Showing papers in "Iet Systems Biology in 2009"

Moment-closure approximations for mass-action models

Abstract: Although stochastic population models have proved to be a powerful tool in the study of process generating mechanisms across a wide range of disciplines, all too often the associated mathematical development involves nonlinear mathematics, which immediately raises difficult and challenging analytic problems that need to be solved if useful progress is to be made. One approximation that is often employed to estimate the moments of a stochastic process is moment closure. This approximation essentially truncates the moment equations of the stochastic process. A general expression for the marginal- and joint-moment equations for a large class of stochastic population models is presented. The generalisation of the moment equations allows this approximation to be applied easily to a wide range of models. Software is available from http://pysbml.googlecode.com/ to implement the techniques presented here.

Genetic network identification using convex programming

Abstract: Gene regulatory networks capture interactions between genes and other cell substances, resulting in various models for the fundamental biological process of transcription and translation. The expression levels of the genes are typically measured as mRNA concentration in micro-array experiments. In a so-called genetic perturbation experiment, small perturbations are applied to equilibrium states and the resulting changes in expression activity are measured. One of the most important problems in systems biology is to use these data to identify the interaction pattern between genes in a regulatory network, especially in a large scale network. The authors develop a novel algorithm for identifying the smallest genetic network that explains genetic perturbation experimental data. By construction, our identification algorithm is able to incorporate and respect a priori knowledge known about the network structure. A priori biological knowledge is typically qualitative, encoding whether one gene affects another gene or not, or whether the effect is positive or negative. The method is based on a convex programming relaxation of the combinatorially hard problem of L O minimisation. The authors apply the proposed method to the identification of a subnetwork of the SOS pathway in Escherichia coli , the segmentation polarity network in Drosophila melanogaster , and an artificial network for measuring the performance of the method.

Optimal experimental design with the sigma point method

Abstract: Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their variances. To obtain highly predictive models, very precise parameters are needed. The optimal experimental design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher information matrix. The application of this traditional method has at least two shortcomings for models that are nonlinear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, the authors show that by applying the sigma point (SP) method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the SP method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The SP method is demonstrated for the example of a widely used biological model.

Optimal control policy for probabilistic Boolean networks with hard constraints

Abstract: It is well known that the control/intervention of some genes in a genetic regulatory network is useful for avoiding undesirable states associated with some diseases like cancer. For this purpose, both optimal finite-horizon control and infinite-horizon control policies have been proposed. Boolean networks (BNs) and its extension probabilistic Boolean networks (PBNs) as useful and effective tools for modelling gene regulatory systems have received much attention in the biophysics community. The control problem for these models has been studied widely. The optimal control problem in a PBN can be formulated as a probabilistic dynamic programming problem. In the previous studies, the optimal control problems did not take into account the hard constraints, i.e. to include an upper bound for the number of controls that can be applied to the captured PBN. This is important as more treatments may bring more side effects and the patients may not bear too many treatments. A formulation for the optimal finite-horizon control problem with hard constraints introduced by the authors. This model is state independent and the objective function is only dependent on the distance between the desirable states and the terminal states. An approximation method is also given to reduce the computational cost in solving the problem. Experimental results are given to demonstrate the efficiency of our proposed formulations and methods.

Steady-state and dynamic flux balance analysis of ethanol production by Saccharomyces cerevisiae

