text:
Many mathematical models characterizing mechanisms of cell fate decisions have been constructed recently. Their further study may be impossible without development of methods of model composition, which is complicated by the fact that several models describing the same processes could use different reaction chains or incomparable sets of parameters. Detailed models not supported by sufficient volume of experimental data suffer from non-unique choice of parameter values, non-reproducible results, and difficulty of analysis. Thus, it is necessary to reduce existing models to identify key elements determining their dynamics, and it is also required to design the methods allowing us to combine them.
Here we propose a new approach to model composition, based on reducing several models to the same level of complexity and subsequent combining them together. Firstly, we suggest a set of model reduction tools that can be systematically applied to a given model. Secondly, we suggest a notion of a minimal complexity model. This model is the simplest one that can be obtained from the original model using these tools and still able to approximate experimental data. Thirdly, we propose a strategy for composing the reduced models together. Connection with the detailed model is preserved, which can be advantageous in some applications. A toolbox for model reduction and composition has been implemented as part of the BioUML software and tested on the example of integrating two previously published models of the CD95 (APO-1/Fas) signaling pathways. We show that the reduced models lead to the same dynamical behavior of observable species and the same predictions as in the precursor models. The composite model is able to recapitulate several experimental datasets which were used by the authors of the original models to calibrate them separately, but also has new dynamical properties.
Model complexity should be comparable to the complexity of the data used to train the model. Systematic application of model reduction methods allows implementing this modeling principle and finding models of minimal complexity compatible with the data. Combining such models is much easier than of precursor models and leads to new model properties and predictions.
Systems biology aims to study complex interactions in living systems and focuses on analysis and modeling their properties. Mathematical modeling provides several ways to describe biological processes based on experimental information of different kind. However, creation of detailed models not supported by enough experimental data often makes their analysis and interpretation difficult [1]. Several aspects of the same process can be modeled using different levels of abstraction involving different reaction chains, chemical kinetics, and incomparable sets of parameters. Such models are difficult to merge. Meanwhile, merging is an important approach for creation of complex models. Thus, development of efficient methods and software, allowing us to combine models, is the object of intense study in systems biology. In our work, we focused on the fact that, generally, complexity of models is not comparable to the volume of experimental data used to adjust their parameters. Due to this fact, we turn to the methods of model reduction allowing us to minimize model's complexity without affecting the model simulation dynamics.
Model reduction is a well-established technique in many fields of biochemical research and engineering. It has been used for many years in chemical kinetics (for reviews, see [2-4]) and has already found multiple applications in systems biology, including discrete modeling [5] and modeling of metabolic pathways [6,7]. The principles of this technique have been applied in computational biology [8] and implemented as a part of widely used pathway simulators such as BioUML [9], BIOCHAM [10], COPASI [11], and GINsim [12]. Model reduction led to new insights in mechanisms of translation regulation by microRNAs [13,14] and was applied for analysis of such signaling pathways as JAK-STAT [15], NF-κB [16], and EGFR [17].
In our investigation, we used the principles of model reduction to construct reasonably accurate minimal size approximations of two different models describing the CD95 signaling pathways [18,19]. The first model explores pro-apoptotic properties of CD95 after stimulation by its natural ligand CD95L or by agonistic antibodies anti-CD95 implying formation of the death-inducing signaling complex (DISC) [18,20]. DISC consists of oligomerized CD95, death domain-containing adaptor FAS-associated molecule (FADD), procaspases-8 and −10, and two isoforms of cellular FLIP (CFLAR) protein (cFLIP long and cFLIP short). Caspase-8 leads to activation of effector caspase-3 directly (type I cells) or via stimulation of cytochrome C release from the mitochondria (type II cells) [21]. The latter step requires formation of the apoptosome complex and activation of caspase-9. Once activated, caspase-3 cleaves poly(ADP-ribose) polymerase (PARP), thereby making the apoptotic process irreversible. The second model describes the state when CD95 not only activates the pro-apoptotic pathway, but also induces transcription factor NF-κB that is an important regulator of cell survival functioning [19]. This is possible due to cFLIPL cleavage in the DISC complex. The cleaved p43-FLIP directly interacts with the IKK complex and activates it. The activated IKK performs phosphorylation of the IκB protein and thereby frees NF-κB.
The authors of the models have evaluated concentration changes of major apoptotic molecules by Western blot analysis and represented them as relative values at given time points. Using the systematic methodology [2] implemented in the BioUML software, we reduced the models so that they still satisfy these data. This allowed us to simplify the overlapping components of the models and find a way for their composition.
Model reduction
Mathematical modeling of biological processes based on the classical theory of chemical kinetics assumes that a model consists of a set of species S = (S1,…,Sm) associated with a set of variables C(t) = (C1(t), …, Cm(t)) depending on time t ∈ [0, T], T ∈ R+ and representing their concentrations, and a set of biochemical reactions with rates v(t) = (v1(t), …, vn(t)) depending on a set of kinetic constants K. Reaction rates are modeled by mass-action or Michaelis-Menten kinetics. A system of ordinary differential equations (ODE) representing a linear combination of reaction rates is used to describe the model behavior over time:
Here N is a stoichiometric matrix of n by m. We say that CSS is a steady state of the system (1) if
Model reduction implies transformation of the ODE system to another one with smaller number of equations without affecting dynamics of variables C1(t), …, Cs(t), which is fixed by a set of experimental points Ciexp(tij) at given times tij, j = 1, …, ri, where ri is number of such points for the concentration Ci(t), i = 1, …,s. To check dynamics preservation in the course of model reduction, we consider the function of deviations defined as a normalized sum of squared differences [11]:
where weights are calculated as mean squared values of experimental concentrations for each variable and the normalizing factor ωmin/ωi is used to make all concentration trajectories to have similar importance.
Reducing kinetic model is possible when some quantities are much smaller than other quantities and can be neglected. Usually, this implies some qualitative relations (much bigger, much smaller) between model parameters. When these relations satisfy certain rules, we can approximate the detailed model by a simpler one. If the parameters are (approximately) determined, as in our case, we find an approximation specific for a region of the parameter space. However, if we want to investigate the model behavior for the entire space, we need to decompose it into regions characterized by asymptotically different behaviors of the dynamical systems. Afterwards, a specific reduction should be performed for each region (Figure 1).
Figure 1. Schematic representation of the model reduction technique. A model consisting of four species (A, B, C, and D) and two reactions (r1 and r2) was reduced taking into account the relations between time-dependent concentrations CA(t) and CB(t), as well as reaction rates vr1(t) and vr2(t). In the case when CA(t) ≫ CB(t), the concentration of A can be considered constant for some period of time. The same simplification could be applied to B. If vr1(t) ≈ vr2(t), then C could be removed, resulting in direct formation of D triggered by the binding of A and B only.
We define the minimal complexity model as a reduced model with the minimal number of elements (species and reactions) so that the deviation function value (3) calculated for the reduced model is different from the original model no more than 20%. Such threshold is explained by the fact that in this work we considered experimental data obtained by Bentele et al.[18] and Neumann et al.[18] using Western blot technology with the standard deviation 15-20%.
Reduction of mathematical model complexity is achievable by different methods [2]. Description of the methods directly used in our work is provided below.
(MR1)Removal of slow reactions. We say that reaction r1 is much slower than reaction if , where k=10-2. When such reactions do not affect experimental dynamics of species, we neglect them. Note, that in some cases, it is sufficient to consider k = 10−1 or even k = 1.
(MR2)Quasi-steady-state approximation[22] assumes that all variables C(t) of the model are split in two groups: basic variables Cs(t) and quasi-stationary variables Cf(t) for which we could write:
where ɛ is small parameter. We consider the approximation ɛ → 0 resulting in the equation Nf · vf(C, K, t) = 0. Thus, the chain of reactions S → I → P with a quasi-stationary species I can be reduced to the form S → P.
(MR3)Lumping analysis refers to reducing the number of model variables by grouping some species. In particular, this can be illustrated by reactions
with kinetic rates and . If k1 = k2 and , then the system (4) can be replaced by a single reaction
where , and k = k1 = k2. Note, that in this example lumped variables , and , are linearly dependent: however, this is not required in general case. For conditions on lumpability in monomolecular reaction networks, see [23].
(MR4)Removal of approximately linearly dependent variables. If variables A(t) and B(t) (species concentrations or reaction rates of the model) are approximately linearly dependent:
then we can replace one of them with another in all kinetic laws of the model.
(MR5)Simplification of the Michaelis-Menten kinetics. Consider a reaction r of the form S –E → P, where an enzyme E converts a substrate S into product P. Reaction rate of such reaction is frequently defined by the Michaelis-Menten formula
where the enzyme concentration is a dynamic variable allowing to use the same kinetics in different regions of the phase space. If Km ≫ CS(t), then we can reduce this formula to the form: . On the other hand, if CS(t) ≫ Km, then (5) can be replaced by the equation vr(t) = k · CE(t).
(MR6)Simplification of equations based on the law of mass action when one reactant dominates others. Consider a reaction r of the form S1 + S2 → P with the kinetic law
When for t ∈ [0, T], the formula (6) can be replaced by the linear equation . The time T of validity of such pseudo-lineary approximation is defined as a period during which the relative change of does not exceed some ε, i.e. .
One way to perform the model reduction is to apply the foregoing methods in the numerical order (Figure 2). Note that the methods MR5 and MR6 are of the same type, so it does not matter which one to use first. This way assumes that we calculate the value of the distance function (3) at each reduction step to test whether approximation of the experimental data is still within allowable limit or not.
Figure 2. Flow chart of the model reduction. The methods of model reduction are presented in the order of their application. The last two methods are of the same type, so this is a choice of the systems biologist which one to use first.
Model analysis and comparison
Model comparison using Akaike information criterion (AIC). This criterion [24] defines the relative complexity of a model based on the goodness of experimental data fit and the number of model parameters |K| (initial concentrations of species are not considered):
The function χ2 is defined by the formula (3) with weights 1/ σij2 (instead of ωmin/ωi) [15], where mean deviations σij of experimental values Ciexp(tij) are calculated using smoothing spline [25]:
For j + k < 0 and j + k > ri we assumed Ci(ti,j+k) = Ciexp(ti,j+k) = 0.
Models can be compared using the Akaike criterion, if they approximate the same experimental data. When the AIC value of one model is less than of others, we say that this model is simpler in terms of this criterion.
Model comparison with the mean AIC. When we want to compare models approximating different sets of experimental data, we could calculate the mean AIC coefficients by the formula
where nexp determines the number of experimental points.
Steady-state analysis finds values of species concentrations according to the rules (2). It is desirable to reduce a model so that steady-state concentrations of all experimentally measured chemical species have not changed significantly.
Sensitivity analysis reveals steady-state concentrations response to parameter perturbations. The local sensitivities Ciss, i = 1, …, m, for all parameters pj, j = 1, …, |K|, are calculated via finite difference approximations:
It is useful to compute the mean log sensitivity for all fitted species:
where np is the number of all parameters |K| or the number of parameters retained after the model reduction.
Modular modeling
Considering the mathematical models of CD95 signaling pathways [18,19], we decomposed them into functional modules. This step allowed us to identify overlapping components of the models and simplify their analysis. We defined a module as a submodel (including several species, reactions and parameters of the model) with input, output and contact ports. The first two types of ports characterized variables calculated in one module and passed to another through a directed connection. The contact ports declared common variables of modules via undirected connections (for more details of modular modeling, see [26]).
Preliminary analysis, problems and inconsistencies in the precursor models
The mathematical model by Bentele et al. (Figure 3A) consists of 43 species including a virtual variable xaa intended for quantification of "apoptotic activity" caused by active caspases-3, -6 and -7 and calculated by the formula
where k36act, k7act, Km367act ∈ K. The variable xaa specifies a process of degradation in the model introduced as an exponential decay function fdegr(xaa). This function is defined by the formula kd · xaa2 + kds with kd,kds ∈ K for all active caspases and complexes containing their cleaved products, and by the formula kd · xaa2 for all other molecules besides cPARP (cleaved PARP), where fdegr(xaa) is constant. All species in the model are degraded with the exception of cytochrome C and Smac stored in the mitochondria, whose concentrations are constant.
Figure 3. The model by Bentele et al. and results of its reduction. A. The original model decomposed into modules according to three steps of apoptosis: activation of caspases-8 and -9 and inactivation of PARP. The species retained after the model reduction are colored. B. The modular view of the model. The dashed connections were deleted during the model reduction. C. The minimal reduced model. D. The graphical notation used for representation of the models A-C.
In total, the model contains 80 reactions (Table 1) including 24 reactions based on mass action kinetics, 12 reactions taken with kinetics of Michaelis-Menten, 41 reactions of degradation, the reaction of xaa production specified above and two reactions of cytochrome C and Smac release from the mitochondria modeled using a discrete event. The latter implies complete cytochrome C and Smac release within 7 minutes as soon as tBid reaches a certain level in comparison to Bcl-2/Bcl-XL. Since the authors did not provide exact form of the release function, we proposed the sigmoid function which has the expected behavior:
where ttrigger is the time when tBid concentration reaches a value of Bcl-2/Bcl-XL, trelease is the start time of release and kcontr is the contraction coefficient.
Table 1. Summary of reactions from the original model by Bentele et al. and the reduced model
Additional file 1: Table 1S. Notations of parameters used in the paper and in the original models. Table 2S. Table of all reactions (excepting degradation) and rate constants in the composite model. Table 3S. Table of degraded species and kinetic laws of degradation in the composite model. Table 4S. Table of nonzero initial concentrations in the composite model. Table 5S. Steady state analysis of the Bentele's model and the composite model. Species. Table 6S. Steady state analysis of the Neumann's model and the composite model, Table 7S. Calculation of the mean sensitivity for the investigated apoptosis models. Table 8S. Analysis of predictions regarding apoptosis in HeLa cells as formulated by Neumann et al. Table 9S. Predictions of the models for SKW 6.4 cells. Table 10S. Parametric constraints of the models by Bentele et al. and Neumann et al.
Format: PDF Size: 544KB Download file
This file can be viewed with: Adobe Acrobat Reader
The model comprises 43 species (including xaa) and 45 kinetic parameters, which the authors estimated based on the experimental data obtained by Western blot analysis for the human cell line SKW 6.4. Cells were stimulated by 5 μg/ml and 200 ng/ml of anti-CD95 (fast and reduced activation scenarios, respectively) and dynamics of several proteins (Bid, tBid, PARP, cPARP, procaspases-2, -3, -7, -8, -9, cleaved product of procaspase-8 p43/p41, and caspases-8) were measured.
We could not reproduce the dynamics of the original model using the parameter values provided by the authors. In particular, there was too rapid consumption of procaspases-2, -3, -7, -8 in the case of 5 μg/ml of anti-CD95 and procaspases-2, -9 in the case of 200 ng/ml. Degradation rates of procaspase-8 and caspases-8 was insufficient for both activation scenarios. Thus, we had to make several modifications of the original model to obtain the same dynamics as described in the original paper. Namely, we multiplied the rate constants of all the bimolecular reactions by the value 5∙ 10-5 and specified kd equal to 3.56 min-1 and 0.62 min-1 (instead of 0.891 min-1 and 0.184 min-1) for fast and reduced activation scenarios, respectively.
The model by Neumann et al. includes 23 species, 23 reactions constructed according to the law of mass action, and 17 kinetic parameters (Figure 4A). It reproduces experimental measurements of 8 entities (total amount of procaspase-8, its cleaved product p43/p41, caspase-8, procaspase-3, caspase-3, IκB-α, phosphorylated IκB-α and cleaved p43-FLIP) obtained using Western blot technology for HeLa cells stably overexpressing CD95–GFP and treated with three different concentrations of agonistic anti-CD95 antibodies (1500, 500 and 250 ng/ml). This is the reduced model suggested by the authors for description of the CD95-mediated pathways of cell death and NF-κB activation. Model reduction was based on intuition about what is important in the biochemical mechanisms. It was performed as long as the parameter estimation procedure (repeated after each step of the reduction) was able to provide a good fit of the experimental data. Particularly, the details of some complex formations were omitted as well as some non-measured species were removed. The authors submitted the model to the BioModels database [27]. Thus, we had no problems reproducing it.
Figure 4. The original model by Neumann et al. and results of the model reduction. A. The original model decomposed into modules according to three steps of the CD95 signaling pathways: activation of caspase-8, pro-apoptotic pathway resulting in caspase-3 activation and anti-apoptotic pathway regulated by NF-κB. The species retained during the model reduction are colored; reactions are represented by solid lines. B. The modular view of the model. Activation of caspase-8 and p43-FLIP (product of cFLIPL cleavage) occurs at the DISC complex and triggers simultaneous processes of cell death and survival.
Reduction of the CD95-signaling model
We started the Bentele's model reduction by excluding the direct dependence of the virtual species xaa on caspases-6 and -7. For this purpose, we approximated the amount of caspases-7 by the linear function of caspase-3 concentration:
where a = 0.18 for both activation scenarios. In addition, we considered inequalities holding for the parameters in the formula (10):
and simplified it:
After that we decomposed the model into modules (Figure 3B) corresponding to three biological steps: activation of caspase-8, cytochrome C-induced activation of caspase-9 and PARP cleavage down-regulated by these caspases.
Below we provide detailed description of the reduction process of all modules. The process is based on the flow chart represented in the Figure 2. If it is enough for a reader to have a general idea of model reduction without going into full details, we suggest to go directly to the last two paragraphs of this section, where you find the summary of the model reduction procedure.
