Causal mapping as a tool to mechanistically interpret phenomena in cell motility: Application to cortical oscillations in spreading cells

Abstract

Biological processes that occur at the cellular level and consist of large numbers of interacting elements are highly nonlinear and generally involve multiple time and spatial scales. The quantitative description of these complex systems is of great importance but presents large challenges. We outline a new systems biology approach, causal mapping (CMAP), which is a coarse-grained biological network tool that permits description of causal interactions between the elements of the network and overall system dynamics. On one hand, the CMAP is an intermediate between experiments and physical modeling, describing major requisite elements, their interactions and paths of causality propagation. On the other hand, the CMAP is an independent tool to explore the hierarchical organization of cell and the role of uncertainties in the system. It appears to be a promising easy-to-use technique for cell biologists to systematically probe verbally formulated qualitative hypotheses. We apply the CMAP to study the phenomenon of contractility oscillations in spreading cells in which microtubules have been depolymerized. The precise mechanism by which these oscillations are governed by a complex mechano-chemical system is not known but the data observed in experiments can be described by a CMAP. The CMAP suggests that the source of the oscillations results from the opposing effects of Rho activation leading to a decreased level of myosin light chain phosphatase and a cyclic calcium influx caused by increased membrane tension and leading to a periodically enhanced activation of myosin light chain kinase.

Mechanical and Biochemical Modeling of Cortical Oscillations in Spreading Cells

“…Such oscillations with well-defined periods suggest that complex phenomena like these might be fertile ground to explore theoretical explanations of the interactions of the microfilament-microtubule systems that would give rise to such global behavior. Indeed, recently we used a coarse-grained method, causal mapping (CMAP) (10), to determine the system components and interactions needed to produce cortical oscillations. CMAP analysis suggested that the mechanism underlying the observed cortical oscillations relies on a time-delayed negative feedback loop.…”

In Silico Generation of Alternative Hypotheses Using Causal Mapping (CMAP)

“…2 and Table 1), including the one previously tested [15]. In our previous model, it was assumed that the Rho pathway was not influenced by the other elements of the system.…”

“…In the previous work [15] we assumed that this maximum step can not exceed the interval size p j determined by the set size, i.e. f max  =  p  = 1/K.…”

Towards predictive stochastic dynamical modeling of cancer genesis and progression

“…For example, the deterministic force f can be obtained by modeling the activation as sigmoidal or S-shaped typical in engineering, threshold functions varying between 0 and 1 (Zhu et al , 2010), a procedure similar to those in fuzzy cognitive maps (Kosco, 1997; Miao et al ., 2001; Weinreb et al , 2006). Our own convenient choice is, for activation, $$f_A(y)={\text{italicay}}^n/(1+{\text{italicay}}^n),$$ and for inhibition, $$f_I(y)=1-f_A(y)=1/(1+{\text{italicay}}^n),$$ with numerical values are chosen to be a = 10 and n = 3.…”