text:
cvc/cvce and cvc/c v v c words- Freebie -Two pages filled with those tricky words that some students need extra practice with.
Students read the 2 words in each box while they watch for the final "e" sound or look for the 2 vowels together while switching back and forth from a short to a long vowel sound.
Use with small group: Listen to students read the list of words. Students could take turns reading one box at a time as they read around the table.
Use at a reading center: Set several copies at a reading center for students to partner read. Students can take turns reading each box.
Use for fluency: How many words can the students read correctly in one minute?
CVC and CVCE Picture Cards help students practice writing these words. This pack includes 20 task cards. Each task card has 9 pictures. The pictures are either a CVC word or a CVCE word. Students need to think about which word to write and to write it correctly.
Need some silent e resources? Try these!
Silent e Games:
Silent e Worksheets:
Thanks for stopping by today!
Until next time,


text:
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subset: commoncrawl


text:
NEW YORK (AP) Maria Sharapova simply couldn't bear the thought of a U.S. Open taking place without her.
So while sidelined with a torn shoulder a year ago, she refused to follow the tournament on TV. Basically pretended it wasn't even happening.
On Tuesday night, Sharapova was right where she likes to be: on the Grand Slam stage and in the spotlight. The 2006 U.S. Open champion returned to the tournament with an impressive 6-3, 6-0 victory over Tsvetana Pironkova of Bulgaria.
DJOKOVIC DIARY: 'I love the New York crowd'
"I was in the physical therapy office every single day, and the tennis was on. But I made a point not to watch it," Sharapova explained. "When you're not participating in a tournament that you very much love, and you've had success at, as an athlete and as a competitor, to not be there and not be competing is pretty tough."
Against her 98th-ranked opponent, Sharapova's game was as glittery as her black-and-silver dress, an outfit she described as a tribute to New York's skyline. The three-time Grand Slam title winner produced 29 winners — 23 more than Pironkova. And Sharapova's game was particularly clean in the second set, when she hit 16 winners and only five unforced errors.
Apart from four double-faults, Sharapova showed no signs of the shoulder injury that forced her to have surgery in October and kept off the tour for nearly 10 months.
"This is a Grand Slam. You've got to get going from the first match," Sharapova said. "After being gone, this is what it's all about."
Tell that to Ana Ivanovic. Or Dinara Safina.
Earlier Tuesday, Safina came perilously close to becoming the first No. 1-seeded woman to lose in the U.S. Open's first round. But she eked out a victory over an 18-year-old from Australia who is ranked 167th and needed a wild-card invitation to get into the tournament.
The worst showing ever by a top-seeded woman in New York came last year, when Ivanovic exited in the second round. Now seeded 11th, Ivanovic did herself one worse this time, losing in the first round to 52nd-ranked Kateryna Bondarenko 2-6, 6-3, 7-6 (7-5).
"It hurts. I can tell you that," Ivanovic said. "I'm sure I will have sleepless nights."
At least the 2008 French Open champion had a big support group in the stands, cheering for her wildly. Safina, in contrast, would look up at her coach for positive body language, and instead, he'd cover his eyes with his hands or turn his head with a wince.
Nearly undone by 11 double-faults and 48 total unforced errors, Safina was a point away from a 4-0 deficit in the third set before coming back to beat Olivia Rogowska 6-7 (5-7), 6-2, 6-4.
Safina, younger sister of 2000 U.S. Open champion Marat Safin, is used to faring well in the early stages of Grand Slam tournaments. Usually, it's later on that problems arise: She is 0-3 in major finals, all lopsided losses, and managed to win only one game against Venus Williams in the Wimbledon semifinals in July.
"I was surprised that, you know, she was giving me free points," said Rogowska, who never has defeated anyone ranked better than 47th.
As Rogowska spoke, her eyes were red, and she fiddled with a well-worn tissue.
"I'm disappointed I lost," she said, "and I didn't expect to say that after playing the No. 1 player in the world. It's a bit weird."
Ivanovic was not the only seeded player who was upset: 276th-ranked Jesse Witten of Naples, Fla., knocked off No. 29-seeded Igor Andreev of Russia 6-4, 6-0, 6-2; Nicolas Lapentti beat No. 19 Stanislas Wawrinka 4-6, 3-6, 7-6 (6), 7-6 (3), 6-3; and Ivan Navarro beat No. 27 Ivo Karlovic 6-4, 7-6 (8), 7-6 (5).
Yanina Wickmayer of Belgium defeated No. 16 Virginie Razzano of France 6-4, 6-3; and Shahar Peer of Israel eliminated No. 32 Agnes Szavay of Hungary 6-2, 6-2.
Otherwise, winners included 2004 U.S. Open champion Svetlana Kuznetsova, past runners-up Elena Dementieva and Jelena Jankovic, No. 9 Caroline Wozniacki and No. 13 Nadia Petrova.
Men's winners included No. 2-seeded Andy Murray, last year's U.S. Open runner-up, who beat Ernests Gulbis of Latvia 7-5, 6-3, 7-5 in Tuesday night's last match.
Also advancing were 2008 Australian Open champion Novak Djokovic and that tournament's runner-up, Jo-Wilfried Tsonga, along with No. 10 Fernando Verdasco, No. 11 Fernando Gonzalez, No. 16 Marin Cilic, No. 17 Tomas Berdych, No. 22 Sam Querrey of Thousand Oaks, Calif., and Taylor Dent of Newport Beach, Calif.
Dent, playing in the U.S. Open for the first time since 2005, eliminated Feliciano Lopez of Spain 4-6, 7-6 (6), 6-3, 7-5.
Neither Safina nor Rogowska played particularly well. They combined for 24 double-faults, 113 unforced errors and 15 service breaks over 2½ hours.
"I put a lot of pressure on her serve," Rogowska said, "and it seemed to crumble a bit."
Afterward, Safina found two things to be happy about: She didn't break any rackets — something big brother Marat is known for — and she didn't receive any warnings from the chair umpire. So, yes, the mental fragility she's acknowledged is an issue for her on court was a factor in her play, but at least Safina managed to keep it in check.
"It happens that you have a bad day and you want to ... say, 'I hate everything,"' Safina said. "But at the end of the day, you win the match, even like this — I would say a little bit ugly. But you come in the hotel, and you are like, 'I made it."'
Rogowska, too, tried to focus on the positive.
A year ago, after all, she was back home in Melbourne, watching the U.S. Open on television. On Tuesday, she was playing in the tournament and nearly winning — against the woman who is ranked No. 1, no less.
"My heart was just going crazy, and I was breathing, like, really fast," Rogowska said. "So next time, I guess, I'm just going to have to learn to stay calm, and, you know, not get too excited."
Sounds like good advice for Safina.
Copyright 2009 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.
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text:
She's still the same old LiLo. READ MORE »
She's still the same old LiLo. READ MORE »
Gotta respect it. READ MORE »
Depending on the booze he drinks, maybe he'll launch into a slurred rap. READ MORE »
To her credit, she did have one awesome policy proposal: banning Republicans from public bathrooms. READ MORE »
Just leave them alone already. READ MORE »
Everytime beautiful and wealthy people marry, I have another glass of wine before 5 p.m. READ MORE »
Looks like it's your move, Taylor. READ MORE »
This will never end. READ MORE »
There's no official word yet, but she's lost her bling. READ MORE »
What Jones has undergone on Twitter is a symptom of the widespread verbal abuse black women and other women of color on social media regularly face. READ MORE »
The alien visitation actually makes a good deal of sense given his space-like aesthetics and quick ascent to increased fame after leaving the bonds of One Direction. READ MORE »
How did we as a society get here? READ MORE »
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Looks like it's going to be a great Fourth of July weekend this year! With plenty of hot sun, warm weather, and fun events to keep the entire family entertained, it's sure to be a holiday weekend to remember.
For so many reasons, this is one of the best times of the year to live in New England. We are finally fully ensconced in summer here, and our patience with the long, snowy winter has paid off. Yes, it's true: berry season is upon us! Whether you are a fan of raspberries, strawberries, blackberries or blueberries, this month marks the time when you have local access to pretty much all of them. Pick them yourself or head over to your local farmers' market and stock up. Berries don't last long, but there are so many ways to preserve them that take very little time and effort. You can make a quick jam using this easy recipe; wash and freeze them for months to come; or you can make them into a simple and healthy dessert that everyone will love: homemade popsicles.
What could be better than an icy pop made up of local, fresh berries and yogurt? Getting your kids involved in the fun- after all, there are very few things that are more fun than getting down and dirty with a bowl full of strawberries that you are allowed to "smush"- with your HANDS!