Caspase-8 activation module includes 20 species and 14 reactions (besides the reactions of degradation), which could be divided into three groups: cleavage of procaspase-8 at the DISC complex, its activation triggered by caspase-3, and inhibition of complexes containing DISC by cFLIPL and cFLIPS (Table 1, Figure 3A, reactions br1-br14).
Firstly, we eliminated slow reactions br12 and br13 according to the method MR1. Next, we applied the quasi-steady-state analysis (MR2) to the module and removed quasi-stationary intermediates CD95R:CD95L, DISC:pro8, DISC:pro82, DISC:p43/p41 and DISC:cFLIPL. Thus, in particular, we got two main reactions instead of br1-br6: fast formation of the DISC complex (Table 1, Figure 3B, br1*) and slower activation of caspase-8 in this complex (br2*).
Further, we noticed that the consumptions of cFLIPL and cFLIPS satisfied the same kinetic laws. Therefore, these species could be lumped (MR3) resulting in the reaction br4*:
cFLIP + 2∙ DISC + pro8 → cFLIP:DISC:pro8,
where cFLIP indicated two isoforms cFLIPL and cFLIPS so that CcFLIP = CcFLIPL = CcFLIPS.
We approximated the concentration of caspase-6 by the linear function b · Ccasp3, b = 0.145 (MR4), and merged reactions br7 and br8 of caspases-8 activation induced by caspases-3 and mediated by caspases-6 into one reaction br3*:
pro8 –casp3 → casp8.
Since the reaction br8 followed the Michaelis-Menten kinetics with the constants k68 and Km68, then the reaction rate of br3* was provided by the kinetic law
where k38 = 0.145 · k68 and Km38 = Km68. Analysis of this kinetic law for low level of CD95L ensured that Cpro8 ≫ Km38. In addition, in the case of the fast activation scenario the value of vbr3* was much lower than the rate of caspase-8 activation mediated by CD95. Thus, we established vbr3* = k38·Ccasp3 without significant changes in the results of the model simulation (MR1, MR5).
Complementing the above reduction steps, we removed the elements that were unnecessary to fit the experimental dynamics provided by Bentele et al. These elements were degradation reactions of CD95L, CD95R and FLIP, and the blocked DISC complex (inactivated DISC). As a result, we introduced the conservation law:
where L0 and R0 denote initial concentrations of the ligand and receptor, respectively. Solving the differential equation
we obtained the analytical function for the receptor concentration:
The module of caspase-9 activation consisted of 19 species and 14 reactions (besides the reactions of degradation) including activation of caspase-9 triggered by cytochrome C, cleavage/activation of Bid by caspases-2 and -8, IAP inhibition of caspase-9 activity and binding of inhibitors by Smac (br15-br26, br35, br38). Based on the method MR1, we eliminated the last two reversible reactions, as well as the slow reaction br20 of the apoptosome complex dissociation. Further, since this complex was a quasi-stationary intermediate and the rate of br15 was linearly dependent on a difference of br16 and br17 rates, we reduced the chain of procaspase-9 activation (br15-br20), using the methods MR2 and MR4, to the form:
Accordingly to Bentele et al., we have the following rule of cytochrome C release from mitochondria:
Here frelease(t) satisfies the formula (11). Taking into account (15) and ignoring degradation of the complex Cyt C:Apaf-1, we got
where c = 0.59 was the coefficient of linearity.
Then, we noticed that the experimental measurements of procaspase-9 concentration were presented by Bentele and his colleagues only for 200 ng/ml of anti-CD95. In this case, degradation of procaspase-9 was insignificant. Thus, neglecting it and considering the kinetic law kApop·Cpro9·CCytC:Apaf-1 of the second reaction in (15), we obtained the differential equation of procaspase-9 dynamics:
Solving it, we found:
Finally, analyzing reactions of Bid activation (br21-br23), we removed the slower reaction mediated by caspase-2. The similar reaction involving caspase-8 followed the Michaelis-Menten kinetics with the constant Km28Bid ≫ CBid. Therefore, we redefined the kinetics of this reaction based on the law of mass action (MR5):
The module of PARP inactivation contained 13 species (including the virtual species xaa) and 11 reactions (excepting reactions of degradation). Six reactions (activation of caspases-3 and -7 by caspases-8 and -9, and cleavage/inactivation of PARP) were based on the Michaelis-Menten kinetics (br27-br32), four reactions reproduced the reversible inhibition of caspases-3 and -7 based on the law of mass action (br33, br34, br36, br37), and one corresponded to the production of xaa (br38), simplification of which was discussed above.
We deleted slow reactions of casp3:IAP and casp7:IAP complexes dissociation and ignored slow degradation of procaspase-7 and IAP. Then analyzing the cleavage of procaspases-3 and -7, we eliminated reactions triggered by caspase-9, which were slower in comparison to the similar reactions induced by caspase-8. For the same reason we ignored the reaction of PARP inactivation by caspase-3 (MR1).
Considering the remaining reactions with the Michaelis-Menten kinetics (br29, br32), we used the following inequalities Km78 ≫ Cpro7 and Km376act ≫ CPARP, which, in combination with MR5 and (12), led to the following kinetic laws:
where k3act = 0.18 · k7act
Thus, the CD95-signaling model consisting of 43 species (including one virtual species), 80 reactions and 45 kinetic parameters was approximated by a model with 18 species, 26 reactions and 25 parameters, except the constant concentration of Cytochrome C (Figure 3C). Figure 5 shows the comparison of simulated concentrations of these models with experimental dynamics obtained by Bentele et al. for the 11 species mentioned above. Since this dynamics was expressed in arbitrary units, we uniquely translated it into precise values for all proteins with non-zero initial values. However, for such molecules as caspase-8, p43/p41, tBid and cPARP, precise values directly depended on the concentration levels at the end or in the middle of time series. Accordingly, we computed these levels during the model reduction and recalculated experimental dots if necessary.
Figure 5. Results of the composite model approximation to the experimental data by Bentele et al. The experimental data (dots) were obtained by Bentele et al.[17] using Western blot analysis and expressed as relative values. Once simulated values (curves in the figure) were found for the original Bentele's model (solid red), the reduced model (dashed black) and the composite model (solid blue), experimental points were recalculated taking into account these values. Wherever blue or black dots are missing, they coincide with the red dots. Note that considering the concentration of procaspase-8 in the original model, we observed experimental dynamics for the separate species only, but not for the total amount as expected from experiments. Thus, validating parameters of the composite model, we evaluated the total amount of procaspase-8.
Species without experimental evidence (CD95L, DISC, cFLIP, DISC:pro8:cFLIP, IAP, caspase-3 and virtual species xaa) and reactions br1*-br13* directly affect the simulated dynamics of the experimentally measured concentrations (Table 2). Thus, further reduction of the model by removing these elements is impossible. Regarding the degradation process, we agree with Bentele et al. that experimental data cannot be matched if this process is fully ignored. Actually, if we remove any of the retained reactions of degradation, then excepted concentration dynamics will be impaired. Thus, we found the minimal complexity approximation of the original model.
Table 2. The role of species and reactions in the apoptotic process described by the reduced model
Reduction of the CD95-mediated and NF-κB signaling model
As was mentioned above, Neumann et al. simplified their model in order to reduce the large number of free parameters. The authors noted that further simplification of the model was not possible because the model fit significantly decreased. However, we removed slow reactions (nr4, nr11-nr13, Figure 4A) using the method MR1, and removed the reaction of NF-κB degradation (nr23), which was not significant for reproducing the experimental data of the original model. Note that we retained the slow reactions nr6 and nr7, the former of which regulates apoptosis inhibition in the case of high levels of cFLIPL and procaspase-8 in accordance with the precursor model prediction (see the analysis of the predictions below), and the latter of which will be required to combine this model with the Bentele's model hereafter.
Based on the method MR6, we also took into account the inequality CIKK ≫ Cp43−FLIP and simplified the kinetic law
of the reaction nr19 to the form
Therefore, we reduced the number of model species from 23 to 20, the number of reactions from 23 to 18 and the number of kinetic parameters from 17 to 15 (besides the constant concentration of IKK). These modifications did not change the fit to the experimental data provided by Neumann et al. (Figure 6).
Figure 6. Comparison of the composite model simulation results with the experimental data by Neumann et al. The simulated concentrations of the original and reduced models (solid lines), as well as the simulated values of the composite model (dashed lines) were obtained by Neumann et al.[18] for three different concentrations of anti-CD95: 1500 ng/ml (black), 500 ng/ml (blue), and 250 ng/ml (red). We did not recalculate the relative experimental data (dots) as in the case of the Bentele's model due to a slight difference between the results of the composite and precursor models. An exception was made for values of procaspase-3 and caspase-3, which were normalized for the composite model by the term 0.1 for convenience of the visual plots comparison.
