text:
I will design awesome logo and UI for mobile apps
About This Gig
Do you want to get Custom Design for your mobile App?
I am a professional designer & a professional mobile App Developer.
I have 5 year experience in this field.
I will design a unique, professional and modern mobile app UI for you. My design will support all resolutions of Phone for any platform like iOS and Android
What Type of UI I will provide
- Material Design Mobile App UI
- Social Apps UI
- Latest Flat Designs
- One Page Flat Webpage UI
- iPhone Mockup
Order Details
2 days delivery 2 Revisions
Basic App or app icon or Splash Screen JPG & PNG
- 1 Image


text:
pRnvinpn Core C has both research and service goals, with the overall theme of developing new and useful imaging and dosimetry approaches to help optimize PDT in preclinical models and clinical studies. The systems used by each project vary considerably,yet the file systems, data analysis, planning and dosimetry concepts can be centralized and inter-project communication in this area can significantly enhance the quality of research. The core is subdivided into four distinct aims, including (!) Structural and functional imaging and dosimetry;(ii) Photophysical imaging/monitoring in vivo;(iii) Molecular imaging in vivo;and (iv)Technology translation.
These aims all work with the projects to ensure that developments from one project may assist in another, and that methods, doses, image files, and developed softwaregets used to the highest potential. There are specific areas in structural dosimetry which will be developed including optical imaging translation, clinical dosimetry, mesh creation and light modeling tools, and visualization software. The core will assist Projects 1 and 2 in establishing functioning dosimetry system for all clinical trials, complete with instrumentation to measure the light and PS, as well as treatment planning software which has the capabilities to adapt the light doses in real time. The photophysical dosimetry will involve development of a specialized high resolution fluorescence imaging system for skin cancer treatment mapping. The variance of PS concentration will be studied in both skin and pancreatic cancer models, as well as installation and testing of singletoxygen dosimetry in collaboration with PSI. The recent developments in molecular imaging will be extended into imaging in vivo, and be used to quantify the expression EGFR, VEGF levels, and expression of other key proteins in vivo. Integrated optical tomography with MRI, US, CT will be used to study these with high image resolution.
The final aim tackles the complex issue of technology transfer, and when to spend time on patenting and shareware distribution of technology. We have partners in several companies, and these will be leveraged to help guide our next steps, as well as working through the technology transfer offices of each institution, and the CIMIT center at MGH to fulfill the NIH Roadmap goals of private public partnerships. The core will administer and update a share ware site for distribution of software tools and dosimetry designs, for systems, which do not have immediate commercial potential, yet would benefit the field of PDT in general by distribution to other academic centers. The core is centered at Dartmouth and MGH, as these sites have been the locus of technology developments in the past funding period, yet the key personnel and collaborators at each site have planned bi-annual meetings and more often weekly meetings planned during clinical trials. Enhanced file transfer and customized software tools will improve the interactions planned and make this core significantly improve the quality of research at each of the project sites. The potential benefits to public health that this Core provides is in the form of new dosimetry and imaging tools for better treatment outcomes and initiating commercialization of research in the Program in partnership with industry.
|O'Brien, Darragh P; Sandanayake, Neomal S; Jenkinson, Claire et al. (2015) Serum CA19-9 is significantly upregulated up to 2 years before diagnosis with pancreatic cancer: implications for early disease detection. Clin Cancer Res 21:622-31
|Samkoe, Kimberley S; Tichauer, Kenneth M; Gunn, Jason R et al. (2014) Quantitative in vivo immunohistochemistry of epidermal growth factor receptor using a receptor concentration imaging approach. Cancer Res 74:7465-74
|Skipworth, J R A; Keane, M G; Pereira, S P (2014) Update on the management of cholangiocarcinoma. Dig Dis 32:570-8
|Huggett, Matthew T; Passant, Helen; Hurt, Chris et al. (2014) Outcome and patterns of care in advanced biliary tract carcinoma (ABC): experience from two tertiary institutions in the United Kingdom. Tumori 100:219-24
|Jermyn, Michael; Davis, Scott C; Dehghani, Hamid et al. (2014) CT contrast predicts pancreatic cancer treatment response to verteporfin-based photodynamic therapy. Phys Med Biol 59:1911-21
|Spring, Bryan Q; Abu-Yousif, Adnan O; Palanisami, Akilan et al. (2014) Selective treatment and monitoring of disseminated cancer micrometastases in vivo using dual-function, activatable immunoconjugates. Proc Natl Acad Sci U S A 111:E933-42
|Spring, Bryan Q; Palanisami, Akilan; Hasan, Tayyaba (2014) Microscale receiver operating characteristic analysis of micrometastasis recognition using activatable fluorescent probes indicates leukocyte imaging as a critical factor to enhance accuracy. J Biomed Opt 19:066006
|Kanick, Stephen Chad; Davis, Scott C; Zhao, Yan et al. (2014) Dual-channel red/blue fluorescence dosimetry with broadband reflectance spectroscopic correction measures protoporphyrin IX production during photodynamic therapy of actinic keratosis. J Biomed Opt 19:75002
|Anand, Sanjay; Rollakanti, Kishore R; Horst, Ronald L et al. (2014) Combination of oral vitamin D3 with photodynamic therapy enhances tumor cell death in a murine model of cutaneous squamous cell carcinoma. Photochem Photobiol 90:1126-35
|Keane, Margaret G; Bramis, Konstantinos; Pereira, Stephen P et al. (2014) Systematic review of novel ablative methods in locally advanced pancreatic cancer. World J Gastroenterol 20:2267-78
Showing the most recent 10 out of 101 publications

subset: commoncrawl


text:
> Classifieds
> Job
1. English native speaker with teaching experience preferred 2. Enthusiastic, active, passionate and good at communication3. Flexible working time Please send your CV to our email: firstname.lastname@example.com:159-2166-8157
Shanghai is internationally famous, technologically mind-blowing and industrially incredible. Working and living in Shanghai is an opportunity few ever get to experience. With an ultra-modern, fast-paced way of life Shanghai can be compare...


text:
How to Make New Year's Resolutions that Save You Money
Making New Year's Resolutions is a grand tradition that illustrates the desire of people in our society to get better each year. But many resolutions are short lived as we return to our settled ways after a number of weak attempts to change. This year can be different, though, if we make concrete goals that help us save money as we achieve them. Here are some areas to focus on.
Quit Smoking
If you are a smoker make this coming year, in January in fact, the time to quit smoking forever. Search for, find, and print out pictures of diseased lungs, throats, etc., and tape them to your mirror because that's you or will be. Sit down and calculate the direct cost of smoking and see how much you will save per year of not smoking. If smoking costs you $30 a week, that's $1500 a year. If you expect to live another 30 years, that's $45,000 you would have saved, not including the compound growth if you saved or invested that money each year. You'll also have fewer sicknesses and medical bills. You can do it!
Reduce Consumption of Sweets and Alcohol
If you are overweight and want to lose pounds and inches, resolve to do it this year. And do it in ways that will save you money, not cost you money. First, resolve to eliminate packaged snacks and desserts, except for special celebrations. Those are costly luxuries that are unhealthful as well as fattening. Use fruits and vegetables as snacks instead. If you drink alcohol take a year off from consuming it. Or at least have several alcohol-free days a week. Cutting back on sweets and alcohol will save you real money over the course of a year.
Do Aerobic Exercise
Next, begin an exercise program, even if it's just walking around the block or in a mall. Resolve to develop and follow an aerobic exercise plan at least. But get your doctor's approval first. Regular exercise five or more times a week will save you medical expenses down the road.
Aerobic exercise at a moderate intensity level (like brisk walking) for 150 or more minutes per week will deliver major health benefits.
Walk Everywhere You Can
Resolve to walk everywhere that is safe instead of driving to every errand. This will save you fuel and increase your physical activity.
Car Pool If You Commute by Car
Resolve to car pool to work, at least three days a week. Share expenses and save on fuel. That should be doable for many people. Car pool with a friend when you go shopping, too. More money saved.
Save Money in the Home
Resolve to examine every way possible to save money in the home, and do it starting in January. Significantly reduce heating, air conditioning and water heating usage and you will save a lot of money each year. Contact your electric (and gas if applicable) utility to get specific ways to save energy and money.
Final Thoughts on Making Resolutions that Save You Money
If you don't smoke and are not overweight you still have four resolutions above that will save you money, and probably save you hundreds of dollars per year. Also:
- Write all your resolutions down with specific steps to accomplish them. Post these prominently in your home. Review them often. Commit publicly and then it should be easier to keep your commitments. You can do it!
- Always check with your doctor to get medical clearance before beginning or dramatically changing an exercise plan.
More by this Author
- 4
The Mayo Clinic Diet offers a complete roadmap to healthy weight loss. Permanent changes to eating and activity habits are required, but there are sufficient resources for success.
- 0
One of the four cardinal virtues, prudence is the good habit of selecting the best means to achieve a worthy goal. It is acquired by learning, experience and practice.
- 1
Setting and achieving personal goals is a shortcut to success in many areas of life. Goals focus attention and energy on things that are important to achieve and then action plans detail what needs to be done to reach...
No comments yet.


text:
Welcome to Mobile Add-ons.
Add extra features and styles to make Mobile your own.Close
Review for Restartless Restart by nag73
Rated 5 out of 5 stars
Cheers, works like a charm.This review is for a previous version of the add-on (8.1-signed.1-signed).
To create your own collections, you must have a Mozilla Add-ons account.