While the recipe below features a mixed-berry approach of strawberries and blueberries to celebrate this weekend's patriotic festivities, feel free to use any kind of berry, or stone fruits (plums, peaches, etc.) as we get into August and September. Another fun idea? Keep the berries separate and make three different batches of popsicles: each to represent the colors of the flag. If you have several popsicle molds on hand, make one batch that is just strawberry, one that is all blueberry, and for the "white," try your hand at an all banana-yogurt popsicle. If you don't have popsicle molds, here are a few source ideas, or feel free to use what we did growing up: paper cups and popsicle sticks.
Patriotic Mixed-Berry Pops
Yields 6 popsicles
1 cup strawberries, mashed
1 cup blueberries
1/4 cup sugar
1/4 cup water
juice of 1/2 of a lemon, about 2-3 tablespoons
1/3 cup yogurt (I used plain Greek)
Heat the sugar and water in a small saucepan until the sugar dissolves into the water completely. Squeeze the lemon into the simple syrup, stir and put aside. Wash and hull the strawberries, and slice them into rough chunks. With clean hands, smush and mash the strawberries until you have "strawberry soup," with some whole pieces of berries suspended in strawberry juice. Add the blueberries, the yogurt, and the lemon-y simple syrup: stir well until yogurt and syrup is mixed in completely.
Pour the fruit-yogurt mixture into a large liquid measuring cup (especially if it has a pourer- this will make it easier to pour the liquid into the molds). A funnel might also come in handy. Pour the mixture into your molds, leaving a bit of room at the top of each mold as the mixture will expand when frozen. Cap the molds and put in the freezer for at least 4 hours. If you have extra, simply pour into a small jar and freeze for an extra bonus. I have also mixed in more yogurt with my extras to create something a bit different that is more frozen yogurt-like and less-popsicle like.


text: O Jesus, I Have Promised Look Inside O Jesus, I Have Promised SATB choir, keyboard - Moderately EasyComposed by David Ashley White (1944-). Year C Pentecost13; Catholic Year C Ordinary20. Ordination, Confirmation, Ordination/Installation, Commitment/Discipleship, Community/Fellowship, Stewardship. Octavo. Published by MorningStar Music Publishers (MN.50-9055). Usually leaves our warehouse: Within 2 to 3 weeks (Minimum order: 8) More info Add to Cart { "catalogRefId":"17324621", "productId":"prod17324621", "quantity":"1" }


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Skip to comments.Irish coach: Brittney Griner plays "like a guy"
Posted on 04/04/2012 7:18:34 AM PDT by ConservativeStatement
(AP) DENVER - A postgame comment by Notre Dame coach Muffet McGraw about the prowess of Baylor star Brittney Griner caused a stir in the world of social media Tuesday night.
(Excerpt) Read more at cbsnews.com ...
Would have been worse if the Coach said she plays like a girl.
Personally, I would have taken it as a compliment...............
Unlike the One who throws like a girl.
He meant that as a compliment. Why can't we just leave it there?
Obligatory Austin Powers' "That's a man, baby!" picture or Juwanna Mann reference in 3...2...1...
>> He meant that as a compliment.
"Muffet" McGraw is a "she". Dude, don't you remember your nursery rhymes? "Little *Miss* Muffet, tuffet, curds, whey, spider, frightened, &etc? :-)
Just sayin.
Well Laz?
She's one of the few women basketball players that can dunk the ball.
She's probably the only college basketball player who would be competeetive on a men's team.
She's good. It should be considered an accurate statement.
They need a Barr Cheek Cell Test. Many of these 'female' athletes are actually mutants: XXXY, XXY and many other genetic variations. If I was a female LPGA player I ask for a genetics test on Yani Tseng. The question then becomes if they are predominantly 'female' and only partially genetically 'male', should they still be allowed to play?
I agree! I was astounded when I heard her voice. If she is not really a he, I would be amazed.
Of course, what does it matter these days? They let the so-called transgendered compete in women's sports and even beauty contests. According to liberals, there are no differences between men and women and we all choose what we want to be. What a crazy world.
Didn't Laz say his hitting days were over?
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.


text:
Ok, i'm wondering if I should get Reptile, Sub-Zero, or Scorpion's klassic kharacter skin, I know it's last minute but, I really want an opinion. And they all have advantages...
Reptile= Best design, since his other one is his lizard form, which I hate.
Sub-Zero= Best character, I found him to be the best in the demo.
Scorpion= Sweet fatality!!!


text:
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With our extensive experience in multiple sectors, Kier offers you impeccable quality, competitive pricing and a history of successful projects.
On every project, Kier rely on a strategic, consultative approach that often provides significant savings for our clients. And by getting to understand your needs we can help you achieve diverse goals – including environmental, social and health targets.
While our Group gives you the potential to reduce interfaces and costs, our regional businesses carry out projects – giving you the feel of a small, local partner while drawing on local resources.
Kier is a thriving business with a bright future, and we seek long-term, mutually-beneficial alliances with every client. So when you choose Kier you can be certain of our support for many years to come.
Kier works extensively with central government and local authority clients.
Providing corporate clients with dynamic solutions.
From prisons to police stations, Kier helps clients meet tough targets.
Kier delivers and maintains a range of learning environments.
Wide ranging expertise from power stations to waste processing solutions.
Developing solutions that centre around your patient's needs.
Kier creates living spaces and provides support to the social housing sector.
From manufacturing plants to warehouses, we can help streamline your business.
Delivering technically challenging projects around the world.
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From single unit supermarkets to full retail parks, Kier can build, fit out and refurbish.
Kier understands the exacting needs of this specialist sector.
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Army to set bar for each MOS as women enter more jobs
The Army is establishing gender-neutral standards to identify who is capable and qualified to get the job done — any job.
Combat fields opening to women will be the first to see the change, but standards will be set for every military occupational specialty.
Officials are adamant this will neither lower standards so women can qualify, nor raise standards to exclude them from certain jobs. The goal: Identify the physical requirements demanded of each MOS and use that measure as a go or no-go for entry into the career field regardless of gender.
Get all the details in this week's Army Times, on newsstands now.
New center, school to bring signals, cyber, EW together
Army Chief of Staff Gen. Ray Odierno approved a new cyber school for soldiers to consolidate training of the Army's growing cyber force in one location at Fort Gordon, Ga., the first step in what could be a significant reorganization of soldiers with connections to cyberspace operations.
The new Cyber Center of Excellence will incorporate the Signals Center of Excellence and unify training and modernization efforts for cyberspace operations, electronic warfare, cyber electromagnetic activity and cyber-related signals intelligence, Army officials said.
Training and Doctrine Command commander Gen. Robert W. Cone publicly called for the cyber school and also for a cyber career field, and plans to create the latter are underway. Read all about it in the July 1 issue of Army Times, on sale now.
Early-outs expand to Active Guard and Reserve officers
The 15-year early retirement option has been expanded to include federalized National Guard officers of the Active Guard and Reserve who are selected for involuntary separation because of the drawdown.
The option applies to federalized officers who have at least 15 but fewer than 20 years of active service, and who are selected for separation by an Army National Guard force shaping board. Army Secretary John McHugh issued a directive June 10 authorizing the option. The 15-year early retirement option, officially the Temporary Early Retirement Authority, was established by McHugh last fall as the Army prepared to launch a series of retention screening boards for officers and senior noncommissioned officers of the active and reserve components.
Find out more in the latest Army Times.
Army Times Army Careers site
Looking for promotion lists, cutoff scores or this year's board schedules? Find everything you need to know and more on the Army Times careers site, at armytimes.com/career/


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Baptist leaders in Lebanon and France respond to bombings
- November 19, 2015
- By Eron Henry / Baptist World Alliance
Baptists in Lebanon and France reacted to attacks by the Islamic State—also known as ISIS or ISIL—that occurred in their countries.
Evangelicals ponder Christian response to Paris attacks
- November 19, 2015
- By Timothy Morgan / Religion News Service
American evangelical leaders remain at odds over whether the best response to the bloody terrorist attacks in Paris is a war on terrorism and militant Islamic ideology or Christian reconciliation and pacifism.
State Department religious freedom report focuses on terror groups
- October 19, 2015
- By Lauren Markoe / Religion News Service
Secretary of State John Kerry released the annual International Religious Freedom Report and called terror groups the world's greatest threat to religious freedom.
Nepal adopts secular constitution but retains anti-conversion language
- September 17, 2015
- By Ken Camp / Managing Editor
Lawmakers in Nepal rejected an effort to declare the Himalayan nation a Hindu state, adopting a new constitution Sept. 14 defining Nepal as a secular republic but retaining a controversial anti-conversion clause.