Model composition
Analysis of the reduced models based on the Akaike criterion (7) confirmed that they had lower complexity than the original models (Table 3). The difference between the mean AIC coefficients (8) of the models decreased by 60%, relative to the initial value. In addition, the reduced Neumann's model better approximated experimental data. Therefore, we used it as the basis for the model composition.
Table 3. Comparison of the investigated models according to Akaike's information criterion ( AIC )
We took into account that the considered experimental data were obtained with SKW 6.4 [18] and HeLa [19] cells, which were shown to behave as type I [21] and type II [28] cells, respectively. In this regard, we assumed that:
(A) initial species concentrations could vary for different cell lines;
(B) kinetic parameters of all reactions (besides the degradation rate modeled as the function kd · xaa2) have the same values for both cell lines, whereas the value of kd could be regulated by various entities and, moreover, is dependent on the initial concentration of anti-CD95 [18];
(C) type I and type II cells conform to different reaction chains of caspases-3 activation [21].
We constructed the composite model of CD95 and NF-κB signaling in the following way. Firstly, according to the assumption (C), we replaced reaction nr15 in the Neumann's model by a chain of three reactions:
The first reaction of this chain had the same kinetic law as br7*. The other reactions represented br6* and nr15 with kinetics modified using the law of mass action. Such modification of br6* was necessary to get the slow increase of caspase-3 concentration experimentally described by Neumann et al.[19]. Modification of nr15 consisted in substitution of Ccasp9 for Ccasp8 .
Secondly, we supplemented the Neumann's model with reaction of caspase-3 inhibition by IAP and evaluated parameters in this reaction together with parameters in (17) using the corresponding data by Neumann et al. and optimization tools of BioUML [29].
Thirdly, we analyzed the changes of the initial concentrations and parameters of the derived model required to reproduce the Bentele's experimental data fixing levels of procaspases-3, -8, cleaved product p43/p41, and caspase-8 (Table 4). All the changes, except step 4, agreed with assumptions (A) and (B). To reproduce the species dynamics, we had to increase the initial concentration of procaspase-3 in the case of HeLa cells by an order of magnitude.
Table 4. Modifications of the reduced Neumann's model to reproduce the experimental data by Bentele et al
Finally, we combined the modules of caspase-8 and NF-κB activation with the modules of caspase-9 activation and PARP inactivation (Figure 7). For this purpose, we modified the last two modules based on (17) and refitted their parameters as well as the concentrations mentioned in Table 4, using experimental data by Bentele et al. For better fit we also supplemented the model by degradation reactions of some species (procaspase-9, caspase-9, DISC:pro8 and DISC:pro8:FLIPS).
Figure 7. Creation of the composite model. The modules of caspase-8 and NF-κB activation were taken from the reduced Neumann's model and combined with the modules of caspase-9 activation and PARP inactivation isolated from the reduced Bentele's model. In addition, two last modules were supplemented by reactions from the modified module of caspases-3 activation.
The resulting composite model (Figure 8) consists of 30 species (including one virtual species), 38 reactions (including 15 reactions of the species degradation) and 30 kinetic parameters, except for the constant concentration of IKK (Additional file 1: Table 2S, Additional file 1: Table3S, Additional file 1: Table4S). The model showed a good fit between the simulation results and the experimental data (Figures 5 and 6).
Figure 8. The composite model of the CD95- and NF-κB-signaling. A. The model integrating pro- and anti-apoptotic machinery described by the models by Neumann et al. and Bentele et al. Reactions with the "nr" titles were taken from the first model, while the "br" titles indicate reactions from the second one. The "*" symbol marks reactions defined in the reduced models. The subscript "m" means that reaction was modified for the models composition. B. The modular view of the model. Activation of caspase-8 triggered by CD95 leads to NF-κB activation and cell survival, on the one hand, and PARP cleavage resulted in the cell death, on the other hand.
Calculation of the mean AIC coefficient for this model revealed that it has the same level of complexity as the reduced models (Table 3). We also noted that reduction of both models did not significantly alter the steady-state concentrations (Additional file 1: Table 5S, Additional file 1: Table6S). However, the composite model has different steady-states, which are more stable according to the mean sensitivities (9) in the cases of SKW 6.4 cells and HeLa cells stimulated with 250 ng/ml of anti-CD95 (Additional file 1: Table 7S).
The reduced models are equivalent to the precursor models with respect to their biological predictions
Analyzing the models constructed by Neumann et al. and Bentele et al., we divided predictions made by them into two groups: qualitative and quantitative. The first group concerned the model network and described mechanisms of the protein-protein interactions. It is this group to which we assigned the experimentally validated Neumann's predictions that processed caspases are not required for NF-κB activation, as well as that pro-apoptotic and NF-κB pathways diverge already at DISC. The corresponding network of reactions was preserved in the reduced model. Thus, the prediction remained valid.
The second group of predictions characterized behavior of the models after changing concentrations of some species, such as CD95L, CD95R, procaspase-8, and inhibitors cFLIPL, cFLIPS, and IAP. Analyzing the predictions of the models by Neumann et al. and Bentele et al. listed in the Tables 5 and 6 respectively, we concluded that the reduction of the first of them did not alter the species dynamics (Additional file 1: Table 8S). For the second reduced model, we detected some minor changes in the predictions. However, in general, the model behavior remained in a good agreement with the Bentele's experiments (Additional file 1: Table 9S).
Table 5. Analysis of predictions regarding apoptosis in HeLa cells as formulated by Neumann et al
Table 6. Predictions of the models for SKW 6.4 cells
Model composition modifies some properties of the precursor models and leads to new predictions
Considering the predictive ability of the composite model, we found that in the case of HeLa cells it was completely preserved (Table 5).
In the case of SKW 6.4 cell line, we estimated the value of degradation rate parameter kd based on the experimental observations by Bentele et al. for 1–10 ng/ml of anti-CD95 (Table 6). When performing simulation experiments of the model for this cell line, we used three different values of kd depending on whether the initial concentration of CD95L was within the range 1–100 ng/ml, within the range 100–1000 ng/ml or greater than 1000 ng/ml (Additional file 1: Table 3S).
Analyzing the model predictions, we detected differences in the behavior of the Bentele's and the composite models (Table 6). The first of them describes a threshold mechanism for CD95-induced apoptosis implying that this process is completely stopped when CD95L concentration is below the critical value. However, the model predicts a sharp increase of cPARP immediately when the level of CD95L exceeds the threshold (Table 6, № 1). In contrast, the composite model shows a gradual increase of cPARP with increase of the ligand level. To determine the apoptotic threshold in this case, we found concentration of CD95L for which cPARP ratio is equal to 10% of the initial PARP amount [30]. As in the original model, this concentration was in the range of 1–10 ng/ml. Additionally, the models revealed sensitivity of the threshold to the concentration of cFLIP (Table 6, № 2). Both of them predicted the cell death phenotype upon stimulation by 1 ng/ml anti-CD95 and the level of cFLIP decreased by ~50%.
The next prediction, which we observed for SKW 6.4 cells, considers a delay of caspase-8 activation caused by low concentrations of anti-CD95 (Table 6, № 3). The maximal delay predicted by the Bentele's model was about 2500 min, whereas the composite model detected a much lower value (700–800 min). Analysis of dependence of caspase-3 concentration on initial values of IAP and CD95L (Table 6, № 4) also demonstrated differences in the models' predictions. Thus, low level of IAP (less than 1 nM) in the original model results in complete cell death. However, under the same condition the composite model shows a smooth increase of caspase-3 levels with CD95L changing from 0.3 nM to 1000 nM. If the amount of the ligand is less than 0.3 nM, IAP blocks apoptosis completely. In addition, the Bentele's model predicts that high concentration of IAP prevents a significant increase of caspase-3 even for high levels of the ligand, whereas in the composite model high concentration of CD95L leads to cell death.
Limitations of the composite model
We analyzed a set of parametric constraints which allowed us to reduce the precursor models (Additional file 1: Table 10S). Following them, we can recover a detailed description of the investigated process. Connection of the composite model with the original model by Neumann et al. was preserved, whereas with the original model by Bentele et al. it was partially lost since the chains of species interactions were changed for the sake of combining the models together. In particular, the pathway of caspase-8 activation in DISC was derived from the Neumann's model as well as the reaction chain of procaspase-9 cleavage was modified. However, following the constraints of Additional file 1: Table 10S, we can complete the composite model with such reactions as Bid truncation by caspase-2 and PARP cleavage triggered by caspase-7. We can also recover the details of caspase-9 activation mediated by cytochrome C and Smac release from mitochondria but with altered kinetics of release. For now, the question of admissibility of such modifications as well as extension of the composite model based on other apoptosis models remains open and is a challenge for further research.