Abstract: Steady-state and dynamic flux balance analysis (DFBA) was used to investigate the effects of metabolic model complexity and parameters on ethanol production predictions for wild-type and engineered Saccharomyces cerevisiae. Three metabolic network models ranging from a single compartment representation of metabolism to a genome-scale reconstruction with seven compartments and detailed charge balancing were studied. Steady-state analysis showed that the models generated similar wild-type predictions for the biomass and ethanol yields, but for ten engineered strains the seven compartment model produced smaller ethanol yield enhancements. Simplification of the seven compartment model to two intracellular compartments produced increased ethanol yields, suggesting that reaction localisation had an impact on mutant phenotype predictions. Further analysis with the seven compartment model demonstrated that steady-state predictions can be sensitive to intracellular model parameters, with the biomass yield exhibiting high sensitivity to ATP utilisation parameters and the biomass composition. The incorporation of gene expression data through the zeroing of metabolic reactions associated with unexpressed genes was shown to produce negligible changes in steady-state predictions when the oxygen uptake rate was suitably constrained. Dynamic extensions of the single and seven compartment models were developed through the addition of glucose and oxygen uptake expressions and transient extracellular balances. While the dynamic models produced similar predictions of the optimal batch ethanol productivity for the wild type, the single compartment model produced significantly different predictions for four implementable gene insertions. A combined deletion/overexpression/insertion mutant with improved ethanol productivity capabilities was computationally identified by dynamically screening multiple combinations of the ten metabolic engineering strategies. The authors concluded that extensive compartmentalisation and detailed charge balancing can be important for reliably screening metabolic engineering strategies that rely on modification of the global redox balance and that DFBA offers the potential to identify novel mutants for enhanced metabolite production in batch and fed-batch cultures.

Proper lumping in systems biology models

Abstract: An algorithm for automatic order reduction of models defined by large systems of differential equations is presented. The algorithm was developed with systems biology models in mind and the motivation behind it is to develop mechanistic pharmacokinetic/pharmacodynamic models from already available systems biology models. The approach used for model reduction is proper lumping of the system's states and is based on a search through the possible combinations of lumps. To avoid combinatorial explosion, a heuristic, greedy search strategy is employed and comparison with the full exhaustive search provides evidence that it performs well. The method takes advantage of an apparent property of this kind of systems that lumps remain consistent over different levels of order reduction. Advantages of the method presented include: the variables and parameters of the reduced model retain a specific physiological meaning; the algorithm is automatic and easy to use; it can be used for nonlinear models and can handle parameter uncertainty and constraints. The algorithm was applied to a model of NF-κB signalling pathways in order to demonstrate its use and performance. Significant reduction was achieved for the example model, while agreement with the original model was proportional to the size of the reduced model, as expected. The results of the model reduction were compared with a published, intuitively reduced model of NF-κB signalling pathways and were found to be in agreement, in terms of the identified key species for the system's kinetic behaviour. The method may provide useful insights which are complementary to the intuitive reduction approach, especially in large systems.

Crosstalk between p53 and nuclear factor-κB systems: pro- and anti-apoptotic functions of NF-κB

Abstract: Nuclear factors p53 and NF-kappaB control many physiological processes including cell cycle arrest, DNA repair, apoptosis, death, innate and adaptive immune responses, and inflammation There are numerous pathways linking these systems and there is a bulk of evidence for cooperation as well as for antagonisms between p53 and NF-kappaB In this theoretical study, the authors use earlier models of p53 and NF-kappaB systems and construct a crosstalk model of p53-NF-kappaB network in order to explore the consequences of the two-way coupling, in which NF-kappaB upregulates the transcription of p53, whereas in turn p53 attenuates transcription of NF-kappaB inhibitors IkappaBalpha and A20 We consider a number of protocols in which cells are stimulated by tumour necrosis factor-alpha (TNFalpha) (that activates NF-kappaB pathway) and/or gamma irradiation (that activates p53 pathway) The authors demonstrate that NF-kappaB may have both anti- and pro-apoptotic roles TNFalpha stimulation, preceding DNA damaging irradiation, makes cells more resistant to irradiation-induced apoptosis, whereas the same TNFalpha stimulation, when preceded by irradiation, increases the apoptotic cell fraction The finding suggests that diverse roles of NF-kappaB in apoptosis and cancer could be related to the dynamical context of activation of p53 and NF-kappaB pathways

Nested uncertainties in biochemical models

Abstract: Dynamic modelling of biochemical reaction networks has to cope with the inherent uncertainty about biological processes, concerning not only data and parameters but also kinetics and structure. These different types of uncertainty are nested within each other: uncertain network structures contain uncertain reaction kinetics, which in turn are governed by uncertain parameters. Here, the authors review some issues arising from such uncertainties and sketch methods, solutions and future directions to deal with them.

