Stochastic neural network models for gene regulatory networks

Recent advances in gene-expression profiling technologies provide large amounts of gene expression data. This raises the possibility for a functional understanding of genome dynamics by means of mathematical modelling. As gene expression involves intrinsic noise, stochastic models are essential for better descriptions of gene regulatory networks. However, stochastic modelling for large scale gene expression data sets is still in the very early developmental stage. In this paper we present some stochastic models by introducing stochastic processes into neural network models that can describe intermediate regulation for large scale gene networks. Poisson random variables are used to represent chance events in the processes of synthesis and degradation. For expression data with normalized concentrations, exponential or normal random variables are used to realize fluctuations. Using a network with three genes, we show how to use stochastic simulations for studying robustness and stability properties of gene expression patterns under the influence of noise, and how to use stochastic models to predict statistical distributions of expression levels in population of cells. The discussion suggest that stochastic neural network models can give better description of gene regulatory networks and provide criteria for measuring the reasonableness o mathematical models

Emerging properties of animal gene regulatory networks

Gene regulatory networks (GRNs) provide system level explanations of developmental and physiological functions in the terms of the genomic regulatory code. Depending on their developmental functions, GRNs differ in their degree of hierarchy, and also in the types of modular sub-circuit of which they are composed, although there is a commonly employed sub-circuit repertoire. Mathematical modelling of some types of GRN sub-circuit has deepened biological understanding of the functions they mediate. The structural organization of various kinds of GRN reflects their roles in the life process, and causally illuminates both developmental and evolutionary process

High-dimensional switches and the modeling of cellular differentiation

Many genes have been identified as driving cellular differentiation, but because of their complex interactions, the understanding of their collective behaviour requires mathematical modelling. Intriguingly, it has been observed in numerous developmental contexts, and particularly hematopoiesis, that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism, before one is upregulated and others downregulated. We characterise conditions under which 3 classes of generic "master regulatory networks", modelled at the molecular level after experimentally-observed interactions (including bHLH protein dimerisation), and including an arbitrary number of antagonistic components, can behave as a "multi-switch", directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than 2 possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low (a simple characterisation is derived). Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins; the speed of response varies with the initial conditions the network is subjected to, which could explain some aspects of cell behaviour upon reprogramming.The coexistence of antagonistic factors at low levels, early in the differentiation process or in pluripotent stem cells, could be an intrinsic property of the interaction between those factors, not requiring a specific regulatory system

Mathematical modelling plant signalling networks

During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This sub-cellular analysis paves the way for more comprehensive mathematical studies of hormonal transport and signalling in a multi-scale setting

A Biologically Informed Hylomorphism

Although contemporary metaphysics has recently undergone a neo-Aristotelian revival wherein dispositions, or capacities are now commonplace in empirically grounded ontologies, being routinely utilised in theories of causality and modality, a central Aristotelian concept has yet to be given serious attention – the doctrine of hylomorphism. The reason for this is clear: while the Aristotelian ontological distinction between actuality and potentiality has proven to be a fruitful conceptual framework with which to model the operation of the natural world, the distinction between form and matter has yet to similarly earn its keep. In this chapter, I offer a first step toward showing that the hylomorphic framework is up to that task. To do so, I return to the birthplace of that doctrine - the biological realm. Utilising recent advances in developmental biology, I argue that the hylomorphic framework is an empirically adequate and conceptually rich explanatory schema with which to model the nature of organism

Measurement of plant growth in view of an integrative analysis of regulatory networks

As the regulatory networks of growth at the cellular level are elucidated at a fast pace, their complexity is not reduced; on the contrary, the tissue, organ and even whole-plant level affect cell proliferation and expansion by means of development-induced and environment-induced signaling events in growth regulatory processes. Measurement of growth across different levels aids in gaining a mechanistic understanding of growth, and in defining the spatial and temporal resolution of sampling strategies for molecular analyses in the model Arabidopsis thaliana and increasingly also in crop species. The latter claim their place at the forefront of plant research, since global issues and future needs drive the translation from laboratory model-acquired knowledge of growth processes to improvements in crop productivity in field conditions

A local regulatory network around three NAC transcription factors in stress responses and senescence in Arabidopsis leaves

A model is presented describing the gene regulatory network surrounding three similar NAC transcription factors that have roles in Arabidopsis leaf senescence and stress responses. ANAC019, ANAC055 and ANAC072 belong to the same clade of NAC domain genes and have overlapping expression patterns. A combination of promoter DNA/protein interactions identified using yeast 1-hybrid analysis and modelling using gene expression time course data has been applied to predict the regulatory network upstream of these genes. Similarities and divergence in regulation during a variety of stress responses are predicted by different combinations of upstream transcription factors binding and also by the modelling. Mutant analysis with potential upstream genes was used to test and confirm some of the predicted interactions. Gene expression analysis in mutants of ANAC019 and ANAC055 at different times during leaf senescence has revealed a distinctly different role for each of these genes. Yeast 1-hybrid analysis is shown to be a valuable tool that can distinguish clades of binding proteins and be used to test and quantify protein binding to predicted promoter motifs

The impact of cellular characteristics on the evolution of shape homeostasis

The importance of individual cells in a developing multicellular organism is well known but precisely how the individual cellular characteristics of those cells collectively drive the emergence of robust, homeostatic structures is less well understood. For example cell communication via a diffusible factor allows for information to travel across large distances within the population, and cell polarisation makes it possible to form structures with a particular orientation, but how do these processes interact to produce a more robust and regulated structure? In this study we investigate the ability of cells with different cellular characteristics to grow and maintain homeostatic structures. We do this in the context of an individual-based model where cell behaviour is driven by an intra-cellular network that determines the cell phenotype. More precisely, we investigated evolution with 96 different permutations of our model, where cell motility, cell death, long-range growth factor (LGF), short-range growth factor (SGF) and cell polarisation were either present or absent. The results show that LGF has the largest positive impact on the fitness of the evolved solutions. SGF and polarisation also contribute, but all other capabilities essentially increase the search space, effectively making it more difficult to achieve a solution. By perturbing the evolved solutions, we found that they are highly robust to both mutations and wounding. In addition, we observed that by evolving solutions in more unstable environments they produce structures that were more robust and adaptive. In conclusion, our results suggest that robust collective behaviour is most likely to evolve when cells are endowed with long range communication, cell polarisation, and selection pressure from an unstable environment

Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems

A generic mechanism - networked buffering - is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems. \ud \u