Europe's refugee crisis stirs consciences, but responses vary
- September 11, 2015
- By Tom Heneghan / Religion News Service
Europe's refugee crisis has inspired faith communities across the continent to open their doors to the newcomers and advocate for more state and private help, but the urgency of their calls and the depth of responses to them vary from country to country.
Advocates urge Nepal to avoid criminalizing religious conversion
- August 19, 2015
- By Ken Camp / Managing Editor
An international coalition spearheaded by the 21st Century Wilberforce Initiative, with significant Baptist involvement, urged government officials in Nepal to remove from the nation's proposed constitution language criminalizing "any act to convert another person from one religion to another."
Baptist leader celebrates Ebola-free Liberia
- May 14, 2015
- By Bob Allen / Baptist News Global
A Liberian Baptist leader celebrated the World Health Organization's declaration the country is Ebola-free, making it the first of the three hardest-hit West African nations to bring the epidemic to a formal end.
Updated: Baptists respond to needs in earthquake-ravaged Nepal
- April 28, 2015
- By Staff / Baptist Standard
Baptists in Nepal and their global missions partners joined in urging prayer and disaster relief after a 7.8-magnitude earthquake claimed more than 5,800 lives.
Islam's Sunni/Shiite divide explained
- February 27, 2015
- By Kimberly Winston / Religion News Service
Sunni and Shiite Muslims, two main sects of Islam, have been in conflict for more than a millennium. Here's a primer on that ancient division.
International community castigated for ignoring terrorism in Nigeria
- January 23, 2015
- By Eron Henry / Baptist World Alliance
The international community has devalued Nigerian lives by ignored terrorist violence and attacks in Nigeria, insisted Samson Ayokunle, president of the Nigerian Baptist Convention.
Persecution of Christians reached historic levels in 2014. Will 2015 be worse?
- January 8, 2015
- By Jonathan Merritt / Religion News Service
From imprisonment to torture to beheadings, more Christians worldwide live in fear for their lives than at any time in the modern era.
Archaeologists may have uncovered site of Jesus' trial
- January 8, 2015
- By Michele Chabin / Religion News Service
The site where Jesus may have been tried, prior to his crucifixion, now is open to the public for the first time.
Liberian Baptist leader returns home after delay due to Ebola
- December 9, 2014
- By Robert Dilday / Baptist News Global
Liberian Baptist leader Emile Sam-Peal is finally going home after being stranded five months in America because of Ebola-related flight cancellations
Orphans abandoned and shunned in Africa's Ebola crisis
- October 25, 2014
- By Sheilia Passewe / USA TODAY
As Ebola continues its rampage across Liberia and elsewhere in West Africa, thousands of children are taking a double hit: losing parents to the fatal virus and then being shunned by relatives who fear they will catch the disease.
Mideast Christians appeal for action
- September 19, 2014
- By Bob Allen / ABPnews/Herald
Christian minorities are in danger of being eradicated in the Middle East, leaders of evangelical and Protestant denominations in Syria and Lebanon said in a joint statement.


text:
News By Tag
* Fitness Training
* Triathlon Training
* Bicycle Fitness
* CompuTrainer Center
* Indianapolis
* More Tags...
Industry News
News By Location
Industry News
Indianapolis Road Bike and Tri Shop to Open Pro Fit Cycling Center Indoor Computrainer Facility
Just in time for shorter, colder days, legendary road bike and triathlon shop, T3 Multisport, is opening a new indoor fitness center designed to help any cyclist take it to the next level. Everyone from beginners to pro's welcome starting Oct 31.
The centerpiece of the new facility will be the CompuTrainer Multi-Rider center. CompuTrainers allow cyclists to ride their own bike indoors while providing data such as heart rate, cadence, power, speed, distance, and caloric expenditure. The rear wheel attaches to a flywheel which adjusts the resistance to simulate outdoor riding and creates the perception of varying terrain indoors! There are hundreds of triathlon and cycling courses where friends can compete or prepare for upcoming races. Changes in fitness are easily tracked and quantified by performing periodic power tests and noting the power numbers during workouts.
Owner and triathlete, Vern LaMere, explains that the new center will be perfect for triathletes and cyclists of all levels, from beginners to advanced. "Those who want to train for sprints and those who want to prepare for Ironman triathlons can gain in strength and endurance. For those who have specific goals such as increased power, aerobic and anaerobic endurance, lactate threshold, hill climbing ability, and for cyclists who simply want to increase their overall fitness and lose weight, we have sessions that will help them achieve any or all of these goals.
While some would suggest that the use of an indoor CompuTrainer might be boring compared to having the wind in your face out on the road, LaMere points to a long list of benefits other that the obvious weather issues like rain, snow, sleet, and freezing temperatures. "Serious athletes know the benefits associated with riding CompuTrainers (see more details at http://www.t3multisport.com/
● There are very few interruptions such as stop lights, traffic, unwanted downhills, potholes, or dogs to disrupt focus and efficiency of the workout.
● Workout time is maximized. It is generally accepted that to convert an outdoor training ride to indoor workout, reduce the total ride time by 20% since more energy is expended on an indoor trainer.
● The controlled environment allows for better management of target zones, cadence, interval times, etc.
● Very few variables mean it is easy to quantify improvement by comparing data from one workout to the next.
● The involved process of deciding what to wear and putting on layers of clothing in the winter is never an issue with consistent indoor room temperatures.
Stationary riding allows one to work on technique exercises such as single leg drills and fast pedaling.
● The limitations and sometimes negative aspects of group riding and training partners are eliminated.
● Riding can be done at any time of the day, (assuming the studio is open!) in all weather conditions.
● It is what the pros do! Top level professional triathletes actually do the majority of their training indoors all year long.
The addition of the new Pro Fit Cycling Center adds to the growing list of services available to triathletes and road cyclists at T3 Multisport (see website at http://T3Multisport.com) such as the professional fitting studio and personal coaching. The shop is widely known for the top brands in professional cycling and triathlons, such as Cervelo, Felt, Guru, Look, Litespeed, and Quintano Roo.
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A federal court in Minnesota scheduled a hearing on April 6 for the antitrust suit the NFLPA filed against the NFL last week.
At the hearing, currently scheduled to be heard by Judge Susan Nelson, the NFLPA is expected to ask for injunctive relief against the lockout league owners imposed on Saturday after the expiration of the collective bargaining agreement.
Nelson was the third judge assigned to the case after two previous judges recused themselves.
It's not yet known whether the case will make its way before Judge David Doty -- who has traditionally heard arguments between the league and the NFLPA.
If the court grants injunctive relief to the NFLPA, the lockout could be invalidated and league operations (including free agency and other player movement) could then resume at some point thereafter. Currently, almost all operations between players and teams have ceased.
The NFLPA decertified as a union on Friday, and it is expected to argue that the NFL cannot lock out their players since they are no longer represented by a union.
The sides broke off talks last week after failing to reach agreement on a new CBA as they bicker over how to split the league's roughly $9 billion in annual revenue.
