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Predicting network modules of cell cycle regulators using relative protein abundance statistics
- Cihan Oguz1Email authorView ORCID ID profile,
- Layne T. Watson2, 3, 4,
- William T. Baumann5 and
- John J. Tyson1
DOI: 10.1186/s12918-017-0409-1
© The Author(s) 2017
Received: 23 September 2016
Accepted: 17 February 2017
Published: 28 February 2017
Parameter estimation in systems biology is typically done by enforcing experimental observations through an objective function as the parameter space of a model is explored by numerical simulations. Past studies have shown that one usually finds a set of "feasible" parameter vectors that fit the available experimental data equally well, and that these alternative vectors can make different predictions under novel experimental conditions. In this study, we characterize the feasible region of a complex model of the budding yeast cell cycle under a large set of discrete experimental constraints in order to test whether the statistical features of relative protein abundance predictions are influenced by the topology of the cell cycle regulatory network.
Using differential evolution, we generate an ensemble of feasible parameter vectors that reproduce the phenotypes (viable or inviable) of wild-type yeast cells and 110 mutant strains. We use this ensemble to predict the phenotypes of 129 mutant strains for which experimental data is not available. We identify 86 novel mutants that are predicted to be viable and then rank the cell cycle proteins in terms of their contributions to cumulative variability of relative protein abundance predictions. Proteins involved in "regulation of cell size" and "regulation of G1/S transition" contribute most to predictive variability, whereas proteins involved in "positive regulation of transcription involved in exit from mitosis," "mitotic spindle assembly checkpoint" and "negative regulation of cyclin-dependent protein kinase by cyclin degradation" contribute the least. These results suggest that the statistics of these predictions may be generating patterns specific to individual network modules (START, S/G2/M, and EXIT). To test this hypothesis, we develop random forest models for predicting the network modules of cell cycle regulators using relative abundance statistics as model inputs. Predictive performance is assessed by the areas under receiver operating characteristics curves (AUC). Our models generate an AUC range of 0.83-0.87 as opposed to randomized models with AUC values around 0.50.
By using differential evolution and random forest modeling, we show that the model prediction statistics generate distinct network module-specific patterns within the cell cycle network.
KeywordsParameter optimization Differential evolution Ensemble modeling Machine learning Random forests Budding yeast Cell cycle Systems biology
In systems biology research, mathematical models of sufficient predictive power allow researchers to interrogate biological systems under a wide variety of experimental conditions that may be difficult to achieve in the laboratory. Such in-silico experiments may lead to discoveries that affect life in important ways, for example, in understanding the molecular basis of certain diseases and in designing drugs for their treatment [1, 2]. What makes a model reliably predictive? Before using a model for predictive purposes, it is essential to show that the model is capable of reproducing major known experimental trends. In other words, incorporation of experimental data into a model by parameter optimization is a critical first step. Due to limitations in direct experimental measurements of kinetic parameters, a common approach is to estimate all unknown model parameters by minimizing the difference between model simulations and experimental data [3]. This approach often generates a set of parameter vectors with equivalent (or comparable) performance. Such parametric uncertainty can be used to advantage by extracting information about critical and dispensable parts of a model using global sensitivity analysis or identifying the most informative future experiments. This information can be used to constrain the model's parameters [4] or to refine the model's structure [5].
Creating an ensemble of parameter vectors with similar (or identical) performance (with respect to a known set of experimental observations) is especially useful when one would like to predict the potential outcome(s) of novel experimental designs. We refer the reader to [6] for a comprehensive survey of experimental design studies (with an emphasis on objective function formulations) from several fields including systems biology. More recent work in the area of experimental design within systems biology includes a study that compares the performances of several alternative methods with and without a predetermined network topology [7] and a novel framework for model selection implemented for both stochastic and deterministic models [8].
In the literature, "ensemble modeling" is a common term used to describe studies of multiple models [5, 9, 10] or a single model with multiple parameter vectors [11]. Here, we focus on the latter case with a complex model of the budding yeast cell cycle (more than 100 model parameters). Of special interest to us is parameter space exploration with a discontinuous objective function that is the sum of many discrete constraints. Recent work in ensemble modeling includes using simulated annealing with a multi objective function to extract robust and fragile model features [12], implementation of Metropolis Monte Carlo and multi ellipsoidal sampling [11], exploration of parameter space by adaptive sparse grids with control objectives [13], and identifying model fragilities with random walks [14]. More recently, ensembles of parameter vectors were generated to understand parameter adaptations underlying phenotypic transitions [15] with an application in pharmacological intervention [16]. In [17], Rumschinski introduced a set-based framework for detecting incorrect model hypotheses and refining parameter estimates with the help of infeasibility certificates and a bisection algorithm that identifies parts of parameter spaces consistent with incomplete and noisy experimental data. This approach was illustrated using two simple models with four species and 3–5 parameters. More recently, Rodriguez-Fernandez et al. implemented a mixed-integer nonlinear programming (MINLP) formulation to simultaneously perform model selection and parameter estimation using in silico generated data of homeostasis in E. coli [18]. For this biological system, the authors identified the best model among 1700 nested models in a computationally efficient manner rather than fully analysing each candidate model separately. Starting with 21 model parameters, the resulting solution showed that parameters were precisely estimated, while identifiability issues and scalability to models of larger complexity were mentioned as limitations of this model identification approach [18].
A common element in these ensemble modeling studies is the use of time-series data for optimizing parameters and for exploring the parameter space for alternative "feasible" vectors that provide acceptable fits to the data. Here, we use an ensemble modeling methodology for complex models when the constraining data are not quantitative time-series of model variables (which are often unavailable in experimental studies of cell physiology) but discrete qualitative observations (in our case, the observed phenotypes of many different yeast strains carrying mutations of cell cycle genes). In addition, the model we consider is much more complex, with many more adjustable parameters and much more experimental data, than the models studied in the work cited above.
Ensemble modeling with qualitative constraints has recently been explored by Pargett et al. [19], who combined "optimal scaling" and gradient-based multi-objective optimization for incorporating a heterogeneous set of experimental constraints into ODE models of stem cell regulation in Drosophila. Starting from a core model with 10 states and 18 unknown parameters, the authors generated several additional models by considering alternative connections between components of the regulatory network. Following the parameter optimization step, experimental design was implemented (based on ranking the predictive variances of measurements) in order to decrease the uncertainty of model parameter values and model structure. Each candidate model was represented by ensembles of optimal parameter vectors and Pareto optimality was used for comparing model performance and for identifying informative experiments.
In [20], temporal logics (typically used with discrete models) was implemented to express the dynamical features of a continuous (ODE-based) model of an enzymatic reaction network involved in cancer. Furthermore, global robustness and sensitivity analysis was used for identifying the boundaries between distinct regions of the model's parameter space (producing different states such as stable steady states and oscillations) and for generating several novel biological insights regarding system's dynamics [20].
For a recent review on the use of qualitative data for estimating the parameters of continuous models, we refer the reader to [21]. This review covers the application of alternative data normalization techniques depending on the nature of the experimental data at hand (qualitative vs. quantitative), formulation of multi-objective optimization using heterogeneous experimental data sets, and Pareto optimality based analysis of tradeoffs between such multiple objectives.
The proposed approach in this paper extends our recent work on parameter optimization of a complex model of the budding yeast cell cycle [22]. Starting from an ensemble of optimally performing parameter vectors, we propose several ways to explore the parameter space for more such vectors. In this search, our aim is to find parameter vectors with diverse predictions (i.e., an extended range of predictions for the phenotypes of novel genetic strains). We demonstrate that differential evolution (DE) [23], which is a metaheuristic method, can effectively find feasible parameter vectors with extended predictive ranges provided an additional feasibility criterion (in addition to the criterion of optimal model performance) is enforced so that the search does not get stuck in a small region of parameter space. We show how DE can be forced to widen the range of predictions during the search for optimal parameter vectors.
The application of DE in similar contexts include [24] in which DE is hybridized with Kalman Filter for improving the parameter estimation accuracy compared to pure DE and genetic algorithm (GA) based approaches. In [24], simple models of glycolysis and the cell cycle, with artificially generated noisy time series data, are used to demonstrate the improved performance of the hybrid approach. More recently, the 18 parameters of an ODE-based dynamic model of endocytosis are optimized with several metaheuristic methods including DE under different observability settings (complete vs. incomplete observability of system variables), multiple levels of measurement noise, and with real and artificially generated time series data [25]. In this study, DE turned out to be the best performer in terms of estimation accuracy and convergence speed while practical parameter identifiability problems suggested the need for additional experimental data to further constrain the model's parameters. Recent studies on the use of metaheuristic methods in a wide range of science and enginnering applications are surveyed in [26] with more than 200 references (including the applications of several DE variants). An earlier review paper focuses on the application of metaheuristic methods to systems biology problems [27] including experimental design [28–30] and parameter identifiability [31–33].