text:
Hotels in Pangkalan Bun
Selection of 7 cheap hotels in Pangkalan Bun with prices from
Hotel reservation
Pangkalan Bun
Hotel rooms in Pangkalan Bun
There are not so many hotel rooms in Pangkalan Bun, just 7, still everyone can find an offer to suit his choice. The most common offers in this city are 3 и 4 stars, they count 2 out of 7, and their prevalent location is central district. According to our practice, it is the most profitable to book a hotel in the west of Pangkalan Bun, as it is the location of the hotels with optimal cost and quality offers along with the cheap hotels. Taking into account the small size of the city, there is no need to dwell hotel reservation on the location: the road to the city center would take less then half an hour, so one can book a hotel in any district of Pangkalan Bun. The most populated with hotels district of Pangkalan Bun is the north, 71% of cheap hotel rooms are concentrated here. Pangkalan Bun is an ideal place for couple and business, such travellers rate hotels there 7.1 out of 10 on average. The view to pool from the hotel room can serve as a pleasant addition to the journey. Apart from all these, hotels in Pangkalan Bun offer their customers laundry service, restaurant/cafe, wi-fi in public areas and concierge service. The staff of the most hotels is multilingual: it speaks english. The most appreciated amenities in Pangkalan Bun hotels are breakfast and service. According to the visitors reviews, hotels in Pangkalan Bun has fantastic service and tasty breakfast. Take a look at our selection of the cheap hotel rooms in Pangkalan Bun to make a well-informed choice for your reservation!
Cheap hotel rates in Pangkalan Bun
Currently Hotellook offers cheap hotels with discounts varying from 5 to 60%. The largest discount found by our users in Pangkalan Bun was 13%. We collected all discount hotel deals in Pangkalan Bun together to make it easier for you to find the really cheap one!
discount 11%
good hotel
5.2 km from the city center
Grand Kecubung Hotel
Check In
Check Out
discount 13%
Fair Hotel
4.6 km from the city center
Hotel Swiss-Belinn Pangkalan Bun
Check In
Check Out
All discount hotels in Pangkalan Bun
hotel collections
Pangkalan Bun hotels with restaurants
average price
average rating
Love to eat? So do we :) That's why we've collected hotels with restaurants in Pangkalan Bun in one place. Cheap hotel rates here start from
Show hotels
All hotel collections in Pangkalan Bun
Best hotels in Pangkalan Bun
Hotels in Pangkalan Bun are spread around the city within the distance of 23.1 kilometers. Those who are keen on antique should definitely fall in love with
Swiss-Belinn Pangkalan Bun
, the oldest hotel of Pangkalan Bun, constructed in 2012. This hotel is located 4.6 km away from the city center. If you like everything shine and bright, Pangkalan Bun can offer
Rimba Orangutan Eco Lodge
for you, the most expensive hotel, where you can find wi-fi in public areas, restaurant/cafe and laundry service. The most popular accommodations in Pangkalan Bun is
Swiss-Belinn Pangkalan Bun
, 3 stars hotel located in a 4.6 kilometers from the city center. The optimal choice for the ones who want to save some money would be
Hotel Bahagia
, the really cheap hotel located in the east of Pangkalan Bun.
The best hotels are here and now. Try them!
All cities in Indonesia


text:
Insulation is material that has the ability to reduce heat or cold transmission.
Insulation Terms:
BTU Amount of heat necessary to raise the temperature of one pound of water one degree Fahrenheit.
K-value Laboratory-determined value of the thermal conductance of a material.
R-value Ability of a material to retard the transmission of heat. The higher the R-value, the better the insulating performance.
U-value Amount of heat, in BTU, transmitted through one square foot of material (the door) in one hour at a temperature difference of one degree Fahrenheit from one side to the other. The lower the U-value, the better the insulation.
Register your door
Awards & Recognition
Clopay Plastic Products
Griffon Corporation
Press Room Clopay Blog Privacy
Terms & Conditions
Careers Sitemap Dealer Log-in en español | en français
February 2017
Award-winning architect Phil Kean selected two distinctive, and distinctly different, Clopay garage door models to feature on the 2017 The New American Home [Read More...]
Designer Christopher Kennedy used contemporary Clopay glass garage doors in the transformation of a midcentury home in Palm Springs. The project is featured in [Read More...]
CONNECT WITH US © Copyright 1996-2017 Clopay Building Products


text:
Your list is empty.
Save musicians, entertainers, speakers and services, and they'll appear here.
Hire Celtic Music in Bennington, VT
Tell us about your event:
Complete the form below to receive FREE no-obligation quotes from Celtic Music in Bennington, VT.
Celtic Music
North Adams, MA
Kate Brittenham has played the harp for 17 years, and only grown more passionately…
Celtic Music
Albany, NY
Harpist / Celtic Music
Ballston Lake, NY
Bagpiper / Celtic Music
Schenectady, NY
Bagpiper / Celtic Music
Amherst, MA
Celtic Music
Lunenburg, MA
Wendy Kerner is a Juilliard graduate whose clients rave about her music, her professionalism…
Harpist / Celtic Music
Hartford, CT
Celtic Music
Hartford, CT
Bagpiper / Celtic Music
East Hartford, CT
Irish / Scottish Entertainment / Celtic Music
Pepperell, MA
Blackstone Cúil (pronounced Kool) is a four-piece band performing unique arrangements…
With a blend of traditional Celtic classics and Cape Breton influenced originals,…
Blackstone Cúil (pronounced Kool) is now a four-piece band performing unique arrangements…
Acoustic Band / Celtic Music
Auburn, MA
1- The Kelly Girls are a lively and talented four piece all female band. Enjoy our…
Celtic Music
Groton, MA


text:
Capsized is a 2D physics based platformer that tasks the player with escaping a hostile alien world.
Generic user.
Hardcore gamer and Associate Producer at the Army Game Studio. Been working in games for almost a decade now, looking forward to decades to come!
The vagrant gamer! Play/stream damn near anything and everything under the sun. Feel free to join me in a game or two, just find me via steam!


text:
For status, comments and chat
Copy the emoticon.
Click on icon on Facebook.
Paste the emoticon in the File name field and click Open.
Each image in our birthday gallery will help you wish someone you know a happy birthday. Share this dog and its bones with a Facebook pal. Free to use, these images will enhance your fun on Facebook. Each image can make your message a bit more special and personalized.


text:
Watch What's in the Basket? (2012) Free Online
What's in the Basket?
IMDB Link:
Rating: 6.2/10 (18 votes)
Director: David Gregory
Writer: N/A
Stars: Beverly Bonner, James Glickenhaus, John Caglione Jr., Kevin Haney
FULL CAST: What's in the Basket? (2012) - Full Cast and Crew
Runtime: 78 min
Rated: N/A
Type: movie
Year: 2012
Genre: Documentary
Quality: HD
Language: English
Released: N/A
|Storyline: A documentary on the making of Frank Henenlotter's Basket Case trilogy.
Home » Documentary » What's in the Basket? (2012)


text:
Is Vuyo's Taxi/Cab Service incorrect or missing key business information? Update your Hotfrog listing today.
Contact details
Are these details correct?
Hotfrog SouthAfrica provides information regarding Vuyo's Taxi/Cab Service in Grahamstown Eastern Cape. Vuyo's Taxi/Cab Service is located at 5623 Ext 6 Joza Location, Grahamstown Eastern Cape 6139 and provides taxi services. Contact them on 0736653558.
Is Vuyo's Taxi/Cab Service in 5623 Ext 6 Joza Location, Grahamstown Eastern Cape 6139 your business? Claim your listing and attract more leads by adding more content, photos and other business details.
We have more taxi services in Grahamstown Eastern Cape available on Hotfrog SouthAfrica. You can update your search for Grahamstown taxi by location, keyword or service options.
25 Hill Street Grahamstown Eastern Cape 6140
POBox 94 Grahamstown Eastern Cape 6140
PO Box 186 Grahamstown Eastern Cape 6140
Sasko Complex Rautenbach Road Grahamstown Eastern Cape 6140
Small Business Hub
Sharing tips, ideas and advice to help grow your small business.
Your profile without ads
Have you considered upgrading to Hotfrog AdVantage? No competitor advertising means exclusive focus on your business. You take centre stage.
Create your free Hotfrog business profile
Follow Hotfrog on:
Share on:
Hotfrog Small Business Hub


text:
KOOZIE Duplex Lunch KoolerSKU #: NW-15696
Item DescriptionMore InformationAdditional Information
Perfect for a lunch on the go, this cooler features multiple storage areas. The bottom opens to reveal a large insulated area, while the handles open to reveal a zippered main storage area. A front slip pocket provides added storage for condiments. Two large zippered main compartments. Bottom compartment ideal for plastic container. Front slip pocket. Dual integrated carrying handle. PEVA sewn interior liner. Price includes: 1-color imprint, 1 location
Price includes the cost of a one color imprint in one location. Please contact us at 888-206-3047 for more print options, a custom project, or additional print locations.
|Imprint Dimensions
|4"w x 3"h
|Standard Production Time


text:
Become a Q Club Member today and enjoy unlimited entry and other great benefits!
Byte Wise
Have you ever had to turn something off and on again to fix it? Why did that work?
Find out at Byte Wise as it explores maths and computational thinking at Questacon this summer, all thanks to Supporting Partner Samsung Electronics Australia.
Count in binary and take on a mechanical computer in a battle of wits. Learn about the maths behind the perfect hole in one in mini-golf—and the maths behind how to make the shot impossible!
Sort your friends and family with the algorithm search engines use to sort information, and find out about the geometry that's saving us all from giant spiders.
See how digital screens display their images—and until 1 March 2017, go into the running to see it in action on your new Samsung HDTV!
Visit Mathamazing and Byte Wise at Questacon to be in the running to win a 65 inch Samsung Series 9 SUHD curved TV valued at $6299! Visiting school groups will have the chance to win a 65 inch Samsung interactive smartboard and a class set of 30 Samsung Galaxy Tab A tablets, valued at a total of $11,599.
Find colourful new ways to put computational thinking on the map at Byte Wise this summer.


text:
Antique Circa 1815 Portrait Miniature Watercolour Faux Effect Tortoiseshell Mount Regency Era
This decorative watercolor on paper side profile depicts an elegant young lady and dates to the beginning of the 19th century, circa 1815. The female sitter is dressed in traditional regency clothing, she is wearing a light blue off the shoulder dress with short puffed sleeve. We adore her coral necklace. She has short, very fashionable curled brown hair - the latest fashion from Paris not quite an à la brutus or à la titus haircut but along those lines. The watercolor is housed beneath a very unusual and very gorgeous reverse painted old bubbled glass mount that was very cleverly painted to imitate expensive tortoiseshell. The 19th century frame features a wonderful Rosewood veneer and external gilt slip, complete with original rear suspension loop.
Measuring: Frame 5.75" (14.5 cm) by 6 5/8" (17 cm). Watercolor approximately 2 3/8" (6 cm) by 2 6/8" (7 cm). Internal 3 3/8" (8.5 cm) by 4 4/8" (11.5 cm).
Condition: This item is in very good condition for its vast age but it is not pristine. The watercolor is crisp and in very good condition, a small black spot is seen on the paper ground to the left of the lady's nose, there is minor mottling to the ground. We have not opened this picture and so you can see some old dust debris trapped under the glass and to the reverse of the glass. The mount is in good condition with only a small dent to the mount at 9 o clock, we believe that the inner gilt oval card mount has been at some point re-gilded. There is some minor wear to the tortoise shell effect reverse painting at 12 and 6 o clock. The frame and gilt slip are in good condition with natural patina, there are some minor bumps to the frame which is to be expected. The frame has been re-backed at some point.
This decorative little watercolor is perfect for anyone who appreciates all things Regency or wouldn't it work superbly well with your existing antique miniature watercolor collection?
3 other shoppers have this item in their Cart or Wish List .
Embracing the past with tempting antique European textiles, prints, paintings and porcelain.
English Platinum rated shop with over 1000 international sales. FREE World shipping on most items, layaway too.