Nate Davis is a reporter, blogger and editor who's been at USA TODAY since 2000. He has covered the NFL since 2005. No, he did not play quarterback for Ball State. Davis' succession of our esteemed colleague Sean Leahy at The Huddle is considered a Brady-for-Bledsoe swap by most "insiders."More about Nate


text:
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Doctor Hoff's Biography
Contact Information
Full Name:Samuel 'Doctor' B. Hoff
Family:Wife: Phyllis
Birth Date:06/07/1957
Birth Place:Williamsport, PA
Home City:Dover, DE
- PhD, Political Science, State University of New York, Stony Brook, 1987
- MA, Political Science, State University of New York, Stony Brook, 1983
- MA, Political Science, American University, 1981
- BA, Political Science, Susquehanna University, 1979
- Candidate, United States President, 2012
- Candidate, United States President, 2004
- Candidate, United States President, 2000
- Member, Suffolk County, New York Democratic Party Committee, 1984-1986
- Member, Delaware Humanities Forum, Visiting Scholar Speakers Bureau, 2002-present
- Chair, Human Relations Commission, Delaware, 2005-2010
- Graduate Director, College of Humanities and Social Sciences, Delaware State University, 2011-present
- Commentator, WHYY-TV12, 2007-present
- Law Studies Director, College of Humanities and Social Sciences, Delaware State University, 2004-present
- Commentator, WBOC-TV, Dover Bureau, 1991-present
- Professor, Delaware State University, 1989-present
- Graduate Director, Historic Preservation Program, Delaware State University, 2005-2011
- Chair, Department of History, Political Science, and Philosophy, Delaware State University, 2000-2003
- Director, ROTC, Delaware State University, 1993-1999
- Visiting Professor, Wichita State University, 1988-1989
- Assistant Professor, State University of New York, College at Geneseo, 1987-1988
- Assistant Professor, Ohio Wesleyan University, 1986-1987
- Adjunct Professor, Wittenberg University, 1987
- Consultant, Elliott Sluhan Productions, Toldeo, Ohio, 1985
- Adjunct Professor, New York Institute of Technology, Old Westbury, 1985
- Staff Assistant, United States Senator Jacob Javits, 1983-1985
- Staff, Clean Water Action Project, 1980
- Research Assistant, United States House Subcommittee on Human Resources, 1980
- Warehouse Staff, Hoff Supply Company, Pennsylvania, 1972-1979
- Intern, Congressman Allen Ertel, 1978
- Board of Directors/Secretary, Society of the War of 1812, Pennsylvania Division, 2007-present
- Board of Directors/President, Delmarva Discussions, Delaware, 2006-present
- Legal Assistance, Paralegal Advisory Board, Delaware Technical and Community College, 2006-present
- Member, Academy of Political Science
- Member, American Political Science Association
- Member, Center for the Study of the Presidency
- Member, Central Delaware Chapter of National Association for the Advancement of Colored People
- Member, Delaware Medal of Honor Historical Association
- Member, Friends of the Vietnam Center
- Member, George Washington Society
- Member, Lincoln Club of Delaware
- Member, Midwest Political Science Association
- Vice President, Military Awards, General Society of the War of 1812, 2009-present
- Member, National Capitol Area Political Science Association
- Member, National Social Science Association
- Member, New York State Political Science Association
- Member, Northeastern Political Science Association
- Member, Pennsylvania Political Science Association
- Member, Society for Military History
- Member, Southern Political Science Association
- Member, Western Political Science Association
- Board of Directors, Underground Railroad Coalition of Delaware, 2010-2013
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Invoketress' Biennial Bellydance Fusion Show
8pm - 11pm - Saturday, November 12th
The River Run Centre - 35 Woolwich Street, Guelph
Click HERE to purchase tickets
The Mosaic is the 11th biennial theatrical Bellydance fusion show put on by Guelph's own, Invoketress Dance.
Join us for an innovative and imaginative evening of dance featuring some of Southern Ontario's finest, as they perform their interpretations of this year's theme: Evoking Otherworldly Beings.
Guests include:
Internationally-acclaimed Shades of Araby, Hamilton.
The incomparable Roula Said, Toronto.
Award-winning Ishra Blanco, Guelph.
Members of the twice Juno-nominated Eccodek, Andrew McPherson and Brent Rowan.
Dance Artist at Dance Theatre David Earle, Georgia Simms, Guelph.
Royal Academy of Dance TCP and Canadian Dance Teachers Associate, Crystal Reia, Kitchener.
Musical mastermind, Gary Diggins, Guelph.
Award-winning duo, Raqs Mahasti, Hamilton.
The innovative, Rinceoiri Celtica, Guelph.
Twitter @invoketress | Instagram @invoketress |
www.facebook.com/invoketress | www.youtube.com/invoketress |
History of the Mosaic
For over the past decade, Ishra and Invoketress have been pushing the creative envelope by organizing and hosting their much-anticipated Bellydance fusion show – a production that takes Bellydance and fuses it with the many other dance forms that exist. This highly acclaimed show was formerly known as the "Mish Mash Belly Bash." In 2012, Invoketress changed the name to "MOSAIC" Bellydance Fusion Show to represent the melding of artistic expressions and dance styles with Bellydance. The show is also now held every two years in order to properly prepare for and create outstanding numbers for a truly memorable, professional, high caliber show. Guest performers are carefully selected by their talent and innovation. Each show has a theme that focuses the show's pieces and to build context.
Invoketress prides itself on presenting the finest in Bellydance Fusion from Southwestern Ontario.
Past Guests Include:
- Arabesque Earthshakers
- Audra Simmons and Lavish
- Belly Up's Ala Nar
- Dance Sister Dance
- Denise Mireau
- Flying Dance Company
- Iman from KAMA Entertainment
- Rinceoiri Celtica
- Shades of Araby
- Karimah from Ancient Moves Dance Co.
- Sandstorm Studio
- and more
Past Musical Guests Include:
- Amber McLean
- Cuneyt Yetkiner
- The Bhadra Collective
- Andrew McPherson of Eccodek
- The Light of East Ensemble
"Thank you again Ishra, Invoketress and volunteers for making MOSAIC one of the events I always look forward to all year. Great to see old friends and support each other in an environment of love and creativity!" - Jaenne
"The Flying Dance Company loved being part of an amazing group of talented ladies and man. We hope we can get more men appreciating and joining us as we all celebrate dance in all forms, may it be in Belly Dancing, Flamenco, Argentine Tango, Salsa, Highland Dance and more. Thank you to Ishra and the amazing people at Invoketress for hosting us all – see you all on the dance floor!" - Nico of Flying Dance Company
"Ishra…thank you so much for having Ala Nar and myself perform last night! What a fun night and a fabulous venue! Thank you again for all that you do!" - Joharah of Belly Up
"Outstanding show last night! It just keeps getting better and better!!" - Lorraine
Arabesque Earthshakers
"Arabesque Earthshakers had a brilliant time performing at Mosaic! Many thanks to Ishra and her awesome crew for creating such a lovely show!" - Arabesque Earthshakers
Dance Sister Dance
"Ishra and crew, thank you so much for including Dance Sister Dance in the Mosaic show. We thoroughly enjoyed sharing our dance with the audience and sharing the stage with so many beautiful performances. Much love and blessed be." – Dance Sister Dance
"Wonderful job tonight ladies! best show yet!!! Loved watching you all!" – Crystal, Dance Instructor and Choreographer
2010 -2014 Posters designed by Mandy Habermehl
Video Archive


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|Hua Dong1, 2, Yanghua Xiao3, Wei Wang3, Li Jin1,4, Momiao Xiong1, 2*
|1Laboratory of Theoretical Systems Biology and Center for Evolutionary Biology, State Key Laboratory of Genetic Engineering, School of Life Science, Fudan University, Shanghai 200433, China
|2Human Genetics Center, University of Texas School of Public Health, Houston, TX 77030, USA
|3Department of Computing and Information Technology, Fudan University, Shanghai 200433, China
|4Chinese Academy of Science-Max-Planck-Gesellschaft Partner Institute for Computational Biology, Shanghai Institutes for Biological Science, CAS, Shanghai, 200433, China
|Corresponding Author :
|Dr. Momiao Xiong,
Phone : 713-500-9894,
Fax : 713-500-0900,
Email : [email protected]
|Received: December 14, 2008; Accepted: December 24, 2008; Published: December 26, 2008
|Citation: Hua D, Yanghua X, Wei W, Li J, Momiao X (2008) Symmetry of Metabolic Network. J Comput Sci Syst Biol 1: 001-020. doi:10.4172/jcsb.1000001
|Copyright: © 2008 Hua D, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Previous studies of properties of metabolic works have mainly focused on the statistic properties of networks, including the small world, and power-law distribution of node degree, and building block of network motifs. Symmetry in the metabolic networks has not been systematically investigated. In this report, symmetry in directed graph was introduced and an algorithm to calculate symmetry in directed and disconnected graphs was developed. We calculated several indices to measure the degree of symmetry and compared them with random networks. We showed that metabolic networks in KEGG and BioCyc databases are generally symmetric and in particular locally symmetric. We found that symmetry in metabolic networks is distinctly higher than that in random networks. We obtained all the orbits in networks which are defined as structurally equivalent nodes and found that compound pairs in the same orbit show much more similarity in chemical structures and function than random compound pairs in network, which suggests that symmetry in the metabolic network can generate the functional redundancy, increase the robustness and play an important role in network structure, function and evolution.