Problem formulation
The cell cycle is the ordered sequence of events that govern cell growth, replication of the cell's genome, and division into two daughter cells that are capable of repeating this cycle in successive generations [34, 35]. The four phases of the cell cycle are DNA synthesis (S phase) and mitosis (M phase) separated by two gaps (G1 and G2). G1, S, G2 and M phases progress sequentially in a repeated manner, which is crucial to maintaining a constant number of chromosomes per cell after each cycle of DNA replication and cell division. Furthermore, the duration of a single cell cycle (i.e., from birth to division) has to be balanced (on average) with the time needed for doubling the amounts of all other cellular components. If this condition is not met (i.e., the mass doubling time is substantially different from the cell cycle time), then average cell size becomes progressively smaller or larger leading to cell death. In addition, a number of "checkpoints" prevent G1-S-G2-M progression in cases such as DNA damage or improper alignment of replicated chromosomes on the mitotic spindle. All of these features of cell cycle progression are controlled by the periodic activation of cyclin-dependent kinases (CDKs) [34]. Since the fundamental molecular mechanisms governing the activation of CDKs are similar among all eukaryotes, an improved understanding of cell cycle controls has potential benefits far beyond the intrinsic challenge of unraveling this complex molecular control system.
START module: START (or G1/S transition) is an event in G1 phase when a new round of DNA synthesis and mitosis are committed by a cell. The most critical step of the START transition is the translocation of Whi5, a stoichiometric inhibitor of SBF and MBF (transcription factors of Cln2 and Clb5 synthesis modeled as a single variable named SBF), from nucleus to cytoplasm. In early G1, SBF is not active since it is inhibited by Whi5. As the cells grow, Cln3 and Bck2 concentrations rise enough to phosphorylate Whi5 (inhibitor of SBF), and as a result SBF becomes active, promoting Cln2 and Cln5 synthesis. Increasing concentrations of Cln2, Cln3, and Clb5 support progression of bud emergence.
S/G2/M module: Increasing Cln2 concentration following the START transition leads to phosphorylation and degradation of CKI. As a result of this, Clb5 is released. The active form of Clb5 promotes DNA synthesis, further inhibiting CKI through phosphorylation. Cln2 and Clb5 inhibit Cdh1 (responsible from Clb2 degradation) and Clb2 concentration increases resulting in the activation of Mcm1 (transcription factor of Clb2), and further Clb2 accumulation. By phosphorylating and inactivating SBF, Clb2 also halts the synthesis of Cln2 and Clb5 and the cells get ready for mitotic exit. Activation of APC by Clb2 and the cooperation of APC with Cdc20 are some of the key steps required for metaphase-anaphase transition and mitotic cyclin degradation. For Clb2 and Clb5 to be degraded, APC has to be phosphorylated and spindle assembly checkpoint needs to be released. Both of these processes are driven by Clb2.
EXIT module: Activation of Cdc14 is the most critical event in the EXIT module since it is essential for exit from mitosis and return to G1 state. Cdc14 dephosphorylates several proteins previously phosphorylated by CDKs in S/G2/M, thereby leading to the activation of Cdh1 and CKI, as well as the repression of Clb2 and Clb5. Two pathways, namely FEAR (Cdc fourteen early anaphase release) and MEN (mitotic exit network), are involved in the activation of Cdc14. The release of Esp1 from Pds1 (through Cdc20 activity) in the FEAR pathway leads to chromatid separation and phosphorylation of Net1. As a result, Cdc14 is released from Net1:Cdc14 complex and free Cdc14 drives exit from mitosis. In order for budding yeast cells to return to G1 state by the robust phosphorylation of Net1, the FEAR pathway is supported by the MEN pathway through the activation of Cdc15 and Tem1 that form a complex (MEN). This results in the full release of Cdc14, activation of Cdh1, complete degradation of Clb2, as well as the stabilization of CKI and a fully restored G1 phase.
In [22], starting from an initial parameter vector that captured 72 of the 119 experimental phenotypes in the Training Set, we improved the number of captured phenotypes to 111. In the process, the optimization algorithm produced more than 3000 parameter vectors that captured the same 111 phenotypes of the Training Set. We call this collection an ensemble of "feasible" parameter vectors. (The ranges of model parameter values in this ensemble are given in Additional file 1: Tables S3 and S4.) In this paper, our goal is to extend the ensemble of feasible parameter vectors identified by [22] to maximize the range of model predictions for a specific group of novel mutant strains (the Prediction Set). These mutants were not included in the Training Set because their phenotypes have not yet been characterized experimentally.
Phosphorylation and dephosphorylation reactions that induce synthetic lethality upon their elimination
Eliminated reaction
Single mutation strains that are viable before and
(rate constant)
inviable after setting the rate constant to zero
Whi5 phosphorylation by Bck2 (k p i5k2)
cln3 Δ, Multicopy BCK2, cdh1 Δ, sic1 Δ, swi5 Δ,
CLB5-db Δ, net1-ts, GAL-CLB2, APC-A
CKI phosphorylation by Cln2 (e k i,n2)
bck2 Δ, GAL-SIC1, net1-ts, APC-A
CKI phosphorylation by Clb2 (e k i,b2)
GAL-CLN3, cdh1 Δ, GAL-CLB5, CLB1 clb2 Δ
CKI dephosphorylation by Cdc14 (k d p k i,14)
bck2 Δ, cdh1 Δ, GAL-CLB2, APC-A
Whi5 phosphorylation by Cln3 (k p i5n3)
bck2 Δ, cdh1 Δ, APC-A
SBF phosphorylation by Clb2 (k p b f b2)
cdh1 Δ, CLB5-db Δ, APC-A
Whi5 phosphorylation by Cln2 (k p i5n2)
bck2 Δ, APC-A
Whi5 dephosphorylation by Cdc14 (k d p i514)
Net1 dephosphorylation by PPX (k d p n e t,p x )
Multicopy CDC15
The range of model predictions
where \( {p}^{(i)}_{j}\in \left \{ {0, 1, 2}\right \}\) characterizes the phenotype for the jth novel genetic strain for the ith parameter vector and l is the total number of novel strains. Phenotype values are set according to the following rules. If, during the simulation of a novel strain, cell size exceeds 25 (arbitrary units) at any time, then the strain's phenotype is inviable (\({p}^{(i)}_{j}=2\)). On the other hand, if cell size at last division is within 5% of the cell sizes at the two previous divisions, then the phenotype is viable (\({p}^{(i)}_{j}=1\)). Finally, if the model generates cycles of multiple periodicity and cell size at division oscillates between values that differ by more than 5%, then the phenotype is "multiply periodic" (\({p}^{(i)}_{j}=0\)). The number S(P) of unique rows in P is defined as the range of the prediction vectors in P. As we explore different schemes for computing prediction matrices, we compute S values for the ensembles created by these schemes. For each ensemble generation scheme, the sampling efficiency (e S ) is computed as S/n tot , where n tot is the total number of samples taken from the parameter space. This measure allows us to compare different ensemble generation schemes based on the ranges of phenotypic predictions they produce.
Based on our previous study [22], which demonstrated that DE is an effective tool for exploring the parameter space of our high dimensional model given a discrete multi objective function (i.e, the number of phenotypes in the Training Set captured by the model), we continue using DE, this time for identifying the range of model predictions. While searching for an implementation of DE to meet this objective with efficient sampling, we encounter technical limitations with the standard implementation of DE that is typically used for parameter optimization, and we surmount these limitations by (i) improving the selection of the ensemble that serves as the starting point of DE, and (ii) adding new constraints to DE that force the method to search for feasible parameter vectors expanding the range of model predictions.
Differential Evolution
Let E D denote real D-dimensional Euclidean space, and let x=(x 1, …, x D )∈E D be a vector of parameter values. The vector x includes both the 126 kinetic constants in the model and the 26 ODE initial conditions (D=152). For each vector x∈E D proposed by the optimization algorithm, we calculate the phenotype \( {p}^{(i)}_{j}\in \left \{ {0, 1, 2}\right \}\) (for the jth strain for the ith parameter vector) for each of the 119 yeast strains in the Training Set. The objective function O(x) is an integer-valued function that counts the number of phenotypes in the Training Set that are correctly captured by the model, given the parameter values in the vector x.