text:
NC Dotted Anti-slip Heat Insulated Silicone Mat
This anti-slip heat insulated mat is made of silicone and is perfect for office and home use.
For more info and to Buy, visit - https://goo.gl/hkmBbT
Best electronic products at our electronics online shopping store at the best price with free shipping.
For more electronic products and accessories, visit - http://shrsl.com/?e4xf
Ad ID: 293297


text: Item is not available Find Another One Others Looked At... Beretta A300 Outlander Turkey 12ga J30TH... SELLER: Silver Creek Outfitters 1 $798.00 Beretta A400 Xtreme Max-5 12ga LEFT HAND... SELLER: Silver Creek Outfitters 1 $1,698.00 BERETTA A-400 XTREME 12GA *MINT CONDITIO... SELLER: SPORTSMENS OUTPOST INC 1 $1,399.99 Beretta A400 Lite Synthetic 12ga 28" SELLER: Silver Creek Outfitters 1 $1,398.00 Beretta A300 Outlander Max-5 12ga SELLER: Silver Creek Outfitters 1 $748.00 NIB BERETTA A300 OUTLANDER 12GA!!! SALE!... SELLER: Parker Custom Arms LLC 1 $699.99 Guns Shotguns Beretta Shotguns Autoloaders Hunting Beretta AL URIKA Optima Ga OBF | 86 | 80 | Lc | 328.1269ms Beretta AL391 URIKA Optima 12 Ga 28" OBF For Sale from Bob Wards | Positive feedback: 100% View | Verified Seller | 197 Completed Sales View Sellers Items This item is no longer available. /UserImages/96827/999054874 3521361.jpg /UserImages/96827/999054874 3521362.jpg /UserImages/96827/999054874 3521363.jpg /UserImages/96827/999054874 3521364.jpg /UserImages/96827/999054874 3521365.jpg /UserImages/96827/999054874 3521366.jpg /UserImages/96827/999054874 3521367.jpg Description Shipping and Payment More Info Gauge: 12 Barrel length: 28" Locking system: elevated locking block Receiver: light alloy with recoil dampener Barrel: steel,chrome plated bore and chamber Rib: ventalated Saftey: cross bolt Front sight: metal bead Magazine: 3 rounds Buyer pays shipping Trades Accepted: We only offer trades in store. Bob Wards is a 4th generation family owned sporting goods store in Montana started 1917. over 4000 guns in stock. Returns are accepted on defective items if notified within 3 days of receiving item. Condition: New In Box Brand: Beretta UPC: j391121 Caliber: 12 Gauge Location: MT Share Item Item #: 999054874 Stock No.: j391121 This item is no longer available. Price: Shipping: See Description (or Arrange local transfer) Accepted Payment Methods: Returns: Only if Defective Bob Wards Seller Since: Jul. 2008 Seller Level: Local Seller This seller is an FFL City: Missoula State: MT Your Recently Viewed Items


text:
DIY Photographer Services
Camera Hire
D.I.Y. Photographers Services is one of the leading wedding photographers in Sydney. We rent out professional cameras to help capture any event in the finest quality.
We at D.I.Y Photographers Services understand how important a personal touch is for good photography. If you have a personal connection to the person or scene you're capturing, you'll put your whole heart and soul into the camerawork, and the resulting pictures will reflect your love, affection and warmth. For a professional photographer, each event is a job and they treat it like they would any job - efficiently and competently, but without that depth of feeling.
We offer you the opportunity to hire your own camera and take pictures at your own pace and time, capturing moments that tug at your heart and not just those that would look good in an album.
We give you a chance to hire multiple cameras so all your loved ones can capture moments they like best, thereby giving you a diverse range of pictures to build your memories with.
We understand that, after a long party or wedding, it is difficult to sift through and download hundreds of captured images. This is why we offer to do it for you! After we pick up the cameras post-event, we download all your pictures and we deliver them in softcopy form via Dropbox. We save you the hassle of processing and downloading the pictures, whilst simultaneously giving you the pleasure of handling your own photography. You take the pictures and we do the processing work! We also have form a rewarding partnership with the award-winning printing company, NuShot. Throughout collaboration, we are able to offer you the best of both worlds- great cameras and a top-class printing services, so you can get quality prints of images you've taken.
Print this page
Create your free Hotfrog business profile
Follow Hotfrog on:
Share on:
Hotfrog Small Business Hub


text:
The Prostacet Prostate formula is a powerful, natural solution designed to:
- Support the Health of the Prostate
- Maintain Healthy Prostate Function
- Support Bladder Health and Normal Urine Flow
Kitmaroc.free.fr - For Order Prostate Health Supplement by Prostacet
Buy Herbal Prostate Health Supplement by Prostacet Kitmaroc.free.fr -
The Prostacet Formula delivers key ingredients to nutritionally support a healthy prostate. Prostacet is an outstanding formula that supports prostate health with Serenoa repens (saw palmetto) which works to nourish this vital organ. Prostacet also contains a healthy dose of lycopene, the remarkably potent antioxidant phytonutrient that has been shown to counteract oxidative tissue damage. Reinforced by other herbs, amino acids, vitamins and minerals, Prostacet has emerged as a premier natural prostate health formula.
Prostate health is a serious issue that affects every part of a man's life. The frequent urination many men experience can make it difficult to visit friends, dine out, or see a movie. It can even interrupt important sleep. Although changes in prostate health are indefinitely part of every man's life, the signs and symptoms that are associated with this condition often prove too embarrassing for most men to even mention. Prostate enlargement is also known as benign prostatic hyperplasia, or BPH. It remains one of the most prevalent problems for men over the age of 60. Moreover, 90% of all men will experience at least some signs and symptoms by age 80.
90 Day Money Back Guarantee Return Policy.
We take great pride in the superior quality of our products and want you to be pleased with your purchase. We believe in offering the very best value, quality and selection to our customers. You may return any unused and unopened item purchased from us for any reason within Ninety (90) days of your purchase. Customer Care
Order Online or Call Toll-Free 24 Hours a Day
Ref Code: 997720 Click here for Local and Iinternational Phone Numbers
All the links and descriptions on this page are taken from public sources such as search engines (google.com, yahoo.com, bing.com). However, if you think any data on this page violates your copyright, please send an message from "Contact Us" page and the links and descriptions of full page will be removed.
January 17, 2017. 12secondes.free.fr (12secondes-free.fr) - 12secondes.free... (http://statrr.com/overview/12secondes.free.fr) xpiroro.free.fr: 0.05%: 26: 0.00%... kitmaroc.free.fr: 0.05%: 60: 0.07%: solito.free.fr: 0.05%... user-reviews of websites inside its resource and reserves the...
January 15, 2017. cartoon6r.free.fr (http://cartoon6r.free.fr/) Untitled Document
January 16, 2017. Dolgital | Dolgital.Free.fr | HTMLCorner (http://www.htmlcorner.com/dolgital.free.fr) cartoon6r.free.fr
January 19, 2017. brc17.free.fr (http://brc17.free.fr/courcon) Free Games Online - Play Java and Flash Games for Fun - Online Freegames. STRATEGY GAMES - BOARD. Chess Game Chinese Checkers Checkers 1 Reversi Game Solitair 1
January 13, 2017. Free | Cycols.Free.fr | HTMLCorner (http://www.htmlcorner.com/cycols.free.fr) Free - Red Hot Tiki
January 18, 2017. bulltricker.free.fr - JEUX EN LIGNE GRATUIT (http://bulltricker.free.fr/) 12secondes.free.fr is a website that ranks 160 in Alexa. 12secondes.free.fr is ranked 501 on statisy and has 261 backlinks according to Alexa. The hostname or fully...
January 12, 2017. Free | Bysirdas.Free.fr | HTMLCorner (http://www.htmlcorner.com/bysirdas.free.fr) Free - KA Home Page
January 14, 2017. Free | 3emedragons.Free.fr | HTMLCorner (http://www.htmlcorner.com/3emedragons.free.fr) kitmaroc.free.fr: 0.3%: 9.6: 0.1%: ophtasurf.free.fr: 0.3%: 35.0: 0.1%: forumfetc.free.fr: 0.3%: 44.7: 0.4%: ddlsearch.free.fr: 0.3%: 6.0: 0.1%: xmaths.free.fr: 0.3%...
January 11, 2017. Assistance Free (https://assistance.free.fr/) Free - MRSC'S PLACE
Popular pages:
Order Online or Call Toll-Free 24 Hours a Day
Ref Code: 997720 Click here for Local and Iinternational Phone Numbers


text:
Greetings Guest!!Dismiss Notice
In order to combat SPAM on the forums, all users are required to have a minimum of 2 posts before they can submit links in any post or thread.
That is IT! I JUST CANCELLED MY SUBSCRIPTION!!!
Discussion in 'EA Land/The Sims Online Stratics Forums' started by Guest, Feb 22, 2008.


text: Seller: katsmeow-2 (95) 100%, Location: Alhambra, California, Ships to: US, Item: 152335001559 Vintage set 7 Bakelite Butterscotch Handles,Knobs,Drawer Pulls. All the knobs are in great pre-owned, used condition. The backs do have old paint. They come with there original screws. Please see pics for overall condition. If you have any questions please ask anytime. Thank you, good luck and happy bidding.