|symmetry; metabolic network; structural equivalence; orbit
|Metabolic networks are composed of consecutive chemical reactions to produce energy and various molecules. They are represented as directed hyper-graphs, with compounds and(or) enzymes as nodes and the reactions activated by the enzymes as hyper-arcs. How to characterize the structure of metabolic networks and how to link their structure with function are important in gaining deep understanding of metabolic networks. In the last decade, we have witnessed the great progress in theories and models of complex networks, which provide new powerful tools for study of metabolic networks. Previous research in complex networks have primarily focused on finding the statistical properties of various networks, such as small world properties(Jeong et al., 2000; Ma and Zeng, 2003; Wagner and Fell, 2001; Watts and Strogatz, 1998); power-law distribution of node degree(Mahadevan and Palsson, 2005; Samal et al., 2006); building block of network motifs(Eom, Lee and Jeong, 2006; Milo et al., 2002) and hierarchical structure of the network topology(Guimera and Nunes Amaral, 2005; Ravasz et al., 2002) . A lot of research exploiting the theory or model of complex networks has been dedicated towards metabolic networks. Jeong et al(Jeong et al., 2000), Mat and Zeng(Ma and Zeng, 2003) calculated the average path length of the metabolic networks and concluded that metabolic network belongs to small-world network. The small-world characteristic implies that information and energy can be rapidly transferred to the whole network and the cell can response quickly to perturbation of environments. Jeong(Jeong et al., 2000) also calculated the degree distribution and concluded that metabolic network follows the power-law distribution with exponential index r ≈ 2.2 . However, the small-world property is still disputing(Arita, 2004). R. Milo(Milo et al., 2002) introduced the concept of'network motifs' and developed algorithms for their identification. Young-Ho Eom (Eom et al., 2006) applied the concept of network motifs to metabolic network and identified the network motifs and the statistically significant subgraph patterns as well. Ravasz (Clauset, Moore and Newman, 2008; Guimera and Nunes Amaral, 2005; Ravasz et al., 2002) proposed the hierarchical-modular model according to the characteristics of metabolic network. They calculated the average clustering coefficient for 43 different organisms as a function of the number of distinct substrates present in their metabolism. They found that, for all 43 organisms, the average clustering coefficient is about an order of magnitude larger than expected for a scale-free network of similar size.
|However, symmetry, a universal property of real networks, has been rarely studied for metabolic network. Symmetry characterizes the invariance under possible transformations and implies conservation laws of nature (Hatcher, 2002; MacArthur, 2008; MacArthur and Anderson, 2006). Symmetry provides redundancy and robustness against perturbation of environments. There is increasing recognition that the universal evolution is caused by symmetry break, generating diversity and increasing complexity and energy(Mainzer, 2005; Quack, 2003). Symmetry break is often followed by addition of functional modules that usually show local symmetry, increasing network robustness(Felder et al., 2001). Until recently, after the concept of symmetry based on the automorphism has been utilized to explore real networks, quantitative methods for investigation network symmetry have been developed. MacArthur(MacArthur, 2008; MacArthur and Anderson, 2006) first found that large real networks are quite symmetric and such symmetry in real networks can be attributed to the local symmetry which is hidden in local substructures. Xiao(Xiao et al., 2008b; Xiao et al., 2008c) then proposed a principle referred to as "similar linkage pattern", which means that nodes with similar properties such as degree tend to have similar linkage targets, to explain the emergence of symmetry. In Ref. [19], symmetry is exploited to characterize the structural heterogeneity of complex networks. Symmetry in real networks has been further used to characterize the simplicity hidden in networks and consequently has been utilized to simplify the network while reserving many key properties of original networks, such as complexity and communication(Xiao et al., 2008a).
|To date, symmetry in metabolic networks and the relations between the structural symmetry and function of the network have rarely been investigated. It is still unknown whether symmetry exits in metabolic networks. If it does, the existence of such symmetry also begs a biological explanation. Purposes of this report are (1) to examine the symmetry of the metabolic networks, (2) to measure the abundance of the symmetry in metabolic networks, (3) to obtain the orbits (structurally equivalent nodes) through restricted network quotient and (4) to explore biological implication of the symmetry of the metabolic networks. To accomplish this, we first reconstruct metabolic networks for 705 organisms in KEGG and 373 in BioCyc databases. Then, we study the influence of connectivity of the reconstructed networks on the symmetry of metabolic networks. Previous works about symmetry in the general networks have focused on undirected graphs. However, the metabolic networks are usually handled as directed graphs. Hence, it's necessary to explore symmetry in directed graphs and develope algorithms to find symmetry in the directed and disconnected networks. Based on these results, we then systematically investigate the properties of symmetry in metabolic networks, including the degree of symmetry, restricted network quotient. To explore functional implications of the structural symmetry of metabolic networks, we test the chemical structure similarity of the symmetric compounds in metabolic networks of 705 organisms which allow us to reveal the relationships between the network symmetry and its function.
|Results and Discussion
|Reconstruction of Metabolic Network
A metabolic network is represented as a directed graph G (N,E) with node set N representing compounds and the edge set E representing the chemical reactions which the compounds participate in. The direction of each edge implies the direction of the chemical reaction. We downloaded the metabolic network data from two major metabolic network databases: KEGG(Kanehisa and Goto, 2000) and BioCyc.
|KEGG is a collection of simplified metabolic networks which are manually drawn pathway maps representing knowledge on reactions, while currency metabolites such as H2Oand ATP are not included. Xml files of all metabolic pathways for 705 organisms were downloaded from KEGG FTP. We reconstructed the metabolic networks according to the reactions data extracted from the xml files and visualized the network by Pajek(Batagelj and Mrvar, 2003). According to KEGG metabolic functions classification, we integrated single pathways into functional modules. Finally we integrated 11 functional modules into a whole metabolic network. See Figure 1 (a) (b) for Drosophila melanogaster's Cofactors and Vitamins Metabolism module and the integrated metabolic network.
|The BioCyc collection of Pathway/Genome Databases (DBs) provides electronic reference sources on the pathways and genomes of different organisms. We collected metabolic pathways of 373 organisms, extracted the reaction data of each organism and integrated the reactions to a network for each organism. Direction of reactions is not given in BioCyc database but currency metabolites are included in. So we finally got 373 undirected graphs including currency metabolites from BioCyc. We first analyze symmetry of KEGG networks and replicate our experiment for BioCyc networks to validate whether our conclusions are ubiquitous in metabolic networks. See additional files 1 for organisms and pathways in KEGG and BioCyc.
|The Connectivity of Metabolic Networks
For the integrated networks of 705 organisms in KEGG, the number of the connected subgraphs (NCS) varies from 1 to 271. Only 5 networks (0.7%) contain less than 10 connected subgraphs. The maximum connected subgraph (MCS) contains 7.8%-100% nodes of the whole network. The proportion of MCS, which is defined as the ratio of the number of the nodes in MCS over the total number of nodes in the network, in 99.6% and 56% of the constructed metabolic networks is less than 80% and 60%, respectively. So we can conclude that the connectivity of metabolic is quite low. We introduced normalized entropy based on the connected subgraph (NECS) to measure the degrees of the connectivity of the network (See Materials and Methods). The larger NECS, the less the network connected. NECS value of the metabolic networks ranges from 0 to 0.778064 with the mean value 0.410917.
|For the integrated networks of 373 organisms in BioCyc, the number of the connected subgraphs (NCS) varies from 2 to 76, which is distinctly less than that in KEGG. The maximum connected subgraph (MCS) contains 92.1%-99.3% nodes of the whole network, definitely larger than that in KEGG. NECS value of the metabolic networks ranges from 0.007 to 0.075 with the mean value 0.0347128. As the currency metabolites were included in BioCyc , the connectivity of metabolic network is significantly increased.
|To gain deeper understanding of the connectivity in metabolic networks, we compared it with the random networks. For each real graph, we generate 100 randomized networks by rewiring the local edges(Maslov, Sneppen and Zaliznyak, 2004). Then we compute the MCS, NCS and NECS for every network and summarize the mean and variance over the 100 randomized networks. From the error bar in Figure 2, we can see clearly that: most of the NCS in real metabolic network is larger than that in random network (89.8%); most of the MCS in real metabolic network is lower than that in random network (96.9%); NECS in real network is obviously larger than the corresponding random network (96.9%). We also compared the connectivity of BioCyc network with their random networks using the same method. In spite of relatively larger connectivity compared with that in KEGG, the connectivity in BioCyc metabolic network is still smaller than that in random networks. The results are shown in Supplementary Figure 1. The results of NCS, MCS and NECS value for 705 real networks and their corresponding randomized networks for both KEGG and BioCyc networks were shown in additional data file 2. The results above imply that the connectivity in metabolic network is rather small. Consequently connectivity has to be taken into account when exploring the network reduction of metabolic networks.