In DE, parameter vectors are propagated from generation to generation by processes of mutation, crossover, and selection. Each generation (indexed by t=0,1,…) consists of N parameter vectors x (t,i). Hence, the real number \({x}^{(t,i)}_{j}\) is the value of the jth parameter in the ith parent in the tth generation. Let u (t,i) be the trial parameter vector born from the ith parent in the tth generation, whose components are constructed in two steps called "mutation" and "crossover". Then, given the parent parameter vector x (t,i) and trial parameter vector u (t,i), a decision is made as to which one is propagated to generation t+1.
- 1.Mutation. First, for each i, 1≤i≤N, we create a "mutant" vector$$ v^{(t,i)}=x^{(t,i)}+F\cdot d^{(t,i)}=x^{(t,i)}+F\cdot \left(x^{(t,i')}-x^{(t,i^{\prime\prime})}\right) $$(3)
by perturbing a parental parameter vector x (t,i), where the perturbation vector d (t,i) is the difference between the parameter vectors of two distinct additional parents i ′ and i ″ chosen at random from the tth generation of parents, and 0<F<1 (F=0.1 in this study).
- 2.Crossover. For each i (1≤i≤N) and j (1≤j≤D), and uniform [ 0,1] random variables U i,j , define the offspring by$$\begin{array}{@{}rcl@{}} {u}^{{(t,i)}_{j}}= \left\{ \begin{array}{rl} {v}^{(t,i)}_{j} &, {0} \leq {U}_{i,j} \leq {C}, \\ {x}^{(t,i)}_{j} &\text{, otherwise.} \end{array} \right. \end{array} $$(4)
We choose the "crossover probability" C=0.5 so that neither parental values nor mutant values are given an advantage during the crossover step.
- 3.Selection. The next generation parent x (t+1,i) is either the parent x (t,i) or the trial vector u (t,i). As DE explores the parameter space under different settings in this study, depending on the settings of the particular DE run, we impose three distinct feasibility criteria for selection, which are described below.
Feasibility Criterion 1 (F C 1): Trial vector u (t,i) satisfies F C 1 if the model it defines captures the 111 phenotypes listed in Additional file 1: Table S7 out of the 119 phenotypes in the Training Set. F C 1 is always enforced by DE for creating Ensembles 1 through 16 in Table 2. For each ensemble generation scheme, the efficiency of sampling in terms of identifying parameter vectors that satisfy F C 1 (\(\phantom {\dot {i}\!}e_{{FC}_{1}}\)) is computed as \(n_{{FC}_{1}}/n_{tot}\phantom {\dot {i}\!}\), where \(\phantom {\dot {i}\!}n_{{FC}_{1}}\) is the number of parameter vectors that satisfy F C 1 and n tot is the total number of samples taken from the parameter space.Table 2
Ensembles of feasible vectors generated with different schemes
Selection of
Feasibility criteria
# generations
the initial DE
used in selection
per DE run
DE runs
(Range of
population from
step of DE
Ensemble 1
Parameter vectors
Ensemble generated
satisfy F C 1
in optimization [22]
Parameter vectors
Ensemble extracted
satisfy F C 1
from 50,000
LHS samples
Randomly selected
parameter vectors
V max (10)
V max (10)
F C 1 and F C 2
V max (10)
F C 1 and F C 2
V max (123)
F C 1 and F C 2
V max (123)
F C 1 and F C 2
S max & V max (123)
F C 1 and F C 2
S max & V max (123)
F C 1 and F C 2
S max & V max (123)
F C 1, F C 2, and F C 3
S max & V max (123)
F C 1, F C 2, and F C 3
S max & V max (123)
F C 1 and F C 3
S max & V max (123)
F C 1 and F C 3
S max & V max (123)
F C 1, F C 2, and F C 3
S max & V max (123)
F C 1 and F C 3
Feasibility Criterion 2 (F C 2): F C 2 requires that trial vector u (t,i) can only replace parent vector x (t,i) if u (t,i) leads to an expansion in the feasible region's estimated volume. For this, we compute the estimated volumes of two Ensembles X 1 and X 2. The first ensemble X 1 consists of all the parent vectors of the current tth generation of DE (all satisfying F C 1) including x (t,i). This ensemble excludes u (t,i) since it is not a parent vector. The second ensemble X 2 includes u (t,i) in addition to all the parent vectors excluding x (t,i). F C 2 dictates that the trial vector u (t,i) can only replace x (t,i) if the estimated volume of the second ensemble is greater than the estimated volume of the first one (V(X 2)>V(X 1)). (We describe our approach for estimating the volume spanned by an ensemble of parameter vectors in Section 1 of the Additional file 2: Supplementary Text.) With ensemble creation Schemes 4 to 7 in Table 2, DE enforces F C 2 together with F C 1 so that a trial vector replaces the corresponding parent if and only if the trial vector that reproduces the 111 target phenotypes of the Training Set, and leads to an expansion in the feasible region's estimated volume.
Feasibility Criterion 3 (F C 3): F C 3 requires that trial vector u (t,i) can only replace parent vector x (t,i) if u (t,i) yields a prediction vector for the 129 mutant strains of the Prediction Set that has not been derived from any parent vector up through the tth generation of DE. In other words, if a trial vector u (t,i) satisfies F C 1, u (t,i) replaces its parent x (t,i) if and only if the prediction vector \(\hat {\mathbf {p}}\) generated by u (t,i) is not among the rows of the prediction matrix generated by all the parent vectors up through the point of generation of u (t,i). For creating Ensembles 11, 12, and 15 in Table 2, DE enforced all three criteria so that a trial vector replaces the corresponding parent if and only if the trial vector defines a model that captures the 111 target phenotypes of the Training Set, leads to an expansion in the feasible region's estimated volume, and produces a new phenotypic prediction vector for the 129 novel mutants in the Prediction Set. Ensembles 13, 14, and 16 are created by enforcing only first and the third criteria.
Results and discussion
Exploring the parameter space with Latin hypercube sampling
Our starting ensemble in this study is derived from the 3415 feasible parameter vectors identified in [22]. The size of this ensemble is reduced by 8% since only 3146 of these vectors are F C 1-feasible when truncated to 32-bit IEEE single precision. (We are eliminating parameter vectors that are very sensitive with respect to F C 1.) We call this collection of vectors "Ensemble 1". (Throughout this paper, parameter vectors are considered feasible only if their truncated 32-bit values are also feasible.) Applying Ensemble 1 to the Prediction Set, we generate 30 unique prediction vectors.
We explore this initial feasible region by Latin hypercube sampling (LHS). The bounds of the hypercube are formed by the minimum and maximum values of each parameter from Ensemble 1. 50,000 samples are generated as described in Section 2 of the Additional file 2: Supplementary Text. Out of these sample vectors, only 243 (0.5% of the total) are F C 1-feasible. These feasible vectors form Ensemble 2, which produces 51 unique prediction vectors; a 70% improvement (51/30) in the total range of predictions (previously defined as the number of unique prediction vectors).
Exploring the parameter space with DE
The results of LHS point out the possibility of finding feasible parameter vectors with a wider range of model predictions compared to those of Ensemble 1. We next investigate the possibility of using DE to identify alternative feasible ensembles with wider prediction ranges.
First, we created an initial random selection of 19 parameter vectors from Ensemble 1. (The population size of 19 is dictated by computational limitations imposed by the complexity of the model and the size of the Training Set [22]). Starting from this initial population of parameter vectors, DE explores the parameter space with mutation, crossover, and selection operations (described in Methods). (Rather than maximizing the total number of captured phenotypes by the model as we did previously [22], we only look for parameter vectors that capture the the 111 phenotypes listed in Additional file 1: Table S7 while missing the remaining eight phenotypes (Additional file 1: Table S8). Such vectors are feasible according to F C 1 as described earlier). In 400 generations, DE generates 7143 vectors (Ensemble 3 in Table 2) whose truncated 32-bit values satisfy F C 1. Despite its large size, Ensemble 3 yields only six unique prediction vectors for the 129 strains in the Prediction Set.
Why did DE perform so poorly compared to LHS even though, in our previous study, it was superior to random sampling in optimizing model performance (capturing phenotypes in the Training Set)? The answer comes from a comparison of the volumes the parameter space that are spanned by Ensembles 2 and 3. Ensemble 3 has an estimated volume that is 83 orders of magnitude smaller than that of Ensemble 2. In other words, DE zooms into a much smaller region of parameter space than LHS.
The ten most critical model parameters
Parameter name
Total amount of Cdc14
SPN synthesis rate
Total amount of Esp1
Total amount of Net1
Degradation rate of Cdc20
PPX inactivation by Esp1
Efficiency of Cdc14-Net1 complex (RENT) formation
Time scale for protein activation
Net1 phosphorylation by Clb2
Total amount of Mcm1
Therefore, to prevent this drop in dynamic volume, we introduce a new constraint (F C 2) as described in the Methods section. To enforce F C 2, the estimated volumes of two distinct ensembles are computed every time a new trial vector that satisfies F C 1 is found. The first ensemble includes all parameter vectors satisfying F C 1 until that point of DE, except the newest trial vector generated. Hence, this ensemble includes the trial vector's competitor: the parent vector. The second ensemble is generated by including the trial vector instead of the parent vector, with the remaining members being identical to those of the first ensemble. If the estimated volume of the second ensemble is greater than that of the first one, the trial vector replaces the parent vector in the next generation of DE in the search for feasible vectors. Otherwise, the parent vector is not replaced, but the trial vector is recorded since it satisfies F C 1 and its predictions for the phenotypes of the Prediction Set are evaluated after DE is complete. Succinctly, F C 2 allows a trial vector to replace a parent only if it leads to an expansion of the feasible region. As shown in Fig. 3 (green and red lines), this new feasibility criterion prevents the volume of the feasible region from shrinking as the generations pass (two independent DE runs). Additional file 3: Figure S1 (blue line) and Additional file 1: Table S9 show that without this volume maximization strategy, the ranges of nearly all parameters are diminished after 400 generations. On the other hand, with estimated volume maximization, the majority of the parameters have about a 10% variation after 400 generations (green line in Additional file 3: Figure S1). These parameter ranges are calculated by dividing the maximum parameter values by the minimum parameter values among all parent vectors at the 400 th generation. Due to this improvement in the parameter ranges, we allow DE to explore for an additional 1200 generations. Additional file 3: Figure S1 (red line) shows that about 10% range for most parameters is still preserved among the parent vectors in the 1600 th generation. We perform two realizations of DE with this approach for 1600 generations, thereby creating two more ensembles (Ensembles 5 and 6 in Table 2). These ensembles generate 64 and 69 unique phenotypic prediction vectors, respectively.
A further improvement comes from selecting the initial DE population to maximize the volume spanned by the vectors with respect to all 123 kinetic parameters rather than just the 10 most critical parameters. (Note that the kinetic parameters k s n2, f, and MDT have fixed values in Additional file 1: Table S3.) Two independent DE realizations for 1600 generations produce an average of 87 unique phenotypic prediction vectors (Ensembles 7 and 8 in Table 2) further increasing the range of predictions compared to those of Ensembles 5 and 6. This is also a significant improvement over LHS (51 unique prediction vectors) even though DE required about 30,000 samples (1600 generations × 19 vectors) to identify ∼70% wider (87/50) range of predictions compared to 50,000 LH samples. Having gotten DE to a point where it is more efficient than random sampling in terms of exploring the feasible region, we next seek ways to improve the performance of DE even further.
Increasing the phenotypic diversity of the initial population of DE
As we previously stated, 3146 feasible parameter vectors from the initial DE optimization run on the Training Set [22] (Ensemble 1) generate 30 unique phenotypic prediction vectors for the Prediction Set. Interestingly, 97% of these vectors generate only five of the total 30 prediction vectors as shown in Additional file 3: Figure S2. Due to this, the initial population of parameter vectors used in the last two DE runs (Scheme 5 in Table 2) produces a total of four unique prediction vectors all of which are in this set of five dominant prediction vectors. In other words, the diversity of the initial population in terms of phenotypic predictions is very low, only 13% (4 /30) of the diversity is utilized. Therefore, to increase this diversity, we select the initial population of feasible parameter vectors such that each one generates a different prediction vector (a total of 19) for the 129 strains in the Prediction Set. While using this initial selection scheme, we also maximize the estimated volume spanned by the selected vectors (Scheme 6 in Table 2). The details of this diversification procedure are in the Additional file 2: Supplementary Text (Section 5). This strategy further expands the range of predictions, with two independent runs (each for 1600 generations) increasing the average number of unique prediction vectors from 87 to 106 (Table 2). Thus, improved predictive diversity among the parent parameter vectors in the initial population results in feasible vectors (generated during DE) that are predictively more diverse.
Enforcing an increased range of predictions during DE
In order to explore the phenotypic prediction space of the model further, we enforce a third criterion during DE. With this new criterion, a parent parameter vector is only replaced by a trial vector if the trial vector generates a new prediction vector, one not heretofore generated by any feasible parameter vector during this DE run. (For the descriptions of parent and trial parameter vectors, refer to Methods section.) In other words, with this modification, the trial parameter vector has to satisfy three constraints to replace the parent vector. It should reproduce 111 phenotypes in Additional file 1: Table S7 (F C 1), increase the estimated volume of the feasible region upon replacing the parent vector (F C 2), and generate a new prediction vector (F C 3). Two independent realizations with this new scheme (for 1600 generations) increase the average number of unique predictions from 106 to 122.5 (average of Ensembles 11 and 12 in Table 2). We note that since the occurrence of a trial vector that satisfies the first two criteria is not very frequent (less than 10% among the samples generated by DE), simulating the 129 mutant strains of the Prediction Set on-the-fly (during DE) adds negligible computational time compared to the time required to run DE for 1600 generations with the 119 phenotypes in the Training Set.
Comparison of the two most efficient ensemble generation schemes
In order to compare the performances of Schemes 7 and 8 more thoroughly, we perform four DE runs with each scheme (2200 generations per run). As shown in Table 2, Scheme 8 produces 671 unique prediction vectors (from 15050 feasible parameter vectors in Ensemble 16), whereas the number of unique prediction vectors is 293 for Scheme 7 (from 15520 feasible parameter vectors in Ensemble 15), reiterating our previously stated conclusion that Scheme 8 is more efficient in exploring the phenotypic prediction space. Lower performance of Scheme 7 suggests that maximizing the feasible estimated volume during DE (through F C 2) may have no benefit.
The ten most fragile phenotypes
Phenotype #
Phenotype name
CLB2-db Δ multicopy SIC1 (Viable)
cln1 Δ cln2 Δ cdh1 Δ (Viable)
CLB2-db Δ clb5 Δ clb6 Δ in galactose (Viable)
cdc15 Δ net1-ts cdh1 Δ (Viable)
GAL-CLB2 cdh1 Δ (Inviable)
cln1 Δ cln2 Δ cdh1 Δ GAL-CLN2 (Viable)
CLB2-db Δ in galactose (Inviable)
APC-A (Viable)
APC-A sic1 Δ (Viable)
CLB5-db Δ pds1 Δ (Viable)
\({\hat {R}_{i}}=900\) is the highest possible robustness score for a feasible parameter vector that satisfies F C 1 prior to perturbations. One way to compare different ensembles in terms of robustness is to compare the distributions of \({\hat {R}_{i}}\).
From these results, we conclude that by forcing the DE search to expand the range of predictions, one can explore the prediction space effectively as demonstrated by Scheme 8's superior predictive diversity over its alternatives (Table 2). However, by forcing DE to maximize the feasible region's estimated volume, it is possible to improve the robustness of the model in reproducing experimentally verified phenotypes, but at the expense of predictive diversity. Therefore, one should select the appropriate scheme for parameter space exploration, depending on one's preference between higher robustness (Scheme 7) or diversity of model predictions (Scheme 8). Higher robustness against parametric perturbations may be enforced in some cases. For instance, one may need to modify the values of parameters in feasible vectors in order to capture additional experimental constraints while still capturing the original data [42], and this would favor the selection of Scheme 7 over Scheme 8.
Relative protein abundance predictions
Up to this point, we have only considered the phenotypic prediction range for the 129 mutant strains in the Prediction Set. Next, we consider predictions of relative protein abundances. In simulations, the time average concentration of a protein represents the model's prediction for that protein's abundance in an asynchronous population of budding yeast cells. For theoretical and experimental reasons, it is better to focus on relative protein abundances, i.e., the ratio of the abundance of one protein with respect to another. Relative abundances of proteins are typically measured by Western Blotting [43] or mass spectrometry [44]. Relative abundance measurements have been useful in estimating the parameters of systems biology models in the past [45, 46].