text:
Eff you af, Eff you!!!!!!
silly cow came to visit today so onto month 5 for us.
Congrats Debster and Roxy, hope those lines get darker for you
Made with Love, how did your lines go this morning??
Hi girls :-) i havnt been on for a while.. Wow congrats to all the bfp mamas yay how fantastic! Big hugs everyone with bfn fx for next month..
Afm welli tested this morn-bfn - no sign of af yet though. Any advice on the best hpt to use?
Have symptoms but could b me just making too much out of them i think. Im pretty down today over this whole journey of losses and bfns we hav had. Xo
I'm actually not all that excited by this mornings test. With the storms I didn't get a wink of sleep so must have gone to the loo a hundred times. It's pretty much the same darkness as it was at 11dpo. I'm 13dpo today and honestly thought they would be getting pretty solid by now. I'm blaming my frequent wee's.
Still have symptoms. My lower back was so sore last night and nausea and boobs being sore are still in full force so I guess that's comforting.
Off for bloods tomorrow. FX its a big number and rising.
I don't know what they normally do but I was going to ask for two sets of bloods two days apart and an early scan around 7 weeks so we can see a healthy heart beat. I'm probably being over cautious but it will definitely help to relieve the caution and worry we are both feeling since we only just had an mc last cycle.
Thats still a positive line. Fingers crossed your bloods show good results
When is AF due MWL?
Good luck with your bloodtest MWL
Ok tested again this afternoon. Last one at the bottom it wasn't even 3min when I took this pic so it got darker still. AF is due tomorrow. I hope she stays away. I usually get spotting on cd14 followed by full on AF the next day /cd1.
Thks ladies. xx
Pregnant for the first-time?
Not sure where to start? We can help!
Our Insider Programs for pregnancy first-timers will lead you step-by-step through the 14 Pregnancy Must Dos!


text: Indovision 59,915pages on this wiki Add New Page Edit History Talk0 Share ????-present Add a photo to this galleryExternal links Indovision Retrieved from "http://logos.wikia.com/wiki/Indovision?oldid=782745" Ad blocker interference detected! Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers Wikia is not accessible if you've made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected. Categories: Direct broadcast satellite services Indonesia


text:
30 Days with Justin
By: xian lingyun
Welcome to the walkthrough for the iOS game 30 Days with Justin, if you are looking for ways to make it to the next level, and to improve gaming experience as a master player, you've come to the right place. Here you will find 30 Days with Justin tips, tricks and guides, as well as the opportunity to share your own discoveries to help others move on and beat the game.
If you can't find the answer to your question you are welcome to post it in the comments section below. This way others who know the answer can help you by sharing their own tips and advices.
30 Days with Justin game app is developed by xian lingyun and available on iTunes and Google Play. For more details on the app, check out our review.
- App name: 30 Days with Justin
- Seller: xian lingyun
- Category: Music
- Updated: Aug 29, 2012
30 Days with Justin iOS/Android Gameplay
Check out these tutorial for all levels of 30 Days with Justin. We'll continue to update this list with the latest answers as new levels are released.
30 Days with Justin Answers
- Basic Game Guide Part One - lite iphone gameplay video
Hit like if this helped you!
Until the Walkthrough is completed, feel free to ask for help in the comments section.


text:
Through Saturday, March 7 Read More
With five New York art spaces showing maps, charts, and diagrams, it's a great moment for flowchart art Read More
A collaboration between MoMA curators and the Columbia Business School depicts early modernism as a vast social network. It's the latest in a long line of charts showing that no ism is an island Read More
A growing number of artists are poking fun at art-world inequities in their work—even as they participate in the system they critique Read More
Your cart is empty.
Sign up to receive Breakfast with ARTnews, our new daily morning e-newsletter, a selection of what our editors are reading.
Sign up to receive ARTnews Today, our new daily afternoon e-newsletter, with up-to-the-minute ARTnews articles, criticism, and a note from our editors.


text:
Alexz Johnson photo
Most popular Alexz Johnson photos, ranked by our visitors.
Top pics of Alexz Johnson
Alexz Johnson photo galley
Check out full gallery with 18 pictures of Alexz Johnson. Only high quality pics and photos with Alexz Johnson. Last update date: 21 January 2011.
1280x1024 2
667x1000 2
1600x983 1
1600x1176 1
1000x1534 2
Photogallery of Alexz Johnson updates weekly. We update gallery with only quality interesting photos. If you have good quality pics of Alexz Johnson, you can add them to Photo-forum. Good photos will be added to photogallery.
Popular photo galleries of celebrities
Most popular celebrity photogalleries:
© ThePlace2.ru - Celebrity photos
mail: email@example.com
design: eto design


text:
From excellent coffees to a wide selection of regular, herbal green or decaf teas Fresh Start Coffee has it all. For a Morning breakfast to mid-morning snack, to a healthy lunch the Staff at Fresh Start Coffee can provide it.
The have freshly baked muffins, danishes, croissants, and bagels
An assortment of Tarts, squares, cookies and puff pasteries
A fresh variety of seasonal fruits and berries, beautifully decorated and presented.
A selection of farm-fresh cheeses with an assortment of crackers.
Large and tasty sanwiches prepared an a variety of fresh breads. From Roasr beef to turkey, Black Forest Ham, Tuna Salad and Egg Salad.
Sandwiches on freshly baked Panini and Focaccia. With your choices ranging from Prosciutto, to Calbrese Salami, Sun dried Tomato, goat cheese, and more...
From Chicken Salad, Tuna Salad, Seafood Salad, and Vegetable Hummus.
Triangle/Pinwheel style sandwiches wide a wide variety of fillings to choose from.
Greek, Ceasar, Red Potato, Penne & vegetable, Greek Pasta Salads and more are available
If you desire something else, then give us a call. Special requests? No problem!
Please allow 24 hour for catering orders on groups of 10 people or more.


text:
Listen to Darius Rucker Radio on iHeartRadio
Get your holiday wagon wheels rolling with Darius Rucker. He performed in New York City as past of the iHeartRadio Country Live series. Get ready for the holidays with Darius in celebration of his latest album Home for the Holidays.
During his exclusive and intimate iHeartRadio Country Live show, Darius performed songs off of his recent holiday album, a few Darius Rucker classics, and will talk about his holiday album in a special Q&A.
The best part is everyone will be able to celebrate the holidays with Darius -- the more the merrier!
Kick back with a glass of eggnog and get ready to celebrate the holidays with Darius Rucker! Check out these 3 songs from the show!


text:
Pharrell Designs Puffy Vests, Abercrombie & Fitch Presents 176 Pages Of Beefcakes, And More Fashion News
• Pharrell Williams designed puffy coats for the outerwear company Moncler, and a couple of them look like bulletproof vests. We discourage anyone from checking to see if they actually repel gunfire. {Fashion Indie}
• Abercrombie & Fitch is bringing back its super-sexy quarterly magazine (its last one came out eight years ago). 176 pages of hotties? 'Nuff said. {Stylewatch/People}
• Vogue's July issue talks smack on Katy Perry and Ke$ha. But not everyone does! See here and here for proof. {Styleite}
• Kristin Cavallari from The Hills rocked a black leather studded dress in the middle of this hot summer day and didn't get sweaty. Miracles do happen. {Gawker}
• Royal hottie Prince Harry is in America for the annual Veuve Cliquot polo match this weekend! Elle picked out a few hats you can wear in his honor. {Elle}


text:
- Hi there, welcome to Tribesmart. Log in to get started...
Geyser Tube
Guide price: £6
Last updated on 20th Apr 2013
Tags: geek
Geyser Tube
If you must conduct crackpot experiments with mints and fizzy pop you might as well do them properly. How? By loading Mentos into this bottle-top contraption and pulling the pin. As the sweeties react with the soda a powerful geyser blasts up to 30ft in the air. Whoosh!
Login or Register to add this to your wish list or favourites.


text:
View, Coats-Walston House, Tarboro, North Carolina
Coats-Walston House (Tarboro, N.C.)
Item information
- Title:
- View, Coats-Walston House, Tarboro, North Carolina
- Topics:
- Subjects:
- Item identifier:
- buch0216
- Photographer:
- Buchman, Tim more info on Buchman, Tim
- Builder:
- Coats, Thomas H. more info on Coats, Thomas H.
- Created Date:
- circa to
- Created Date:
- Description:
- Provenance: Thomas H. Coats (contractor), first owner | Architectural Note: The home was constructed from a pattern in Minard Lafever's "Architectural Instructor." The property also houses a brick kitchen and a board-and-batten smokehouse. | Historical Note: The property is listed on the National Register of Historic Places.
- Genre:
Architectural photographs
- Location:
Tarboro (N.C.)
- Digital Project:
Built Heritage
Source information
- Repository:
- Preservation North Carolina
- Collection:
- Tim Buchman Photographs, 1988-1998 (MC00583) held by Preservation North Carolina
- Note field:
- Not all materials from the physical collection may have been scanned. Images may have been enhanced for web access.
- Rights:
- Reproduction and use of this material requires permission from Preservation North Carolina. For general information see the Preservation North Carolina website (http://www.presnc.org).
- Funding:
- Digitization of this image was partially supported with federal Library Services and Technology Act (LSTA) funds made possible through a grant from the Institute of Museum and Library Services, and administered by the State Library of North Carolina, a division of the Department of Cultural Resources.
Building: Coats-Walston House (Tarboro, Edgecombe County, North Carolina)
- Built:
- Street:
- 1311 St Andrew St
- Community:
- Tarboro
- State:
- Zip:
- 27886
- Provenance note:
- Thomas H. Coats (contractor), first owner
- Architectural note:
- The home was constructed from a pattern in Minard Lafever's Architectural Instructor. The property also houses a brick kitchen and a board-and-batten smokehouse.
- Historical note:
- The property is listed on the National Register of Historic Places.
- General note:
- The date is approximate.
- Location:
Tarboro (N.C.)
- Subjects:
Housing, Single family
National Register of Historic Places
Historic buildings
- Latitude, Longitude:
- 35.906245, -77.538692


text:
5 Bedrooms Detached House for sale
Proudly presented to you by move estate agents; the unique manor barn stands beautifully within its plot of approximately seven acres of level land and offers an enviable location,…
£1,399,000 Guide Price
6 Bedrooms Detached House for sale
Church Lane, Eldersfield, GL19
A handsome 6 bedroom victorian residence with an annexe and office/studio set down a winding driveway in excess of 3 acres. eldersfield village is in unspoilt countryside close to…
4 Bedrooms Detached House for sale
Apperley Village, Gloucestershire, GL19 4DL
Accessed via electric gates to 3/4 acre plot with views to the malvern hills and stable block. recently refurbished 4 bed detached home offering fantastic living accommodation with…
£489,000 Guide Price
3 Bedrooms Detached House for sale
Deerhurst, Gloucester, Gloucestershire, GL19
A wonderful single storey property that has been subject to a major programme of refurbishment and decoration, set in a magical location adjacent to the historic odda's chapel.…
4 Bedrooms Detached House for sale
Long Green, Forthampton, Gloucester
Backing onto fields and sitting centrally within its delightful gardens, this is a characterful semi rural cottage full of charm and surprisingly, space!
3 Bedrooms Detached Bungalow for sale
The Old Pitch, Tirley, Gloucester
A spacious detached home in an elevated position - uniquely arranged with accommodation on one level and garaging beneath.
Ashleworth, GLOUCESTERSHIRE, GL19 4JL
Drive through the iron gates and think "i love where i live'' this will happen every day, it's a place you wont want to leave and can't wait to get back to.…
Orchard Park, Lower Apperley, Gloucester, Gloucestershire, GL19…
A well positioned 13 x 39 park home situated on a small holiday park in lower apperley. the home has views over fields and countryside from the raised decking area. there are two bedrooms,…
Free Instant Valuation
Find out if you are charging enough rent or what your property would be worth if you were to sell now