In this paper, we considered two approaches to development of mathematical models of cell fate decisions. The first concerns the methodology of model reduction and involves approximation of one model by another one of lower dimension without affecting dynamics of experimentally measured species. The second implies composition of the models and aims at reproducing experimental dynamics of all precursor models.
There are many advantages of working with low-dimensional models [8]. In particular, the researcher has a clear vision of the most important biochemical reactions taking place in the modeled system as well as better understanding of them. Low-dimensional models are easier to analyze and faster to simulate. This helps to save time and enhances productivity. The main limitation of model reduction consists in loss of biological information. However, it should be noted that even if some information (for example, about very slow biochemical reactions) may be lost, it can result in a more clear understanding of the most important interactions and allows focusing on the decisive processes in the model, predictive ability of which is reasonably preserved. Hence, this limitation can be transformed into an advantage.
Model composition aiming at getting a single model from several ones is useful because in such a case a computational biologist is able to investigate the composite model behavior under different conditions that cannot be performed in the precursor models separately. For example, our model allows studying the role of p43-FLIP or IAP in the type I SKW 6.4 or type II HeLa cells, respectively, that might become a task for the future work. In other words, we constructed the model that describes pro- and anti-apoptotic signal transduction in different cell types with reasonable accuracy instead of a couple of different models. Whenever necessary, some reaction chains and parameters can be switched off giving opportunity to simulate a certain type of cells. In addition, the composite model covers experimental data obtained from all precursor models, each of which separately satisfies its own data only.
Model composition sometimes causes modification of some properties of the initial models, resulting in new testable predictions. In our case, such predictions were related to SKW 6.4 cells, and some simulation results were different from the corresponding results of the original Bentele's model. Nonetheless, the composite model behavior remained in good agreement with experimental data used in modeling by Bentele et al. Thus, the question of what model (original or composite) is more realistic requires further experimental investigation.
One of the questions that can be asked concerns the need of reducing models in order to combine them. An attempt to construct the composite modular model of apoptosis was made in [26]. This attempt revealed multiple conceptual and methodological difficulties. The main obvious obstacles included:
choice of elements in the overlapping parts of different models;
incomparable sets of parameters;
the lack of experimental data, as well as inability to use the data obtained for different cell lines or in different ways (e.g. single-cell or cell culture measurements);
inability to make accurate predictions.
Model reduction allows solving some of these problems. In particular, reducing the number of model elements, we reduce the overlapping parts as well. This may be essential for direct combining of models. In addition, the complexity of the reduced model become comparable with the complexity of available experimental data. Therefore, the risk of model overfitting is decreased.
In the case when two models are directly related (for example, one model was emerged from the other), their composition may be significantly easier in comparison to composition of quite different models. In our work, the models by Bentele et al. and Neumann et al. are not directly related, as it could be expected as these models were constructed in the same research group. For example, they use different reaction chains of caspase-8 activation and different values of kinetic parameters in the overlapping reactions.
Another quite useful principle that we used in modeling was modular structure of the developed model. This principle provides flexibility for future extensions. Thus, we are planning to extend the composite model and supply it with modules and data from studies of TRAIL [31-33] and TNF-α [34,35] signaling, apoptosome-dependent caspase activation [36] and p53 oscillation system [37]. It is noteworthy that the model by Laussmann et al.[33], describing TRAIL-induced activation of caspase-8, emerged from the original study by Bentele et al.[18]. This fact may help us in our future work.
Characterising the models used in our work, we can say that we saved our time working with the model by Neumann et al.[19] derived from the BioModels database [27], and spent a lot of time to reproduce the model by Bentele et al.[18] that had not existed in a ready-to-use format. Thus, we would like to emphasize that for the common benefit, the systematic application of biological standards in modeling (e.g. SBML [38] and SBGN [39]) and depositing the working models in public databases (e.g. BioModels [27]) would significantly facilitate analysis of existing biomathematical models and using them as the base for development of new composite systems.
Finally, we believe that the composite model itself may be useful for further investigation of apoptosis.
Mathematical modeling provides a powerful tool for studying the properties of biological processes. Methods of model reduction allowed us to take a first step towards validation of the modular model of apoptosis [26]. Using these methods, we composed two models describing pathways of CD95- and NF-κB-signaling in one without affecting the fit to the experimentally measured dynamics and model predictions. For the model reduction and composition, we used the BioUML software that was extended by the required methods of analysis.
The models by Bentele et al. and Neumann et al. reconstructed in BioUML and represented using SBML format and SBGN notation, as well as their reduced and decomposed versions are available at http://ie.biouml.org/bioumlweb/#de=databases/The%20composite%20model%20of%20CD95%20and%20NF-kB%20signaling webcite.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
EK performed reduction, integration and analysis of the apoptosis models. AZ coordinated the model reduction part of the study. RS and FA coordinated the study of the apoptosis machinery. FA also led implementation of the analysis toolbox in the BioUML software. All authors have participated in writing and editing the manuscript, as well as read and approved the final manuscript.
This work was supported by FP6 grant 037590 "Net2Drug", FP7 grant 090107 "LipidomicNet", EU FP7 (project APO-SYS) and Agence Nationale de la Recherche (project ANR-08-SYSC-003 CALAMAR). AZ is a member of the team "Systems Biology of Cancer," Equipe labellisée par la Ligue Nationale Contre le Cancer.
Hlavacek WS: How to deal with large models?
Gorban AN, Radulescu O, Zinovyev AY: Asymptotology of Chemical Reaction Networks.
Gorban AN, Karlin IV, Zinovyev AY: Constructive methods of invariant manifolds for kinetic problems.
Klonowski W: Simplifying principles for chemical and enzyme reaction kinetics.
Calzone L, Tournier L, Fourquet S, Thieffry D, Zhivotovsky B, Barillot E, Zinovyev A: Mathematical modelling of cell-fate decision in response to death receptor engagement.
Liebermeister W, Baur U, Klipp E: Biochemical network models simplified by balanced truncation.
Bruggeman FJ, Westerhoff HV, Hoek JB, Kholodenko BN: Modular response analysis of cellular regulatory networks.
Radulescu O, Gorban AN, Zinovyev A, Noel V: Reduction of dynamical biochemical reactions networks in computational biology.
Kolpakov FA, Valeev IT, Tolstyh NI, Kisele I, Kondrakhin YV, Kutumova EO, Yevshin IS: BIoUML - open source Integrated platform for building virtual cell and virtual physiological 1 human.
Virtual Biology
in press, DOl: 10.127041vb1e12
Calzone L, Fages F, Soliman S: BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge.
Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U: COPASI — a COmplex PAthway SImulator.
Naldi A, Berenguier D, Fauré A, Lopez F, Thieffry D, Chaouiya C: Logical modelling of regulatory networks with GINsim 2.3.
Zinovyev A, Morozova N, Nonne N, Barillot E, Harel-Bellan A, Gorban AN: Dynamical modeling of microRNA action on the protein translation process.
Morozova N, Zinovyev A, Nonne N, Pritchard L-L, Gorban AN, Harel-Bellan A: Kinetic signatures of microRNA modes of action.
Quaiser T, Dittrich A, Schaper F, Mönnigmann M: A simple workflow for biologically inspired model reduction – application to early JAK-STAT signaling.
Radulescu O, Gorban AN, Zinovyev A, Lilienbaum A: Robust simplifications of multiscale biochemical networks.
Conzelmann H, Saez-Rodriguez J, Sauter T, Bullinger E, Allgöwer F, Gilles ED: Reduction of mathematical models of signal transduction networks: simulation-based approach applied to EGF receptor signalling.
Bentele M, Lavrik I, Ulrich M, Stößer S, Heermann DW, Kalthoff H, Krammer PH, Eils R: Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis.
Neumann L, Pforr C, Beaudouin J, Pappa A, Fricker N, Krammer PH, Lavrik IN, Eils R: Dynamics within the CD95 death-inducing signaling complex decide life and death of cells.
Krammer PH, Rüdiger A, Lavrik IN: Life and death in peripheral T cells.
Scaffidi C, Fulda S, Srinivasan A, Friesen C, Li F, Tomaselli KJ, Debatin K-M, Krammer PH, Peter ME: Two CD95 (APO-1/Fas) signaling pathways.
Choi J, Yang KW, Lee TY, Lee SY: New time-scale criteria for model simplification of bio-reaction systems.
Wei J, Kuo JC: A lumping analysis in monomolecular reaction systems: Analysis of the exactly lumpable system.
Akaike H: A new look at the statistical model identification.
Schilling M, Maiwald T, Hengl S, Winter D, Kreutz C, Kolch W, Lehmann WD, Timmer J, Klingmüller U: Theoretical and experimental analysis links isoform-specific ERK signaling to cell fate decisions.