The ten novel phenotypes with highest predictive variance
Mutant #
Mutation 1
Mutation 2
Mutation 3
e k i,n2=0
k p b f b2=0
k d p i514=0
e k i,n2=0
k p b f b2=0
k p i5k2=0
e k i,b2=0
k d p i514=0
k p i5k2=0
e k i,b2=0
e k i,n2=0
k p i5n3=0
k p b f b2=0
k p i5k2=0
e k i,b2=0
k d p n e t,p x =0
e k i,n2=0
k d p k i,14=0
k p b f b2=0
k p b f b2=0
k d p i514=0
k d p n e t,p x =0
k p b f b2=0
k d p n e t,p x =0
e k i,b2=0
k p b f b2=0
k d p n e t,p x =0
Similar approaches have been used in two previous model driven experimental design studies [47, 48]. In [47], Dong et al. presented an experimental design process called "Computing Life" and illustrated it for the biological clock of Neurospora crassa. At each experimental design cycle, the authors chose the Maximally Informative Next Experiment (MINE) from a large set of potential network models and microarray experiments using a criterion that enforced maximal independence between observables. This analysis identified several genes (from a total of 11,000 genes) under the direct control of a key clock oscillator and also discovered a link between this clock and ribosome biogenesis. In [48], Donahue et al. implemented a sparse grid approximation using polynomials to explore their objective function (based on time series data) in order to discriminate simultaneously between uncertainties in model structure and in parameter values (without an initially determined feasible region). One disadvantage of the sparse grid search is the required smoothness of the objective function, whereas typically rugged objective function landscapes [49] are observed for large and nonlinear network models. This is especially the case in our study where many discrete experimental constraints determine the feasibility of model parameter vectors. For detailed theoretical discussions regarding the use of prediction variability statistics in model-based experimental design, we refer the reader to two excellent reviews [4, 6].
Ranking cell cycle proteins and biological processes in terms of prediction variability
In order to study the potential relationships between the variabilities of relative abundance predictions linked to individual cell cycle proteins and the topology of the cell cycle network, we first identified the total variability associated with each of the 26 proteins. To this end, for each protein, we computed the sum of the CV values for each protein abundance ratio with that particular protein in its numerator. We refer to this sum as the "variability score" of the protein. (We have verified that our ranking of proteins based on their variability scores does not depend on whether we use the protein in the numerator or denominator in the summation process (data not shown)).
Cell cycle regulators ordered in terms of their variability scores (decreasing from top to bottom)
Variability score
Network module
Class label
High variability
High variability
High variability
High variability
High variability
High variability
Polo A
High variability
High variability
High variability
High variability
Clb5 T
High variability
High variability
Cdh1 A
High variability
Low variability
Polo T
Low variability
Low variability
Pds1 T
Low variability
Clb2 T
Low variability
Low variability
Low variability
V (Mass)
Low variability
Low variability
Low variability
Low variability
Low variability
Swi5 T
Low variability
Ten regulators in the S/G2/M module, on the other hand, were evenly distributed among both categories. Two regulators in this module, namely Cdc20A-APC and Cdc20A-APCP had strikingly different predictive variability scores. Cdc20A-APC complex has the highest score of 231.4), whereas Cdc20A-APCP complex was ranked 20 th with a score of 115.58. These two complexes are responsible from the degradation of Clb5, Clb2, and Pds1 through ubiquitin-mediated proteolysis [51]. Interestingly, Cdc20A-APCP is 9.3, 3.8, and 6.5–fold more potent than Cdc20A-APC (based on the average parameter values in Ensemble 16) in terms of degrading Clb5, Clb2, and Pds1, respectively. Hence, a potent (or critical) regulator turned out to have less predictive variability compared to a weaker regulator in our model once again pointing to a potential relationship between the cell cycle network and the variability scores of individual model variables (more critical variables have less predictive variance). After ranking cell cycle proteins by denominator-based formation of relative abundance-network module pairs (i.e., each relative abundance is matched to the module of the protein in its denominator), we computed the Pearson correlation coefficient between the vectors formed from the order of the two rankings (numerator-based vs. denominator-based) as 0.99. Hence, the ranking of cell cycle proteins was independent of the way network modules were assigned to relative abundance values.
Biological processes ordered in terms of predictive variability which decreases from top to bottom
Biological process
Regulation of cell size
164.38 ±42.18
Negative regulation of transcription involved in
160.63 ±0.00
G1/S transition of mitotic cell cycle
Regulation of transcription involved in
157.89 ±71.29
G1/S transition of mitotic cell cycle
Positive regulation of transcription involved in
156.26 ±0.00
G1/S transition of mitotic cell cycle
Positive regulation of transcription from RNA polymerase II promoter
156.26 ±0.00
Regulation of cyclin-dependent protein kinase activity
154.81 ±38.41
Mitotic spindle orientation checkpoint
147.02 ±0.00
Exit from mitosis
147.02 ±0.00
Establishment of mitotic spindle localization
147.02 ±0.00
Regulation of mitotic spindle assembly
139.93 ±0.00
Positive regulation of DNA replication
139.93 ±0.00
G1/S transition of mitotic cell cycle
130.11 ±13.89
Positive regulation of spindle pole body separation
129.07 ±15.36
G2/M transition of mitotic cell cycle
129.07 ±15.36
Positive regulation of protein ubiquitination
124.20 ±0.00
Negative regulation of spindle pole body separation
124.20 ±0.00
Regulation of cell cycle
120.28 ±0.00
Positive regulation of gene expression
120.28 ±0.00
Mitotic sister chromatid segregation
119.01 ±0.00
Regulation of mitotic spindle elongation
118.21 ±0.00
Negative regulation of protein dephosphorylation
118.21 ±0.00
Positive regulation of mitotic metaphase/anaphase transition
116.62 ±10.73
Activation of APC-Cdc20 complex activity
116.62 ±10.73
Protein phosphorylation
109.39 ±0.00
Mitotic cytokinesis
109.39 ±0.00
Regulation of exit from mitosis
109.29 ±0.14
Negative regulation of cyclin-dependent protein kinase by cyclin degradation
109.03 ±0.00
Mitotic spindle assembly checkpoint
109.03 ±0.00
Positive regulation of transcription involved in exit from mitosis
107.48 ±0.00
Based on Table 7, the biological processes associated with the smallest predictive variability values (1 s t -12 th percentile range) were identified as the positive regulation of transcription involved in exit from mitosis (and also its simpler form "regulation of exit from mitosis"), mitotic spindle assembly checkpoint, and negative regulation of cyclin-dependent protein kinase by cyclin degradation. These processes are associated with Swi5 (the transcription factor for CKI), Net1 (stoichiometric inhibitor of Cdc14), Cdc15 (responsible for Net1 phosphorylation), and Cdc20 (required for Clb5, Clb2, and Pds1 degradation) that all play critical roles for mitotic exit which is the cell cycle network module with least predictive variability as we previously stated.
The findings that we summarize in this section, when taken together, suggest that the statistics generated from the model predictions are influenced by the topology of the cell cycle network and that these statistics may also be generating distinct patterns that are specific to individual network modules. In order to test this hypothesis, we next implemented the "random forest" classification method and developed statistical models to predict the network modules in which individual cell cycle regulators operate (i.e., biological functions of these regulators) using model prediction statistics.
Predicting biological functions (or network modules) of cell cycle regulators using relative abundance statistics
In order to predict the biological functions (or network modules) of cell cycle regulators using relative abundance statistics, we implemented the random forest classification method using the Statistics and Machine Learning ToolboxTM of Matlab®; [57]. For each relative abundance (a total of 47850 relative abundances with finite CV values), four features were used for predicting the network modules of individual cell cycle proteins, namely the mean, standard deviation, and CV values of the particular relative abundance and the ID-number of the viable novel mutant (of the 129 strains in the Predictive Set plus the wild type strain) that is simulated to generate the relative abundance prediction. The true class of each relative abundance was identified as the network module to which the protein in the numerator belonged. (We later tested if the predictive accuracy significantly changed when the denominator was taken as the reference point for identifying the true class labels and found out that our predictive ability was not dependent on this choice.) Predictive accuracy is computed by generating receiver operating characteristic (ROC) curves (true positive rate vs. the false positive rate obtained using several classifier output thresholds) and quantifying the areas under these curves (AUC) for each network module as the positive class vs. the negative class generated by combining the remaining two modules (i.e., START module vs. S/G2/M and EXIT modules, S/G2/M module vs. START and EXIT modules, and EXIT module vs. START and S/G2/M modules). We performed 100 runs (per set of features or model inputs) and reported the average AUC and its p-value based on a Z-test with respect to a random model with two classes (i.e., AUC=0.5) [58], an approach commonly taken for computing the statistical significance of AUC in ROC based predictive modeling studies. When the p-value computed from the AUC is less than 0.05, the predictive performance measured by the AUC value is deemed statistically significant. We also generated randomized models by permuting the class labels (or network modules) attached to each relative abundance in 100 independent realizations. The p-values associated with the predictive performances of these randomized models were expected to be higher than 0.05 in order to verify the statistical significance achieved by the non-randomized models trained and tested by the true network modules associated with all the relative abundances.