SysBioMed report: Advancing systems biology for medical applications

Abstract: The following report selects and summarises some of the conclusions and recommendations generated throughout a series of workshops and discussions that have lead to the publication of the Science Policy Briefing (SPB) Nr. 35, published by the European Science Foundation. (Large parts of the present text are directly based on the ESF SPB. Detailed recommendations with regard to specific application areas are not given here but can be found in the SPB. Issues related to mathematical modelling, including training and the need for an infrastructure supporting modelling are discussed in greater detail in the present text.)The numerous reports and publications about the advances within the rapidly growing field of systems biology have led to a plethora of alternative definitions for key concepts. Here, with ‘mathematical modelling’ the authors refer to the modelling and simulation of subcellular, cellular and macro-scale phenomena, using primarily methods from dynamical systems theory. The aim of such models is encoding and testing hypotheses about mechanisms underlying the functioning of cells. Typical examples are models for molecular networks, where the behaviour of cells is expressed in terms of quantitative changes in the levels of transcripts and gene products. Bioinformatics provides essential complementary tools, including procedures for pattern recognition, machine learning, statistical modelling (testing for differences, searching for associations and correlations) and secondary data extracted from databases.Dynamical systems theory is the natural language to investigate complex biological systems demonstrating nonlinear spatio-temporal behaviour. However, the generation of experimental data suitable to parameterise, calibrate and validate such models is often time consuming and expensive or not even possible with the technology available today. In our report, we use the term ‘computational model’ when mathematical models are complemented with information generated from bioinformatics resources. Hence, ‘the model’ is, in reality, an integrated collection of data and models from various (possibly heterogeneous) sources. The present report focuses on a selection of topics, which were identified as appropriate case studies for medical systems biology, and adopts a particular perspective which the authors consider important. We strongly believe that mathematical modelling represents a natural language with which to integrate data at various levels and, in doing so, to provide insight into complex diseases: 1. Modelling necessitates the statement of explicit hypotheses, a process which often enhances comprehension of the biological system and can uncover critical points where understanding is lacking. 2. Simulations can reveal hidden patterns and/or counter-intuitive mechanisms in complex systems. 3. Theoretical thinking and mathematical modelling constitute powerful tools to integrate and make sense of the biological and clinical information being generated and, more importantly, to generate new hypotheses that can then be tested in the laboratory.Medical Systems Biology projects carried out recently across Europe have revealed a need for action: 4. While the need for mathematical modelling and interdisciplinary collaborations is becoming widely recognised in the biological sciences, with substantial implications for the training and research funding mechanisms within this area, the medical sciences have yet to follow this lead. 5. To achieve major breakthroughs in Medical Systems Biology, existing academic funding schemes for large-scale projects need to be reconsidered. 6. The hesitant stance of the pharmaceutical industry towards major investment in systems biology research has to be addressed. 7. Leading medical journals should be encouraged to promote mathematical modelling.

Evolution of gene auto-regulation in the presence of noise.

Abstract: Auto-regulatory negative feedback loops, where the protein expressed from a gene inhibits its own expression are common gene network motifs within cells. We investigate when will introducing a negative feedback mechanism be beneficial in terms of increasing a fitness function that is given by the probability of maintaining protein numbers above a critical threshold. Our results show the existence of a trade-off as introducing feedback decreases the average number of protein molecules driving this number closer to the critical threshold (which decreases fitness) but also reduces stochastic fluctuations around the mean (which increases fitness). We provide analytical conditions under which a negative feedback mechanism can evolve, that is, introducing feedback will increase the above fitness. Analyses of these conditions show that negative feedbacks are more likely to evolve when (i) the source of noise in the protein population is extrinsic (i.e. noise is caused by fluctuations in exogenous signals driving the gene network) and not intrinsic (i.e. the randomness associated with mRNA/protein expression and degradation); (ii) the dynamics of the exogenous signal causing extrinsic noise is slower than the protein dynamics; and (iii) the critical threshold level for the protein number is low. We also show that mRNA/protein degradation rates are critical factors in determining whether transcription or translational negative feedback should evolve. In particular, when the mRNA half-life is much shorter than the protein's half-life, then a transcriptional negative feedback mechanism is more likely to evolve. On the other hand, a translational negative feedback mechanism is preferred with more stable mRNAs that have long half-lifes.