Kutumova EO, Kiselev IN, Sharipov RN, Lavrik IN, Kolpakov FA: A modular model of the apoptosis machinery.
Le Novère N, Bornstein B, Broicher A, Courtot M, Donizelli M, Dharuri H, Li L, Sauro H, Schilstra M, Shapiro B, Snoep JL, Hucka M: BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems.
Engels IH, Stepczynska A, Stroh C, Lauber K, Berg C, Schwenzer R, Wajant H, Jänicke RU, Porter AG, Belka C, Gregor M, Schulze-Ostho K, Wesselborg K: Caspase-8/FLICE functions as an executioner caspase in anticancer drug-induced apoptosis.
Kutumova EO, Ryabova AS, Valeev TF, Kolpakov FA: BI0UML plug-in for nonlinear parameter estimation using multiple experimental data.
Virtual Biology 1
in press. DOl: 10.127041vb1e10
Gaudet S, Spencer SL, Chen WW, Sorger PK: Exploring the contextual sensitivity of factors that determine cell-to-cell variability in receptor-mediated apoptosis.
Albeck JG, Burke JM, Aldridge BB, Zhang M, Lauffenburger DA, Sorger PK: Quantitative analysis of pathways controlling extrinsic apoptosis in single cells.
Albeck JG, Burke JM, Spencer SL, Lauffenburger DA, Sorger PK: Modeling a snap-action, variable-delay switch controlling extrinsic cell Death.
Laussmann MA, Passante E, Hellwig CT, Tomiczek B, Flanagan L, Prehn JH, Huber HJ, Rehm M: Proteasome inhibition can impair caspase-8 activation upon submaximal stimulation of apoptotic tumor necrosis factor-related apoptosis inducing ligand (TRAIL) signaling.
Rangamani P, Sirovich L: Survival and apoptotic pathways initiated by TNF-alpha: modeling and predictions.
Cho K-H, Shin S-Y, Lee H-W, Wolkenhauer O: Investigations into the analysis and modeling of the TNFα-mediated NF-κB-signaling pathway.
Rehm M, Huber HJ, Dussmann H, Prehn JH: Systems analysis of effector caspase activation and its control by X-linked inhibitor of apoptosis protein.
Hamada H, Tashima Y, Kisaka Y, Iwamoto K, Hanai T, Eguchi Y, Okamoto M: Sophisticated framework between cell cycle arrest and apoptosis induction based on p53 dynamics.
Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H, Arkin AP, Bornstein BJ, Bray D, Cornish-Bowden A, Cuellar AA, Dronov S, Gilles ED, Ginkel M, Gor V, Goryanin II, Hedley WJ, Hodgman TC, Hofmeyr JH, Hunter PJ, Juty NS, Kasberger JL, Kremling A, Kummer U, Le Novère N, Loew LM, Lucio D, Mendes P, Minch E, Mjolsness ED: The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models.
Le Novère N, Hucka M, Mi H, Moodie S, Schreiber F, Sorokin A, Demir E, Wegner K, Aladjem MI, Wimalaratne SM, Bergman FT, Gauges R, Ghazal P, Kawaji H, Li L, Matsuoka Y, Villéger A, Boyd SE, Calzone L, Courtot M, Dogrusoz U, Freeman TC, Funahashi A, Ghosh S, Jouraku A, Kim S, Kolpakov F, Luna A, Sahle S, Schmidt E: The Systems Biology Graphical Notation.


text:
Dhananjay Munde, NCP MLC and the estranged nephew of senior BJP leader Gopinath Munde, today met MNS president Raj Thackeray at his residence here, raising a few eyebrows.
Dhananjay called on Raj at 'Krushnakunj' in suburban Dadar and termed it as a personal visit.
He said he shares good relations with Raj and clarified that it was not a political meet.
"It was just a courtesy call. In the past too, I have met him several times. There is no need to derive any political meaning out of it," Dhananjay, who quit BJP to join the Sharad Pawar-led outfit in July last year, said.
Dhananjay walked out of BJP over alleged differences with his uncle, who instead nominated his daughter Pankaja Palve-Munde from Parli constituency in Beed district.
He formally quit the BJP after resigning as a legislator even when he had three years of tenure left.

subset: commoncrawl


text:
Article ID: 889251 - View products that this article applies to.
On This Page
This step-by-step article describes how to spawn a process that runs under the context of the impersonated user in Microsoft ASP.NET pages. To spawn a process that runs under the context of the impersonated user, you cannot use the System.Diagnostics.Process.Start method. This is because in ASP.NET, impersonation is performed at the thread level and not at the process level. Therefore, any process that you spawn from ASP.NET will run under the context of the ASP.NET worker process and not under the impersonated context.
Description of the techniqueTo work around this issue, you must make platform invoke (P/Invoke) calls to the following Win32 APIs:
Steps to spawn a processMicrosoft provides programming examples for illustration only, without warranty either expressed or implied. This includes, but is not limited to, the implied warranties of merchantability or fitness for a particular purpose. This article assumes that you are familiar with the programming language that is being demonstrated and with the tools that are used to create and to debug procedures. Microsoft support engineers can help explain the functionality of a particular procedure, but they will not modify these examples to provide added functionality or construct procedures to meet your specific requirements. To spawn a process that runs under the context of the impersonated user, follow these steps:
For more information, click the following article number to view the article in the Microsoft Knowledge Base:
(https://support.microsoft.com/kb/306158/ )How to implement impersonation in an ASP.NET application
(https://support.microsoft.com/kb/321748/ )How to create a local Web server ASP.NET application
(https://support.microsoft.com/kb/842790/ )A System.Security.SecurityException exception occurs when you try to impersonate a user from a secondary thread in an ASP.NET Web application
Article ID: 889251 - Last Review: June 2, 2005 - Revision: 4.6
Give Feedback


text:
A psychohistory of Mary Cleave would begin at the age of two, on the potty, where her mother taught her to read. From that time on, Mary always associated toilet training with higher education, eventually earning a doctorate in the field of sanitary engineering. Her mother was a high school biology teacher in Long Island, the third generation of a line of naturalists; her father was a trumpet player and conductor. For extra income the Cleaves operated a summer camp on Lake Champlain, in the cool Adirondacks. Mary, the second of three daughters, was the counselor in charge of the waterfront. It was there—confronted with the approaching death of that once limpid and thriving body of water, now strangled in sewage and the volatile wastes of industrial society—that Mary committed herself to regenerating the beauty of the natural world.
That is one motif in Mary's life. Another is flying. By the age of ten she had assembled nearly every model airplane in the Revell line. She remembers an Armed Forces Day when her parents took her to an Air Force base, where she could clamber through the actual jets on display. We can picture Mary then as an undergrown tomboy with a crooked smile and gray-green eyes that are still twice as sharp as normal—great pilot's eyes. "Boy, I'd like to fly one of these babies!" she exclaimed, and an airman stationed there assured her, "You'll never fly one of these, young lady." He was doing her a favor. Women didn't fly jet airplanes: it was a simple truth. But somewhere in Mary's mind, as she looked at the jet, a seed was planted, and part of her would never sleep until she saw it flower.
When the manned space age began in 1961 with Yuri Gagarin streaking over the atmosphere singing, "I am eagle! I am eagle!" Mary was fourteen and already in the air. "She learned to fly before she learned to drive," her mother remembers. "I would take her to the airport in the car, and then she would take me for a ride in the airplane." In her love for flying, Mary was no different from the men who formed the early nucleus of the astronaut corps, but unlike those men, for whom space travel was new, Mary and the people of her generation would view it as a fact of life. By the time Mary would be old enough to join the astronaut corps, the first great age of space exploration would be over. The people of her generation would not be expected to conquer space, only to civilize it. That was fine with them; they grew up wanting to do exactly that.
Mary's standard equipment in the cockpit was a pair of pillows, one behind her back so she could reach the pedals and one on the seat so she could see over the instrument panel. "It was not a sight to inspire confidence in my passengers," Mary admits. She might have dreamed of becoming a commercial pilot if she had been a man, but instead she decided to become a stewardess. She would dangle from the top of a door in ski boots, urging her body to grow, but it stopped at five feet one and a half inches, two and a half inches short of the airlines' minimum. If it wasn't the sex it was the size.
Her imagination grew fat on science fiction and weekly doses of Star Trek. In times of stress or whenever she craved solace, she would sink into science fiction and simply vanish from society. Out of the mountain of pulpy paperbacks she consumed, one would plant another seed in her mind—a novel by Robert Heinlein titled Space Cadet, about a new recruit in the space academy. That was one book she never forgot.
