Cell signaling networks regulate a variety of developmental and physiological processes, and changes in their response to external stimuli are often implicated in disease initiation and progression. To elucidate how different responses can arise from conserved signaling networks, we have developed a mathematical model of the well-characterized Caenorhabditis vulval development network involving EGF, Wnt and Notch signaling that recapitulates biologically observed behaviors. We experimentally block a specific element of the EGF pathway (MEK), and find different behaviors in vulval development in two Caenorhabditis species, C. elegans and C. briggsae. When we separate our parameters into subsets that correspond to these two responses, they yield model behaviors that are consistent with observed experimental results, despite the initial parameter grouping based on perturbation in a single node of the EGF pathway. Finally, our analysis predicts specific parameters that may be critical for the theoretically and experimentally observed differences, suggesting modifications that might allow intentional switching between the two species' responses. Our results indicate that all manipulations within a signal transduction pathway do not yield the same outcome, and provide a framework to identify the specific genetic perturbations within a conserved network that will confer unique behaviors on the network.
Polarization, whereby a cell defines a spatial axis by segregating specific determinants to distinct regions, is an essential and highly conserved biological process. The process of polarization is initiated by a cue that breaks an initially symmetric distribution of determinants, allowing for a spatially asymmetric redistribution. The nature of this cue is currently not well understood. Utilizing the conservation of polarization process and its determinants, we theoretically investigate the nature of the cue and the regulation of contractility that enables the establishment of polarity in early embryos of the nematode worm Caenorhabditis elegans (C. elegans). Our biologically based model, which consists of coupled partial differential equations, suggests that a biochemical but not mechanical cue is sufficient for symmetry breaking, and inhibition of contractile elements by specific determinants is needed for sustained spatial redistribution.
Centrosomes serve as a site for microtubule nucleation and these microtubules will grow and interact with the motor protein dynein at the cortex. The position of the centrosomes determines where the mitotic spindle will develop across all cell types. Centrosome positioning is achieved through dynein and microtubule-mediated force generation. The mechanism and regulation of force generation during centrosome positioning are not fully understood. Centrosome and pronuclear movement in the first cell cycle of the Caenorhabditis elegans early embryo undergoes both centration and rotation prior to cell division. The proteins LET-99 and GPB-1 have been postulated to have a role in force generation associated with pronuclear centration and rotation dynamics. When the expression of these proteins is perturbed, pronuclear positioning exhibits a movement defect characterized by oscillatory ("wobble") behavior of the pronuclear complex (PNC). To determine if this movement defect is due to an effect on cortical dynein distribution, we utilize RNAi-mediated knockdown of LET-99 and GPB-1 to induce wobble and assay for any effects on GFP-tagged dynein localization in the early C. elegans embryo. To compare and quantify the movement defect produced by the knockdown of LET-99 and GPB-1, we devised a quantification method that measures the strength of wobble ("wobble metric") observed under these experimental conditions. Our quantification of pronuclear complex dynamics and dynein localization shows that loss of LET-99 and GPB-1 induces a similar movement defect which is independent of cortical dynein localization in the early C. elegans embryo.
Mathematical models of complex systems rely on parameter values to produce a desired behaviour such as bistability. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. Here we propose a novel method for generating a large number of simulation outcomes using the Markov-chain based algorithm that we term the Modified Metropolis-Hastings (MMH). We provide rigorous proof of the MMH properties and demonstrate that MMH is more efficient for parameter generation than current algorithms, especially for complex models with high-dimensional parameter space and/or diverse outputs. We apply the method to a model of protein phosphorylation to discover characteristic dynamics that identify the mechanism of bistability in protein levels. Our application shows that the proposed methodology can be used to provide unique information about a complex system using the parameters generated by MMH.
Mathematical models of natural processes rely on parameter values to produce scientifically meaningful simulation behaviour such as bistability or oscillations. Frequently, the parameter values cannot be estimated from experimental data and have to be randomly selected and then evaluated whether they satisfy system constraints. Evaluating these constraints for a randomly chosen vector of parameter values can be computationally very costly, preventing efficient learning of the model parameter space. We propose a novel application of a Markov chain methodology to generate a large number of parameter vectors for high-dimensional models with potentially complicated parameter space structures. The method is based on a modification of the Metropolis-Hastings algorithm which learns the parameter space as the chain progresses, reducing unnecessary evaluations of model constraints and resulting in many working parameter vectors that generate a desired model behaviour. We show that the method outperforms commonly used parameter generating schemes in terms of speed and accuracy of parameter space learning. Further, we demonstrate how the learned parameter space can be used to identify bistability mechanisms in a model of protein phosphorylation. The method can be applied to any mathematical or computational models for efficient parameter generation and discovery of underlying parameter space structure.
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