Related papers: A dynamic p53-mdm2 model with delay kernel
Active materials take advantage of their internal sources of energy to self-organize in an automated manner. This feature provides a novel opportunity to design micron-scale machines with minimal required control. However, self-organization…
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
The different cell types in a living organism acquire their identity through the process of cell differentiation in which the multipotent progenitor cells differentiate into distinct cell types. Experimental evidence and analysis of…
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…
Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey-predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than…
The tumor suppressor p53 plays a central role in cell fate decisions after DNA damage. Programmed Cell Death 5 (PDCD5) is known to interact with the p53 pathway to promote cell apoptosis. Recombinant human PDCD5 can significantly sensitize…
Rhythmic and sequential subdivision of the elongating vertebrate embryonic body axis into morphological somites is controlled by an oscillating multicellular genetic network termed the segmentation clock. This clock operates in the…
We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…
Transcription factor binding to the surface of DNA regulatory regions is one of the primary causes of regulating gene expression levels. A probabilistic approach to model protein-DNA interactions at the sequence level is through Position…
This paper focuses on molecular communication (MC) systems using two types of signaling molecules which may participate in a reversible bimolecular reaction in the channel. The motivation for studying these MC systems is that they can…
Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
Large multidimensionality of high-throughput datasets pertaining to cell signaling and gene regulation renders it difficult to extract mechanisms underlying the complex kinetics involving various biochemical compounds (e.g., proteins,…
We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
In this work, we investigate the dynamical properties of a reaction-diffusion system arising from tumor-therapy modelling that features both nonlinear interactions and nonlocal delay. By applying the Lyapunov-Schmidt reduction, we establish…
The understanding of mechanisms that control epigenetic changes is an important research area in modern functional biology. Epigenetic modifications such as DNA methylation are in general very stable over many cell divisions. DNA…