Related papers: Master regulators as order parameters of gene expr…

Understanding how gene regulatory networks (GRNs) give rise to stable and dynamic cellular states remains a central challenge in theoretical biology, particularly when slow epigenetic feedback reshapes the underlying regulatory landscape.…

In this paper we look at a class of random optimization problems that arise in the forms typically known as Hopfield models. We view two scenarios which we term as the positive Hopfield form and the negative Hopfield form. For both of these…

Modeling the time-series of high-dimensional, longitudinal data is important for predicting patient disease progression. However, existing neural network based approaches that learn representations of patient state, while very flexible, are…

The evolution of the genome has led to very sophisticated and complex regulation. Because of the abundance of non-coding RNA (ncRNA) in the cell, different species will promiscuously associate with each other, suggesting collective dynamics…

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one…

Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation…

We recently introduced the joint gramian for combined state and parameter reduction [C. Himpe and M. Ohlberger. Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems. arXiv:1302.0634, 2013], which is…

We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low…

A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…

Models of transcriptional regulation that assume equilibrium binding of transcription factors have been very successful at predicting gene expression from sequence in bacteria. However, analogous equilibrium models do not perform as well in…

The biological processes of cellular decision making and differentiation involve a plethora of signalling pathways and gene regulatory circuits. These networks, in their turn, exhibit a multitude of motifs playing crucial parts in…

Selective control in a population is the ability to control a member of the population while leaving the other members relatively unaffected. The concept of selective control is developed using cell death or apoptosis in heterogeneous cell…

Temporal gene expression data (Wen, et. al.) was analyzed using the recently introduced inverse modeling technique of Embedded Complex Logistic Maps (ECLM). Preliminary results indicate scale-free structure in the gene regulatory network…

We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…

The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and…

Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although…

Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in…

We introduce a simple cellular-network model to explain the capacity of the plants as memory devices. Following earlier observations (Bose \cite{Bose} and others), we regard the plant as a network in which each of the elements (plant cells)…

Gene regulation in Eukaryotes is mainly effected through transcription factors binding to rather short recognition motifs generally located upstream of the coding region. We present a novel computational method to identify regulatory…

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce…