Parameter estimate of signal transduction pathways

Targeting the Cation-Chloride Co-Transporter NKCC1 to Re-Establish GABAergic Inhibition and an Appropriate Excitatory/Inhibitory Balance in Selective Neuronal Circuits: A Novel Approach for the Treatment of Alzheimer's Disease

GABA, the main inhibitory neurotransmitter in the adult brain, depolarizes and excites immature neurons because of an initially higher intracellular chloride concentration [Cl-]i due to the delayed expression of the chloride exporter KCC2 at birth. Depolarization-induced calcium rise via NMDA receptors and voltage-dependent calcium channels is instrumental in shaping neuronal circuits and in controlling the excitatory (E)/inhibitory (I) balance in selective brain areas. An E/I imbalance accounts for cognitive impairment observed in several neuropsychiatric disorders. The aim of this review is to summarize recent data on the mechanisms by which alterations of GABAergic signaling alter the E/I balance in cortical and hippocampal neurons in Alzheimer's disease (AD) and the role of cation-chloride co-transporters in this process. In particular, we discuss the NGF and AD relationship and how mice engineered to express recombinant neutralizing anti-NGF antibodies (AD11 mice), which develop a neurodegenerative pathology reminiscent of that observed in AD patients, exhibit a depolarizing action of GABA due to KCC2 impairment. Treating AD and other forms of dementia with bumetanide, a selective KCC2 antagonist, contributes to re-establishing a proper E/I balance in selective brain areas, leading to amelioration of AD symptoms and the slowing down of disease progression.

Petri Net computational modelling of Langerhans cell Interferon Regulatory Factor Network predicts their role in T cell activation

Langerhans cells (LCs) are able to orchestrate adaptive immune responses in the skin by interpreting the microenvironmental context in which they encounter foreign substances, but the regulatory basis for this has not been established. Utilising systems immunology approaches combining in silico modelling of a reconstructed gene regulatory network (GRN) with in vitro validation of the predictions, we sought to determine the mechanisms of regulation of immune responses in human primary LCs. The key role of Interferon regulatory factors (IRFs) as controllers of the human Langerhans cell response to epidermal cytokines was revealed by whole transcriptome analysis. Applying Boolean logic we assembled a Petri net-based model of the IRF-GRN which provides molecular pathway predictions for the induction of different transcriptional programmes in LCs. In silico simulations performed after model parameterisation with transcription factor expression values predicted that human LC activation of antigen-specific CD8 T cells would be differentially regulated by epidermal cytokine induction of specific IRF-controlled pathways. This was confirmed by in vitro measurement of IFN-γ production by activated T cells. As a proof of concept, this approach shows that stochastic modelling of a specific immune networks renders transcriptome data valuable for the prediction of functional outcomes of immune responses.

Mathematical and Computational Modeling in Complex Biological Systems

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

Combining in silico evolution and nonlinear dimensionality reduction to redesign responses of signaling networks

The rational design of network behavior is a central goal of synthetic biology. Here, we combine in silico evolution with nonlinear dimensionality reduction to redesign the responses of fixed-topology signaling networks and to characterize sets of kinetic parameters that underlie various input-output relations. We first consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm (EA) to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 orders of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. We also consider a network with both positive and negative feedback and use the EA to evolve oscillatory responses with different periods in response to a change in input. For each targeted input-output relation, we conduct many independent runs of the EA and use nonlinear dimensionality reduction to embed the resulting data for each network in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the cases considered, the network topologies exhibit significant flexibility in generating alternative responses, with distinct patterns of kinetic rates emerging for different targeted responses.

Analysis of Network Topologies Underlying Ethylene Growth Response Kinetics

Most models for ethylene signaling involve a linear pathway. However, measurements of seedling growth kinetics when ethylene is applied and removed have resulted in more complex network models that include coherent feedforward, negative feedback, and positive feedback motifs. The dynamical responses of the proposed networks have not been explored in a quantitative manner. Here, we explore (i) whether any of the proposed models are capable of producing growth-response behaviors consistent with experimental observations and (ii) what mechanistic roles various parts of the network topologies play in ethylene signaling. To address this, we used computational methods to explore two general network topologies: The first contains a coherent feedforward loop that inhibits growth and a negative feedback from growth onto itself (CFF/NFB). In the second, ethylene promotes the cleavage of EIN2, with the product of the cleavage inhibiting growth and promoting the production of EIN2 through a positive feedback loop (PFB). Since few network parameters for ethylene signaling are known in detail, we used an evolutionary algorithm to explore sets of parameters that produce behaviors similar to experimental growth response kinetics of both wildtype and mutant seedlings. We generated a library of parameter sets by independently running the evolutionary algorithm many times. Both network topologies produce behavior consistent with experimental observations, and analysis of the parameter sets allows us to identify important network interactions and parameter constraints. We additionally screened these parameter sets for growth recovery in the presence of sub-saturating ethylene doses, which is an experimentally-observed property that emerges in some of the evolved parameter sets. Finally, we probed simplified networks maintaining key features of the CFF/NFB and PFB topologies. From this, we verified observations drawn from the larger networks about mechanisms underlying ethylene signaling. Analysis of each network topology results in predictions about changes that occur in network components that can be experimentally tested to give insights into which, if either, network underlies ethylene responses.

An improved constraint filtering technique for inferring hidden states and parameters of a biological model

MOTIVATION

In systems biology, kinetic models represent the biological system using a set of ordinary differential equations (ODEs). The correct values of the parameters within these ODEs are critical for a reliable study of the dynamic behaviour of such systems. Typically, it is only possible to experimentally measure a fraction of these parameter values. The rest must be indirectly determined from measurements of other quantities. In this article, we propose a novel statistical inference technique to computationally estimate these unknown parameter values. By characterizing the ODEs with non-linear state-space equations, this inference technique models the unknown parameters as hidden states, which can then be estimated from noisy measurement data.

RESULTS

Here we extended the square-root unscented Kalman filter SR-UKF proposed by Merwe and Wan to include constraints with the state estimation process. We developed the constrained square-root unscented Kalman filter (CSUKF) to estimate parameters of non-linear state-space models. This probabilistic inference technique was successfully used to estimate parameters of a glycolysis model in yeast and a gene regulatory network. We showed that our method is numerically stable and can reliably estimate parameters within a biologically meaningful parameter space from noisy observations. When compared with the two common non-linear extensions of Kalman filter in addition to four widely used global optimization algorithms, CSUKF is shown to be both accurate and computationally efficient. With CSUKF, statistical analysis is straightforward, as it directly provides the uncertainty on the estimation result.

AVAILABILITY AND IMPLEMENTATION

Matlab code available upon request from the author.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Static network structure can be used to model the phenotypic effects of perturbations in regulatory networks

MOTIVATION

Biological processes are dynamic, whereas the networks that depict them are typically static. Quantitative modeling using differential equations or logic-based functions can offer quantitative predictions of the behavior of biological systems, but they require detailed experimental characterization of interaction kinetics, which is typically unavailable. To determine to what extent complex biological processes can be modeled and analyzed using only the static structure of the network (i.e. the direction and sign of the edges), we attempt to predict the phenotypic effect of perturbations in biological networks from the static network structure.

RESULTS

We analyzed three networks from different sources: The EGFR/MAPK and PI3K/AKT network from a detailed experimental study, the TNF regulatory network from the STRING database and a large network of all NCI-curated pathways from the Protein Interaction Database. Altogether, we predicted the effect of 39 perturbations (e.g. by one or two drugs) on 433 target proteins/genes. In up to 82% of the cases, an algorithm that used only the static structure of the network correctly predicted whether any given protein/gene is upregulated or downregulated as a result of perturbations of other proteins/genes.

CONCLUSION

While quantitative modeling requires detailed experimental data and heavy computations, which limit its scalability for large networks, a wiring-based approach can use available data from pathway and interaction databases and may be scalable. These results lay the foundations for a large-scale approach of predicting phenotypes based on the schematic structure of networks.