text:
My Comments
and Angel card?? I have my package but it came with a letter, shirt and dog tag
Replied To: Angel Pin ()
On: Dec 28, 2011
what is an Angel PIN
Replied To: Angel Pin ()
On: Dec 28, 2011
Hi ladies, my site was down for some reason but im back and i'll follow u guys...#followback
Replied To: Trey Angels and Twitter ()
On: Nov 28, 2011
KG ur right, the only difference is between kids and adults the number doesnt matter lol. I know somebody's grandma is a fan too lol :-)
Replied To: Trey Angels and Twitter ()
On: Nov 18, 2011
@Jamroc my bad girl I was getting my stories mixed up...im back on track now.
Replied To: Story - Made To Be Together ()
On: Nov 18, 2011
Member name:
About Me:
I'm 23 years old and full of FUN. I was born and raised in Petersburg Virginia and has only seen Trey ONCE in my life. I am a HUGE fan of music and art. I sing, draw and make scrapbooks during my free time. I'm currently a full-time worker and I have no kids as of now. My favorite quote is "You've gotta dance like there's nobody watching, love like you'll never be hurt, sing like there's nobody listening, and live like it's heaven on earth." ~William Purkey
United States
Twitter Name:
[{"parent":{"title":"Get on the list!","body":"
Get exclusive information about STARTER SITE tour dates, video premieres and special announcements","field_newsletter_id":"6010047","field_label_list_id":"50","field_display_rates":"0","field_preview_mode":"false","field_lbox_height":null,"field_lbox_width":null,"field_toaster_timeout":"60000","field_toaster_position":"From Top","field_turnkey_height":"1000","field_mailing_list_params_toast":"&autoreply=no","field_mailing_list_params_se":null}}]


text:
The resource has been added to your collection
Materi ini menyajikan bagaimana berkomunikasi secara efektif dalam bentuk tampilan SLIDE POWER POIN
This resource has not yet been reviewed.
Not Rated Yet.
Our Terms of Service and Privacy Policies have changed. By logging in, you agree to our updated Terms and Policies.


text:
If England were to keep playing Australia at Lord's every four years, it would have had to happen some time, but the victory finally achieved a little before the scheduled lunch interval yesterday ended perhaps the oldest sporting hoodoo of all. If the formbook is a fair guide, it will be about 56 years before England win an Ashes Test at the home of cricket again.
Only one man in the world came close to witnessing this rare sporting phenomenon three times in a lifetime. Henry Allingham, the First World War veteran who died on Saturday at the age of


text:
mauddib512 Review
its luggage
Its luggage, built to hold stuff while traveling. its fine for what it is. and the price was good. which had more color options.
- How accurate was the sizing? very
- Please tell us about the quality of the product. uality was fine
- Was the product free of any manufacturer defects? yes
Was This Review Helpful?


text:
Car & Dog Wash Cranbourne
Car Wash
Why choose a LaserWash® touch free car wash?
Not only can you get the best clean for your vehicle 7 days a week, but the Cranbourne North LaserWash® comes with all the most innovative features that combine to create a car wash experience that will make you come back over and over.
Open Bay Wash makes it easier to pull your car in the car wash without worrying about damaging your tyres and rims. It's safe and comfortable!
Environmentally Friendly! Our soaps and solutions are 100% bio-degradable.
Hot Fresh Water to give your vehicle the best cleaning possible
Underbody Wash & Side Blast cleans the undercarriage of vehicles more effectively than any other car wash system available.
Clear Coat Protectant protects the paint from acid rain and UV rays to help keep cars cleaner, longer.
OverGlow High Gloss Application is applied with purchase of the Extreme wash.
Extreme Air Dry delivers breakthrough dryer performance that dries vehicles better than any car wash, while using less energy with an Extreme Wash.
Print this page
We only use the Best Car Wax "Turtle wax ICE"
Car Care Centre Vending Machines ArmorAll Original Sponge Applicator (Renews & revitalises vinyl, rubber & plastic) Micro Fibre Towel
Welcome to the Cranbourne Spray & Wash, we are open 7 days a week from 6am – Midnight.
we offer 5 self serve car wash bays and 1 fully automated car wash bay
We are open 7 days from 7am-10pm that means you can use the carwash when it suits you.
• Vacuum & Vending Machines
• Boats, Jet Ski's welcome
• Dog wash facility (Enclosed area, you can treat your best friend to a wide range of available services).
• 24 hours Security Cameras
Create your free Hotfrog business profile
Follow Hotfrog on:
Share on:
Hotfrog Small Business Hub