|Symmetry in Metabolic Networks
Given a metabolic network G(N,E), a one-to-one mapping, or bijective mapping, from N onto itself is called a permutation on N. Two nodes are adjacent if there is an arc from one node to the other node. Among all the permutations in S(N), where S(N) is the set of permutations acting on N, some permutations can preserve the adjacency of the nodes and these permutations are called automorphisms acting on the node set. The set of automorphisms under the product of permutations forms a group: Aut(G)(Tinhofer and Klin, 1999).Two nodes x and y are automorphically equivalent to each other if there is an automorphism that transforms node x to node y. In the context without confusion, such equivalence relation of nodes is also called structural equivalence. A set of structurally equivalent nodes is defined as an orbit of Aut(G). According to such equivalent relation on node set, we can get a partition P={N1,N2,…Nm}, called as automorphism partition, which is composed of orbit sets N1,N2,…Nm . An orbit is non-trivial when it contains more than one node, otherwise it's trivial. A network is called symmetric if we can find at least one non-trivial orbit in this network, otherwise the network is asymmetric. The quotient graph of an undirected graph is defined as a reduced graph which has every orbit (structurally equivalent nodes) as its new node and adds an edge to connect two nodes if there is at least one edge from any one node in the orbit to any one node in another orbit. The quotient graph of a directed graph is similar to that of undirected graph except that the direction of the arcs is preserved in the quotient of directed graph.
|Consider the undirected graph G0 in Figure 3(A), the automorphism partition is P0={N1,N2,N3, N4}, where N1={1,2}, N2={3}, N3={4}, and N4={5,6,7}. There are four orbits which are classified by different colours. The quotient graph of G0 is shown in G1. The four orbits of G0 are reduced to four nodes in G1 , and as long as there is an edge between any two orbits of G0, the corresponding nodes in G1 are adjacent. For directed graph G0 in Figure 3(B) , the automorphism partition is P0={N1,N2,N3,N4,N5}, where N1={1,2}, N2={3}, N3={4}, and N4={5,6} and N5={7}. The five orbits of G0 are reduced to five nodes in G1 , and as long as there is an arc from one orbit to another orbit in G0, there is an arc from one corresponding node to another corresponding node in G1 (shown in Figure 3(B)). Please note that in the directed graph G0 in Figure 3(B), the edges between orbits N1 and N2 and that between N2 and N3 are both bidirectional, which determines that the edge between corresponding nodes in G1 are bidirectional. Because the direction of arc <7, 4> is different from that of <4, 5> and<4, 6>, nodes 5 and 6 belong to the fourth orbit while node 7 belongs to the fifth orbit.
|Consider Figure1 (A) where we take the Drosophila melanogaster's Cofactors and Vitamins metabolism module as a real example. There are 100 nodes and 96 arcs in this module. The NCS(number of connected subgraph) is 25, which implies the connectivity of this network is very small. There are 12 non-trivial orbits in the network, each of which is marked in green ellipse.
|To measure the degree of the symmetry of metabolic networks, we calculate α: the size of Aut(G), β: the relative degree of network symmetry of 705 metabolic networks1 α. reflects the absolute symmetry degree of network directly. β is used to measure the symmetry of networks with different sizes. Generally, the larger α and β is, the more symmetric the network is. Among all the tested metabolic networks, 99.3% of them have α larger than 1010 and 82.3% of them have α larger than 10100, which implies that most of metabolic networks are far away from asymmetric network. Hence, generally metabolic networks can be characterized as symmetric networks. Statistics of β shows that 98.7% of the metabolic network has β smaller than 0.1 and 83.3% of the metabolic network has β smaller than 0.01, which suggests that relative symmetry degree of metabolic network is quite low compared to the maximal symmetry degree of networks with equivalent number of nodes.
|We also summarize φ: the degree of global symmetry for the networks. For some networks, there is some of automorphisms moving all the nodes or most of nodes. The action of such automorphism on node set will have global influence on the structure of the graph. However, for some other networks, all the automorphisms only move a small part of vertices or only action on the local subgraph of the network. Hence, when studying symmetry of networks, it's necessary to characterize the degree of global symmetry or local symmetry of the network. Generally, the larger φ is, the more globally symmetric the network is. Among all the tested metabolic networks, 98.6% of which has φ smaller than 0.1 and 72.8% has φ between 0.05-0.01, which suggest that metabolic network is very local symmetric.
|To validate our conclusion, we replicate our experiment using BioCyc datasets. Among all the tested metabolic networks, 97.6% of them have α larger than 1010 and only one network (metaCyc) has α larger than 10100. Statistics of β shows that only 1metabolic network has β smaller than 0.001 and 5 of the metabolic networks has β larger than 0.01, β values of the other networks (98.4%) are all between 0.001 and 0.01. φ of BioCyc data varies from 0.002071 to 0.0434783 with a mean value of 0.008364. Please see additional data file 3 for the results of α, β and φ value for metabolic networks in KEGG and BioCyc.
|To further investigate the symmetry of metabolic network, we compared three indices α, β and φ of metabolic network with corresponding randomized networks. For each real metabolic networks for703 organisms, we generated 100 randomized networks with the same number of nodes and edges as the real network following Erdos-Renyi random graph model (Erdos and Renyi, 1960)2 .(Two organisms: Debaryomyces hansenii (dha) and Legionella pneumophila Corby (lpc) were not included because they cannot produce Erdos-Renyi random networks due to their small network size). Then we compute α, β and φ for every random network and summarize the mean and variance over the 100 randomized networks for each real network. The comparisons of α, β and φ between real network and random networks are shown in Figure 4. We can see clearly from Figure 4 that 99.4% of α, 99.4% of β and 99.9% of φ in real metabolic network is larger than that in random network. These results demonstrated that the symmetry in metabolic network is obviously strong than that in random network, suggesting that symmetry is an important and nonignored feature in metabolic network.
|Again, we replicated our study in BioCyc metabolic networks. We found that in spite of relatively less symmetry compared with KEGG, the symmetry in BioCyc network is still substantially larger than that in random networks, suggesting that metabolic network is far away from asymmetric network. The comparisons of α, β and φ between real network in BioCyc and random networks are shown in Supplementary Figure 2. Please see additional data file 4 for the results of α, β and φ value for randomized networks in both KEGG and BioCyc.
|Comparison of the Cconnectivity and Symmetry of Metabolic Networks between KEGG and BioCyc Datasets
In table 1, we compared the range, mean value and variance of three connectivity indices NCS, MCS, NECS and three symmetry indices α, β and φ between networks of 705 species in KEGG and networks of 373 species in BioCyc. We can see clearly that for all the six measures, the range and variances in BioCyc datasets is significantly less than that in KEGG datasets. (For the range of log10 α in BioCyc, if we get rid of the largest value 612.608 and the smallest value 0.903; remaining values range from 6.85-96.367). The mean values of NCS and NECS of BioCyc datasets are less than that in KEGG datasets, however, MCS of BioCyc is larger than that of KEGG. All these facts suggest that metabolic network in BioCyc is more connected. Since symmetry is typically greater for lower connectivity and shorter branches networks (MacArthur, 2008), it's naturally to find that symmetry in BioCyc networks is less than that in KEGG networks.
|However, for both datasets, we clearly found that symmetry in real networks is obviously larger than that in randomized networks. No matter which metabolic network reconstruction methods were used, we came to the same conclusion that the symmetry of metabolic network, specifically, local symmetry, does exist.
|Inferring Functional Equivalence from Structural Equivalence
We calculated the automorphism group (See material and methods for its definition) and obtained the orbits (structurally equivalent nodes) considering the connectivity and direction constraints for the reconstructed metabolic networks of all 705 organisms in KEGG. Since nodes in the same orbit are structurally equivalent to each other, it motivates us to further explore whether structurally equivalent nodes are functional equivalent. To accomplish this, we first generated two datasets which consist of similarity scores (See Materials and Methods for definition of similarity score). One dataset is referred to as orbit dataset. For each orbit in the metabolic network we calculated similarity scores for all pairs of compounds in the orbit and averaged them as the similarity score of the orbit. All similarity scores of the orbits in the networks of 705 organisms in KEGG were collected to form the orbit dataset where the replicated orbits were just calculated once. Another dataset which is referred to as random dataset was generated by collections of similarity scores of all pairs of compounds in the metabolic modules of all 705 organisms in KEGG. We used t statistics and wilcoxon rank sum statistics(Pagano and Gauvreau, 2000) to test whether there were significant differences in the similarity scores between orbit dataset and random dataset3
|The results were shown in Table 2, from which we can see that in all pathway/modules, the compounds in the orbit showed significant evidence of similarity in compound chemical structures, which implied that the structurally equivalent nodes in metabolic networks are similar in their chemical structure. The compounds with similar chemical structure will have similar functions and play similar roles in biochemical reactions(Gutteridge, Kanehisa and Goto, 2007). In Table 3, we listed the values of similarity of the compounds in all the orbits in Glycolysis/Gluconeogenesis and TCA cycle pathways. In Glycolysis/Gluconeogenesis pathway, 92.7% of orbits' similarity is larger than 0.5, while in TCA cycle pathways 55% of orbits' similarity is larger than 0.5. To gain further understanding of the nature of similarity among the compounds in the orbit, we presented the results of Glycolysis/ Gluconeogenesis pathway and TCA cycle pathway.
|(1) The orbit [C00668, C01172] in Glycolysis/Gluconeogenesis pathway.
