Related papers: A Constructive Approach to Gene Expression Dynamic…
Evolution is the theory that plants and animals today have come from kinds that have existed in the past. Scientists such as Charles Darwin and Alfred Wallace dedicate their life to observe how species interact with their environment, grow,…
It is well known that the structural deformations (stressed states) of DNA molecule play a crucial role in its biological functions including gene expression. For instance, looping in DNA (often mediated by protein binding) is a crucial…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
Motivated by a recent article on open problems in artificial life, here I postulate three laws which form a mathematical framework to describe artificial life evolutionary dynamics. They are based on a continuous approximation of population…
Numerous transcription factors self-assemble into different order oligomeric species in a way that is actively regulated by the cell. Until now, no general functional role has been identified for this widespread process. Here we capture the…
Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these…
Modelling gene regulatory networks not only requires a thorough understanding of the biological system depicted but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to…
Complex systems, such as life and languages, are governed by principles of evolution. The analogy and comparison between biology and linguistics\cite{alphafold2, RoseTTAFold, lang_virus, cell language, faculty1, language of gene, Protein…
A gene expression compendium is a heterogeneous collection of gene expression experiments assembled from data collected for diverse purposes. The widely varied experimental conditions and genetic backgrounds across samples creates a…
Adaptation mechanism of cells on the basis of stochastic gene expression and epigenetic modification is proposed. From marginally stable states generated by epigenetic modification, a gene expression pattern that achieves greater cell…
Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases…
In many longitudinal microarray studies, the gene expression levels in a random sample are observed repeatedly over time under two or more conditions. The resulting time courses are generally very short, high-dimensional, and may have…
We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with step-function production term, we…
Regulation of intrinsic noise in gene expression is essential for many cellular functions. Correspondingly, there is considerable interest in understanding how different molecular mechanisms of gene expression impact variations in protein…
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of…
We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
The processes of gene expression are inherently stochastic, even for essential genes required for growth. How does the cell maximize fitness in light of noise? To answer this question, we build a mathematical model to explore the trade-off…