Systems biology最新文献

As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states (expressed or not expressed) for each gene or protein in the network, as well as a high level of synchronisation among the various regulatory processes. Two possible methods of adapting qualitative models to incorporate the continuous-time character of regulatory networks, are discussed and compared. The first method consists of introducing asynchronous updates in the Boolean model. In the second method, the approach introduced by Glass is adopted to obtain a set of piecewise linear differential equations that continuously describe the states of each gene or protein in the network. Both methods are applied to a Boolean model of the segment polarity gene network of Drosophila melanogaster. The dynamics of the model is analysed, and a theoretical characterisation of the model's gene pattern prediction is provided as a function of the timescales of the various processes.

In two earlier papers, means were provided to decide the capacity of complex chemical reaction networks, taken with mass-action kinetics, to admit multiple equilibria in the context of the isothermal homogeneous continuous flow stirred tank reactor (CFSTR). In such a reactor, all species are deemed to be in the outflow, a fact which has an important bearing on the nature of the governing equations. In contrast, one can imagine CFSTR-like models of the cell in which certain large molecules (e.g., enzymes) remain entrapped within the cell, whereas smaller ones (e.g., metabolites) are free to diffuse through the cell boundary. Although such models bear a strong physical resemblance to the classical CFSTR picture, there are substantive differences in the corresponding mathematics. Without a presumption of mass-action kinetics, this research is intended to indicate a general way in which results about uniqueness of equilibria in the classical CFSTR context extend to entrapped species models.

Parameter estimation is a major challenge for mathematical modelling of biological systems. Given the uncertainties associated with model parameters, it is important to understand how sensitive the model output is to variations in parameter values. A local sensitivity analysis determines the model sensitivity to parameter variations over a localised region around the nominal parameter values, whereas a global sensitivity analysis (GSA) investigates the sensitivity over the entire parameter space. Using a T-cell receptor-activated Erk-MAPK signalling pathway model as an example, the authors present a comparative study of a variety of different sensitivity analysis techniques. These techniques include: local sensitivity analysis, existing GSA methods of partial rank correlation coefficient, Sobol's, extended Fourier amplitude sensitivity test, as well as a weighted average of local sensitivities and a new GSA method to extract global parameter sensitivities from a parameter identification routine. Results of this study revealed critical reactions in the signalling pathway and their impact on the signalling dynamics and provided insights into embedded regulatory mechanisms such as feedback loops in the pathway. From this study, a recommendation emerges for a general sensitivity analysis strategy to efficiently and reliably infer quantitative, dynamic as well as topological properties from systems biology models.

The manipulation of organisms using combinations of gene knockout, RNAi and drug interaction experiments can be used to reveal regulatory interactions between genes. Several algorithms have been proposed that try to reconstruct the underlying regulatory networks from gene expression data sets arising from such experiments. Often these approaches assume that each gene has approximately the same number of interactions within the network, and the methods rely on prior knowledge, or the investigator's best guess, of the average network connectivity. Recent evidence points to scale-free properties in biological networks, however, where network connectivity follows a power-law distribution. For scale-free networks, the average number of regulatory interactions per gene does not satisfactorily characterise the network. With this in mind, a new reverse engineering approach is introduced that does not require prior knowledge of network connectivity and its performance is compared with other published algorithms using simulated gene expression data with biologically relevant network structures. Because this new approach does not make any assumptions about the distribution of network connections, it is suitable for application to scale-free networks.

The unexpectedly long, and still unfinished, path towards a reliable mathematical model of glycolysis and its regulation in Lactococcus lactis is described. The model of this comparatively simple pathway was to be deduced from in vivo nuclear magnetic resonance time-series measurements of the key glycolytic metabolites. As to be expected from any nonlinear inverse problem, computational challenges were encountered in the numerical determination of parameter values of the model. Some of these were successfully solved, whereas others are still awaiting improved techniques of analysis. In addition, rethinking of the model formulation became necessary, because some generally accepted assumptions during model design are not necessarily valid for in vivo models. Examples include precursor-product relationships and the homogeneity of cells and their responses. Finally, it turned out to be useful to model only some of the metabolites, while using time courses of ubiquitous compounds such as adenosine triphosphate, inorganic phosphate, nicotinamide adenine dinucleotide (oxidised) and nicotinamide adenine dinucleotide (reduced) as unmodelled input functions. With respect to our specific application, the modelling process has come a long way, but it is not yet completed. Nonetheless, the model analysis has led to interesting insights into the design of the pathway and into the principles that govern its operation. Specifically, the widely observed feedforward activation of pyruvate kinase by fructose 1,6-bisphosphate is shown to provide a crucial mechanism for positioning the starving organism in a holding pattern that allows immediate uptake of glucose, as soon as it becomes available.

During the evolution of endosymbiosis, only one orthologous gene, either from the invader or the invaded genome, is preserved. Genetic and environmental factors are usually invoked to explain this gene preference. How biochemical parameters can play a role in the selection of genes that code for enzymes that constitute a metabolic pathway is explored. Simple Michaelis-Menten-like enzymes are considered whose kinetic parameters are randomly generated to construct two parallel homologous pathways to account for the contributions of the invaded and the invader. Steady-state fluxes as targets of natural selection are focused. Enzymes are eliminated one by one so that the total flux through the pathway is least disturbed. Analysis of the results, done by different criteria, indicate that the maximal velocities, both forward and backward, are more influential in selection than the respective Michaelis constants. This inclination disappears as metabolite concentrations are increased. It is shown that kinetic selection criteria can result in a mosaicism of enzymes in the same pathway in terms of their genetic origin. Analysis of the results using the control coefficient paradigm disclosed an expected robust correlation between flux control coefficients of enzymes and their selective elimination. Similar analyses, performed for the case of single gene transfer or for gene replication with subsequent mutation, yielded essentially similar results. The results conform with the phenomenon of genetic mosaicism found in phylogenetic analyses of single or double endosymbioses and lateral gene transfer.

The problem of disentangling complex dynamic systems is addressed, especially with a view to identifying those variables that take part in the essential qualitative behaviour of systems. The author presents a series of reflections about the methods of formalisation together with the principles that govern the global operation of systems. In particular, a section on circuits, nuclei, and circular causality and a rather detailed description of the analytic use of the generalised asynchronous logical description, together with a brief description of its synthetic use (OreverseO logic). Some basic rules are recalled, such as the fact that a positive circuit is a necessary condition of multistationarity. Also, the interest of considering as a model, rather than a well-defined set of differential equations, a variety of systems that differ from each other only by the values of constant terms is emphasised. All these systems have a common Jacobian matrix and for all of them phase space has exactly the same structure. It means that all can be partitioned in the same way as regards the signs of the eigenvalues and thus as regards the precise nature of any steady states that might be present. Which steady states are actually present, depends on the values of terms of order zero in the ordinary differential equations (ODEs), and it is easy to find for which values of these terms a given point in phase space is steady. Models can be synthesised first at the level of the circuits involved in the Jacobian matrix (that determines which types and numbers of steady states are consistent with the model), then only at the level of terms of order zero in the ODE's (that determines which of the steady states actually exist), hence the title 'Circular casuality'.

Biological complexity and limited quantitative measurements pose severe challenges to standard engineering methodologies for modelling and simulation of genes and gene products integrated in a functional network. In particular, parameter quantification is a bottleneck, and therefore parameter estimation, identifiability, and optimal experiment design are important research topics in systems biology. An approach is presented in which unmodelled dynamics are replaced by fictitious 'dependent inputs'. The dependent input approach is particularly useful in validation experiments, because it allows one to fit model parameters to experimental data generated by a reference cell type ('wild-type') and then test this model on data generated by a variation ('mutant'), so long as the mutations only affect the unmodelled dynamics that produce the dependent inputs. Another novel feature of the approach is in the inclusion of a priori information in a multi-objective identification criterion, making it possible to obtain estimates of parameter values and their variances from a relatively limited experimental data set. The pathways that control the nitrogen uptake fluxes in baker's yeast (Saccharomyces cerevisiae) have been studied. Well-defined perturbation experiments were performed on cells growing in steady-state. Time-series data of extracellular and intracellular metabolites were obtained, as well as mRNA levels. A nonlinear model was proposed and was shown to be structurally identifiable given data of its inputs and outputs. The identified model is a reliable representation of the metabolic system, as it could correctly describe the responses of mutant cells and different perturbations.

Systems biology aims to study the properties of biological systems in terms of the properties of their molecular constituents. This occurs frequently by a process of mathematical modelling. The first step in this modelling process is to unravel the interaction structure of biological systems from experimental data. Previously, an algorithm for gene network inference from gene expression perturbation data was proposed. Here, the algorithm is extended by using regression with subset selection. The performance of the algorithm is extensively evaluated on a set of data produced with gene network models at different levels of simulated experimental noise. Regression with subset selection outperforms the previously stated matrix inverse approach in the presence of experimental noise. Furthermore, this regression approach enables us to deal with under-determination, that is, when not all genes are perturbed. The results on incomplete data sets show that the new method performs well at higher number of perturbations, even when noise levels are high. At lower number of perturbations, although still being able to recover the majority of the connections, less confidence can be placed in the recovered edges.

It has long been hypothesised that futile cycles in cellular metabolism are involved in the regulation of biochemical pathways. Following the work of Newsholme and Crabtree, a quantitative theory was developed for this idea based on open-system thermodynamics and metabolic control analysis. It is shown that the stoichiometric sensitivity of an intermediary metabolite concentration with respect to changes in steady-state flux is governed by the effective equilibrium constant of the intermediate formation, and the equilibrium can be regulated by a futile cycle. The direction of the shift in the effective equilibrium constant depends on the direction of operation of the futile cycle. High stoichiometric sensitivity corresponds to ultrasensitivity of an intermediate concentration to net flow through a pathway; low stoichiometric sensitivity corresponds to super-robustness of concentration with respect to changes in flux. Both cases potentially play important roles in metabolic regulation. Futile cycles actively shift the effective equilibrium by expending energy; the magnitude of changes in effective equilibria and sensitivities is a function of the amount of energy used by a futile cycle. This proposed mechanism for control by futile cycles works remarkably similar to kinetic proofreading in biosynthesis. The sensitivity of the system is also intimately related to the rate of concentration fluctuations of intermediate metabolites. The possibility of different roles for the two major mechanisms within cellular biochemical regulation, namely reversible chemical modifications via futile cycles and shifting equilibrium by macromolecular binding, are discussed.