Molecular Networks
Networks exhibiting "accelerating" growth have total link numbers growing faster than linearly with network size and can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at…
Template directed replication of nucleic acids is at the essence of all living beings and a major milestone for any origin of life scenario. We here present an idealized model of prebiotic sequence replication, where binary polymers act as…
A complex network approach to protein folding is proposed. The graph object is the network of shortcut edges present in a native-state protein (SCN0). Although SCN0s are found via an intuitive message passing algorithm (S. Milgram,…
The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the…
In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we…
We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and…
Existing mathematical models of the shoot apical meristem (SAM) explain nucleation and confinement of a stem cell domain by Turing's mechanism, assuming that the diffusion coefficients of the activator (WUSCHEL) and inhibitor (CLAVATA) are…
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…
Discovering disease pathways, which can be defined as sets of proteins associated with a given disease, is an important problem that has the potential to provide clinically actionable insights for disease diagnosis, prognosis, and…
Abnormal metabolism is an emerging hallmark of cancer. Cancer cells utilize both aerobic glycolysis and oxidative phosphorylation (OXPHOS) for energy production and biomass synthesis. Understanding the metabolic reprogramming in cancer can…
Clusters of circulating tumor cells (CTCs), although rare, may account for more than 95% of metastases. Inflammatory breast cancer (IBC) is a highly aggressive subtype that chiefly metastasizes via CTC clusters. Theory suggests that…
The recent development of single-cell transcriptomics has enabled gene expression to be measured in individual cells instead of being population-averaged. Despite this considerable precision improvement, inferring regulatory networks…
We present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct…
Background: Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cy-cles (TICs) causing unbounded metabolic flux ranges…
The mathematical modelling of genetic-metabolic networks is of out most importance in the field of systems biology. Different formalisms and a huge variety of classical mathematical tools have been used to describe and analyse such…
In this paper we derive several quasi steady-state approximations (QSSAs) to the stochastic reaction network describing the Michaelis-Menten enzyme kinetics. We show how the different assumptions about chemical species abundance and…
Retroactivity arises when the coupling of a molecular network $\mathcal{U}$ to a downstream network $\mathcal{D}$ results in signal propagation back from $\mathcal{D}$ to $\mathcal{U}$. The phenomenon represents a breakdown in modularity of…
Organisms across all domains of life regulate the size of their cells. However, the means by which this is done is poorly understood. We study two abstracted "molecular" models for size regulation: inhibitor dilution and initiator…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
The major biochemical networks of the living cell, the network of interacting genes and the network of biochemical reactions, are highly interdependent, however, they have been studied mostly as separate systems so far. In the last years an…