Per decision tree, approximately 64% of the samples are retained to be used for model training, whereas the remaining samples are used for model testing. These test samples are referred to as "out-of-bag" (OOB) samples, whereas the training samples are expanded by bootstrapping [59] (or sampling with replacement) up to the sample size of the original data [60] prior to model training. Classification of the test samples are based on the complete ensemble of trees (a total of 100 trees) with a voting scheme. For example, a test sample (i.e., the protein in the numerator of a relative abundance) is predicted to be in the "START" module if the number of trees that predict this outcome is higher than the ones that predict the protein's network module as "S/G2/M" or "EXIT".
Predictive performances of the random forest models developed using relative abundance statistics along with the p-values corresponding to mean AUC values in 100 independent realizations (STD corresponds to standard deviation)
Positive class
AUC (Mean ±STD)
AUC (Mean ±STD)
with randomized modules
with randomized modules
0.8667 ±0.0004
0.4996 ±0.0046
0.8326 ±0.0005
0.5003 ±0.0038
0.8366 ±0.0005
0.5008 ±0.0038
Recent studies have indicated that abundances of proteins are regulated in a biological function-dependent manner [61–63]. For example, in general, production and degradation rates of regulatory proteins are trained by evolution to quickly respond to certain stimuli, whereas proteins produced by housekeeping genes and structural proteins that are critical for the integrity of an organism are relatively more stable [61]. Furthermore, it is now also clear that protein abundance signatures are shaped not only by transcriptional and post-transcriptional regulation [64] but also by translation and post-translational regulation, which play prominent roles in determining both dynamic and steady-state behaviours of protein abundances [61, 62, 65]. The cell cycle model used in our study takes into account all of these individual modes of regulation and successfully predicts the network modules of individual cell cycle regulators (related to their biological functions) from model prediction statistics. This outcome demonstrates the critical importance of developing comprehensive and accurate models of important biological processes (such as cell cycle control) for correctly predicting various dynamic and steady-state behaviours shaped by a complex interplay between several modes of regulation. Generating correct predictions despite such complexity holds the key to elucidating critical components and their interactions in complex biological networks in a context-dependent manner.
Previously [22], we demonstrated a practical approach for fitting a complex dynamical model of the budding yeast cell cycle [40, 41] to a large set of qualitative experimental observations (viability/inviability of mutant strains of yeast). Taking a further step in this work, we characterize the feasible region of this model in order to test whether the statistical features of relative protein abundance predictions are influenced by the topology of the cell cycle regulatory network.
Using differential evolution (DE), we generate an ensemble of feasible parameter vectors that reproduce the phenotypes (viable or inviable) of wild-type yeast cells and 110 mutant strains (we call these 111 strains the Training Set). We use this ensemble to predict the phenotypes of 129 mutants (the Prediction Set) for which experimental data is not available. We identify 86 novel mutants that are predicted to be viable and then rank the cell cycle proteins in terms of their contributions to cumulative variability of relative protein abundance predictions. Of the three modules in the cell cycle control system (START, S/G2/M, and EXIT), the EXIT module (the most fragile module identified in [22]) has the least predictive variability, whereas the START module has the highest predictive variability. When we compile all of the gene ontology based biological processes associated with the cell cycle proteins in the model, we identify that the proteins involved in "regulation of cell size" and "regulation of G1/S transition" contribute most to predictive variability, whereas proteins involved in "positive regulation of transcription involved in exit from mitosis", "mitotic spindle assembly checkpoint", and "negative regulation of cyclin-dependent protein kinase by cyclin degradation" contribute the least. These results suggest that the statistics of these predictions may be generating patterns specific to individual network modules (START, S/G2/M, and EXIT). To test this hypothesis, we develop random forest models for predicting the network modules of cell cycle regulators using relative abundance statistics as model inputs. Predictive performance is assessed by the areas under receiver operating characteristics curves (AUC). Our models generate an AUC range of 0.83-0.87 as opposed to randomized models with AUC values around 0.50. By using differential evolution and random forest modeling, we show that the model prediction statistics generate distinct network module-specific patterns within the cell cycle network.
Area under the curve
Coefficient of variation
Differential evolution
Latin hypercube sampling
Ordinary differential equation
Wild type
Cihan Oguz performed this work when he was employed at Virginia Tech. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health, the Department of Health and Human Services, or the United States government.
Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under award number R01 GM078989-07 to JJT and WTB. We are grateful to the Advanced Research Computing Lab at Virginia Tech for computing resources. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health, the Department of Health and Human Services, or the United States government.
Availability of data and materials
The prediction ranges for all ensembles can be reproduced using Additional file 4 (C++ subroutine that implements the model along with a Matlab script), and Additional files 5, 6, 7, 8 and 9 (Ensembles 1 through 16). DE is implemented using the Matlab code available at http://www1.icsi.berkeley.edu/~storn/code.html.
Authors' contributions
Conceived the study: CO. Developed the methodology, performed the simulations and analysis: CO. Wrote the paper: CO, WTB, LTW, JJT. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Not applicable.
Ethics approval and consent to participate
Not applicable.
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subset: commoncrawl


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Dr. Melanie White*
Institute of Molecular and Cell Biology,
A*STAR, Singapore
Dr Syed Uzair Ahmad
Medical Communication Division, Fresta
Technologies, Beijing, China
Research Consultant
Dr. Ajay Singh
Centre for Insect Systematics, School of Environmental Science and Natural Resources, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia.
Xavier Marquínez
Haramaya University, College of Agriculture and Environmental Science, School of Plant Science, Department of Plant Breeding and Genetics, Dire Dawa, Ethiopia., Ethiopia.
David Pimentel
South Eastern Kenya University, Kenya.
Dr. Rajib Roychowdhury
Okinawa Agricultural Research Center, Japan.
Yee-Joo Tan
Animal Genetic Engineering Laboratory, Department of Zoology and Genetics, Federal University of Pelotas, Campus Universitário Capão do Leão s/n°, caixa postal 354, CEP: 96010-900, Pelotas, Rio Grande do Sul, Brazil.
Shahin S Ali
1703 East West Hwy, Apt. 709, Silver Spring, MD 20910, USA, United States.
Nathalie Balaban
The Hebrew University of Jerusalem, Israel.
SyAnna Huttenlocher
University of Wisconsin–Madison, USA Cell migration, chemotaxis, innate immunity and inflammation, zebrafish immunity, wound healing and cancer biology, leukocyte migration, regenerationstems biology, biophysics, nanoscience, bacteriology.
Anders Hedenström
Lund University, Sweden
Biomechanics, flight, aerodynamics, movement, migration, ecology and evolution of animal flight, high-speed wing motion analysis, airflow visualization, force measurement.
Graham Taylor
University of Oxford, UK Biomechanics, flight dynamics, swimming, control systems, sensory systems, sensory ecology (also: avian palaeontology, animal navigation, migration)
Connie Eaves
Terry Fox Laboratory, Canada Hematopoiesis, leukemic stem cells, chronic myeloid leukemia, breast cancer, mammary stem cells, transplantation, single cell studies.
Sophie Martin
University of Lausanne, Switzerland Cell polarity, cytoskeleton, membrane fusion/trafficking, cell cycle (also: yeast cell biology)
Marianne Bronner
Caltech, USA Developmental neurobiology, neural crest, epigenetics of development, evo-devo, early patterning and morphogenesis (also: stem cell biology, cell biology, neuroscience)
Cecilia Lo
University of Pittsburgh, USA Cardiovascular development, congenital heart disease, cilia biology, ciliopathies, left–right patterning, mouse models, developmental genetics (also: neurodevelopment, live cell and embryo imaging, general embryology, gap junction biology)
Elisa Izaurralde
Max Planck Institute for Developmental Biology, Germany Post-transcriptional regulation of mRNA, RNA biology, P-bodies, RNA silencing.