It included C00668 (alpha-D-Glucose 6-phosphate) and C01172 (beta-D-Glucose 6-phosphate). Their chemical structures were shown in Table 3. C01172 is an isomer of C0066, so their chemical structures are identical. We examined the pathways which two compounds C00668 and C01172 participate in and the enzymes catalyzing the biochemical reactions of these two compounds. We found that they shared most of the pathways and enzymes (some enzymes are the same; some enzymes are in the same category, like 184.108.40.206 and 188.8.131.52). Interested readers please see Table 4 for details.
|(2) The orbit [C00158, C00311, C00417] in TCA cycle pathway.
Their names, chemical structures, pathways which they participate in and enzymes they were catalyzed by were shown in Table 5. The compound C00311 (Isocitrate) is the isomer of the compound C00158 (Citrate). C00417 (cis- Aconitate) is the product of dehydrolysis from C00158 and C00311. In TCA cycle, the three reactions among these three compounds are catalyzed by the same enzyme EC188.8.131.52:
R01325: Citrate<=> cis-Aconitate + H2O
R01900: Isocitrate <=> cis-Aconitate + H2O
R01324: Citrate <=> Isocitrate
From the Table 5 we can see clearly that three compounds C00158, C00311 and C00417 participated in the same pathways and were catalyzed by same enzymes in most cases.
Since metabolic function is mainly determined by chemical structure(Gutteridge et al., 2007), our work showed that structural equivalent nodes in the metabolic networks were more likely to have the same or similar function.
|Recently, symmetry in general complex networks has attracted certain research interest. All previous works (MacArthur, 2008; Xiao et al., 2008a; Xiao et al., 2008b; Xiao et al., 2008c)about symmetry in the networks have focused on undirected graphs. To explore symmetry in the metabolic networks, in this report we first introduced the concept of symmetry and developed algorithms to search symmetry in the directed networks. Then we further systematically investigated the symmetry properties of metabolic network, including the degree of symmetry, restricted network quotient. We observed much higher symmetry in metabolic networks which are reconstructed from KEGG and BioCyc datasets than that in random networks. Our preliminary results showed that metabolic networks are generally symmetric and in particular locally symmetric. To explore functional implications of the structural symmetry of metabolic networks, we tested significance of the chemical structure similarity of the compounds in the same orbit of the network. We found that compounds that are structurally equivalent to each other tend to have high similarity in chemical structures and that the structurally equivalent compounds often take part in the activities of the same pathway and are catalyzed by same enzymes. This may suggest that the symmetry in the metabolic network can generate the functional redundancy, and increase the robustness and the ability against attack of external disturbances.
|Symmetry may arise from duplications in evolution of metabolic networks. In this report, we have focused on the symmetry of the metabolic networks. Due to the strong correlation between symmetry and duplication (a universe mechanism in biological networks) (Bhan, Galas and Dewey, 2002; Chung et al., 2003; Teichmann and Babu, 2004), symmetry is expected to be ubiquitous in a variety of other biological networks and to play an important role in the evolution of biological networks.
|Despite increasing interests in exploring the role of symmetry in evolution of networks, mechanism of evolution of symmetry has not been well investigated. It is worth studying the mechanism of generating symmetry of the networks and the role of structurally equivalent compounds in cell and molecular functions in the future.
|Materials and Methods
|Metabolic Network Reconstruction
|At present, two major metabolic reconstruction methods are usually used. One method is introduced in Ma and Zeng(Ma and Zeng, 2003), where "currency" metabolites like H2O, ATP, ADP are not included as nodes in network. This simplified metabolic network is biochemically meaningful in calculating path length. KEGG PATHWAY database uses the simplified metabolic network reconstruction method. The xml files of totally 152 metabolic pathways for every organism (705 organisms in total) were downloaded from KEGG FTP(Release date: Dec. 18, 2007). Reaction data were read from the xml files and represented as directed graph. The direction of each link implies the direction from an input compound (reactant) to an output compound (product) (See Figure 1(a)). Single pathways are combined to modules according to their metabolic functions, such as Carbohydrate Metabolism, Metabolism of Cofactors and Vitamins. There are 11 modules and each module contains 2-23 pathways. See additional data file 1. We also integrated all the 152 metabolic pathways into a metabolic network for every organism. Another metabolic network reconstruction method includes currency metabolites as nodes in network(Jeong et al., 2000), which makes metabolic network more connected. The metabolic network reconstruction in BioCyc database is a representative of this method. Totally 373 available Pathway/Genome Databases was downloaded (Release date: Oct. 15, 2008. Each database in the BioCyc collection describes the genome and
metabolic pathways of a single organism, including another independent database AraCyc which has not been combined into BioCyc yet). We processed the tabular flat files of reaction data and combined the reactions into an integrated network for each organism. Direction information was not given in reaction files of BioCyc. So the integrated networks are unidirectional networks.
|Connectivity of Metabolic Networks
|Since many enzymes have not been found in some organisms yet, the reactions (edges in network) which are catalyzed by these enzymes are absent in the current network. Hence, we expect that the connectivity of metabolic network is quite low compared to corresponding randomized synthetic networks. To verify such conjecture, we use the number of connected subgraphs (NCS) and ratio of size of maximum connected subgraph to the whole network size (MCS) to measure the connectivity of metabolic network. We calculate the number of connected subgraph (NCS) in every single network. Apparently, the larger the NCS is, the lower the connectivity of metabolic network is; the larger MCS is, the more connected the network is. Furthermore, based on these concepts, we can define a new index: entropy based on connected subgraph (ECS) to measure the average connectivity of a metabolic network:
| ECS = - Σ pi log pi
0 ≤ i ≤ |c|
|, where C is the set of connected subgraphs of the network and pi is the probability that a node belongs to a connected subgraph Cj. Given all connected subgraphs C={C1 , C2 ,…, Ck}, we can calculate pi as:
|pi = |Ci| / Σ j |Cj| = |Ci| / N
|, where N is the number of nodes in a graph. Clearly, for networks with N nodes, ECSmax =logN when pi=1/N for each 0 ≤ i ≤ |c| (in this case, every node in the network is isolated from each other); ECSmin =0, when the network is a connected graph and consequently p=1 . Thus, we can define normalized entropy based on ECSmax and ECSmin :
|NECS = ECS - ECSmin / ECSmax - ECSmin = ECS / log( N )
|In general, networks that contain a large connected subgraph tend to have a relatively small value under the measurement of NECS. Whereas metabolic networks are expected to be less connected and consequently the value of NECS is expected to be relatively large. The connectivity statistics including NCS, MCS and NECS in this section are summarized from the underlying graphs of the metabolic networks, where the direction and self loops were removed from the original network.
|Assessing Symmetry of Complex Networks
|The degree of the symmetry of a graph G usually could be quantified by the following formula:
|α = | Aut(G) |
|which is the size of the automorphism group of graph G. Generally, α is very large and we usually use log10|Aut(G)| .
|In order to compare the symmetry of networks with different sizes, symmetry measure β is often used, which is defined as:
|β = ( α / N! )1/N ,
where N is the node number of network, β measures the symmetry relative to maximal possible automorphism group of a graph with N nodes.
|In general, for empirical networks, when network grows its symmetry is often destroyed. As evolution proceeds we rarely find global symmetry in the network, which means we can rarely find automorphisms that transforms most of nodes. In fact, many real networks have been shown to be locally symmetric(MacArthur, 2008) , which means that we can only find automorphisms which transform only small part of nodes in the network. Here, we use φ to quantify the degree to which graph G is globally symmetric(Xiao Y et al., "Efficiently Indexing Shortest Paths by Exploiting Symmetry in Graphs". In Proceedings of the 12th International Conference on Extending Database Technology (EDBT'09), March 23-26, 2009.):
|φ = max{ |supp(g)| : g ε ID(G)} / N ,
|where supp(g)={ vi : vig ≠ vi } and ID(G) is the set of indecomposable automorphisms of graph G. An indecomposable automorphism of Aut(G) is a non-identity automorphism in Aut(G) that can not be decomposed into the product of two automorphisms g1 and g2 such that g1 ≠ e and g2 ≠ e and supp(g1) Π supp(g2) = φ , where e is the identity permutation that transform each vertex to itself.
