Browsing by Author "Kessler, David A."
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Item Confluent and nonconfluent phases in a model of cell tissue(American Physical Society, 2018) Teomy, Eial; Kessler, David A.; Levine, HerbertThe Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and size, and the interaction between adjacent cells is a by-product of this additive energy. We generalize this model so as to allow zero or partial contact between cells. We identify several phases, two of which (solid confluent and liquid confluent) were found in previous studies that imposed confluency as well as others that were not. Transitions in this model may be relevant for understanding both normal development as well as cancer metastasis.Item How input fluctuations reshape the dynamics of a biological switching system(2012) Hu, Bo; Kessler, David A.; Rappel, Wouter-Jan; Levine, Herbert; National Science Foundation; Center for Theoretical Biological Physics; American Physical SocietyAn important task in quantitative biology is to understand the role of stochasticity in biochemical regulation. Here, as an extension of our recent work [Phys. Rev. Lett. 107, 148101 (2011)], we study how input fluctuations affect the stochastic dynamics of a simple biological switch. In our model, the on transition rate of the switch is directly regulated by a noisy input signal, which is described as a non-negative mean-reverting diffusion process. This continuous process can be a good approximation of the discrete birth-death process and is much more analytically tractable.Within this setup, we apply the Feynman-Kac theorem to investigate the statistical features of the output switching dynamics. Consistent with our previous findings, the input noise is found to effectively suppress the input-dependent transitions.We show analytically that this effect becomes significant when the input signal fluctuates greatly in amplitude and reverts slowly to its mean.Item Nonlinear self-adapting wave patterns(IOP Publishing, 2016) Kessler, David A.; Levine, Herbert; Center for Theoretical Biological PhysicsWe propose a new type of traveling wave pattern, one that can adapt to the size of physical system in which it is embedded. Such a system arises when the initial state has an instability for a range of wavevectors, k, that extends down to k = 0, connecting at that point to two symmetry modes of the underlying dynamical system. The Min system of proteins in E. coli is such a system with the symmetry emerging from the global conservation of two proteins, MinD and MinE. For this and related systems, traveling waves can adiabatically deform as the system is increased in size without the increase in node number that would be expected for an oscillatory version of a Turing instability containing an allowed wavenumber band with a finite minimum.Item Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process(Springer, 2015) Kessler, David A.; Levine, Herbert; Center for Theoretical Biological PhysicsOne of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size NN is large and mutation rates are low, but not necessarily small compared to 1/N1/N. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy αα-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form