text:
|Home | About | Journals | Submit | Contact Us | Français
Maximum Likelihood (ML) processing of transmission electron microscopy images of protein particles can produce reconstructions of superior resolution due to a reduced reference bias. We have investigated a ML processing approach to images centered on the unit cells of two-dimensional (2D) crystal images. The implemented software makes use of the predictive lattice node tracking in the MRC software, which is used to window particle stacks. These are then noise-whitened and subjected to ML processing. Resulting ML maps are translated into amplitudes and phases for further processing within the 2dx software package. Compared with ML processing for randomly oriented single particles, the required computational costs are greatly reduced as the 2D crystals restrict the parameter search space. The software was applied to images of negatively stained or frozen hydrated 2D crystals of different crystal order. We find that the ML algorithm is not free from reference bias, even though its sensitivity to noise correlation is lower than for pure cross-correlation alignment. Compared with crystallographic processing, the newly developed software yields better resolution for 2D crystal images of lower crystal quality, and it performs equally well for well-ordered crystal images.
Electron crystallography of two-dimensional (2D) crystals is a commonly used technique to obtain high-resolution three-dimensional (3D) structures of proteins (for a recent review, see Renault et al., 2006). The technique was developed mainly by Henderson and co-workers (Henderson and Unwin, 1975) and one of its first applications led to an atomic model of bacteriorhodopsin (Henderson et al., 1990). Many other structures have been solved at a resolution that allowed an interpretation with an atomic model. The data collected from 2D crystals come in two flavors: Images and electron diffraction pattern. Electron diffraction data provide intensities of diffraction spots, much like X-ray diffraction of 3D crystals. These can be measured, and their square root gives the amplitude components of the protein structure. The images of the 2D crystals can be Fourier transformed, and both, amplitudes and phases of the calculated diffraction spots can then be measured by Fourier extraction. This is in contrast to the situation in X-ray crystallography, where phases are not directly observable. Therefore, to collect a complete data set from 2D crystals by electron crystallography, both electron diffraction and imaging are usually performed.
Images also offer another advantage over X-ray crystallography. If disorder is present in a crystal and limits the resolution in a diffraction pattern, the crystal distortions in an image of the crystal can be corrected computationally. This procedure is commonly referred to as "unbending" and significantly improves the resolution attainable by Fourier extraction from 2D crystal images. For the unbending process, a reference image containing only a small number of unit cells is generated either from a filtered version of the image itself, or by projecting an already existing 3D reference structure using the program MAKETRAN (Kunji et al., 2000). A cross-correlation map is then calculated between the reference and the image to determine the location of each unit cell in the crystal. Using the autocorrelation function of the reference, the correlation map can be searched for peaks and unit cell locations are recorded. The MRC program QUADSEARCH (Crowther et al., 1996) performs such a search and exploits the a-priori knowledge of the approximate location of the peaks. It uses an iterative refinement process to predict the peak location in the cross-correlation map, and then searches for the actual local maximum in that map within a limited radius of the predicted location. A coordinate list of the identified lattice nodes is then generated, which is used by the MRC program CCUNBEND to correct the crystal distortions in the image by one of two methods: A better ordered crystal image is generated by either smoothly warping the image so that the unit cells fall onto a perfect lattice, or by creating a discrete montage of unit cells placed at the crystallographically determined grid points. The Fourier transform of the unbent image is then evaluated to obtain values for the amplitudes and phases of the crystal projection map in that image.
The unbending procedure described above has been applied very successfully in many cases and is in common use, but it also has some limitations. First, in its current implementation, it cannot correct for in-plane rotational disorder. Second, the use of correlation functions for alignment is prone to error when the signal is weak, due to the increased chance of mistaking a noise peak for the correlation peak produced by the signal. The signal in the correlation map depends on the size of the reference area used to find the unit cell locations. A larger reference area will produce stronger signal peaks but will also be less sensitive to short-range disorder in the crystal. To detect and remove short-range disorder, a smaller reference area containing one unit cell or even a single molecule would be desirable.
In the case of strong irregularities in a badly ordered 2D crystal, or variations among the unit cells due to sample heterogeneity, single-particle image processing can be applied to the recorded 2D (pseudo-) crystal images. The goal of the single particle processing is similar to the 2D crystal unbending procedure. In both cases alignment and averaging of individual molecules or their assemblies is done to enhance the signal. Sass et al., 1989, have combined phases from correlation averaging (CA) with amplitudes from electron diffraction, obtaining a 3.5Å projection map of porin. Schultz et al., 1993, imaged negatively stained 2D monolayer crystals by tomographic single-axis tilt series, calculated a 3D reconstruction of the unit cell via single particle methods, and combined two molecules from the unit cell with non-crystallographic symmetry to fill the missing cone. Sherman et al., 1998, applied multivariate statistical analysis to 2D crystal images. Stahlberg et al., 1998, used single particle methods to detect and correct for the non-crystallographic orientation of the photosynthetic reaction center within well-ordered 2D crystal images of the surrounding light-harvesting-complex I. Tahara et al., 2000, could significantly improve the resolution of a Na+/K+-ATPase projection map by applying single particle processing methods to 2D crystal images and allowing for sample heterogeneity.
Here, we apply a maximum likelihood (ML) approach to the single-particle processing of 2D crystal images. The ML processing was introduced for the processing of images of non-crystalline material (single particles), and was shown to have superior performance at low signal-to-noise ratios (SNR, variance ratio of signal over noise) compared with correlation-based alignment (Sigworth, 1998). Combining the single particle processing with an ML approach can therefore lead to an improvement over the currently used unbending process. We utilize a whitening filter to make the ML method applicable to the real data which have nonwhite noise. We discuss here the application of ML to 2D crystals and compare its performance with the traditional correlation-based unbending. Furthermore, we show how the contrast transfer function (CTF) of the electron microscope can be included in the processing.
The application of the ML approach to single particle images has been described previously and employs the iterative expectation maximization algorithm to maximize the likelihood function (Dempster et al., 1977). Since the images we will process as single particles will be centered on unit cells excised from a 2D crystal, it is reasonable to limit the alignment of each particle to an in-plane angle and translation. Individual unit cells may also suffer from out-of-plane tilts, for example due to undulations in the crystal (cryo-crinkling, Vonck, 2000). To perform a full 3D alignment, two additional angles would have to be considered. The computational load associated with the expectation maximization algorithm would be very high in this case and some approximations have to be made (Scheres et al., 2005). However, application of the ML approach to experimental data from 2D crystals (see below), shows that very good results can also be obtained when limiting the alignment to in-plane transformations. We will, therefore, limit our discussion to this case and follow Sigworth's implementation of the maximization algorithm (Sigworth, 1998). Briefly, we assume that we have a set of N images X = {Xi;i = 1…N} and corresponding transformation parameters Φ = {i;i = 1…N} describing how these images are related to the underlying structure A. We further assume that the noise in each image follows approximately a Gaussian distribution and is uncorrelated. This assumption will be discussed further below when considering experimentally observed data. We can write for each image i
where R = {Ri;i = 1…N} are independent Gaussian noise images, and σ is the standard deviation of the noise. The negative sign in front of the transformation i indicates that it describes the transformation needed to bring image Xi into register with structure A. A transformation i consists of i = (qxi,qyi,qαi) where (qxi,qyi) describes an in-plane translation and qαi a rotation applied to each image. Furthermore, we assume that each image is approximately centered on a point (ζx,ζy), and that the deviation from this point can be described by a Gaussian distribution with standard deviation (σx,σy) (for isotropic lattice distortions, σx = σy). For images of single particles, the distribution of in-plane rotations is usually assumed to be uniform. The in-plane angular distribution of unit cells within a 2D crystal, on the other hand, will be quite narrow. It will be represented by a Gaussian distribution centered on the value ζα with a standard deviation σα. The goal of the ML approach is to maximize the probability P(X|Θ) that the set of images X is observed assuming a set of model parameters Θ = (A, σ,ζx,ζy,ζα,σx,σy,σα). Instead of maximizing P(X | Θ), its logarithm L(X | Θ) is maximized. Assuming independent variables associated with each image, P(X | Θ) is the product of probabilities for each image Xi, and we can write for the logarithm
The probabilities P(Xi | Θ) can be written as integration over the product of the probability density P(Xi | ,Θ) for each image given the model parameters Θ and a transformation , and of the probability density f( | Θ) for a transformation given the model parameters Θ:
Using the assumptions made above for the noise in the images and the distribution of transformation parameters, we can now write for the probability density f( | Θ) for the transformation parameters
(Sigworth, 1998). M is the number of pixels in an image. By demanding that the derivative of L(X | Θ) with respect to each model parameter vanishes, an iterative expectation maximization procedure can be established for obtaining improved estimates of each model parameter, given the parameters Θ(n) (Sigworth, 1998):
The formulation in the previous section does not take into account the CTF of the electron microscope and is based on the assumption of independent Gaussian noise. This implies independence of neighboring pixels, an assumption that does not hold in many experimental situations (Scheres et al., 2005). Uncorrelated noise gives rise to a flat power spectrum, which is usually referred to as a white spectrum. As an example, we calculate the power spectrum for the image stack of unit cells from a 2D crystal of bacteriorhodopsin. The images in the stack were padded to four times their original size to achieve finer sampling of the power spectra, and their power spectra were added for averaging. The average spectrum is shown in Figure 1, together with a line scan. The power spectrum exhibits Thon rings (Thon, 1971) and an amplitude falloff and therefore, the assumption of independent noise does not hold. A noise whitening procedure is needed before maximum likelihood estimation can proceed. For single particles, a noise whitening filter has been constructed from circularly-averaged power spectra of a pure noise region (Sigworth, 2004). Based on the noise model described below, we obtained a similar whitening filter for 2D crystals.
The power spectrum in Figure 1 can be described as a composition of four components: The first arises from the crystal and can be identified as the spot pattern visible in the spectrum (Figure 1A). This will be referred to as the signal S since it contains the information that we are trying to extract with the maximum likelihood procedure. The second component is the ring pattern (Thon rings) that shows oscillations characteristic for the CTF (Figure 1A and 1B). This will be referred to as the image background Bi since it is originating from the entire sample including the non-crystalline parts, such as the carbon support film and/or ice. The third component arises from the shot noise of the electrons forming the image. It lacks the CTF modulation but is still affected by a detector modulation transfer function (MTF). This will be referred to as sample-independent background Bs. The fourth component Be is the MTF-independent background, arising from detector noise (film scanner electronics, or CCD camera electronics). The detector-convoluted Bs together with Be contribute to the background, indicated by the red line in Figure 1B. We can write for the power in our spectrum
k is a point in the power spectrum in Figure 1A. The envelope function ENVi contains all the factors affecting the optical properties of the electron microscope, such as spatial and temporal coherence, as well as any reduction in contrast due to sample movement and charging (see, for example, Zhu et al., 1997). Assuming independence of S and Bi, we can write for the power spectrum of the background in the image
where CTF is given by
with (Scherzer, 1948)
k is the magnitude of k. The two constants w1 and w2 are given by the percentage of amplitude contrast, W, in the image:
Usually, the value for W ranges from 0.03 (Toyoshima and Unwin, 1988; Toyoshima et al., 1993) to 0.14 (Smith and Langmore, 1992) for proteins embedded in ice, and 0.19 (Zhu and Frank, 1994) to 0.35 (Erickson and Klug, 1971) for proteins embedded in stain (uranyl acetate). λ is the electron wavelength and Cs is the spherical aberration coefficient of the objective lens. The defocus Δf is given by (Henderson et al., 1986; Mindell and Grigorieff, 2003).
where DF1 and DF2 are the two defocus values describing the defocus in two perpendicular directions in an image when astigmatism is present, αast gives the angle between the first direction (described by DF1) and the x-axis, and αk is the angle between the direction of the scattering vector k and the x-axis. For a particular image, DF1, DF2 and αast can be determined using a fitting procedure that fits a calculated CTF to the observed Thon rings (Mindell and Grigorieff, 2003). Note that in Eqs. (14) and (16) a positive value for the defocus indicates an underfocus.
