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Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling--even if often this step is not made explicit--and any model has to neglect details while still being physically accurate.…
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…
We study the ensemble velocity of non-processive motor proteins, described with multiple chemical states. In particular, we discuss the velocity as a function of ATP concentration. Even a simple model which neglects the strain-dependence of…
In this paper, we investigate a mathematical modeling of biochemical processes which makes it possible to determine the adaptation of a biosystem to open environmental conditions.
In two-sided matching markets with contracts, quantile (or generalized median) stable mechanisms represent an interesting class that produces stable allocations which can be viewed as compromises between both sides of the market. These…
Cytoskeletal networks of biopolymers are cross-linked by a variety of proteins. Experiments have shown that dynamic cross-linking with physiological linker proteins leads to complex stress relaxation and enables network flow at long times.…
We propose a minimal mathematical model to explain long-range coordination of dynamics of multiple cells in epithelial spreading, which may be induced, under different conditions, by a chemical signal, or mechanical stress, or both. The…
The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular,…
Embedding efficient calculation instructions into biochemical system has always been a research focus in synthetic biology. One of the key problems is how to sequence the chemical reaction modules that act as units of computation and make…
Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving,…
We have investigated the relaxational dynamics for a protein model at various temperatures. Theoretical analysis of this model in conjunction with numerical simulations suggests several relaxation regimes, including a single exponential, a…
We study the mechanical unfolding of a simple model protein. The Langevin dynamics results are analyzed using Markov-model methods which allow to describe completely the configurational space of the system. Using transition path theory we…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
The mechanical properties of cells, which influence the properties of the tissue they belong to, are controlled by various mechanisms. Bi et al. theoretically demonstrated that density-independent rigidity transition occurs in…
Protein translation is a multistep process which can be represented as a cascade of biochemical reactions (initiation, ribosome assembly, elongation, etc.), the rate of which can be regulated by small non-coding microRNAs through multiple…
The self-organization of proteins into enriched compartments and the formation of complex patterns are crucial processes for life on the cellular level. Liquid-liquid phase separation is one mechanism for forming such enriched compartments.…
Cells accomplish diverse functions using the same molecular building blocks, from setting up cytoplasmic flows to generating mechanical forces. In particular, transitions between these non-equilibrium states are triggered by regulating the…
Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualitative behavior of…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
There are many problems in biochemistry that are difficult to study experimentally. Simulation methods are appealing due to direct availability of atomic coordinates as a function of time. However, direct molecular simulations are…