Related papers: Master regulators as order parameters of gene expr…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular…
Recent progress in experimental techniques has enabled us to quantitatively study stochastic and flexible behavior of biological systems. For example, gene regulatory networks perform stochastic information processing and their…
Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…
Multipotent stem or progenitor cells undergo a sequential series of binary fate decisions, which ultimately generate the diversity of differentiated cells. Efforts to understand cell fate control have focused on simple gene regulatory…
This paper presents an intracellular feedback control strategy, to regulate the gene expression process dynamics. For this purpose, two types of genetic circuits are designed in order to compare concentrations of the input transcription…
Changes in a cell's external or internal conditions are usually reflected in the concentrations of the relevant transcription factors. These proteins in turn modulate the expression levels of the genes under their control and sometimes need…
We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by…
Tumorigenic transformation of human epithelial cells in vitro has been described experimentally as the potential result of a process known as spontaneous immortalization. In this process a generic series of cell state transitions occur in…
We consider the class of Hopfield models of associative memory with activation function $F$ and state space $\{-1,1\}^N$, where each vertex of the cube describes a configuration of $N$ binary neurons. $M$ randomly chosen configurations,…
High-throughput experiments are shedding light on the topology of large regulatory networks and at the same time their functional states, namely the states of activation of the nodes (for example transcript or protein levels) in different…
Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted…
In our recent work \cite{StojnicHopBnds10} we looked at a class of random optimization problems that arise in the forms typically known as Hopfield models. We viewed two scenarios which we termed as the positive Hopfield form and the…
We consider a model of large regulatory gene expression networks where the thresholds activating the sigmoidal interactions between genes and the signs of these interactions are shuffled randomly. Such an approach allows for a qualitative…
Expression of the Drosophila segment polarity genes is initiated by a prepattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these…
Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are…
Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or…
Connectivity networks have recently become widely used in biology due to increasing amounts of information on the physical and functional links between individual proteins. This connectivity data provides valuable material for expanding our…