Molecular Networks
We discuss several qualitative properties of the solutions of reaction-diffusion systems and equations of the form $u_t = \epsilon^2 D \Delta u + f(u,x,\epsilon t)$, that are used in modeling pattern formation. We analyze the diffusion…
One of the main tasks of post-genomic informatics is to systematically investigate all molecules and their interactions within a living cell so as to understand how these molecules and the interactions between them relate to the function of…
Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding…
Summary: Most cellular tasks are performed not by individual proteins, but by groups of functionally associated proteins, often referred to as modules. In a protein assocation network modules appear as groups of densely interconnected…
To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit…
Understanding the system level adaptive changes taking place in an organism in response to variations in the environment is a key issue of contemporary biology. Current modeling approaches such as the constraint-based flux balance analyses…
In addition to their self-renewal capabilities, hematopoietic stem cells guarantee the continuous supply of fully differentiated, functional cells of various types in the peripheral blood. The process which controls differentiation into the…
Two complementary analyses of a cyclic negative feedback system with delay are considered in this paper. The first analysis applies the work by Sontag, Angeli, Enciso and others regarding monotone control systems under negative feedback,…
This paper contains some immature results. It have been withdrawn.
Cooperative interactions among the binding of multiple signaling molecules is a common mechanism for enhancing the sensitivity of biological signaling systems. It is widely assumed that this increase in sensitivity of the mean response…
Samoilov, Plyasunov, and Arkin provide an example of a chemical reaction whose full stochastic (Master Equation) model exhibits bistable behavior, but for which the deterministic (mean field) version has a unique steady state at least for…
Deciphering regulatory events that drive malignant transformation represents a major challenge for systems biology. Here we analyzed genome-wide transcription profiling of an in-vitro transformation process. We focused on a cluster of genes…
The structure of a stochastic nonlinear gene regulatory network is uncovered by studying its response to input signal generators. Four applications are studied in detail: a nonlinear connection of two linear systems, the design of a logic…
Transcriptional interactions in a cell are modulated by a variety of mechanisms that prevent their representation as pure pairwise interactions between a transcription factor and its target(s). These include, among others, transcription…
We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. Once such a graph has been…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
The transcription factor p53 is an important regulator of cell fate. Mutations in p53 gene are associated with many cancers. In response to signals such as DNA damage, p53 controls the transcription of a series of genes that cause cell…
Mixed-substrate microbial growth is among the most intensely studied systems in molecular microbiology. Several mathematical models have been developed to account for the genetic regulation of such systems, especially those resulting in…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
The TGF-beta pathway plays a central role in tissue homeostasis and morphogenesis. It transduces a variety of extracellular signals into intracellular transcriptional responses that control a plethora of cellular processes, including cell…