Alex Gould
Francis Crick Institute, UK Drosophila metabolism, development, lifespan, physiology, endocrinology, developmental neurobiology (also: cancer metabolism, metabolomics, neural stem cells, cell signaling, cell competition)
Toru Ouchi
PHD, Professor of Oncology Department of Cancer Genetics Roswell Park Cancer Institute Buffalo, NY, USA
Paul Hasty
Ph.D, Department of Molecular Medicine University of Texas Health Science Center at San Antonio
San Antonio, TX 78245-3207, USA.
Shawn S. Li,
Ph.D Department of Biochemistry University of Western Ontario London, Ontario, Canada
Maya Schuldiner
Weizmann Institute of Science, Israel Yeast systems biology and cell biology, translocation into rganelles, protein sorting, membrane contact sites and trafficking.
Ellen Carpenter
Ph.D. Department of Psychiatry and Biobehavioral Science UCLA School of Medicine Los Angeles, CA 90095, USA.
Alberto Diaspro
Ph.D.MicroScoBio Research Center, Department of Physics University of Genoa Genoa, Italy.
David Gius
M.D., Ph.D.Departments of Radiation Oncology Cancer Biology and Pediatrics Vanderbilt Medical School Nashville, TN 37232, USA
Morris Maduro
Ph.D. Department of Biology University of California Riverside, CA, USA.
Wensheng Qin
Ph.D. Biorefining and Biotechnology Laboratory Lakehead University Thunder Bay, Ontario P7B 5E1, Canada.
Alessandro Minelli
Ph.D.Department of Biology University of PadovaPadova, Italy.
Hyun-Mo Ryoo
Ph.D. Department of Cell and Developmental Biology School of Dentistry and Dental Research Institute Seoul National University Seoul, Korea.
Ken-ichi Shinoda
Ph.D.Department of AnthropologyThe National Science Museum Tokyo, Japan.


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This chapter focuses on raster functions that take more than one spatial object. We'll look at raster aggregation functions such as ST_Union. As well as ST_MapAlgebr, ST_Intersection and map algebra family of functions.
First draft completed and on MEAP
Stay tuned for our next book pgRouting: A Practical Guide published by Locate Press due out in hard-copy 4th quarter 2017. Content is now feature complete and can purchase e-Book draft and get final when goes to print.


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Seeking Full-Time Article Writers
This project received 40 bids from talented freelancers with an average bid price of $317 USD.Get free quotes for a project like this
Project Budget$250 - $750 USD
Total Bids40
Project Description
Are you a proficient English writer?
Do you love writing quality articles?
Do you know how to construct search engine optimized (SEO) content?
Can you manage 5 or more 500-word SEO articles per day?
Do you have MS Word and Skype?
If you can answer yes to all of the above, we need you.
We have a demand for SEO articles on a daily basis and need writers who can turn out quality articles fast.
We can't afford to pay the best rates in the industry at this stage (we pay $3/500w) but there is a lot of work, so this could make sense for you in bulk. This is a long term project.
If you feel you have what it takes, please do apply.
Skills Required
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- Set your budget and the timeframe
- Outline your proposal
- Get paid for your work
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- Forbes
- The New York Times
- Time
- Wall Street Journal
- Times Online


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"Every life contains difficulties we are not prepared for. Read, learn, and be prepared for life and healing."
—Bernard S. Siegal, M.D., Author of Love, Medicine & Miracles and Peace, Love, and Healing
"Fascinating! Amazing! A revolutionary exploration of the effects and causes of trauma."
—Mira Rothenberg, Director Emeritus of Blueberry Treatment Centers for Disturbed Children, Author of Children With Emerald Eyes
"It is a most important book. Quite possibly a work of genius."
—Ron Kurtz, Author of Body Reveals and Body-Centered Psychotherapy
"Levine effectively argues that the body is healer and that psychological scars of trauma are reversible—but only if we listen to the voices of our body."
—Stephen W. Porges, Ph.D., Professor of Human Development and Psychology, University of Maryland
"A vital contribution to the exciting emerging science of mind/body interaction in the treatment of disease."
—Robert C. Scaer, M.D., Neurology, Medical Director, Rehabilitation Services, Boulder Community Hospital
"Peter Levine's work is visionary common sense, pure and simple."
—Laura Huxley, lifetime partner and collaborator of Aldous Huxley
"[ Waking the Tiger] is an excellent resource for those who have been traumatized or know someone who suffers from trauma, like a soldier returning from war. Finally, there is help that doesn't ask us to relive what happened and re-experience the pain. Instead, it follows the body's wisdom in its search for renewal and healing."
— Soaring Again
Nature's Lessons in Healing Trauma...
Waking the Tiger offers a new and hopeful vision of trauma. It views the human animal as a unique being, endowed with an instinctual capacity. It asks and answers an intriguing question: why are animals in the wild, though threatened routinely, rarely traumatized? By understanding the dynamics that make wild animals virtually immune to traumatic symptoms, the mystery of human trauma is revealed.
Waking the Tiger normalizes the symptoms of trauma and the steps needed to heal them. People are often traumatized by seemingly ordinary experiences. The reader is taken on a guided tour of the subtle, yet powerful impulses that govern our responses to overwhelming life events. To do this, it employs a series of exercises that help us focus on bodily sensations. Through heightened awareness of these sensations trauma can be healed.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
(Aucun exemplaire disponible)
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Wants and needs, exquisitely met.
Reconnecting shouldn't be left to cell phones, email or social media. It's best done in person. Long Cove's outdoor amenities provide families with the finest forum to laugh, talk and play as new friends. Feel good about letting your kids roam free like you did as a kid. And with a range of activities and facilities at hand, everyone can discover something fun all year-round.


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Sign Up for the 2017 CSA Season TODAY!
Fresh * GMO and Pesticide Free * Local
Click Here for CSA Share Options and Sign-Up Form!
Choose Wellspring to be your Farmer!
Our 30th Season Growing Growers and Food.
Additional CSA information can be found on the following pages of our website:
What's in a CSA Box?
Upcoming Workshops
Herbal Goat Milk Soap Making - taught by Linda Conroy of Moonwise Herbs
Tuesday, April 18th 6-8:30pm
Make Old Fashion Herbal and Goat Milk Soap. Hands-on class explores art of combining Soapanified oils and herbs to create your own special soap. Make from scratch - just like your great grandma used to make with an herbal touch to give your soap that luxurious touch. Each participant will take home soap that we make. $50 by 4/14 or $60 after
From the Garden: Herbal Infused Oils, Salves and Lotion - taught by Linda Conroy of Moonwise Herbs
Tuesday, May 2nd 6-8:30pm
Experienced herbalist Linda Conroy will lead participants through the process of making infused oils, salves and lotions. The focus will be on creating remedies from herbs in the garden. Participants will leave with a list of healing herbs, recipes and preparations made in this workshop.
$50 by 4/28 or $60 after
Call 262-675-6755 to register
Now Accepting Internship Applications for the 2017 Growing Season!
(Applications due NOW - open until internships are filled)
To learn more and to apply, please visit our Wellspring Farm Intern Application page.
We offer a variety of classes, school programs, consultative services and workshops for adults, teens, children and farmers.
Our programs include Farm to School, gardening, food
preparation and preservation, summer camps, farm tours, field trips, workshops and much more!ORGANIC FARM
We are a working organic farm that serves as a model for sustainable growing practices while teaching the next generation of farmers how to grow food.
Through our CSA (Community Supported Agriculture) program, consumers enter into a partnership to receive a weekly "share" of the farm's produce - a box of nourishing, certified-organic produce delivered each week throughout the growing season.
We provide our community – as well as travelers from anywhere – a place to hold events in our conference and retreat center. Guests also have the opportunity to experience farm life by staying in either our Bed & Breakfast or certified International Hostel.
We are open year-round and are available for weddings, anniversaries, family reunions, birthdays, or just a relaxing retreat in nature with a farm fresh breakfast!


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I have a very horny Lion. It was difficult for me not to give him an orgasm last night. He wanted to come. I wanted him to come. It should have been a no-brainer, right? In a "normal" relationship it…
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- Caging Your Man
- So You Want A Chastity Device
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- The Toybox
- Contact Us
- About Us


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Whether you're an expert fisherman or thinking about angling for
the first time, nothing beats the experience of charter fishing. Full-
and half-day charter fishing trips are great for bachelor parties, corporate
team building events, birthdays, and anytime you want to enjoy the sun
and the sea. But why not just take out your own boat or rent one instead
of booking a private charter? Here are some of the benefits of
charter fishing in Plymouth.