Generating probabilistic boolean networks from a prescribed transition probability matrix

Abstract: Probabilistic Boolean networks (PBNs) have received much attention in modeling genetic regulatory networks. A PBN can be regarded as a Markov chain process and is characterised by a transition probability matrix. In this study, the authors propose efficient algorithms for constructing a PBN when its transition probability matrix is given. The complexities of the algorithms are also analysed. This is an interesting inverse problem in network inference using steady-state data. The problem is important as most microarray data sets are assumed to be obtained from sampling the steady-state.

Integrating BioPAX pathway knowledge with SBML models.

Abstract: Online databases store thousands of molecular interactions and pathways, and numerous modelling software tools provide users with an interface to create and simulate mathematical models of such interactions However, the two most widespread used standards for storing pathway data (biological pathway exchange; BioPAX) and for exchanging mathematical models of pathways (systems biology markup language; SBML) are structurally and semantically different Conversion between formats (making data present in one format available in another format) based on simple one-to-one mappings may lead to loss or distortion of data, is difficult to automate, and often impractical and/or erroneous This seriously limits the integration of knowledge data and models In this paper we introduce an approach for such integration based on a bridging format that we named systems biology pathway exchange (SBPAX) alluding to SBML and BioPAX It facilitates conversion between data in different formats by a combination of one-to-one mappings to and from SBPAX and operations within the SBPAX data The concept of SBPAX is to provide a flexible description expanding around essential pathway data - basically the common subset of all formats describing processes, the substances participating in these processes and their locations SBPAX can act as a repository for molecular interaction data from a variety of sources in different formats, and the information about their relative relationships, thus providing a platform for converting between formats and documenting assumptions used during conversion, gluing (identifying related elements across different formats) and merging (creating a coherent set of data from multiple sources) data

Mesoscopic statistical properties of multistep enzyme-mediated reactions

Abstract: Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this study, the authors address this problem by solving the chemical master equations for various enzymatic reactions. A perturbation theory analogous to that used in quantum mechanics allows the determination of the first (n) and the second (σ2) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d(n)/dt (or 'dose-response' curve) and the Fano factor F= σ2/(n) are both realistically measurable quantities, and whereas the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and the authors explore this possibility in the context of four sample multistep enzymatic reactions. Measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.

Exploring mechanisms of oscillations in p53 and nuclear factor-κb systems

Abstract: A number of regulatory networks have the potential to generate sustained oscillations of irregular amplitude, but well conserved period. Single-cell experiments revealed that in p53 and nuclear factor (NF)-κB systems the oscillation period is homogenous in cell populations, insensitive to the strength of the stimulation, and is not influenced by the overexpression of p53 or NF-κB transcription factors. We propose a novel computational method of validation of molecular pathways models, based on the analysis of sensitivity of the oscillation period to the particular gene(s) copy number and the level of stimulation. Using this method, the authors demonstrate that existing p53 models, in which oscillations are borne at a saddle-node-on-invariant-circle or subcritical Hopf bifurcations (characteristic for systems with interlinked positive and negative feedbacks), are highly sensitive to gene copy number. Hence, these models cannot explain existing experiments. Analysing NF-κB system, the authors show the importance of saturation in transcription of the NF-κB inhibitor IκBα. Models without saturation predict that the oscillation period is a rapidly growing function of total NF-κB level, which is in disagreement with experiments. The study supports the hypothesis that oscillations of robust period are based on supercritical Hopf bifurcation, characteristic for dynamical systems involving negative feedback and time delay. We hypothesise that in the p53 system, the role of positive feedback is not sustaining oscillations, but terminating them in severely damaged cells in which the apoptotic programme should be initiated.

