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Recently, energetic variational approach was employed to derive models for non-isothermal electrokinetics by Liu et. al \cite{Liu-Wu-Liu-CMS2018}. In particular, the Poisson-Nernst-Planck-Fourier (PNPF) system for the dynamics of $N$-ionic…
In this paper, a novel approach based on robust stability concepts and tools is introduced to evaluate the unconditional stability of microwave active $\textit{n}$-port devices. An efficient calculation of the Structured Singular Value of…
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle…
Chemical reactions in cell are subject to intense stochastic fluctuations. An important question is how the fundamental physiological behavior of cell is kept stable against those noisy perturbations. In this paper a stochastic model of…
We investigate the structural aspects of genuine multipartite entanglement in Gaussian states of continuous variable systems. Generalizing the results of [Adesso & Illuminati, Phys. Rev. Lett. 99, 150501 (2007)], we analyze whether the…
The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be…
Self-assembly of proteins is a biological phenomenon which gives rise to spontaneous formation of amyloid fibrils or polymers. The starting point of this phase, called nucleation exhibits an important variability among replicated…
Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not…
In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…
In spite of decades of research, much remains to be discovered about folding: the detailed structure of the initial (unfolded) state, vestigial folding instructions remaining only in the unfolded state, the interaction of the molecule with…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
In the protein sequence space, natural proteins form clusters of families which are characterized by their unique native folds whereas the great majority of random polypeptides are neither clustered nor foldable to unique structures. Since…
Fluctuating environments pose tremendous challenges to bacterial populations. It is observed in numerous bacterial species that individual cells can stochastically switch among multiple phenotypes for the population to survive in rapidly…
Energy evaluation using fast Fourier transforms enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods efficient acceleration is achieved only in either…
The concept of a nested canalizing Boolean function has been studied over the course of the last decade in the context of understanding the regulatory logic of molecular interaction networks, such as gene regulatory networks. Such functions…
We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select…
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
Understanding the relationship between protein sequence, function, and stability is a fundamental problem in biology. While high-throughput methods have produced large numbers of sequence-function pairs, functional assays do not distinguish…
Biological systems encode function not primarily in steady states, but in the structure of transient responses elicited by time-varying stimuli. Overshoots, biphasic dynamics, adaptation kinetics, fold-change detection, entrainment, and…
Among the unsolved problems in computational biology, protein folding is one of the most interesting challenges. To study this folding, tools like neural networks and genetic algorithms have received a lot of attention, mainly due to the…