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 statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2 table

Threshold-dominated regulation hides genetic variation in gene expression networks

<p>Abstract</p> <p>Background</p> <p>In dynamical models with feedback and sigmoidal response functions, some or all variables have thresholds around which they regulate themselves or other variables. A mathematical analysis has shown that when the dose-response functions approach binary or on/off responses, any variable with an equilibrium value close to one of its thresholds is very robust to parameter perturbations of a homeostatic state. We denote this threshold robustness. To check the empirical relevance of this phenomenon with response function steepnesses ranging from a near on/off response down to Michaelis-Menten conditions, we have performed a simulation study to investigate the degree of threshold robustness in models for a three-gene system with one downstream gene, using several logical input gates, but excluding models with positive feedback to avoid multistationarity. Varying parameter values representing functional genetic variation, we have analysed the coefficient of variation (<it>CV</it>) of the gene product concentrations in the stable state for the regulating genes in absolute terms and compared to the <it>CV </it>for the unregulating downstream gene. The sigmoidal or binary dose-response functions in these models can be considered as phenomenological models of the aggregated effects on protein or mRNA expression rates of all cellular reactions involved in gene expression.</p> <p>Results</p> <p>For all the models, threshold robustness increases with increasing response steepness. The <it>CV</it>s of the regulating genes are significantly smaller than for the unregulating gene, in particular for steep responses. The effect becomes less prominent as steepnesses approach Michaelis-Menten conditions. If the parameter perturbation shifts the equilibrium value too far away from threshold, the gene product is no longer an effective regulator and robustness is lost. Threshold robustness arises when a variable is an active regulator around its threshold, and this function is maintained by the feedback loop that the regulator necessarily takes part in and also is regulated by. In the present study all feedback loops are negative, and our results suggest that threshold robustness is maintained by negative feedback which necessarily exists in the homeostatic state.</p> <p>Conclusion</p> <p>Threshold robustness of a variable can be seen as its ability to maintain an active regulation around its threshold in a homeostatic state despite external perturbations. The feedback loop that the system necessarily possesses in this state, ensures that the robust variable is itself regulated and kept close to its threshold. Our results suggest that threshold regulation is a generic phenomenon in feedback-regulated networks with sigmoidal response functions, at least when there is no positive feedback. Threshold robustness in gene regulatory networks illustrates that hidden genetic variation can be explained by systemic properties of the genotype-phenotype map.</p

Reliability of Transcriptional Cycles and the Yeast Cell-Cycle Oscillator

A recently published transcriptional oscillator associated with the yeast cell cycle provides clues and raises questions about the mechanisms underlying autonomous cyclic processes in cells. Unlike other biological and synthetic oscillatory networks in the literature, this one does not seem to rely on a constitutive signal or positive auto-regulation, but rather to operate through stable transmission of a pulse on a slow positive feedback loop that determines its period. We construct a continuous-time Boolean model of this network, which permits the modeling of noise through small fluctuations in the timing of events, and show that it can sustain stable oscillations. Analysis of simpler network models shows how a few building blocks can be arranged to provide stability against fluctuations. Our findings suggest that the transcriptional oscillator in yeast belongs to a new class of biological oscillators

