Computational modeling of Caenorhabditis elegans vulval induction

Analysis of Pattern Formation by Colored Petri Nets With Quantitative Regulation of Gene Expression Level

Modeling and simulation are becoming indispensable tools for studying multicellular events such as pattern formation during embryonic development. In this paper, we propose a new approach for analyzing multicellular biological phenomena by combining colored hybrid Petri nets (ColHPNs) with newly devised biological experiments that can control level of a gene quantitatively. With this approach, we analyzed patterning of the boundary cells in the Drosophila large intestine, where one-cell-wide domain of boundary cells differentiate through Delta-Notch signaling. Biological experiments regulating the level of Delta resulted in six distinct patterns of boundary cells correlating with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling. This approach can be easily adapted to address other similar pattern formation issues in the systems biology area.

A computational model predicts genetic nodes that allow switching between species-specific responses in a conserved signaling network

Alterations to only specific parameters in a model including EGF, Wnt and Notch lead to cell behavior differences.

A model of the regulatory network involved in the control of the cell cycle and cell differentiation in the Caenorhabditis elegans vulva

BACKGROUND

There are recent experimental reports on the cross-regulation between molecules involved in the control of the cell cycle and the differentiation of the vulval precursor cells (VPCs) of Caenorhabditis elegans. Such discoveries provide novel clues on how the molecular mechanisms involved in the cell cycle and cell differentiation processes are coordinated during vulval development. Dynamic computational models are helpful to understand the integrated regulatory mechanisms affecting these cellular processes.

RESULTS

Here we propose a simplified model of the regulatory network that includes sufficient molecules involved in the control of both the cell cycle and cell differentiation in the C. elegans vulva to recover their dynamic behavior. We first infer both the topology and the update rules of the cell cycle module from an expected time series. Next, we use a symbolic algorithmic approach to find which interactions must be included in the regulatory network. Finally, we use a continuous-time version of the update rules for the cell cycle module to validate the cyclic behavior of the network, as well as to rule out the presence of potential artifacts due to the synchronous updating of the discrete model. We analyze the dynamical behavior of the model for the wild type and several mutants, finding that most of the results are consistent with published experimental results.

CONCLUSIONS

Our model shows that the regulation of Notch signaling by the cell cycle preserves the potential of the VPCs and the three vulval fates to differentiate and de-differentiate, allowing them to remain completely responsive to the concentration of LIN-3 and lateral signal in the extracellular microenvironment.

A network model for the specification of vulval precursor cells and cell fusion control in Caenorhabditis elegans

The vulva of Caenorhabditis elegans has been long used as an experimental model of cell differentiation and organogenesis. While it is known that the signaling cascades of Wnt, Ras/MAPK, and NOTCH interact to form a molecular network, there is no consensus regarding its precise topology and dynamical properties. We inferred the molecular network, and developed a multivalued synchronous discrete dynamic model to study its behavior. The model reproduces the patterns of activation reported for the following types of cell: vulval precursor, first fate, second fate, second fate with reversed polarity, third fate, and fusion fate. We simulated the fusion of cells, the determination of the first, second, and third fates, as well as the transition from the second to the first fate. We also used the model to simulate all possible single loss- and gain-of-function mutants, as well as some relevant double and triple mutants. Importantly, we associated most of these simulated mutants to multivulva, vulvaless, egg-laying defective, or defective polarity phenotypes. The model shows that it is necessary for RAL-1 to activate NOTCH signaling, since the repression of LIN-45 by RAL-1 would not suffice for a proper second fate determination in an environment lacking DSL ligands. We also found that the model requires the complex formed by LAG-1, LIN-12, and SEL-8 to inhibit the transcription of eff-1 in second fate cells. Our model is the largest reconstruction to date of the molecular network controlling the specification of vulval precursor cells and cell fusion control in C. elegans. According to our model, the process of fate determination in the vulval precursor cells is reversible, at least until either the cells fuse with the ventral hypoderm or divide, and therefore the cell fates must be maintained by the presence of extracellular signals.

Hybrid Modeling of Cell Signaling and Transcriptional Reprogramming and Its Application in C. elegans Development

Modeling of signal driven transcriptional reprogramming is critical for understanding of organism development, human disease, and cell biology. Many current modeling techniques discount key features of the biological sub-systems when modeling multiscale, organism-level processes. We present a mechanistic hybrid model, GESSA, which integrates a novel pooled probabilistic Boolean network model of cell signaling and a stochastic simulation of transcription and translation responding to a diffusion model of extracellular signals. We apply the model to simulate the well studied cell fate decision process of the vulval precursor cells (VPCs) in C. elegans, using experimentally derived rate constants wherever possible and shared parameters to avoid overfitting. We demonstrate that GESSA recovers (1) the effects of varying scaffold protein concentration on signal strength, (2) amplification of signals in expression, (3) the relative external ligand concentration in a known geometry, and (4) feedback in biochemical networks. We demonstrate that setting model parameters based on wild-type and LIN-12 loss-of-function mutants in C. elegans leads to correct prediction of a wide variety of mutants including partial penetrance of phenotypes. Moreover, the model is relatively insensitive to parameters, retaining the wild-type phenotype for a wide range of cell signaling rate parameters.

Quantitative variation in autocrine signaling and pathway crosstalk in the Caenorhabditis vulval network

BACKGROUND

Biological networks experience quantitative change in response to environmental and evolutionary variation. Computational modeling allows exploration of network parameter space corresponding to such variations. The intercellular signaling network underlying Caenorhabditis vulval development specifies three fates in a row of six precursor cells, yielding a quasi-invariant 3°3°2°1°2°3° cell fate pattern. Two seemingly conflicting verbal models of vulval precursor cell fate specification have been proposed: sequential induction by the EGF-MAP kinase and Notch pathways, or morphogen-based induction by the former.

RESULTS

To study the mechanistic and evolutionary system properties of this network, we combine experimental studies with computational modeling, using a model that keeps the network architecture constant but varies parameters. We first show that the Delta autocrine loop can play an essential role in 2° fate specification. With this autocrine loop, the same network topology can be quantitatively tuned to use in the six-cell-row morphogen-based or sequential patterning mechanisms, which may act singly, cooperatively, or redundantly. Moreover, different quantitative tunings of this same network can explain vulval patterning observed experimentally in C. elegans, C. briggsae, C. remanei, and C. brenneri. We experimentally validate model predictions, such as interspecific differences in isolated vulval precursor cell behavior and in spatial regulation of Notch activity.

CONCLUSIONS

Our study illustrates how quantitative variation in the same network comprises developmental patterning modes that were previously considered qualitatively distinct and also accounts for evolution among closely related species.

Automatic inference of multicellular regulatory networks using informative priors

To fully understand the mechanisms governing animal development, computational models and algorithms are needed to enable quantitative studies of the underlying regulatory networks. We developed a mathematical model based on dynamic Bayesian networks to model multicellular regulatory networks that govern cell differentiation processes. A machine-learning method was developed to automatically infer such a model from heterogeneous data. We show that the model inference procedure can be greatly improved by incorporating interaction data across species. The proposed approach was applied to C. elegans vulval induction to reconstruct a model capable of simulating C. elegans vulval induction under 73 different genetic conditions.