By the time she was eighteen Mary was desperate for travel, so she decided to go to school in Colorado, despite her father's dictum that civilization stopped at the western border of Pennsylvania. She went to Colorado State University to become a veterinarian, but after two years she realized she could never be a large-animal vet: her arms were too short. She switched her major, planning to become a biology teacher like her mother, but in the year she spent practice-teaching in Denver she seemed to spend most of her time patrolling the rest rooms. When she left Colorado State, Mary got a job on a "floating campus," tutoring college kids in biology as the ship tramped from port to port. Wherever she went, she took samples of the water. The memory of Lake Champlain never left her; she saw it again and again in all the degraded waters of the world.
In 1971 she decided to go back to school, to Utah State University. She specialized in phycology, which is the study of algae, and worked in the Utah Water Research Laboratory there. Mary soon learned that once you joined the league of science, you left behind the world of common understanding. If she went to a party and told people she was a phycologist, they assumed she had a lisp. "Right away they started telling me about their nervous breakdowns."
Most of the guys in the lab were engineers, and they persuaded her that if she was really serious about cleaning up the environment, she would have to get a doctorate in either civil or environmental engineering. Mary went for both. She fulfilled her compact with Lake Champlain and became a sanitary engineer. The day in 1979 that she finished defending her dissertation, becoming the first woman to earn a Ph.D. in engineering at Utah State, she prepared herself a bubble bath and spent the next two days rereading Frank Herbert's Dune trilogy, which is about space and ecology. The stories are set on the desert planet of Arrakis, where water is so scarce that people have to recycle the moisture and waster of their own bodies. As Mary lounged in


text:
They're standing by your side on your big day — here's your chance to show them how much you appreciate it. From stylish accessories to amazing finds like a 1963 Gibson SG Junior, this sale has everything you need to get your groomsman gift game on lock.
We like our technology just as much as the next guy, but there's a lot to be said for the simple act of putting ink to paper. And that's where this collection of fine pens from the luxury experts at Waterford comes in. From intricately engraved titanium to deep orange resins, each is a work of exceptional craftsmanship that will serve you well for years to come.
The 1 train cuts across the west side of NYC, from the very tip of lower Manhattan, all the way up to the Bronx. No surprise, then, that a whole lot of dapper guys pass through its doors each day on their way to the office. Here, a collection of gear to take you to work in similarly well-appointed style. Go ahead and suit up.


text:
This Week at War: An Arms Race America Can't Win
The United States has no chance in ship-for-ship showdown with China. Luckily, it shouldn't have to have one.
- By Robert HaddickRobert Haddick is managing editor of Small Wars Journal.
In a speech delivered on June 2 to the Shangri-La Security Dialogue conference in Singapore, U.S. Defense Secretary Leon Panetta attempted to convince his audience that America's "rebalancing" strategy to the Asia-Pacific region — previous called a "pivot" — is serious and will be backed by expanded military power. Panetta announced that by 2020, 60 percent of the U.S. Navy will be positioned in the Pacific. He also openly discussed the controversial Air-Sea Battle concept, while denying that the reinforcements and new plans are a challenge to China. He also promised to step up the presence of U.S. military forces in the region, both through new basing arrangements and by an expanded list of training exercises with partner military forces.
Panetta likely hoped his remarks would bolster the credibility of the administration's strategy. On closer examination, there is less to Panetta's Pacific naval buildup than meets the eye. The U.S. Navy's intelligence office, by contrast, expects China's naval expansion this decade to be more substantial, especially when it comes to its submarine force. The reinforcements that Panetta discussed and new ideas like the Air-Sea Battle concept are necessary but insufficient responses to the worsening military trends in the region. The United States should not expect to win an arms race in the Western Pacific. Instead, it will have to find other more enduring advantages if it hopes to craft a sustainable strategy for the region.
Panetta's promise to base 60 percent of the U.S. fleet in the Pacific was not news — Navy Secretary Ray Mabus announced this intention in a speech back in March. Panetta's assertion that there is currently a "50/50 percent split between the Pacific and the Atlantic" is also not quite right. According to the department's website, of the Navy's 186 major conventional warships (aircraft carriers, cruisers, destroyers, amphibious ships, and attack and cruise missile submarines), 101, or 54 percent, current have home ports on the Pacific Ocean. The Navy's latest 30-year shipbuilding plan forecasts 181 of these major combat ships in the fleet in 2020. A 60 percent allocation implies 109 major combatants in the Pacific in 2020, an increase of eight such ships from today.
On the other hand, the U.S. Office of Naval Intelligence (ONI) forecasts that China's navy will own 106 major warships in 2020, up from 86 in 2009. Seventy-two of these are expected to be attack submarines, compared to 29 for the United States in the Pacific in 2020, under the 60 percent allocation assumption. For the two decades beyond 2020, the U.S. Navy's shipbuilding plan projects no increase in the number of major warships. China's long-range shipbuilding plans are unknown; however, its defense budget has increased at an 11.8 percent compound annual rate, after inflation, between 2000 and 2012, with no indications of any changes to that trend.
Of course, counting ships does not tell the whole story. Even more critical are the missions assigned to these ships and the conditions under which they will fight. In a hypothetical conflict between the United States and China for control of the South and East China Seas, the continental power would enjoy substantial structural advantages over U.S. forces.
China, for instance, would be able to use its land-based air power, located at many dispersed and hardened bases, against naval targets. The ONI forecasts China's inventory of maritime strike aircraft rising from 145 in 2009 to 348 by 2020. U.S. land-based air power in the Western Pacific operates from just a few bases, which are vulnerable to missile attack from China (the Cold War-era Intermediate Nuclear Forces Treaty prevents the United States from developing theater-based surface-to-surface missiles with ranges sufficient to put Chinese bases at risk). A comparison of ship counts similarly does not include China's land-based anti-ship cruise missiles, fired from mobile truck launchers. Nor does it account for China's fleet of coastal patrol boats, also armed with anti-ship cruise missiles.
The Air-Sea Battle concept began as an effort to improve staff coordination and planning between the Navy and the Air Force in an effort to address the structural disadvantages these forces would have when going up against a well-armed continental power like China. The concept is about creating operational synergies between the services. An example of this synergy occurred in last year's campaign against Libya, when U.S. Navy cruise missiles destroyed Libya's air defense system, clearing the way for the U.S. Air Force to operate freely over the country.
But Air-Sea Battle still faces enormous challenges in overcoming the "home court" advantage a continental power enjoys deploying its missile forces from hidden, dispersed, and hardened sites. In addition, the United States faces a steep "marginal cost" problem with an opponent like China; additional defenses for U.S. ships are more expensive than additional Chinese missiles. And China can acquire hundreds or even thousands of missiles for the cost of one major U.S. warship.
Given these structural weaknesses, Air-Sea Battle's success will rely not on endlessly parrying the enemy's missiles, but striking deeply at the adversary's command posts, communications networks, reconnaissance systems, and basing hubs in order to prevent missiles from being launched in the first place. Such strikes would mean attacks on space systems, computer networks, and infrastructure, with implications for the broader civilian economy and society. Some critics of Air-Sea Battle reason that raising the stakes in this manner would make terminating a conflict much more difficult and would escalate the conflict into domains — such as space and cyber — that are particular vulnerabilities for the United States.
The United States won't be able to win an arms race against China and currently has no plans to do so. Nor can the Pentagon count on superior military technology; China already has impressive scientific and engineering capabilities, which are only getting better. Instead, U.S. policymakers need to discover enduring strategic advantages that don't require keeping a qualitative or quantitative lead in weapons. Geography may be one such benefit. In a conflict, the so-called First Island Chain that runs from Japan to Taiwan and then to the Philippines could become a barrier to the Chinese navy and provide outposts for U.S. and allied sensors and missiles. China would likely view such preparations as a provocation, but from the allied perspective, they will complicate Chinese military planning.
Second, the United States and its allies are far more experienced at planning and conducting complicated military operations that require coordination across countries and military services. With a long-established network of alliances and partnerships in the region, U.S. commanders and their counterparts have accumulated decades of experience operating together. One aspect of Air-Sea Battle is to further extend this advantage.
The most powerful U.S. advantage is the alliance network itself. Washington's long list of treaty allies and partners provides options for U.S. and allied policymakers and planners. The alliance network could also help convert the threat of escalation to a U.S. advantage. The more U.S. military forces are able to disperse across the region, at temporary or rotational basing arrangements, the more difficult it will be for China to gain an advantage with military power. In order to achieve such an advantage, China will have to attack a wider number of countries, bringing them into a war on the U.S. side. This prospect should deter conflict from beginning.
The more successful U.S. diplomacy is at building up a large network in the region, the stronger the deterrent effect and the less risk assumed by each member. With its outreach to ASEAN countries and others over the past decade, the United States seems to be on this path. New rotational basing deals with Australia, Singapore, and the Philippines are more evidence of this approach. But more diplomatic success will be required as the challenge from China increases.