The construction of transcription factor networks through natural selection

Transcription regulation plays a key role in determining cellular function, response to external stimuli and development. Regulatory proteins orchestrate gene expression through thousands of interactions resulting in large, complex networks. Understanding the principles on which these networks are constructed can provide insight into the way the expression patterns of different genes co-evolve. One method by which this question can be addressed is to focus on the evolution of the structure of transcription factor networks (TFNs). In order to do this, a model for their evolution through cis mutation, trans mutation, gene duplication and gene deletion is constructed. This model is used to determine the circumstances under which the asymmetrical in and out degree distributions observed in real networks are reproduced. In this way it is possible to draw conclusions about the contributions of these different evolutionary processes to the evolution of TFNs. Conclusions are also drawn on the way rates of evolution vary with the position of gene in the network. Following this, the contributions of cis mutations, which occur in the promoters of regulated genes, and trans mutations, which occur in the coding reign of transcription factors, to the evolution of TFNs are investigated. A space of neutral genotypes is constructed, and the evolution of TFNs through cis and trans mutations in this space is characterised. The results are then used to account for large scale rewiring observed in the yeast sex determination network. Finally the principles governing the evolution of autoregulatory motifs are investigated. It is shown that negative autoregulation, which functions as a noise reduction mechanism in haploid TFNs, is not evolvable in diploid TFNs. This is attributed to the effects of dominance in diploid TFNs. The fate of duplicates of autoregulating genes in haploid networks is also investigated. It is shown that such duplicates are especially prone to loss of function mutations. This is used to account for the lack of observed autoregulatory duplicates participating in network motifs. From this work, it is concluded that the relative rates of different evolutionary processes are responsible for shaping the global statistical properties of TFN structure. However, the more detailed TFN structure, such as network motif distribution, is strongly influenced by the population genetic details of the system being considered. In addition, extensive neutral evolution is shown to be possible in TFNs. However, the effects of neutral evolution on network structure are shown to depend strongly on the structure of the space on neutral genotypes in which the TFN is evolving

Towards a Boolean network-based Computational Model for Cell Differentiation and its applications to Robotics

Living organisms are the ultimate product of a series of complex processes that take place within—and among—biological cells. Most of these processes, such as cell differentiation, are currently poorly understood. Cell differentiation is the process by which cells progressively specialise. Being a fundamental process within cells, its dysregulations have dramatic implications in biological organisms ranging from developmental issues to cancer formation. The thesis objective is to contribute to the progress in the understanding of cell differentiation and explore the applications of its properties for designing artificial systems. The proposed approach, which relies on Boolean networks based modelling and on the theory of dynamical systems, aims at investigating the general mechanisms underlying cell differentiation. The results obtained contribute to taking a further step towards the formulation of a general theoretical framework—so far missing—for cellular differentiation. We conducted an in-depth analysis of the impact of self-loops in random Boolean networks ensembles. We proposed a new model of differentiation driven by a simplified bio-inspired methylation mechanism in Boolean models of genetic regulatory networks. On the artificial side, by introducing the conceptual metaphor of the “attractor landscape” and related proofs of concept that support its potential, we paved the way for a new research direction in robotics called behavioural differentiation robotics: a branch of robotics dealing with the designing of robots capable of expressing different behaviours in a way similar to that of biological cells that undergo differentiation. The implications of the results achieved may have beneficial effects on medical research. Indeed, the proposed approach can foster new questions, experiments and in turn, models that hopefully in the next future will take us to cure differentiation-related diseases such as cancer. Our work may also contribute to address questions concerning the evolution of complex behaviours and to help design robust and adaptive robots

Modeling stochasticity and robustness in gene regulatory networks

Motivation: Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations

Hematopoiesis and T-cell specification as a model developmental system

The pathway to generate T cells from hematopoietic stem cells guides progenitors through a succession of fate choices while balancing differentiation progression against proliferation, stage to stage. Many elements of the regulatory system that controls this process are known, but the requirement for multiple, functionally distinct transcription factors needs clarification in terms of gene network architecture. Here, we compare the features of the T-cell specification system with the rule sets underlying two other influential types of gene network models: first, the combinatorial, hierarchical regulatory systems that generate the orderly, synchronized increases in complexity in most invertebrate embryos; second, the dueling ‘master regulator’ systems that are commonly used to explain bistability in microbial systems and in many fate choices in terminal differentiation. The T-cell specification process shares certain features with each of these prevalent models but differs from both of them in central respects. The T-cell system is highly combinatorial but also highly dose-sensitive in its use of crucial regulatory factors. The roles of these factors are not always T-lineage-specific, but they balance and modulate each other's activities long before any mutually exclusive silencing occurs. T-cell specification may provide a new hybrid model for gene networks in vertebrate developmental systems