Parameter estimation using meta-heuristics in systems biology: a comprehensive review

This paper gives a comprehensive review of the application of meta-heuristics to optimization problems in systems biology, mainly focussing on the parameter estimation problem (also called the inverse problem or model calibration). It is intended for either the system biologist who wishes to learn more about the various optimization techniques available and/or the meta-heuristic optimizer who is interested in applying such techniques to problems in systems biology. First, the parameter estimation problems emerging from different areas of systems biology are described from the point of view of machine learning. Brief descriptions of various meta-heuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying meta-heuristics to the systems biology modelling problem are addressed, including the reliability and identifiability of model parameters, optimal design of experiments, and so on. Finally, we highlight some possible future research directions in this field.

Identification of a model of non-esterified fatty acids dynamics through genetic algorithms: the case of women with a history of gestational diabetes

Elevation in non-esterified fatty acids (NEFA) has been shown to modulate insulin secretion and it is considered as a risk factor for the development of type 2 diabetes. Here we present a method that complements a mathematical model of NEFA kinetics with genetic algorithms for model identification. The complemented strategy allowed to assess parameters of NEFA kinetics and to get insight into their relationship with insulin during oral glucose tolerance tests in women with former gestational diabetes: (i) providing a reliable estimation of the model parameters, (ii) assuring the usability of the model, and (iii) promoting and facilitating its application in a clinical context.

A genetic algorithm-based Boolean delay model of intracellular signal transduction in inflammation

Background

Signal transduction is the major mechanism through which cells transmit external stimuli to evoke intracellular biochemical responses. Understanding relationship between external stimuli and corresponding cellular responses, as well as the subsequent effects on downstream genes, is a major challenge in systems biology. Thus, a systematic approach to integrate experimental data and qualitative knowledge to identify the physiological consequences of environmental stimuli is needed.

Results

In present study, we employed a genetic algorithm-based Boolean model to represent NF-κB signaling pathway. We were able to capture feedback and crosstalk characteristics to enhance our understanding on the acute and chronic inflammatory response. Key network components affecting the response dynamics were identified.

Conclusions

We designed an effective algorithm to elucidate the process of immune response using comprehensive knowledge about network structure and limited experimental data on dynamic responses. This approach can potentially be implemented for large-scale analysis on cellular processes and organism behaviors.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

The signaling petri net-based simulator: a non-parametric strategy for characterizing the dynamics of cell-specific signaling networks

Reconstructing cellular signaling networks and understanding how they work are major endeavors in cell biology. The scale and complexity of these networks, however, render their analysis using experimental biology approaches alone very challenging. As a result, computational methods have been developed and combined with experimental biology approaches, producing powerful tools for the analysis of these networks. These computational methods mostly fall on either end of a spectrum of model parameterization. On one end is a class of structural network analysis methods; these typically use the network connectivity alone to generate hypotheses about global properties. On the other end is a class of dynamic network analysis methods; these use, in addition to the connectivity, kinetic parameters of the biochemical reactions to predict the network's dynamic behavior. These predictions provide detailed insights into the properties that determine aspects of the network's structure and behavior. However, the difficulty of obtaining numerical values of kinetic parameters is widely recognized to limit the applicability of this latter class of methods. Several researchers have observed that the connectivity of a network alone can provide significant insights into its dynamics. Motivated by this fundamental observation, we present the signaling Petri net, a non-parametric model of cellular signaling networks, and the signaling Petri net-based simulator, a Petri net execution strategy for characterizing the dynamics of signal flow through a signaling network using token distribution and sampling. The result is a very fast method, which can analyze large-scale networks, and provide insights into the trends of molecules' activity-levels in response to an external stimulus, based solely on the network's connectivity. We have implemented the signaling Petri net-based simulator in the PathwayOracle toolkit, which is publicly available at http://bioinfo.cs.rice.edu/pathwayoracle. Using this method, we studied a MAPK1,2 and AKT signaling network downstream from EGFR in two breast tumor cell lines. We analyzed, both experimentally and computationally, the activity level of several molecules in response to a targeted manipulation of TSC2 and mTOR-Raptor. The results from our method agreed with experimental results in greater than 90% of the cases considered, and in those where they did not agree, our approach provided valuable insights into discrepancies between known network connectivities and experimental observations.