The physiological behaviors of cells (growth and division, differentiation, movement, death, etc.) are controlled by complex Networks of interacting genes and proteins, and a fundamental goal of computational cell biology is to develop dynamical models of
these regulatory networks that are realistic, accurate and predictive. Historically, these models have divided along two basic lines: deterministic or stochastic, and continu- ous or discrete, with scattered efforts to develop hybrid approaches that bridge these divides.
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In chapter 1 of this volume, using the cell cycle control system in eukaryotes as anexample, Singhania and colleagues propose a hybrid approach that combines a con- tinuous representation of slowly changing protein concentrations with a discrete repre-
sentation of components that switch rapidly between “on” and “off” states, combining the deterministic causality of network interactions with the stochastic uncertainty of random events. The hybrid approach can be easily tailored to the available knowledge of control systems, and it provides both qualitative and quantitative results that can be compared to experimental data to test the accuracy and predictive power of the model.
In chapter 2, Head, Briels, and Gompper present the results of numerical simula- tions of a discrete fi lament-motor protein model confi ned to a pressurized cylindri- cal box. Stable spindles, nematic confi gurations, asters, and high-density semi-asters spontaneously emerge. State diagrams are presented delineating each stationary state as the pressure, motor speed and motor density are varied. The authors further high- light a parameter regime where vortices form exhibiting collective rotation of all fi la-
ments, but have a fi nite lifetime before contracting to a semi-aster. They demonstrate that discrete fi lament-motor protein models provide new insights into the stationary and dynamical behavior of active gels and subcellular structures, because many phe- nomena occur on the length-scale of single fi laments.
In yet another scenario, the assembly of the Drosophila embryo mitotic spindle during prophase depends upon a balance of outward forces generated by cortical dy- nein and inward forces generated by kinesin-14 and nuclear elasticity. Myosin II is known to contribute to the dynamics of the cell cortex but how this infl uences the prophase force-balance is unclear. Sommi and her colleagues investigate this ques- tion in chapter 3; they did so by injecting the myosin II inhibitor, Y27632, into early Drosophila embryos. They observed a signifi cant increase in both the area of the dense cortical actin caps and in the spacing of the spindle poles. Their results suggest that two complementary outward forces are exerted on the prophase spindle by the over- lying cortex. Specifi cally, dynein localized on the mechanically fi rm actin caps andthe actomyosin-driven contraction of the deformable soft patches of the actin cortex, cooperate to pull astral microtubules outward. Thus, myosin II controls the size and dynamic properties of the actin-based cortex to infl uence the spacing of the poles of the underlying spindle during prophase.
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