The power spectrum modulation is mainly due to the first term in the sum in Eq. (12), which includes the oscillations of the CTF. Therefore, a whitening filter Hw is obtained by averaging the power spectrum along the path of the thon rings
where k1(ki) = k1(k) indicates the pixels ki in reciprocal Fourier space that are on the same Thon ring as pixel k. N is the number of Fourier pixels along one Thon ring that are averaged. k1(k) is a function that is constant for all k lying on the same Thon ring. In the case of no astigmatism it simply returns the magnitude of k. For the more general case, k1(k) is given by
where k2 is the resolution of the pixel k, (i.e.: k2 = |k|). Eq. (18) is derived in the Appendix.
During calculation of equation (17), Fourier pixels are excluded from the averaging if their power deviates from the average by more than the standard deviation of the power. The latter was calculated from the Fourier pixels for which k1(k) is a constant value, and this value was refined by four times iteratively excluding pixels with an amplitude exceeding the standard deviation of the included pixels. Therefore, strong reflections from the crystal that contain predominantly signal, are mostly excluded from the averaging and the whitening filter reflects mainly the background modulation. The Fourier transform of the background with whitened power spectrum is
where F(k) is the pre-whitening Fourier transform. Eq. (19) includes a multiplication by Sign[CTF(k)] which equals +1 for CTF≥0 and −1 for CTF<0. The multiplication does not change the power spectrum. However, it performs a phase flip according to the CTF that is important when points with different values of the CTF are being averaged. This situation can arise, for example, when there is astigmatism present in an image. Any rotation of an image relative to another image from the particle stack would then result in the averaging of image terms that do not have the same CTF value.
Figure 2 shows the average power spectrum after whitening. As the line scan in Figure 2B shows, the power is now approximately constant. Figure 3 shows that the distribution of densities in both the original the whitened images closely match a Gaussian profile. This shows that the whitening does not significantly alter the density distribution of pixels in an image. The background in the whitened image can now be treated as uncorrelated Gaussian noise and, therefore, satisfies the condition of the likelihood formalism outlined above. Apart from the background term, the whitened image also contains the crystal. However, the SNR of the whitened image is only about 1/170 (see below), making the contribution of the crystal negligible.
The whitening process amplifies the noise level, particularly at high resolution and near CTF zeros. Therefore, the algorithm presented here requires a larger number of particles to obtain the same overall SNR in the final reconstruction, compared with other algorithms that do not require whitening.
The ML procedure described above can be applied to the stack of unit cells excised from the 2D crystal after whitening. The whitened stack is not suitable for determination of the projection structure of the crystal, however, since it does not correct for the CTF of the electron microscope. To obtain a CTF-corrected projection structure of the crystal, a second stack of unit cells has to be generated that contains unaltered amplitudes and phases. Upon convergence of the ML procedure for the stack with the whitened crystal data, an ML estimate of the unaltered crystal can be calculated using Eq. (7) by replacing the data set X with CTF-corrected data set derived from the unaltered crystal. In evaluating Eq. (7), it is important that the probability function γ is calculated using the whitened images.
If is the signal component in the ML estimate of the unaltered crystal, an estimate of the crystal structure S can be obtained by "dividing" by the CTF. However, because the CTF contains regions of small values and zeros, a straight division is not possible. It is customary in these cases to use the well-known Wiener inverse filter (Freiden, 1975). S is then given by
where SNR(k) is the SNR of at point k. The SNR is usually not known at every point in the spectrum. However, an estimate of the average SNR can be obtained from the crystal by comparing the integrated intensity of all diffraction peaks in a power spectrum of the crystal with the integrated intensity of all other points in the spectrum. In a typical low-dose image, such as the image of the bacteriorhodopsin 2D crystal considered below, the average SNR before averaging is about 1/50. After averaging over N unit cells in a stack (for example N=10029 unit cells from the bacteriorhodopsin crystal, see below) the SNR in the average is N times the SNR of the raw image (in our example the average SNR is about 200). If we assume that the SNR is approximately proportional to CTF2,
the average SNR within the considered resolution range, , will be . Here, α is a proportionality constant. It follows for the SNR in the ML estimate from N images that
Using Eq. (22) we can write for the structure S
Eqs. (25) and (26) say that we can correct the observed density by dividing by the CTF at most points. is multiplied by the CTF only where CTF2 becomes small. The value for will be close to 0.5 if the CTF is not significantly attenuated by the envelope ENVi. For a significantly attenuated CTF, the value for the average will be smaller. For example, if the envelope function at the high-resolution end of the considered resolution range attenuates the power spectrum by 90%, the value for is only 0.15. For large values of , for example 200 (see above), the action of the filter (Eq. (26)) will not depend strongly on the precise value of . Therefore, in the following calculations, we will approximate by its upper bound of 0.5.
If the defocus does not change across the image (untilted specimen), the CTF correction factor Ω can be applied to the original image of the 2D crystal before excising the unit cells. Applying the CTF correction to the entire image or at least to larger patches of the original image before excising the unit cells has the advantage that the CTF-dependent point-spread-function (PSF) in the image is not truncated and can be completely included for the CTF correction (Rosenthal and Henderson, 2003; Philippsen et al., 2006).
A further factor affecting the contrast is the resolution-dependent amplitude falloff. To restore the signal at higher spatial frequencies, the amplitudes can be scaled by an exponential function
where a negative temperature factor B determines the amount of amplification. Note that Eq. (27) uses the definition of the temperature factor commonly found in X-ray crystallography. To relate this to the Debye–Waller temperature factor, it has to be divided by 4.
In single particle image processing, the resolution of the final map can be estimated with the help of the Fourier Ring Correlation (FRC) function between the Fourier transformations of two reconstructions that are made from two subsets of the dataset. As described in Stewart and Grigorieff, 2004, this bears the risk of noise correlation, when image data of low SNR are aligned to the same reference with an algorithm suffering from strong reference bias. Therefore, we calculate the FRC between two structures obtained by independent alignment cycles with two different references. As a resolution cut-off, we used FRC = 0.33 to match the crystallographic criterion. A FRC of 0.33 corresponds roughly to a phase error of 45° (Rosenthal and Henderson, 2003). The crystallographic resolution was determined by the IQ-weighted phase residual determined during symmetry averaging, also with a cut-off of 45°.
When applied to averages calculated from a 2D crystal image, the resolution determination by direct FRC generally fails: The Fourier transformation underlying the FRC calculation assumes periodic boundary conditions in the image. As the unit cell stack generated from a 2D crystal image generally does not have window dimensions and orientations that are exactly aligned with the crystal unit cells, the periodic boundary conditions are not met. The discontinuities at the boundaries correspond to strong and sharp contrast features that will lead to spurious correlation in the FRC curve.
We have therefore opted for resolution determination of the final image after application of a circular mask with a smooth edge. In addition, our software extracts the precise crystal unit cell of the final map and re-interpolates this onto a 200 × 200 pixel wide square image, which is then Fourier transformed, and the amplitudes and phases of the Fourier pixels are extracted, following the procedure by Sherman et al., 1998. These values for amplitudes and phases are then directly compatible with the 2D crystallography package of the MRC image-processing suite, and can be used for further processing with the MRC software. Specifically, Fourier merging and lattice line interpolation performed by the MRC software for 3D reconstructions from differently tilted 2D crystal images is made possible.
Crystallographic image processing with the MRC software programs includes the program QUADSEARCH (Crowther et al., 1996), which determines a coordinate list that describes the positions of the unit cells of the 2D crystal. This list is subsequently interpolated into a much finer raster by the program CCUNBEND, which corrects crystal distortions in the real-space image. The corrected image is Fourier transformed and the amplitude and phase values of the diffraction peaks are evaluated. In QUADSERCH, the unit cell positions are found by searching for maxima in a cross-correlation map, calculated by correlating a reference image (extracted from a filtered version of the original image) with the raw image. However, instead of simply determining the locations of global maxima in this cross-correlation map, QUADSERCH can make use of the a-priori knowledge of the approximate crystal unit cell location, and predicts the location of the next unit cell by extrapolating from the last n (usually 6 or 7) identified unit cell locations. Therefore, QUADSERCH only performs a local peak search of the cross-correlation map in the neighborhood of the predicted location. This reduces the risk of mistaking a spurious noise peak for the correct correlation peak indicating the unit cell location. QUADSERCH allows also refinement of the predicted unit cell location table, by extrapolating a specific new unit cell location from the previously determined raster of neighboring unit cell locations, approaching the location in question simultaneously from different sides. This algorithm enables QUADSERCH to find the correct crystal unit cell location with a much higher precision than a simple cross-correlation peak search over the entire unit cell would allow. This allows the usage of a smaller reference particle size, since the prediction algorithm in QUADSERCH can find a correct local peak, even if this peak is only a weak local maximum within the noisy landscape of the cross-correlation map.
A single-particle approach to the processing of images of 2D crystals would have a disadvantage over the crystallographic approach if the unit cells were selected based only on the maxima in the cross-correlation map between reference and 2D crystal image, instead of profiting from the knowledge of the approximately predicted location of the next unit cell. We decided, therefore, to use the list of unit cell locations determined by QUADSERCH. The more accurate centering of the unit cells extracted at the determined locations will lead to a narrow distribution in Eq. (5) (small σx,σy), which acts as a significant constraint in the likelihood maximization. The different steps of processing including QUADSERCH and ML analysis are depicted in Figure 4.
Using the environment of the 2dx software (Gipson et al., 2007a), we utilize the peak position profile determined by QUADSERCH to define the unit cell locations for further processing. The 2dx_image standard-script "Maximum Likelihood" was created, which allows the application of the ML algorithm during the standard image processing sequence. This script calls the program 2dx_ML.exe, which performs the ML calculations. All required parameters and input images for the ML processing are transmitted from the 2dx_image environment, which provides usable default values and offers an interactive help function in form of program-internal manuals, online-documentation and right-mouse-click activated pop-up information windows for the user. The results of the ML processing are channeled back into the 2dx_image graphical user interface (GUI) for further analysis or parameter refinement.
The program 2dx_ML.exe performs noise-whitening according to Eq. (19) on the entire input image, and then windows the particle stack. For the particle selection, the user has the choice of either accepting particles with a QUADSERCH profile correlation value above a given threshold, or explicitly defining the percentage of QUADSERCH particle locations (e.g. 90%) that should be chosen for usage in the ML processing. The program then estimates the ML parameters according to Eq. (4–6, 8–10), and iteratively calculates the next generation of estimates structure A(n+1), according to Eq. (7), with correction of the CTF according to Eqs. (25, 26).
For the first estimate for the iterative processing the user can choose either the average of the noise-whitened particle stack, a computer-generated random noise image, or a randomly chosen unit cell. Upper limits for the translation in form of a circular mask and for the rotational angle search range for the ML profiles can be defined. The iterative calculation of the next estimate can be done by a ML calculation with a weighting scheme according to Eq. (7). The SNR of the data can be increased by applying a 2, 3, 4, or 6-fold rotational symmetry to the calculated estimate, if such symmetry is expected to be present. Application of rotational symmetry automatically centers the result onto the symmetry center. An experimental option to apply a low-pass filter using either sharp cut-off or Gaussian profile to the estimated structure after each ML iteration is available. Application of a low-pass filter during the initial iterations can help the overall convergence of the ML procedure in some cases. The iterations are terminated when either a pre-defined number of iterations is reached or the change of the ML parameters is below a given threshold. For the final reconstruction a negative B-factor can be applied (Eq. 27) to amplify high-resolution terms. The final result is output as an image in MRC format, and can be inspected in the 2dx_image GUI. The final result is also translated into a list of amplitudes and phases following Sherman et al., 1998, for further processing in the 2dx_merge program (Gipson et al., 2007b).