|To compute the above measures, the well known nauty program(McKay, 1981), which is one of the most efficient graph isomorphism algorithms available, is used to calculate the size and structure of automorphism groups.
|Symmetry in Metabolic Networks
|Symmetry in Directed Graph
|In most of the previous studies of complex networks, networks are usually pre-processed as their underlying graphs: where weights, directions and self-loops are omitted. However, in the studies of metabolic network, the direction can't be omitted since many reactions are irreversible and the direction determines the reaction rates and the product output. Hence, when exploring symmetry in metabolic networks, we need to investigate symmetry in directed networks first.
|In general, a directed network is a pair (N, E) with N representing the node set and E representing the set of ordered pairs of N. The related concepts of symmetry in directed graph is completely the same as that in undirected graphs. The fact that we need to highlight when exploring symmetry in directed networks is that any automorphism in a directed network need to preserve the oriented relation instead of un-oriented relation in undirected graph.
|It's trivial to show that if g is an automorphism of a directed graph G, g will also be an automorphism of its underlying graph G'. However the inverse does not necessarily hold true. Hence, if G' is the underlying graph of graph G, we have Aut(G) ⊆ Aut(G'), which implies that the degree of symmetry of G is smaller than that of G'. Consequently, the automorphism partition of the directed graph is finer4 than that of its underlying graph.
|Restricted Network Quotient
|Recall that nodes of a symmetric network can be partitioned into disjoint equivalent classes which are called orbits of the graph according to the automorphic equivalence relation on nodes. Nodes in the same orbit are structurally equivalent and cannot be distinguished from each other(Tinhofer and Klin, 1999) by usual measurement on nodes, such as degree, clustering coefficient. Therefore they can be glued together to create a coarse reduced network, known as the quotient. In Figure 3, G1 are quotient networks of G0. Since metabolic networks possess a non-trivial automorphism partition they carry a significant amount of redundant information in which more than one node plays the same structural role.
|In most of the previous researches about complex network, only the automorphism group of the largest connected subgraph is exploited. In above sections, we have shown that metabolic networks are more disconnected than other empirical networks. Hence it is necessary to explore the symmetry of metabolic networks with all disconnected subgraphs taken into account.
|However, preserving all disconnected subgraphs will pose a challenge to the calculation of quotient of metabolic structure. Please note that when calculating quotient of a graph consisting of two isomorphic disconnected subgraphs, these two subgraphs will be merged into one subgraph under the action of the automorphism group of the graph. Hence, calculation of network quotient should take into account the connectivity constraint so that the isomorphic isolated modules will not be merged into one reduced subgraph in the quotient.
|Specifically, assume that graph G contains pair-wise isomorphic and disconnected subgraphs G1, G2, …Gm. Let H(G) be the set consisting of all those automorphisms that swap nodes between pair-wise and disconnected subgraphs, i.e.
|H(G)={g: xg = y and g ε Aut(G) and x ε V(Gi) and y ε V(Gj) and i ≠ j }.
|Then we can calculate the restricted quotient of graph G under the action of R(G) = Aut(G) - H(G).
|It's easy to show that in the restricted quotient all disconnected subgraphs in the original graph will not be merged and consequently the number of disconnected subgraphs will be preserved. We obtained the orbits in network through the restricted network quotient.
|Given a graph G0 consisting of two isomorphic subgraphs, as shown in Figure5(A). Obviously, the automorphism group of G0 can be decomposed into the wreath product(Rotman, 1999) of Gin and Gout, where Gin is the triangle, shown in Figure 5(B), and Gout is the abstracted outer graph, as shown in Figure 5(C). Note that in Aut(G), there are some automorphisms, such as g=(1,4)(2,5)(3,6) that swap nodes in different isolated subgraphs( e.g. 1 and 4 are transformed to each other in spite of that these two vertices are in different isolated subgraphs). Under the action of such automorphisms, we finally can obtain one single orbit {1,2,3,4,5,6}for G0. Thus the quotient of G0 is just a single node (shown in Figure 5(D)), which contradicts to the fact that two isolated triangle structures often interpreted as two isolated functional modularity for biological networks. However based on the concept of restricted network quotient, the network G0 can be reduced to a quotient network consisting of two isolated nodes (shown in Figure 5(E)).
|In the computation of symmetry of directed networks, we find that nauty program can not ensure the correctness for directed graphs. Hence, we first use nauty to get the automorphism partition of the underlying graph of the network and then refine the automorphism partition. Considering the direction and connectivity of metabolic networks, the algorithm to get the orbits is shown in Algorithm 1. Although theoretically we can not ensure that the resulting partition is equivalent to the automorphism partition under the restricted automorphism group, the resulting partition is practically close to the desired partition and is practically useful in the exploration of functional equivalence of nodes in the same orbits:
|Algorithm1: getOrbits (G )
Input: a metabolic network G
Output: new orbit partition P'
1. P'=φ, G={ G1, G2, …Gm } // get Connected Subgraphs of G ;
2. R(G)=Aut(G)-H(G) // get restricted automorphisms
4. for each Vi ε P such that |Vi|>1
5. for each v ε Vi
6. L(v)=(|N+(v),N-(v)|); // compute the in-degree and out-degree of v
7. Order(Vi) ; // Sort Vi according to lexicographic order of L(v)
8. {Vi1, Vi2,…, Vik} = Subdivide(Vi);
9. P'=P' υ {Vi1, Vi2,…, Vik}
10. return P'
|Analyze Orbit Similarity
|In the above section, we have known that nodes in the same orbit group are structurally equivalent. It is well known that structural equivalence implies functional equivalence. Whether the structurally equivalent nodes in the network are more similar in function has still not been validated. In metabolic networks, nodes are compounds with specific structure which determines its function in reactions. If two compounds are structurally similar to each other, they will function similarly. Alex Gutteridge et.al have found that chemical structure of small molecular compounds often determines compound suitability for use in regulation and how groups of similar compounds can regulate sets of enzymes(Gutteridge et al., 2007). Hence, it is reasonable to believe that whether the structurally equivalent nodes in the network are functionally equivalent can be inferred from the similarity between their chemical structures.
|Many chemical structure comparison methods have been proposed to analyze the compound similarity in the metabolic pathways (Hattori et al., 2003; Nobeli et al., 2003; Raymond, Gardiner and Willett, 2002; Raymond and Willett, 2002). In most of the algorithms, the chemical structure is treated as a two dimensional (2D) object, which can be presented as a graph consisting of nodes (atoms) and edges (bonds). In this paper, we use the method proposed by Masahiro H.(Hattori et al., 2003) to compute the similarities between chemical compounds. In this method, the similarities between compounds are measured by the size of maximal common subgraph (MCS) between two graphs representing these two compounds. A normalized similarity score based on Jaccard coefficient(Watson, 1983) is used in this method, which is defined as the ratio of the size of the maximal common substructure to the size of the nonredundant set of all substructures:
|, where |G| is defined as the number of nodes of graph G.
|After obtaining the similarity of all the compound pairs by Masahiro's algorithm, we compared the compound similarities between nodes in the same orbits to the compound similarity between nodes in the network and test the significance of similarity scores of nodes in the same orbit.
|All similarity score of the orbits in the networks of 705 organisms were collected to form the orbit dataset where the replicated orbits were just calculated once. Another dataset which is referred to as random dataset was generated by collections of similarity scores of all pairs of compounds in the metabolic modules of all 705 organisms.
|Three statistics were used to test differences in the similarity scores between the orbit dataset and random dataset: right tail t-test with equal variance, right tail t-test with unequal variance and Wilcoxon two-sided rank sum test(Pagano and Gauvreau, 2000).
|We assume that the compounds in the same orbit should have similar chemical structure and function. So we use Hattori's maximal-common-subgraph based algorithm with loose weighting condition to do chemical structure comparison. We summarized the average over similarity scores of all compound pairs in the same orbit:
|S = Σ 1 ≤ i < j ≤ n Si,j / n(n-1) / 2
|Authors' Contributions
|Hua Dong analyzed the data and wrote the draft; Yanghua Xiao was responsible for the algorithms and the program. Hua Dong and Yanghua Xiao contribute equally to this work. All authors wrote and approved the final manuscript.
|This work was partially supported by grant from Shanghai Commission of Science and Technology (04dz14003) and Grant from Hi-Tech Research and Development Program of China(863) (2007AA02Z300). Thanks for Hoicheong Siu's help on network reconstruction from BioCyc dataset.
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