Focus on the Fish
When you book a fishing charter, the only thing you and your guests needs
to worry about is showing up and having a great time. Charter fishing
companies in New England will often provide the equipment you need, and
depending on the length of the charter may even provide light snacks or
full meals to you and your guests.
Learn a Thing or Two
Charter fishing boats are captained and staffed with knowledgeable fishing
experts. Spending a day with such knowledgeable fishermen will improve
your own skillset and help you become an even
better angler. If you live in the area, you'll also learn where some of the best
fishing spots are so you can come back with your own boat.
Bring More Friends
Do you have a large fishing boat that can fit up to 70 guest? Probably
not, but charter fishing companies like Captain John Whale Watching &
Fishing Tours does. This means you can book a fishing adventure for a
large group instead of settling for some activity that's less exciting
and less fun than spending the day out on the ocean fishing.
If you want to have a great day of fishing with friends, family, or coworkers,
book a private fishing charter with Captain John Whale Watching &
Fishing Tours of Plymouth, MA. We've been fishing the water of New
England for more than 60 years, and over that time we've learned
the best spots and the best techniques to have a great haul of fish. To
learn more about our full- and half-day fishing charters for up to 70
guests, call us at (508) 927-5575.
Photo courtesy
Provincetown is full of things to do and see, including art galleries,
antique shops, restaurants, and so much more. Located 40 miles out to
sea at the tip of Cape Cod, Provincetown is one of the world's natural
deep water harbors as well as one the premier tourist destinations on
the East Coast. MacMillan Pier, Provincetown's major transportation
hub, is a destination in and of itself, with all sorts of activities and
shops for the entire family.
Captain John Whale Watching & Fishing Tours operates the Plymouth to
Provincetown Fast Ferry to help you take in the sights, sounds, and smells
of P-Town. The
passenger ferry runs from June through September. If you will be bringing a leashed and
well-behaved dog, please call us ahead of time so we can make a note on
your reservation. TO learn more about our ferry services, whale watching
tours, and chartered fishing trips, call us at (508) 927-5575.
Whales are some of the most amazing creatures in the ocean, and perhaps
even the most amazing creatures on the planet! It's no wonder
whale watching tours are such a popular attraction in whale hot spots around the country, including
right here in Plymouth, MA. Whether you want to brush up on whale facts
to impress your friends during a whale watching adventure or you think
your whale knowledge will help convince your family to embark on a tour,
here are six undeniably amazing facts about whales.
If you are as amazed by whales as we are, we'd love to give you a
closer look at these magnificent creatures. With
Captain John Whale Watching & Fishing Tours in Plymouth, whale sightings are
guaranteed. Group rates are available, and we offer free whale watching tours for
active military men and women. Call us at (508) 927-5575 to learn more
about our whale watching tour schedules and rates.
Cape Cod is one of the premier whale watching spots in all of the world.
Here all sorts of whale species put on dazzling displays for those lucky
enough to see them. Just how close can you get to these amazing creatures
on a whale watching tour? And what does it look like to see whales in
their natural environment? Watch this video to see what your typical whale
watching excursion will entail.
If you're interested in a
whale watching trip in Plymouth, book your adventure with the company that's been doing it better
than anyone for over six decades. As the most experienced and continuously
operated whale watch company in Plymouth, we promise an unforgettable
experience no other whale watching tour operator can match. In fact, with
Captain John whale sightings are
guaranteed. Call us at (508) 927-5575 to book your whale watching adventure today.
If you want to make the most of your whale watching trip, there are a few
tips you can use to see as many whales as possible and stay comfortable
through your venture. Watch this video for essential whale watching tips.
Come prepared to your whale watching trip by wearing sunglasses and bringing
binoculars. Keep your eyes on the horizon and look for puffs of mist;
these puffs signal a whale has breached the surface. You can also find
whales by being patient and listening for their songs or the sounds of
their bodies clapping against the water.
Captain John Whale Watching & Fishing Tours is happy to take you whale watching in Plymouth. Our team also specializes
in flounder fishing and deep sea fishing trips, so visit our website or
call us at (508) 927-5575 to book yours. You can also stop by and see
us if you live in the area.


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Ready to order? Call us at +1 (800) 513-1675
Our Unscented Jewelry Candle was created for all of you out there that have allergies to scent or just love the ambiance of a burning candle without any fragrance. Now you can enjoy your Jewelry Candle without any scent at all but still find your hidden jewel.
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What a fun idea right?!?!
Each Chalkboard Jewelry Candle comes with a hidden jewel within it that has a value from $10 to $7500!
You could get a ring, bracelet, anklet, pendant or necklace inside your Chalkboard Jewelry Candles!
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I like typing number 9 since forever. If you have known me for so long, you'll know.
So, what is the story for today?
Let's make ordinary days becoming slightly extra-ordinary!
1. I still continue the (Act) clean eating~!
You think I've stopped right?
Ha! I got you! I haven't! *proud*
Images are taken randomly and I can't really remember which meal is for which day.
Bought favourite fruit juices, because I can!
I said to my parents: "I act healthy! See I bought fruit juices!"
Parents remark: "But you buy two ma! Act healthy your head!"
Okayy, my bad this time.
Hahahaha taken this pics while laughing!
Because ah, I wanted to make a post about (Act) clean eating again so I purposedly put very few fried chicken breast and lots of stinky broccoli.
Then after took the "healthy" lunch pic so I removed lots of the broccoli and added in more more fried chicken breast.
Then I laughed and I took another pic.
And tadah~ My "healthy" lunch!
Felt bad about my "healthy" lunch cheating, so I boiled potato, carrot and chicken breast with garlic, leek (and onion I think, I can't remember).
Really no taste, but I tahan it. Felt so guilty for the last lunch cheating.
Then for dinner, since I couldn't tahan for my glutton to spark real bad--I ate two plates.
Omg, really, now looking at this pic makes me want to cry!
When I cooked the boiled potato-carrot-chicken breast, mum cooked meesua-porridge. So I had it for my dinner, and I was pretty sure that I was super hungry so I cut some boiled vegetables, added in peanut sauce and tadah--my second dinner!
I felt desperate for the two-plates look so I went to refrigerator and opened myself a cooling drink; to cool my head hahahaha.
And today's dinner! The yesterday's meesua.
Surely re-cooked and added more meesua. Plus the porky satay you can see.
I am amazed at how tasteless it is that I didn't even want a second plate.
Wait, I don't mean that usually I have second plate, but, hahahaha nevermind.
2. My hair growsss!
Left: May 2015. Right: September 2015.
I can say this time it grows pretty fast. I had my haircut at almost shoulder length, and it has grown much longer now. Happy~!
And omg, do I grow a double chin now!?!?!?!?
3. I start to jog in the evening!
Okay someone said this girl's running looked really weird!
But it was me! ;__;
And I said "it wasn't me! It was a girl I met during running!"
And I didn't want to bring anything for running today so it's before running pic!
Omg look at that belly, looks so yummy (?)!
The reason why I start to run in the evening: the view is really rewarding!
I love sunsets so much!
Lots of love ♥


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Music & Civilization
Project Leader: Richard
Associate Professor & Acting Chair
Music & Theatre
Facilitators: Dr.
Maureen Horgan, Dr. Chris Hendley
In a music appreciation
class, a great deal of class time is spent listening to
music which decreases the amount of time left for
reflection and discussion. By loading the listening library
into iPods and housing them at the GC&SU library where
students are able to check them out, listening takes place
outside of the classroom freeing up valuable class time
that can better be spent discussing themes, comparing
genres and the like. A student can check out an iPod from
the library, listen to assigned selections while using the
text notes function of the iPod to learn about the social
setting and political climate of the era of composition, or
read biographical information about composers and
musicians. Photos that accompany the music and text bring
composers to life for students as well.


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This page lists every execution for each year since 1998. You can also find information about executions by state, method, or view the current schedule of executions in the U.S.
Select the year200920082007200620052004200320022001200019991998
Get updates on Amnesty's work to protect human rights worldwide.
The Arkansas Supreme Court has issued a stay of execution for Stacey Johnson, who was due to be put to death in Arkansas on 20 April for a murder committed in 1993. It has ordered a lower court to conduct a hearing on a defence motion for DNA testing.
Support human rights with a donation to Amnesty today.
Over 1,634 people were executed in 2015, the highest number of since 1989. It's to the END the death penalty once & for all!