Systems biology最新文献

When the genomic integrity of a cell is challenged, its fate is determined in part by signals conveyed by the p53 tumour suppressor protein. It was observed recently that such signals are not simple gradations of p53 concentration, but rather a counter-intuitive limit-cycle behaviour. Based on a careful mathematical interpretation of the experimental body of knowledge, we propose a model for the p53 signalling network and characterise the p53 stability and oscillatory dynamics. In our model, ATM, a protein that senses DNA damage, activates p53 by phosphorylation. In its active state, p53 has a decreased degradation rate and an enhanced transactivation of Mdm2, a gene whose protein product Mdm2 tags p53 for degradation. Thus the p53-Mdm2 system forms a negative feedback loop. However, the feedback in this loop is delayed, as the pool of Mdm2 molecules being induced by p53 at a given time will mark for degradation the pool of p53 molecules at some later time, after the Mdm2 molecules have been transcribed, exported out of the nucleus, translated and transported back into the nucleus. The analysis of our model demonstrates how this time lag combines with the ATM-controlled feedback strength and effective dampening of the negative feedback loop to produce limit-cycle oscillations. The picture that emerges is that ATM, once activated by DNA damage, makes the p53-Mdm2 oscillator undergo a supercritical Hopf bifurcation. This approach yields an improved understanding of the global dynamics and bifurcation structure of our time-delayed, negative feedback model and allows for predictions of the behaviour of the p53 system under different perturbations.

Despite major advances over the last two decades in our understanding of RNA splicing and (post-) transcriptional regulation in human immunodeficiency virus type-1 (HIV-1), debate continues on the mechanisms and effects of Rev protein on HIV-1 growth. Moreover, arguments that HIV-1 has been optimised for growth have been largely based on speculation. Here, we begin systematically to address these issues by developing a detailed kinetic model for HIV-1 intracellular development. The model accounts for transcription, successive steps in RNA splicing, nuclear export of mRNAs, translation and shuttling of Rev and Tat, Tat-mediated transactivation of transcription, thresholds on Rev in its effects on nuclear export of mRNA, and inhibitory effects of Rev on splicing. Using the model, we found that inefficient splicing of HIV-1 mRNA was generally beneficial for HIV-1 growth, but that an excessive reduction in the splicing efficiency could be detrimental, suggesting that there exists a splicing efficiency that optimises HIV-1 growth. Further, we identified two key contributors to splicing efficiency, the intrinsic splicing rate and the extent of Rev-mediated splicing inhibition, and we showed how these should be balanced for HIV-1 to optimise its growth. Finally, we found that HIV-1 growth is relatively insensitive to different levels of the Rev export threshold, and we suggest that this mechanism evolved to delay viral growth, perhaps to enable evasion of host defensive responses. In summary, our model provides a quantitative and qualitative framework for probing how constituent mechanisms contribute to the complex, yet logical, process of HIV-1 growth.

In previous work, we studied the behaviour of a model of part of the NF-kappaB signalling pathway. The model displayed oscillations that varied both in number, amplitude and frequency when its parameters were varied. Sensitivity analysis showed that just nine of the 64 reaction parameters were mainly responsible for the control of the oscillations when these parameters were varied individually. However, the control of the properties of any complex system is distributed, and, as many of these reactions are highly non-linear, we expect that their interactions will be too. Pairwise modulation of these nine parameters gives a search space some 50 times smaller (81 against 4096) than that required for the pairwise modulation of all 64 reactions, and this permitted their study (which would otherwise have been effectively intractable). Strikingly synergistic effects were observed, in which the effect of one of the parameters was strongly (and even qualitatively) dependent on the values of another parameter. Regions of parameter space could be found in which the amplitude, but not the frequency (timing), of oscillations varied, and vice versa. Such modelling will permit the design and performance of experiments aimed at disentangling the role of the dynamics of oscillations, rather than simply their amplitude, in determining cell fate. Overall, the analyses reveal a level of complexity in these dynamic models that is not apparent from study of their individual parameters alone and point to the value of manipulating multiple elements of complex networks to achieve desired physiological effects.

DNA synthesis and nuclear division in the developing frog egg are controlled by fluctuations in the activity of M-phase promoting factor (MPF). The biochemical mechanism of MPF regulation is most easily studied in cytoplasmic extracts of frog eggs, for which careful experimental studies of the kinetics of phosphorylation and dephosphorylation of MPF and its regulators have been made. In 1998 Marlovits et al. used these data sets to estimate the kinetic rate constants in a mathematical model of the control system originally proposed by Novak & Tyson. In a recent publication, we showed that a gradient-based optimisation algorithm finds a locally optimal parameter set quite close to the 'Marlovits' estimates. In this paper, we combine global and local optimisation strategies to show that the 'refined Marlovits' parameter set, with one minor but significant modification to the Novak & Tyson equations, is the unique, best-fitting solution to the parameter estimation problem.