Detecting drug targets with minimum side effects in metabolic networks

Abstract: High-throughput techniques produce massive data on a genome-wide scale which facilitate pharmaceutical research. Drug target discovery is a crucial step in the drug discovery process and also plays a vital role in therapeutics. In this study, the problem of detecting drug targets was addressed, which finds a set of enzymes whose inhibition stops the production of a given set of target compounds and meanwhile minimally eliminates non-target compounds in the context of metabolic networks. The model aims to make the side effects of drugs as small as possible and thus has practical significance of potential pharmaceutical applications. Specifically, by exploiting special features of metabolic systems, a novel approach was proposed to exactly formulate this drug target detection problem as an integer linear programming model, which ensures that optimal solutions can be found efficiently without any heuristic manipulations. To verify the effectiveness of our approach, computational experiments on both Escherichia coli and Homo sapiens metabolic pathways were conducted. The results show that our approach can identify the optimal drug targets in an exact and efficient manner. In particular, it can be applied to large-scale networks including the whole metabolic networks from most organisms.

Modelling and analysis of the sugar cataract development process using stochastic hybrid systems

Abstract: Modelling and analysis of biochemical systems such as sugar cataract development (SCD) are critical because they can provide new insights into systems, which cannot be easily tested with experiments; however, they are challenging problems due to the highly coupled chemical reactions that are involved. The authors present a stochastic hybrid system (SHS) framework for modelling biochemical systems and demonstrate the approach for the SCD process. A novel feature of the framework is that it allows modelling the effect of drug treatment on the system dynamics. The authors validate the three sugar cataract models by comparing trajectories computed by two simulation algorithms. Further, the authors present a probabilistic verification method for computing the probability of sugar cataract formation for different chemical concentrations using safety and reachability analysis methods for SHSs. The verification method employs dynamic programming based on a discretisation of the state space and therefore suffers from the curse of dimensionality. To analyse the SCD process, a parallel dynamic programming implementation that can handle large, realistic systems was developed. Although scalability is a limiting factor, this work demonstrates that the proposed method is feasible for realistic biochemical systems.

Discrete dynamical system modelling for gene regulatory networks of 5-hydroxymethylfurfural tolerance for ethanologenic yeast

Abstract: Composed of linear difference equations, a discrete dynamical system (DDS) model was designed to reconstruct transcriptional regulations in gene regulatory networks (GRNs) for ethanologenic yeast Saccharomyces cerevisiae in response to 5-hydroxymethylfurfural (HMF), a bioethanol conversion inhibitor. The modelling aims at identification of a system of linear difference equations to represent temporal interactions among significantly expressed genes. Power stability is imposed on a system model under the normal condition in the absence of the inhibitor. Non-uniform sampling, typical in a time-course experimental design, is addressed by a log-time domain interpolation. A statistically significant DDS model of the yeast GRN derived from time-course gene expression measurements by exposure to HMF, revealed several verified transcriptional regulation events. These events implicate Yap1 and Pdr3, transcription factors consistently known for their regulatory roles by other studies or postulated by independent sequence motif analysis, suggesting their involvement in yeast tolerance and detoxification of the inhibitor.

Mixed-integer nonlinear optimisation approach to coarse-graining biochemical networks

Abstract: Quantitative modelling and analysis of biochemical networks is challenging because of the inherent complexities and nonlinearities of the system and the limited availability of parameter values. Even if a mathematical model of the network can be developed, the lack of large-scale good-quality data makes accurate estimation of a large number of parameters impossible. Hence, coarse-grained models (CGMs) consisting of essential biochemical mechanisms are more suitable for computational analysis and for studying important systemic functions. The central question in constructing a CGM is which mechanisms should be deemed ‘essential’ and which can be ignored. Also, how should parameter values be defined when data are sparse? A mixed-integer nonlinear-programming (MINLP) based optimisation approach to coarse-graining is presented. Starting with a detailed biochemical model with associated computational details (reaction network and mathematical description) and data on the biochemical system, the structure and the parameters of a CGM can be determined simultaneously. In this optimisation problem, the authors use a genetic algorithm to simultaneously identify parameter values and remove unimportant reactions. The methodology is exemplified by developing two CGMs for the GTPase-cycle module of M1 muscarinic acetylcholine receptor, Gq, and regulator of G protein signalling 4 [RGS4, a GTPase-activating protein (GAP)] starting from a detailed model of 48 reactions. Both the CGMs have only 17 reactions, fit experimental data well and predict, as does the detailed model, four limiting signalling regimes (LSRs) corresponding to the extremes of receptor and GAP concentration. The authors demonstrate that coarse-graining, in addition to resulting in a reduced-order model, also provides insights into the mechanisms in the network. The best CGM obtained for the GTPase cycle also contains an unconventional mechanism and its predictions explain an old problem in pharmacology, the biphasic (bell-shaped) response to certain drugs. The MINLP methodology is broadly applicable to larger and complex (dense) biochemical modules.

Estimation of metabolic pathway systems from different data sources.

Abstract: Parameter estimation is the main bottleneck of metabolic pathway modelling. It may be addressed from the bottom up, using information on metabolites, enzymes and modulators, or from the top down, using metabolic time series data, which have become more prevalent in recent years. The authors propose here that it is useful to combine the two strategies and to complement time-series analysis with kinetic information. In particular, the authors investigate how the recent method of dynamic flux estimation (DFE) may be supplemented with other types of estimation. Using the glycolytic pathway in Lactococcus lactis as an illustration example, the authors demonstrate some strategies of such supplementation.

Identifying differentially expressed pathways via a mixed integer linear programming model.

Abstract: The identification of genes and pathways involved in biological processes is a central problem in systems biology. Recent microarray technologies and other high-throughput experiments provide information which sheds light on this problem. In this article, the authors propose a new computational method to detect active pathways, or identify differentially expressed pathways via integration of gene expression and interactomic data in a sophisticated and efficient manner. Specifically, by using signal-to-noise ratio to measure the differentially expressed level of networks, this problem is formulated as a mixed integer linear programming problem (MILP). The results on yeast and human data demonstrate that the proposed method is more accurate and robust than existing approaches.

Cross-platform method for identifying candidate network biomarkers for prostate cancer.

Abstract: Discovering biomarkers using mass spectrometry (MS) and microarray expression profiles is a promising strategy in molecular diagnosis. Here, the authors proposed a new pipeline for biomarker discovery that integrates disease information for proteins and genes, expression profiles in both genomic and proteomic levels, and protein-protein interactions (PPIs) to discover high confidence network biomarkers. Using this pipeline, a total of 474 molecules (genes and proteins) related to prostate cancer were identified and a prostate-cancer-related network (PCRN) was derived from the integrative information. Thus, a set of candidate network biomarkers were identified from multiple expression profiles composed by eight microarray datasets and one proteomics dataset. The network biomarkers with PPIs can accurately distinguish the prostate patients from the normal ones, which potentially provide more reliable hits of biomarker candidates than conventional biomarker discovery methods.

Robust control of uncertain context-sensitive probabilistic Boolean networks

Abstract: Uncertainty is an intrinsic phenomenon in control of gene regulatory networks (GRNs). The presence of uncertainty is related to impreciseness of GRN models due to: (1) Errors caused by imperfection of measurement devices and (2) Models' inability to fully capture a complex structure of the GRN. Consequently, there is a discrepancy between actual behaviour of the GRN and what is predicted by its mathematical model. This can result in false control signals, which can drive a cell to an undesirable state. To address the problem of control under uncertainties, a risk-sensitive control paradigm is proposed. Robustness is accomplished by minimisation of the mean exponential cost as opposed to, for instance, minimisation of the mean square cost by risk-neutral controllers. The authors derive an optimal risk-sensitive controller when a GRN is modelled by a context-sensitive probabilistic Boolean network (CSPBN). By using a relation between the relative entropy and free-energy, a relative stability of the cost achieved by the risk-sensitive controller is demonstrated when the distribution of the CSPBN attractors is perturbed, as opposed to the cost of the risk-neutral controller that exhibits increase. The use of the relation between the relative entropy and free-energy to analyse the influence of a particular attractor on the robustness of the controller is studied. The efficiency of the risk-sensitive controller is tested for the CSPBN obtained from the study of malignant melanoma.

Chemotherapy may be delivered based on an integrated view of tumour dynamics.

Abstract: The aim here was to explore the potential of pharmacokinetic (PK)/pharmacodynamic (PD) and physiopathological parameters in explaining the primary effects of an anti-cancer treatment that targets cells in a specific cell cycle phase. The authors applied a theoretical multi-scale disease model of tumour growth that integrates cancer processes at the cellular and tissue scales. The mathematical model at the cell level relies on a dynamic description of cell cycle regulation while the model at the tissue level is based on fluid mechanics considerations. Simulations show that the number of target cells oscillates as the tumour grows after a first cycle of chemotherapy. Both treatment effect and tumour growth processes drive these oscillations. Nonetheless, results indicate that parameters related to physiopathological processes may have greater relevance than classical drug-related parameters in determining the efficacy of a chemotherapy treatment protocol. Physiopathological parameters, in particular those related to cell cycle regulation, may be integrated in PK/PD models aimed at optimising the delivery of phase-specific cytotoxic treatments.

Interampatteness - a generic property of biochemical networks

Abstract: Analysis of gene expression data sets reveals that the variation in expression is concentrated to significantly fewer 'characteristic modes' or 'eigengenes' than the number of both recorded assays ...

Sensitivity Analysis Predicts that the ERK-pMEK Interaction Regulates ERK Nuclear Translocation

Abstract: Following phosphorylation, nuclear translocation of the mitogen-activated protein kinases (MAPKs), ERK1 and ERK2, is critical for both gene expression and DNA replication induced by growth factors. ERK nuclear translocation has therefore been studied extensively, but many details remain unresolved, including whether or not ERK dimerisation is required for translocation. Here, we simulate ERK nuclear translocation with a compartmental computational model that includes systematic sensitivity analysis. The governing ordinary differential equations are solved with the backward differentiation formula and decoupled direct methods. To better understand the regulation of ERK nuclear translocation, we use this model in conjunction with a previously published model of the ERK pathway that does not include an ERK dimer species and with experimental measurements of nuclear translocation of wild-type ERK and a mutant form, ERK1-Δ4, which is unable to dimerise. Sensitivity analysis reveals that the delayed nuclear uptake of ERK1-Δ4 compared to that of wild-type ERK1 can be explained by the altered interaction of ERK1-Δ4 with phosphorylated MEK (MAPK/ERK kinase), and so may be independent of dimerisation. Our study also identifies biological experiments that can verify this explanation.

Genome-wide system analysis reveals stable yet flexible network dynamics in yeast

Abstract: Recently, important insights into static network topology for biological systems have been obtained, but still global dynamical network properties determining stability and system responsiveness have not been accessible for analysis. Herein, we explore a genome-wide gene-to-gene regulatory network based on expression data from the cell cycle in Saccharomyces cerevisae (budding yeast). We recover static properties like hubs (genes having several out-going connections), network motifs and modules, which have previously been derived from multiple data sources such as whole-genome expression measurements, literature mining, protein-protein and transcription factor binding data. Further, our analysis uncovers some novel dynamical design principles; hubs are both repressed and repressors, and the intra-modular dynamics are either strongly activating or repressing whereas inter-modular couplings are weak. Finally, taking advantage of the inferred strength and direction of all interactions, we perform a global dynamical systems analysis of the network. Our inferred dynamics of hubs, motifs and modules produce a more stable network than what is expected given randomised versions. The main contribution of the repressed hubs is to increase system stability, while higher order dynamic effects (e.g. module dynamics) mainly increase system flexibility. Altogether, the presence of hubs, motifs and modules induce few flexible modes, to which the network is extra sensitive to an external signal. We believe that our approach, and the inferred biological mode of strong flexibility and stability, will also apply to other cellular networks and adaptive systems.

Detection of local community structures in complex dynamic networks with random walks

Abstract: Identification of interaction patterns in complex networks via community structures has gathered a lot of attention in recent research studies. Local community structures provide a better measure to understand and visualise the nature of interaction when the global knowledge of networks is unknown. Recent research on local community structures, however, lacks the feature to adjust itself in the dynamic networks and heavily depends on the source vertex position. In this study the authors propose a novel approach to identify local communities based on iterative agglomeration and local optimisation. The proposed solution has two significant improvements: (i) in each iteration, agglomeration strengthens the local community measure by selecting the best possible set of vertices, and (ii) the proposed vertex and community rank criterion are suitable for the dynamic networks where the interactions among vertices may change over time. In order to evaluate the proposed algorithm, extensive experiments and benchmarking on computer generated networks as well as real-world social and biological networks have been conducted. The experiment results reflect that the proposed algorithm can identify local communities, irrespective of the source vertex position, with more than 92% accuracy in the synthetic as well as in the real-world networks.

Role of inhibitory proteins as modulators of oscillations in NFκB signalling

Abstract: The authors discuss the role of the Raf kinase inhibitory protein (RKIP) as a modulator of oscillations in NFκB signalling. A mathematical model of the NFκB signalling pathway was derived and the Lyapunov–Andronov theory was used to analyse dynamical properties of the system. The analytical results were complemented by predictive numerical simulations. Our results suggest that the nature of oscillations, emerging under sustained stimulation of the system, depends on the interplay between the IκB kinase (IKK) stimulation and the inhibitory action of RKIP. The authors found a mathematical relation that defines isoclines in IKK and RKIP levels for which the properties of oscillations are conserved and changes in the stimulation can be compensated by modulating RKIP inhibition. On the other hand, the shifting from the current isocline provokes modulation in either the amplitude (for stronger stimulation) or the frequency (for weaker stimulation).

Synchronisation mechanisms of circadian rhythms in the suprachiasmatic nucleus

Abstract: In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. Each cell in the SCN contains an autonomous molecular clock, and the SCN is composed of multiple single-cell circadian oscillators. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to create an integrated pacemaker that can govern behavioural and physiological rhythmicity and be reset by environmental light. The key is that the heterogeneous network formed by the cellular clocks within the SCN must synchronise to maintain timekeeping activity. To study the synchronisation mechanisms and the circadian rhythm generation, we propose a model based on the structural and functional heterogeneity of the SCN. The model is a heterogeneous network of circadian oscillators in which individual oscillators are self-sustained. The authors show that the dorsomedial region can smooth the periodic light-dark (LD) signal curve and affect its wave form. The authors also study the rhythmic process of the circadian oscillators under the effect of the daily LD cycle, including three courses: information afferent inputs, oscillation and information efferent outputs. The numerical simulations are also given to demonstrate the theoretical results.

Inference of Boolean networks under constraint on bidirectional gene relationships.

Abstract: The coefficient of determination (CoD) has been used to infer Boolean networks (BNs) from steady-state data, in particular, to estimate the constituent BNs for a probabilistic BN. The advantage of the CoD method over design methods that emphasise graph topology or attractor structure is that the CoD produces a network based on strong predictive relationships between target genes and their predictor (parent) genes. The disadvantage is that spurious attractor cycles appear in the inferred network, so that there is poor inference relative to the attractor structure, that is, relative to the steady-state behaviour of the network. Given steady-state data, there should not be a significant amount of steady-state probability mass in the inferred network lying outside the mass of the data distribution; however, the existence of spurious attractor cycles creates a significant amount of steady-state probability mass not accounted for by the data. Using steady-state data hampers design because the lack of temporal data causes CoD design to suffer from a lack of directionality with regard to prediction. This results in spurious bidirectional relationships among genes in which two genes are among the predictors for each other, when actually only one of them should be a predictor of the other, thereby creating a spurious attractor cycle. This paper characterises the manner in which bidirectional relationships affect the attractor structure of a BN. Given this characterisation, the authors propose a constrained CoD inference algorithm that outperforms unconstrained CoD inference in avoiding the creation of spurious non-singleton attractor. Algorithm performances are compared using a melanoma-based network.