U.S. military planners face unfavorable trends in the Western Pacific. Panetta and his lieutenants have sent reinforcements to the region and are rewriting their military doctrines. Although these measures necessary, U.S. policymakers will need another way. Good strategy requires finding enduring advantages. The alliance network in the region provides U.S. commanders with partner military forces, basing options, operational experience, and deterrence against escalation, advantages China won't match any time soon. In this sense, the solution to the challenging military problem U.S. forces face in the Western Pacific will be found as much with more diplomacy as with more firepower.
Related Stories
Is America Pivoting to Asia Fast Enough?James HolmesJames Holmes is an associate professor of strategy at the Naval War College and co-author of Red Star over the Pacific: China's Rise and the Challenge to U.S. Maritime Strategy. The views voiced here are his alone. | Argument |
50 Shares
Will Panetta give any new details on the American pivot to Asia?Josh Rogin
Josh Rogin covers national security and foreign policy and writes the daily Web column The Cable. His column appears bi-weekly in the print edition of The Washington Post. He can be reached for comments or tips at firstname.lastname@example.com.
Previously, Josh covered defense and foreign policy as a staff writer for Congressional Quarterly, writing extensively on Iraq, Afghanistan, Guantánamo Bay, U.S.-Asia relations, defense budgeting and appropriations, and the defense lobbying and contracting industries. Prior to that, he covered military modernization, cyber warfare, space, and missile defense for Federal Computer Week Magazine. He has also served as Pentagon Staff Reporter for the Asahi Shimbun, Japan's leading daily newspaper, in its Washington, D.C., bureau, where he reported on U.S.-Japan relations, Chinese military modernization, the North Korean nuclear crisis, and more.
A graduate of George Washington University's Elliott School of International Affairs, Josh lived in Yokohama, Japan, and studied at Tokyo's Sophia University. He speaks conversational Japanese and has reported from the region. He has also worked at the House International Relations Committee, the Embassy of Japan, and the Brookings Institution.
Josh's reporting has been featured on CNN, MSNBC, C-Span, CBS, ABC, NPR, WTOP, and several other outlets. He was a 2008-2009 National Press Foundation's Paul Miller Washington Reporting Fellow, 2009 military reporting fellow with the Knight Center for Specialized Journalism and the 2011 recipient of the InterAction Award for Excellence in International Reporting. He hails from Philadelphia and lives in Washington, D.C.| The Cable |
33 Shares
Make wealth not war in AsiaClyde Prestowitz
Clyde Prestowitz is the founder and president of the Economic Strategy Institute (ESI), where he has become one of the world's leading writers and strategists on globalization and competitiveness, and an influential advisor to the U.S. and other governments. He has also advised a number of global corporations such as Intel, FormFactor, and Fedex and serves on the advisory board of Indonesia's Center for International and Strategic Studies.| Prestowitz |


text:
Make a Gift Now
FDU Home
FDU News
Career Webinars
FDU Connects
Alumni Awards
Eye on Alumni
Student Spotlight
Main Stage Theater
My Account
Member Photos
Online Directory
FDU Alumni Association
Wroxton College Alumni
Vancouver Alumni
Young Alumni
Black Alumni Chapter
Global Scholars Alumni
FDU Society
South Florida Alumni
Rutherford Alumni
Parents Council
The Fund for FDU
Wroxton College
Scholarship Campaign
Learn about news and alumni events
Find contacts, networks and friends
Alumni Association
and groups
Make a gift or volunteer
FDU News
Career Webinars
FDU Connects
Alumni Awards
Eye on Alumni
Authors and Artists
Class Notes
Myfdu Profiles
Ken Malagiere, BS'05
Simone Portera, BA'07, MAT'08
Peter Knowles, BA'07
Peter Kressaty, BS'90
Cindy Miller, BA'90
Eric Kaplan, BS'74
Serena Bocchino, BA'82
Jim Murphy, DMD'74
Joe, BA'03 and Jen, BSN'03, McCarron
Travis Walvoord, BA'02
Yvette Carscadden, BA'03
Tina Powell, BS'88
Turning Point Videos
Pinnacle Videos
Prominent Alumni
Student Spotlight
Main Stage Theater
Eye on Alumni
Myfdu Profiles
A Conversation with Dr. Predrag B. Markovic, MBA'81
What was life like before you came to FDU?
In 1971, I came to the United States from Yugoslavia on a student visa. I was 22 and alone. I had two bags with me, $20 in my pocket, and I knew 50 words of English.
I found a job cleaning floors after construction in apartments on the Upper East Side of New York City, and learned English by taking classes at the Spanish-American Institute. This enabled me to take the entrance exams for The City University of New York, City College of New York (CCNY).
Next, I worked as a night shift mechanic for a Gnome Bakery, which helped to pay for my tuition. In Yugoslavia, I had graduated Mechanical Technical high school as a mechanical technician. I was always very good at working with my hands. I went to college during the day, taking 21 credits each semester and continuing through each summer, while also working full-time at night in the Woolworth Building Maintenance and Operations Department. Back then, there were many days when I went with little or no sleep.
I met my wife during my last year at City College. She's a registered nurse who came to the U.S. from the Philippines. We were both alone in this country. We got married in my last semester at CCNY. For our wedding, we invited everyone in the U.S. who helped us along the way with advice and suggestions on where to go to school, where to work and live. It was wonderful.
I then served as the operations manager for the Union Carbide Headquarters at 270 Park Avenue in New York City. I learned how a building breathes. I can walk into a building and within a few minutes I can tell you what's wrong and how to fix it. I was recognized for my preventative maintenance practices, which I learned from my grandfather who always said, 'You don't start feeding a suckling pig 2 days before Christmas.' I had tough bosses over the years. I built a strong reputation for organizational leadership, which led to many other opportunities.
Tell us about your construction and renovation projects.
During the mid-1980s, I managed the completion of the Jacob Javitz Convention Center in New York City. We cut $30 million in expenses and finished 3 months ahead of schedule. This led to an opportunity with the Xerox Corporation, where I managed the development of the company's real estate portfolio consisting of 14 office buildings and two mixed-use land development sites.
During the late '90s, I was Vice President for the firm McKissack & McKissack, where I managed the programming of the Walter E. Washington Convention Center in Washington, D.C., a hospital renovation for the National Institutes of Health, and the renovation and restoration of the United States Treasury building, after a fire caused extensive damage in 1996.
I then worked for the New York City School Construction Authority and a number of construction firms. Projects included the New York Public Library for the Performing Arts building at Lincoln Center and train station renovations for the Metro Transit Authority, as well as new facilities for universities, the U.S. Coast Guard and New Jersey State Police, among many others. I built a total of over $4 billion dollars worth of construction projects in North America.
How did FDU prepare you for your career?
FDU opened windows on the world for me. I'm very proud of the education I received from the University, and have always been impressed by the faculty in charge of the MBA program. They have real-world experiences that they bring into the classroom. The professors made us think globally on every case study we worked on, which was excellent.
One course in particular made a significant difference in my life. It focused on the multi-national corporation, and it changed the way I thought about operations and leadership. My FDU professor shared his experience doing business with Saudi Arabia.
What are you up to these days?
I'm taking on new and exciting projects, and I'm also thinking about my legacy. I want to give back to FDU by talking with students, teaching, and sharing my great experiences and advice.
One of FDU's greatest strengths is providing a learning environment that focuses on innovation and global impact. I also want to help the University preserve and expand on this in any way I can.
About Dr. Predrag B. Markovic, MBA'81
Predrag B. Markovic, MBA'81, is Chairman and CEO of P.B. Markovic Project Management, a construction and operations management consulting firm. Markovic earned a bachelor's degree in mechanical engineering from The City University of New York in 1976, and a MBA from Fairleigh Dickinson University's Rutherford Campus in 1981. In 2015, he earned a Doctor of Management in Organizational Leadership from the University of Phoenix.
Fairleigh Dickinson University Alumni Association
Office of Alumni Relations | 1000 River Road | Teaneck, New Jersey 07666
201-692-7013 |
Tell a Friend
Privacy Policy


text:
I'm looking for a webdeveloper to convert PSD on HTML and WordPress !
Here you can view my work : http://d.pr/i/ckds
If anyone is interested and want to talk more about this add me on gmail : email@example.com
Contact me.
Please check your mail.
Helpful Information
- Please read our community guidelines. Self promotion and discussion of piracy is not allowed.
- Open a support ticket if you would like specific help with your account, deposits or purchases.
- Item Support by authors is optional and may vary. Please see the Support tab on each item page.
Most of all, enjoy your time here. Thank you for being a valued Envato community member.


text:
Select department to view salaries for the years 2005-2013, or select "All" for the complete data set. You can also filter results by typing part of an employee's name. (Source: State of Georgia, GHSU/MCG, ASU, GRU, Augusta Technical College, Sept. 16, 2014.)
Please note that the 2013 data in the results set below is the most recent data available.