For comparison with the ML results, a cross-correlation (CC) based single particle algorithm is also implemented. This CC algorithm prepares a set of rotated reference, and calculates the cross-correlation map between the set of rotated references and the particles. A peak search over all cross-correlation maps for each particle is then performed. The particles are then rotated and shifted according to the CC peak location, and subsequently averaged to produce a new reference. As for the ML algorithm, the result is then translated back into amplitudes and phases. The user can choose in the 2dx_image GUI between either the ML or the CC algorithm.
The ML algorithm was first applied to an image of a negatively stained OmpF 2D crystal recorded with a CCD camera. Figure 5 shows the results using the ML algorithm. After noise whitening and five ML iterations the OmpF trimer became visible (Figure 5A). However, further ML iterations tracked the hexagonal background pattern from the CCD camera's fiber taper, superimposed on the crystal structure (Figure 5B, C). This is due to the enhancement of the hexagonal pattern in the power spectrum. Even though in the raw image and in the calculated power spectrum no signature of the CCD camera's fiber optics background was observable, the hexagonal pattern became visible in the power spectrum of the whitened image.
The ML algorithm was therefore extended by a function that excludes Fourier pixels from whitening if their resolution was higher than half the Nyquist frequency and if their amplitude was higher than eight times the local average amplitude. The identified pixels were instead set to an amplitude of one, while the whitening algorithm sets the average of the amplitudes of the remaining pixels to one (see Eq. 17 and 19). This function prevents the signal in the Fourier transformation that originates from the fiber optics pattern at high frequencies from dominating the ML estimate. The modified whitening procedure removed the artifacts seen in the OmpF structure (Figure 5D–F).
We compared results using the new ML procedure with results using another algorithm based on linear cross-correlation alignment, and crystallographic image processing as implemented in the MRC software. These three procedures were applied to 2D crystal images of different SNR and crystalline order: We processed 1) a well-ordered bacteriorhodopsin image (frozen hydrated, image recorded on photographic film and digitized, with an SNR of 1/170, Grigorieff et al., 1995), 2) a partially disordered 2D crystal of the ammonium transporter AmtB (negatively stained, CCD image with an SNR of 1/80, Khademi et al., 2004), and 3) a semi-crystalline membrane patch of the tetrameric potassium channel MloK1 (negatively stained, CCD image with an SNR of 1/30, Chiu et al., 2007). To avoid amplification of noise, whitening was not applied in the CC alignment.
For the well-ordered 2D crystal image of bacteriorhodopsin (bR, Figure 6), 3-fold symmetrization was applied during processing with each method. All processing was done with only one image of bR. For this image, as well as the images of other samples processed for this work, the effect of potential beam tilt was ignored. Using the FRC = 0.33 criterion, the ML approach yielded a resolution of 3.2Å, slightly better than that of the CC alignment (3.4 Å). The crystallographic approach produced results at a similar resolution (3.5Å, IQ-weighted phase residual during symmetrization < 45°). The FRC curves in Figure 6C show the correlation between two structures obtained by two separate ML and CC processes, using two independent reference structures. The FRC curves indicate slightly higher resolution of the ML. The ML process converged after 12 iterations with a translational standard deviation of 0.5 pixels and an angular standard deviation of 0.57°. When the alignment was done with the entire dataset and one common reference, and the FRC was calculated using two subsets of the data, the cross-correlation (CC) alignment showed a slightly higher FRC at high resolution (result not shown). This may have been due to the correlation of noise features between the two structures obtained from subsets of the data using a single reference (Grigorieff, 2000).
ML processing outperformed the other two methods when applied to images of partially disordered 2D crystals of AmtB (Figure 7). The ML reconstruction showed a resolution of 12Å (FRC = 0.33). The CC alignment resulted in a visually lower-resolution map, but similar resolution at the FRC cut-off of 0.33. The ML process converged after 23 iterations with a translational standard deviation of 1.1 pixels and an angular standard deviation of 1.35°. The crystallographic processing of the same micrograph with the MRC software resulted in a projection map at 18Å resolution (IQ-weighted phase residual during symmetrization < 45°).
When applied to a badly ordered 2D crystal of MloK1, the single particle approaches achieved significantly better results than the crystallographic approach (Figure 8). Both the ML and CC algorithms produced structures at a resolution of about 20Å. The similar performance might be due to the high SNR, compared to the other images, produced by the high defocus used when recording the image. At high SNR values, the ML and CC algorithms tend to have similar performance (Sigworth, 1998; Scheres et al., 2005). The ML process converged after 25 iterations with a translational deviation of 3.8 pixels. The unit cells were rotated at 90° steps to detect the deviations from four-fold symmetry. The crystallographic processing of the same micrograph resulted in a blurred reconstruction of 28 Å resolution (IQ-weighted phase residual during symmetrization < 45°).
A major advantage of the ML approach, compared with CC alignment, is the larger convergence radius. This means that the final ML estimate is less likely to be biased by the initial reference (Sigworth, 1998; Scheres et al., 2005). Another problem often found with CC alignment is so-called over-fitting, in which the refinement procedure introduces features in the refined structure that reflect the noise in the data, rather than the signal (Grigorieff, 2000; Stewart and Grigorieff, 2004). A hallmark of over-fitting is a FRC curve that shows artificially high values at high resolution where the SNR is low. Following Stewart and Grigorieff, 2004, we designed a test to detect over-fitting in the ML and CC approach. We constructed a test dataset on the computer, consisting of 2000 images that were generated from a test pattern (Figure 9A) by random translations with a standard deviation of 5 pixels. In-plane rotation was not applied to avoid interpolation errors at high resolution. Each pattern was then overlaid with white Gaussian noise to produce a set of noisy images with a SNR of 1/200, one of which is shown in Figure 9B. Since the signal and noise components of each image were known, a detailed evaluation of the alignment performance could be done.
We used the noise-free structure as the initial reference to perform one round of ML estimation, or one round of CC alignment, depending on which procedure was tested. For the ML procedure, the initial value for the standard deviation of translation was 5 pixels, matching the model parameters that were used to generate the simulated data. The performance of each procedure was evaluated by calculating the new ML estimate (or average of the CC aligned images) from only the noise component of the test images. This allowed us to detect any bias produced by the ML or CC alignment approach. A bias is expected to reveal a replica of the reference in the noise average (Stewart and Grigorieff, 2004). The results in Figure 9C, D suggest that the ML procedure exhibits over-fitting to a lesser extent than CC alignment. Over-fitting becomes significantly more apparent in the ML average after 20 iterations (Figure 9F), but still remains less prominent compared with the result from CC alignment (Figure 9E). Especially at high resolution, the FRC between the noise average produced by the ML procedure and the original pattern is much lower compared with the FRC curve calculated for the average from the CC alignment (Figure 9G).
The performance of the ML and CC alignment procedures can also be evaluated by their alignment error
where sxi and syi are the actual offset of the i-th (1 ≤ i ≤ N) image to the true reference, and and are determined from the coordinates of peaks in the CC map calculated between the i-th image and the final map. The ML alignment showed an error of 2.8 pixels, and the CC alignment an error of 5.2 pixels.
Several recent publications reported data of crystals that diffract to less than 8Å resolution (e.g. Oling et al., 2001; Parcej and Eckhardt-Strelau, 2003; Tahara et al., 2000; Ziegler et al., 2004). In those cases, a single particle approach can lead to a substantial improvement (Tahara et al., 2000). Here we developed and implemented an adaptation of a ML algorithm for computer image processing of 2D crystal images.
The amount of noise correlation in three different alignment methods has been studied by Stewart and Grigorieff, 2004. In their experiments, the phase residual performed worst as a similarity measure, CC alignment performed better, and a newly proposed alignment using a weighted CC performed best. The ability of the new method developed by Stewart and Grigorieff, 2004, to minimize noise correlation is partly due to the weighting function. The ML algorithm can be viewed as using a weighting scheme that is related to the cross correlation profile and the in-plane transformation profile (Eq. 5). The profiles usually result in a frequency low-pass filtration, which presumably renders the ML procedure more resistant to noise over-fitting.
The new ML algorithm uses unit cells centered according to the coordinates written out by the program QUADSERCH. The distribution function describing the in-plane translations of the unit cells converged during the iterative ML processing to a narrow Gaussian-like profile with a width depending on the order of the crystal. In the examples shown here the final profiles had standard deviations of three pixels or less, but did not converge to a single point. The widened profile reflects a difference between the correlation peak locations found by QUADSERCH and unit cell locations estimated by the ML algorithm. The effect of the Gaussian-like profile is similar to the convolution of the reference image with a Gaussian filter during a conventional single-particle cross-correlation alignment. With the narrowing of the Gaussian profile during ML refinement, the influence of high-resolution terms in the images becomes stronger. The dominance of the low-resolution terms at the beginning of the refinement is presumably one of the reasons for the superior convergence radius and reduced initial reference bias of the ML procedure, compared with CC alignment. The Gaussian filter also reduces the over-fitting of noise (see above). This self-adjusting filter is similar to the self-adjusting weighting function used with the weighted CC alignment (Stewart and Grigorieff, 2004).
The rotational distribution for the ML processing is assumed to be Gaussian with a standard deviation that depends on the quality of the crystals, for example +/− 2.5° for relatively well ordered crystals. Some crystal images, however, may be best processed by assuming a uniform distribution of rotations, i.e. equal likelihood for all angles within a specific interval. The newly implemented software allows the specification of an angular search range and step size. A large step size can be used to test for systematic deviations from nominal symmetry. For example, deviations from four-fold symmetry of the tetrameric potassium channel MloK1 can be detected by testing alignments of the unit cells in 90° steps (Chiu et al., 2007). Therefore, a prior knowledge of the distribution of translation and rotation is very important for the ML method, as also been noticed by Scheres et al., 2005.
The whitening procedure is essential for satisfying the current ML theory, and needed for the ML method to work reliably. Further development of the theory to allow also non-white noise distributions may improve the performance of the ML algorithm because it avoids amplification of noise. The described whitening filter was applied to images of entire crystals with subsequent excision of the unit cells, to avoid truncation of the PSF. CTF correction and whitening of smaller areas containing only a small number of unit cells is required for adapting the method to tilted images with different defocus areas (this work is ongoing).
Single particle processing of 2D crystal images has been considered previously for images of 2D crystals (Sherman et al., 1998; Tahara et al., 2000). Here we apply the Maximum Likelihood approach for the first time to 2D crystal images. The correlation of real-space noise of neighboring pixels in the image is eliminated by using a whitening filter. Compared with cross-correlation alignment, the ML method is significantly less sensitive to, but not entirely free of noise-correlation and reference bias. The better performance on data of low SNR makes its application to stacks of images containing unit cells excised from the crystal image possible. The ML approach has its greatest advantage over the crystallographic approach when applied to partially disordered crystals where the disorder would normally limit the attainable resolution. Based on our tests, the ML approach can yield structures at better than 3.5Å resolution, sufficient for their interpretation by atomic models.
The newly developed ML algorithm is available within the software package 2dx (http://2dx.org).
This work was in part supported by the NSF, grant number MCB-0447860, to XZ and HS, and by the National Institutes of Health, grant U54 GM-074929, to HS. NG gratefully acknowledges financial support by the National Institutes of Health, grant 1 P01 GM-62580, and by a research fellowship from the Humboldt Foundation. We thank H.-T. Chou for providing the image of a 2D membrane crystal of AmtB, and P.-L. Chiu for the MloK1 image.
In the absence of astigmatism, Thon rings are circular and the function k1(k) in Eq. 17 corresponds to the identity function k1(k) = |k|. Astigmatism produces elliptical or hyperbolical Thon rings, in which case averaging of the pixels along a Thon ring ellipse requires identifying all pixels k in reciprocal space that lie on the same Thon ring ellipse or hyperbole. This is done by the function k1(k), which assigns to each reciprocal pixel k the resolution of the corresponding pixel on the same Thon-ring in the direction of the largest defocus, which is defined as the direction of DF1 or by αast in Eq. 16. The function k1(k) can be derived by calculating the phase shift χ(k) (Eq. 14) for the Fourier pixel k in question and setting that equal to the phase shift χ(k) for the defocus in direction αast:
This can be transformed into
giving rise to Eq. 18:
The sign of the square root in Eq. A2 can be identified by testing for the non-astigmatic case DF1 = DF2 = Δf (k), which leads to
This is equal to
which resolves to k1 = k2, when the minus sign in Eq. A5 and therefore the plus sign in Eq. A2 is chosen.
Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers.