Related papers: A geometrical perspective on development
Gene expression-based heterogeneity analysis has been extensively conducted. In recent studies, it has been shown that network-based analysis, which takes a system perspective and accommodates the interconnections among genes, can be more…
Regulatory networks describe the interactions between molecular or cellular regulators, like transcription factors and genes in gene regulatory networks, kinases and their receptors in signalling networks, or neurons in neural networks. A…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Due to the increasing heterogeneity and deployment density of emerging cellular networks, new flexible and scalable approaches for their modeling, simulation, analysis and optimization are needed. Recently, a new approach has been proposed:…
The evolutionary origins of structural features in reconstructed gene-regulatory networks (GRNs) remain poorly understood, especially given the random aspects of gene expression. Here, we extend a classical model of GRN evolution to allow a…
Diseases involve complex processes and modifications to the cellular machinery. The gene expression profile of the affected cells contains characteristic patterns linked to a disease. Hence, biological knowledge pertaining to a disease can…
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
Living organisms must respond to environmental changes. Generally, accurate and rapid responses are provided by simple, unidirectional networks that connect inputs with outputs. Besides accuracy and speed, biological responses should also…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
Network neuroscience is the emerging discipline concerned with investigating the complex patterns of interconnections found in neural systems, and to identify principles with which to understand them. Within this discipline, one…
This limited review is intended as an introduction to the fast growing subject of mathematical modelling of cell metabolism and its biochemical pathways, and more precisely on pathways linked to apoptosis of cancerous cells. Some basic…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Morphogenesis is the biological process that causes the emergence and changes of patterns (tissues and organs) in living organisms. It is a robust, self-organising mechanism, governed by Genetic Regulatory Networks (GRN), that hasn't been…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
The dynamics of gene regulatory networks is governed by the interaction between deterministic biochemical reactions and molecular noise. To understand how gene regulatory networks process information during cell state transitions, we study…
Identifying control strategies for biological networks is paramount for practical applications that involve reprogramming a cell's fate, such as disease therapeutics and stem cell reprogramming. Here we develop a novel network control…
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…
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…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…