Under conditions of starvation, populations of the amoebae Dictyostelium discoideum aggregate are mediated by chemical excitation waves of cAMP. Two types of waves can be observed, either spiral or circular-shaped ones. We investigate transitions from rotating spirals to circular shaped waves (target patterns). Two different experiments demonstrating this phenomenon are presented. In the first case a continuous transition from the spiral type pattern to target waves was observed at the later stages of aggregation. In the second case the transition was induced by annihilation of waves by a spatially homogeneous cAMP pulse. Instead of the originally present spiral waves, oscillating spots bearing target patterns emerged. On the basis of a model for Dictyostelium aggregation, we provide a theoretical explanation for such transitions. It is shown that cell density can be an effective bifurcation parameter. Under certain conditions, the system is shifted from the excitable to the oscillatory state while the frequency of oscillations is proportional to the square root of the cell density. Thus, the regions with the highest cell density during the early stages of the spatial rearrangement of the cells become pacemakers and produce target patterns. The analytic results were confirmed in numerical simulations of the model.

Recently a state-space model with time delays for inferring gene regulatory networks was proposed. It was assumed that each regulation between two internal state variables had multiple time delays. This assumption caused underestimation of the model with many current gene expression datasets. In biological reality, one regulatory relationship may have just a single time delay, and not multiple time delays. This study employs Boolean variables to capture the existence of the time-delayed regulatory relationships in gene regulatory networks in terms of the state-space model. As the solution space of time delayed relationships is too large for an exhaustive search, a genetic algorithm (GA) is proposed to determine the optimal Boolean variables (the optimal time-delayed regulatory relationships). Coupled with the proposed GA, Bayesian information criterion (BIC) and probabilistic principle component analysis (PPCA) are employed to infer gene regulatory networks with time delays. Computational experiments are performed on two real gene expression datasets. The results show that the GA is effective at finding time-delayed regulatory relationships. Moreover, the inferred gene regulatory networks with time delays from the datasets improve the prediction accuracy and possess more of the expected properties of a real network, compared to a gene regulatory network without time delays.

To study the network formation of endothelial cells (ECs) in an extracellular matrix (ECM) environment, we have devised an EC aggregation-type model based on a diffusion limited cluster aggregation model (DLCA), where clusters of particles diffuse and stick together upon contact. We use this model to quantify EC differentiation into cord-like structures by comparing experimental and simulation data. Approximations made with the DLCA model, when combined with experimental kinetics and cell concentration results, not only allow us to quantify cell differentiation by a pseudo diffusion coefficient, but also measure the effects of tumor angiogenic factors (TAFs) on the formation of cord-like structures by ECs. We have tested our model by using an in vitro assay, where we record EC aggregation by analysing time-lapse images that provide us with the evolution of the fractal dimension measure through time. We performed these experiments for various cell concentrations and TAFs (e.g. EVG, FGF-b, and VEGF). During the first six hours of an experiment, ECs aggregate quickly. The value of the measured fractal dimension decreases with time until reaching an asymptotic value that depends solely on the EC concentration. In contrast, the kinetics depend on the nature of TAFs. The experimental and simulation results correlate with each other in regards to the fractal dimension and kinetics, allowing us to quantify the influence of each TAF by a pseudo diffusion coefficient. We have shown that the shape, kinetic aggregation, and fractal dimension of the EC aggregates fit into an in vitro model capable of reproducing the first stage of angiogenesis. We conclude that the DLCA model, combined with experimental results, is a highly effective assay for the quantification of the kinetics and network characteristics of ECs embedded in ECM proteins. Finally, we present a new method that can be used for studying the effect of angiogenic drugs in in vitro assays.

Autonomous oscillations at the cellular level are important for various timing and signalling functions. The rhythms depend on environmental influences in a specific manner. In particular, the period of some rhythms has been shown to be very robust to certain environmental factors whereas other rhythms show a high sensitivity towards these factors. It is discussed that the robustness of the systems towards environmental changes results from underlying design principles. However, a comparison of robustness properties of different rhythms is lacking. Here we analyse the sensitivity of the oscillatory period with respect to parameter variations in models describing oscillations in calcium signalling, glycolysis and the circadian system. By comparing models for the same and different rhythms it is shown that the sensitivity depends on the oscillatory mechanism rather than the details of the model description. In particular, we find models of calcium oscillations to be very sensitive, those for glycolytic oscillations intermediately sensitive and models for circadian rhythms very robust. The results are discussed with respect to the temperature dependency of the rhythms. The question of what impact design principles have on the robustness of an oscillator, is addressed more explicitly by a direct comparison of systems with positive and negative feedback regulation for various reaction chain lengths. We find that the systems with negative feedback are more robust than corresponding systems with positive feedback. An increase in the length of the reaction chain under regulation leads to a decrease in sensitivity.