Related papers: Digital clocks: simple Boolean models can quantita…
Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
Embedding efficient command operation into biochemical system has always been a research focus in synthetic biology. One of the key problems is how to sequence the chemical reactions that act as units of computation. The answer is to design…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby…
The colloid cellular automata do not imitate the physical structure of colloids but are governed by logical functions derived from the colloids. We analyse the space-time complexity of Boolean circuits derived from the electrical responses…
Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display…
We leverage data-driven model discovery methods to determine the governing equations for the emergent behavior of heterogeneous networked dynamical systems. Specifically, we consider networks of coupled nonlinear oscillators whose…
Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…
Experiments that compare rhythmic properties across different genetic alterations and entrainment conditions underlie some of the most important breakthroughs in circadian biology. A robust estimation of the rhythmic properties of the…
Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein…
Models of biochemical networks are frequently high-dimensional and complex. Reduction methods that preserve important dynamical properties are therefore essential in their study. Interactions between the nodes in such networks are…
Organisms often use cyclic changes in the concentrations of chemicals species to precisely time biological functions. Underlying these biochemical clocks are chemical reactions and transport processes, which are inherently stochastic.…
We consider a periodic quantum clock based on cooperative resonance fluorescence at zero temperature. In the quantum case, this system has an exact steady state and the limit cycle appears in conditional quantum dynamics under homodyne…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
A van der Pol self sustained oscillator with higher order nonlinearity exhibits a rich dynamics, with multiple periodic attractors, and still the model allows analytical approximations. Some of these properties can be conveniently exploited…
Boolean networks, first developed in the late 1960s as a tool for studying complex disordered dynamical systems, consist of nodes governed by Boolean functions whose evolution is entirely deterministic in that the state of the network at a…
It is possible that there are post-translational circadian oscillators that continue functioning in the absence of negative feedback transcriptional repression in many cell types from diverse organisms. Apart from the KaiABC system from…