Reconstructing nonlinear dynamic models of gene regulation using stochastic sampling

Transcriptional Response in Human Jurkat T Lymphocytes to a near Physiological Hypergravity Environment and to One Common in Routine Cell Culture Protocols

Cellular effects of hypergravity have been described in many studies. We investigated the transcriptional dynamics in Jurkat T cells between 20 s and 60 min of 9 g hypergravity and characterized a highly dynamic biphasic time course of gene expression response with a transition point between rapid adaptation and long-term response at approximately 7 min. Upregulated genes were shifted towards the center of the nuclei, whereby downregulated genes were shifted towards the periphery. Upregulated gene expression was mostly located on chromosomes 16-22. Protein-coding transcripts formed the majority with more than 90% of all differentially expressed genes and followed a continuous trend of downregulation, whereas retained introns demonstrated a biphasic time-course. The gene expression pattern of hypergravity response was not comparable with other stress factors such as oxidative stress, heat shock or inflammation. Furthermore, we tested a routine centrifugation protocol that is widely used to harvest cells for subsequent RNA analysis and detected a huge impact on the transcriptome compared to non-centrifuged samples, which did not return to baseline within 15 min. Thus, we recommend carefully studying the response of any cell types used for any experiments regarding the hypergravity time and levels applied during cell culture procedures and analysis.

NoLiTiA: An Open-Source Toolbox for Non-linear Time Series Analysis

In many scientific fields including neuroscience, climatology or physics, complex relationships can be described most parsimoniously by non-linear mechanics. Despite their relevance, many neuroscientists still apply linear estimates in order to evaluate complex interactions. This is partially due to the lack of a comprehensive compilation of non-linear methods. Available packages mostly specialize in only one aspect of non-linear time-series analysis and most often require some coding proficiency to use. Here, we introduce NoLiTiA, a free open-source MATLAB toolbox for non-linear time series analysis. In comparison to other currently available non-linear packages, NoLiTiA offers (1) an implementation of a broad range of classic and recently developed methods, (2) an implementation of newly proposed spatially and time-resolved recurrence amplitude analysis and (3) an intuitive environment accessible even to users with little coding experience due to a graphical user interface and batch-editor. The core methodology derives from three distinct fields of complex systems theory, including dynamical systems theory, recurrence quantification analysis and information theory. Besides established methodology including estimation of dynamic invariants like Lyapunov exponents and entropy-based measures, such as active information storage, we include recent developments of quantifying time-resolved aperiodic oscillations. In general, the toolbox will make non-linear methods accessible to the broad neuroscientific community engaged in time series processing.

Parametric and non-parametric gradient matching for network inference: a comparison

Background

Reverse engineering of gene regulatory networks from time series gene-expression data is a challenging problem, not only because of the vast sets of candidate interactions but also due to the stochastic nature of gene expression. We limit our analysis to nonlinear differential equation based inference methods. In order to avoid the computational cost of large-scale simulations, a two-step Gaussian process interpolation based gradient matching approach has been proposed to solve differential equations approximately.

Results

We apply a gradient matching inference approach to a large number of candidate models, including parametric differential equations or their corresponding non-parametric representations, we evaluate the network inference performance under various settings for different inference objectives. We use model averaging, based on the Bayesian Information Criterion (BIC), to combine the different inferences. The performance of different inference approaches is evaluated using area under the precision-recall curves.

Conclusions

We found that parametric methods can provide comparable, and often improved inference compared to non-parametric methods; the latter, however, require no kinetic information and are computationally more efficient.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2590-7) contains supplementary material, which is available to authorized users.

Inference of gene networks from gene expression time series using recurrent neural networks and sparse MAP estimation

BACKGROUND

The inference of genetic regulatory networks (GRNs) provides insight into the cellular responses to signals. A class of recurrent neural networks (RNNs) capturing the dynamics of GRN has been used as a basis for inferring small-scale GRNs from gene expression time series. The Bayesian framework facilitates incorporating the hypothesis of GRN into the model estimation to improve the accuracy of GRN inference.

RESULTS

We present new methods for inferring small-scale GRNs based on RNNs. The weights of wires of RNN represent the strengths of gene-to-gene regulatory interactions. We use a class of automatic relevance determination (ARD) priors to enforce the sparsity in the maximum a posteriori (MAP) estimates of wire weights of RNN. A particle swarm optimization (PSO) is integrated as an optimization engine into the MAP estimation process. Likely networks of genes generated based on estimated wire weights are combined using the majority rule to determine a final estimated GRN. As an alternative, a class of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -norm ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> ) priors is used for attaining the sparse MAP estimates of wire weights of RNN. We also infer the GRN using the maximum likelihood (ML) estimates of wire weights of RNN. The RNN-based GRN inference algorithms, ARD-RNN, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -RNN, and ML-RNN are tested on simulated and experimental E. coli and yeast time series containing 6-11 genes and 7-19 data points. Published GRN inference algorithms based on regressions and mutual information networks are performed on the benchmark datasets to compare performances.

CONCLUSION

ARD and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -norm priors are used for the estimation of wire weights of RNN. Results of GRN inference experiments show that ARD-RNN, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -RNN have similar best accuracies on the simulated time series. The ARD-RNN is more accurate than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -RNN, ML-RNN, and mostly more accurate than the reference algorithms on the experimental time series. The effectiveness of ARD-RNN for inferring small-scale GRNs using gene expression time series of limited length is empirically verified.

Construction of Signaling Pathways with RNAi Data and Multiple Reference Networks

Signaling networks are involved in almost all major diseases such as cancer. As a result of this, understanding how signaling networks function is vital for finding new treatments for many diseases. Using gene knockdown assays such as RNA interference (RNAi) technology, many genes involved in these networks can be identified. However, determining the interactions between these genes in the signaling networks using only experimental techniques is very challenging, as performing extensive experiments is very expensive and sometimes, even impractical. Construction of signaling networks from RNAi data using computational techniques have been proposed as an alternative way to solve this challenging problem. However, the earlier approaches are either not scalable to large scale networks, or their accuracy levels are not satisfactory. In this study, we integrate RNAi data given on a target network with multiple reference signaling networks and phylogenetic trees to construct the topology of the target signaling network. In our work, the network construction is considered as finding the minimum number of edit operations on given multiple reference networks, in which their contributions are weighted by their phylogenetic distances to the target network. The edit operations on the reference networks lead to a target network that satisfies the RNAi knockdown observations. Here, we propose two new reference-based signaling network construction methods that provide optimal results and scale well to large-scale signaling networks of hundreds of components. We compare the performance of these approaches to the state-of-the-art reference-based network construction method SiNeC on synthetic, semi-synthetic, and real datasets. Our analyses show that the proposed methods outperform SiNeC method in terms of accuracy. Furthermore, we show that our methods function well even if evolutionarily distant reference networks are used. Application of our methods to the Apoptosis and Wnt signaling pathways recovers the known protein-protein interactions and suggests additional relevant interactions that can be tested experimentally.

Reconstructing Genetic Regulatory Networks Using Two-Step Algorithms with the Differential Equation Models of Neural Networks

BACKGROUND

The identification of genetic regulatory networks (GRNs) provides insights into complex cellular processes. A class of recurrent neural networks (RNNs) captures the dynamics of GRN. Algorithms combining the RNN and machine learning schemes were proposed to reconstruct small-scale GRNs using gene expression time series.

RESULTS

We present new GRN reconstruction methods with neural networks. The RNN is extended to a class of recurrent multilayer perceptrons (RMLPs) with latent nodes. Our methods contain two steps: the edge rank assignment step and the network construction step. The former assigns ranks to all possible edges by a recursive procedure based on the estimated weights of wires of RNN/RMLP (RE_RNN/RE_RMLP), and the latter constructs a network consisting of top-ranked edges under which the optimized RNN simulates the gene expression time series. The particle swarm optimization (PSO) is applied to optimize the parameters of RNNs and RMLPs in a two-step algorithm. The proposed RE_RNN-RNN and RE_RMLP-RNN algorithms are tested on synthetic and experimental gene expression time series of small GRNs of about 10 genes. The experimental time series are from the studies of yeast cell cycle regulated genes and E. coli DNA repair genes.

CONCLUSION

The unstable estimation of RNN using experimental time series having limited data points can lead to fairly arbitrary predicted GRNs. Our methods incorporate RNN and RMLP into a two-step structure learning procedure. Results show that the RE_RMLP using the RMLP with a suitable number of latent nodes to reduce the parameter dimension often result in more accurate edge ranks than the RE_RNN using the regularized RNN on short simulated time series. Combining by a weighted majority voting rule the networks derived by the RE_RMLP-RNN using different numbers of latent nodes in step one to infer the GRN, the method performs consistently and outperforms published algorithms for GRN reconstruction on most benchmark time series. The framework of two-step algorithms can potentially incorporate with different nonlinear differential equation models to reconstruct the GRN.

Using Sub-Network Combinations to Scale Up an Enumeration Method for Determining the Network Structures of Biological Functions

Deduction of biological regulatory networks from their functions is one of the focus areas of systems biology. Among the different techniques used in this reverse-engineering task, one powerful method is to enumerate all candidate network structures to find suitable ones. However, this method is severely limited by calculation capability: due to the brute-force approach, it is infeasible for networks with large number of nodes to be studied using traditional enumeration method because of the combinatorial explosion. In this study, we propose a new reverse-engineering technique based on the enumerating method: sub-network combinations. First, a complex biological function is divided into several sub-functions. Next, the three-node-network enumerating method is applied to search for sub-networks that are able to realize each of the sub-functions. Finally, complex whole networks are constructed by enumerating all possible combinations of sub-networks. The optimal ones are selected and analyzed. To demonstrate the effectiveness of this new method, we used it to deduct the network structures of a Pavlovian-like function. The whole Pavlovian-like network was successfully constructed by combining robust sub-networks, and the results were analyzed. With sub-network combination, the complexity has been largely reduced. Our method also provides a functional modular view of biological systems.

The Local Edge Machine: inference of dynamic models of gene regulation

We present a novel approach, the Local Edge Machine, for the inference of regulatory interactions directly from time-series gene expression data. We demonstrate its performance, robustness, and scalability on in silico datasets with varying behaviors, sizes, and degrees of complexity. Moreover, we demonstrate its ability to incorporate biological prior information and make informative predictions on a well-characterized in vivo system using data from budding yeast that have been synchronized in the cell cycle. Finally, we use an atlas of transcription data in a mammalian circadian system to illustrate how the method can be used for discovery in the context of large complex networks.

Identifying the topology of signaling networks from partial RNAi data

Background

Methods for inferring signaling networks using single gene knockdown RNAi experiments and reference networks have been proposed in recent years. These methods assume that RNAi information is available for all the genes in the signal transduction pathway, i.e., complete. This assumption does not always hold up since RNAi experiments are often incomplete and information for some genes is missing.

Results

In this article, we develop two methods to construct signaling networks from incomplete RNAi data with the help of a reference network. These methods infer the RNAi constraints for the missing genes such that the inferred network is closest to the reference network. We perform extensive experiments with both real and synthetic networks and demonstrate that these methods produce accurate results efficiently.

Conclusions

Application of our methods to Wnt signal transduction pathway has shown that our methods can be used to construct highly accurate signaling networks from experimental data in less than 100 ms. The two methods that produce accurate results efficiently show great promise of constructing real signaling networks.

Systems biology, emergence and antireductionism

This study explores the conceptual history of systems biology and its impact on philosophical and scientific conceptions of reductionism, antireductionism and emergence. Development of systems biology at the beginning of 21st century transformed biological science. Systems biology is a new holistic approach or strategy how to research biological organisms, developed through three phases. The first phase was completed when molecular biology transformed into systems molecular biology. Prior to the second phase, convergence between applied general systems theory and nonlinear dynamics took place, hence allowing the formation of systems mathematical biology. The second phase happened when systems molecular biology and systems mathematical biology, together, were applied for analysis of biological data. Finally, after successful application in science, medicine and biotechnology, the process of the formation of modern systems biology was completed.

Systems and molecular reductionist views on organisms were completely opposed to each other. Implications of systems and molecular biology on reductionist–antireductionist debate were quite different. The analysis of reductionism, antireductionism and emergence issues, in the era of systems biology, revealed the hierarchy between methodological, epistemological and ontological antireductionism. Primarily, methodological antireductionism followed from the systems biology. Only after, epistemological and ontological antireductionism could be supported.

Topological sensitivity analysis for systems biology

Mathematical models of natural systems are abstractions of much more complicated processes. Developing informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise, and a modicum of luck. Except for cases where physical principles provide sufficient guidance, it will also be generally possible to come up with a large number of potential models that are compatible with a given natural system and any finite amount of data generated from experiments on that system. Here we develop a computational framework to systematically evaluate potentially vast sets of candidate differential equation models in light of experimental and prior knowledge about biological systems. This topological sensitivity analysis enables us to evaluate quantitatively the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.

Dynamic probabilistic threshold networks to infer signaling pathways from time-course perturbation data

BACKGROUND

Network inference deals with the reconstruction of molecular networks from experimental data. Given N molecular species, the challenge is to find the underlying network. Due to data limitations, this typically is an ill-posed problem, and requires the integration of prior biological knowledge or strong regularization. We here focus on the situation when time-resolved measurements of a system's response after systematic perturbations are available.

RESULTS

We present a novel method to infer signaling networks from time-course perturbation data. We utilize dynamic Bayesian networks with probabilistic Boolean threshold functions to describe protein activation. The model posterior distribution is analyzed using evolutionary MCMC sampling and subsequent clustering, resulting in probability distributions over alternative networks. We evaluate our method on simulated data, and study its performance with respect to data set size and levels of noise. We then use our method to study EGF-mediated signaling in the ERBB pathway.

CONCLUSIONS

Dynamic Probabilistic Threshold Networks is a new method to infer signaling networks from time-series perturbation data. It exploits the dynamic response of a system after external perturbation for network reconstruction. On simulated data, we show that the approach outperforms current state of the art methods. On the ERBB data, our approach recovers a significant fraction of the known interactions, and predicts novel mechanisms in the ERBB pathway.

Review on statistical methods for gene network reconstruction using expression data

Network modeling has proven to be a fundamental tool in analyzing the inner workings of a cell. It has revolutionized our understanding of biological processes and made significant contributions to the discovery of disease biomarkers. Much effort has been devoted to reconstruct various types of biochemical networks using functional genomic datasets generated by high-throughput technologies. This paper discusses statistical methods used to reconstruct gene regulatory networks using gene expression data. In particular, we highlight progress made and challenges yet to be met in the problems involved in estimating gene interactions, inferring causality and modeling temporal changes of regulation behaviors. As rapid advances in technologies have made available diverse, large-scale genomic data, we also survey methods of incorporating all these additional data to achieve better, more accurate inference of gene networks.

Perturbation biology: inferring signaling networks in cellular systems

We present a powerful experimental-computational technology for inferring network models that predict the response of cells to perturbations, and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is quantified in terms of relative changes in the measured levels of proteins, phospho-proteins and cellular phenotypes such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, Belief Propagation (BP), which is three orders of magnitude faster than standard Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in SKMEL-133 melanoma cell lines, which are resistant to the therapeutically important inhibitor of RAF kinase. The resulting network models reproduce and extend known pathway biology. They empower potential discoveries of new molecular interactions and predict efficacious novel drug perturbations, such as the inhibition of PLK1, which is verified experimentally. This technology is suitable for application to larger systems in diverse areas of molecular biology.

Drugs that target specific effects of signaling proteins are promising agents for treating cancer. One of the many obstacles facing optimal drug design is inadequate quantitative understanding of the coordinated interactions between signaling proteins. De novo model inference of network or pathway models refers to the algorithmic construction of mathematical predictive models from experimental data without dependence on prior knowledge. De novo inference is difficult because of the prohibitively large number of possible sets of interactions that may or may not be consistent with observations. Our new method overcomes this difficulty by adapting a method from statistical physics, called Belief Propagation, which first calculates probabilistically the most likely interactions in the vast space of all possible solutions, then derives a set of individual, highly probable solutions in the form of executable models. In this paper, we test this method on artificial data and then apply it to model signaling pathways in a BRAF-mutant melanoma cancer cell line based on a large set of rich output measurements from a systematic set of perturbation experiments using drug combinations. Our results are in agreement with established biological knowledge, predict novel interactions, and predict efficacious drug targets that are specific to the experimental cell line and potentially to related tumors. The method has the potential, with sufficient systematic perturbation data, to model, de novo and quantitatively, the effects of hundreds of proteins on cellular responses, on a scale that is currently unreachable in diverse areas of cell biology. In a disease context, the method is applicable to the computational design of novel combination drug treatments.

Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information

The extended Kalman filter (EKF) has been applied to inferring gene regulatory networks. However, it is well known that the EKF becomes less accurate when the system exhibits high nonlinearity. In addition, certain prior information about the gene regulatory network exists in practice, and no systematic approach has been developed to incorporate such prior information into the Kalman-type filter for inferring the structure of the gene regulatory network. In this paper, an inference framework based on point-based Gaussian approximation filters that can exploit the prior information is developed to solve the gene regulatory network inference problem. Different point-based Gaussian approximation filters, including the unscented Kalman filter (UKF), the third-degree cubature Kalman filter (CKF₃), and the fifth-degree cubature Kalman filter (CKF₅) are employed. Several types of network prior information, including the existing network structure information, sparsity assumption, and the range constraint of parameters, are considered, and the corresponding filters incorporating the prior information are developed. Experiments on a synthetic network of eight genes and the yeast protein synthesis network of five genes are carried out to demonstrate the performance of the proposed framework. The results show that the proposed methods provide more accurate inference results than existing methods, such as the EKF and the traditional UKF.

Reconstruction of cellular signal transduction networks using perturbation assays and linear programming

Perturbation experiments for example using RNA interference (RNAi) offer an attractive way to elucidate gene function in a high throughput fashion. The placement of hit genes in their functional context and the inference of underlying networks from such data, however, are challenging tasks. One of the problems in network inference is the exponential number of possible network topologies for a given number of genes. Here, we introduce a novel mathematical approach to address this question. We formulate network inference as a linear optimization problem, which can be solved efficiently even for large-scale systems. We use simulated data to evaluate our approach, and show improved performance in particular on larger networks over state-of-the art methods. We achieve increased sensitivity and specificity, as well as a significant reduction in computing time. Furthermore, we show superior performance on noisy data. We then apply our approach to study the intracellular signaling of human primary nave CD4⁺ T-cells, as well as ErbB signaling in trastuzumab resistant breast cancer cells. In both cases, our approach recovers known interactions and points to additional relevant processes. In ErbB signaling, our results predict an important role of negative and positive feedback in controlling the cell cycle progression.

Hub-centered gene network reconstruction using automatic relevance determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data.

Integrated inference and analysis of regulatory networks from multi-level measurements

Regulatory and signaling networks coordinate the enormously complex interactions and processes that control cellular processes (such as metabolism and cell division), coordinate response to the environment, and carry out multiple cell decisions (such as development and quorum sensing). Regulatory network inference is the process of inferring these networks, traditionally from microarray data but increasingly incorporating other measurement types such as proteomics, ChIP-seq, metabolomics, and mass cytometry. We discuss existing techniques for network inference. We review in detail our pipeline, which consists of an initial biclustering step, designed to estimate co-regulated groups; a network inference step, designed to select and parameterize likely regulatory models for the control of the co-regulated groups from the biclustering step; and a visualization and analysis step, designed to find and communicate key features of the network. Learning biological networks from even the most complete data sets is challenging; we argue that integrating new data types into the inference pipeline produces networks of increased accuracy, validity, and biological relevance.

Global transcription regulation of RK2 plasmids: a case study in the combined use of dynamical mathematical models and statistical inference for integration of experimental data and hypothesis exploration

Background

IncP-1 plasmids are broad host range plasmids that have been found in clinical and environmental bacteria. They often carry genes for antibiotic resistance or catabolic pathways. The archetypal IncP-1 plasmid RK2 is a well-characterized biological system, with a fully sequenced and annotated genome and wide range of experimental measurements. Its central control operon, encoding two global regulators KorA and KorB, is a natural example of a negatively self-regulated operon. To increase our understanding of the regulation of this operon, we have constructed a dynamical mathematical model using Ordinary Differential Equations, and employed a Bayesian inference scheme, Markov Chain Monte Carlo (MCMC) using the Metropolis-Hastings algorithm, as a way of integrating experimental measurements and a priori knowledge. We also compared MCMC and Metabolic Control Analysis (MCA) as approaches for determining the sensitivity of model parameters.

Results

We identified two distinct sets of parameter values, with different biological interpretations, that fit and explain the experimental data. This allowed us to highlight the proportion of repressor protein as dimers as a key experimental measurement defining the dynamics of the system. Analysis of joint posterior distributions led to the identification of correlations between parameters for protein synthesis and partial repression by KorA or KorB dimers, indicating the necessary use of joint posteriors for correct parameter estimation. Using MCA, we demonstrated that the system is highly sensitive to the growth rate but insensitive to repressor monomerization rates in their selected value regions; the latter outcome was also confirmed by MCMC. Finally, by examining a series of different model refinements for partial repression by KorA or KorB dimers alone, we showed that a model including partial repression by KorA and KorB was most compatible with existing experimental data.

Conclusions

We have demonstrated that the combination of dynamical mathematical models with Bayesian inference is valuable in integrating diverse experimental data and identifying key determinants and parameters for the IncP-1 central control operon. Moreover, we have shown that Bayesian inference and MCA are complementary methods for identification of sensitive parameters. We propose that this demonstrates generic value in applying this combination of approaches to systems biology dynamical modelling.

Thermodynamically consistent Bayesian analysis of closed biochemical reaction systems

Background

Estimating the rate constants of a biochemical reaction system with known stoichiometry from noisy time series measurements of molecular concentrations is an important step for building predictive models of cellular function. Inference techniques currently available in the literature may produce rate constant values that defy necessary constraints imposed by the fundamental laws of thermodynamics. As a result, these techniques may lead to biochemical reaction systems whose concentration dynamics could not possibly occur in nature. Therefore, development of a thermodynamically consistent approach for estimating the rate constants of a biochemical reaction system is highly desirable.

Results

We introduce a Bayesian analysis approach for computing thermodynamically consistent estimates of the rate constants of a closed biochemical reaction system with known stoichiometry given experimental data. Our method employs an appropriately designed prior probability density function that effectively integrates fundamental biophysical and thermodynamic knowledge into the inference problem. Moreover, it takes into account experimental strategies for collecting informative observations of molecular concentrations through perturbations. The proposed method employs a maximization-expectation-maximization algorithm that provides thermodynamically feasible estimates of the rate constant values and computes appropriate measures of estimation accuracy. We demonstrate various aspects of the proposed method on synthetic data obtained by simulating a subset of a well-known model of the EGF/ERK signaling pathway, and examine its robustness under conditions that violate key assumptions. Software, coded in MATLAB^®, which implements all Bayesian analysis techniques discussed in this paper, is available free of charge at http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.html.

Conclusions

Our approach provides an attractive statistical methodology for estimating thermodynamically feasible values for the rate constants of a biochemical reaction system from noisy time series observations of molecular concentrations obtained through perturbations. The proposed technique is theoretically sound and computationally feasible, but restricted to quantitative data obtained from closed biochemical reaction systems. This necessitates development of similar techniques for estimating the rate constants of open biochemical reaction systems, which are more realistic models of cellular function.

Systematical detection of significant genes in microarray data by incorporating gene interaction relationship in biological systems

Many methods, including parametric, nonparametric, and Bayesian methods, have been used for detecting differentially expressed genes based on the assumption that biological systems are linear, which ignores the nonlinear characteristics of most biological systems. More importantly, those methods do not simultaneously consider means, variances, and high moments, resulting in relatively high false positive rate. To overcome the limitations, the SWang test is proposed to determine differentially expressed genes according to the equality of distributions between case and control. Our method not only latently incorporates functional relationships among genes to consider nonlinear biological system but also considers the mean, variance, skewness, and kurtosis of expression profiles simultaneously. To illustrate biological significance of high moments, we construct a nonlinear gene interaction model, demonstrating that skewness and kurtosis could contain useful information of function association among genes in microarrays. Simulations and real microarray results show that false positive rate of SWang is lower than currently popular methods (T-test, F-test, SAM, and Fold-change) with much higher statistical power. Additionally, SWang can uniquely detect significant genes in real microarray data with imperceptible differential expression but higher variety in kurtosis and skewness. Those identified genes were confirmed with previous published literature or RT-PCR experiments performed in our lab.

DREAM4: Combining genetic and dynamic information to identify biological networks and dynamical models

Background

Current technologies have lead to the availability of multiple genomic data types in sufficient quantity and quality to serve as a basis for automatic global network inference. Accordingly, there are currently a large variety of network inference methods that learn regulatory networks to varying degrees of detail. These methods have different strengths and weaknesses and thus can be complementary. However, combining different methods in a mutually reinforcing manner remains a challenge.

Methodology

We investigate how three scalable methods can be combined into a useful network inference pipeline. The first is a novel t-test–based method that relies on a comprehensive steady-state knock-out dataset to rank regulatory interactions. The remaining two are previously published mutual information and ordinary differential equation based methods (tlCLR and Inferelator 1.0, respectively) that use both time-series and steady-state data to rank regulatory interactions; the latter has the added advantage of also inferring dynamic models of gene regulation which can be used to predict the system's response to new perturbations.

Conclusion/Significance

Our t-test based method proved powerful at ranking regulatory interactions, tying for first out of methods in the DREAM4 100-gene in-silico network inference challenge. We demonstrate complementarity between this method and the two methods that take advantage of time-series data by combining the three into a pipeline whose ability to rank regulatory interactions is markedly improved compared to either method alone. Moreover, the pipeline is able to accurately predict the response of the system to new conditions (in this case new double knock-out genetic perturbations). Our evaluation of the performance of multiple methods for network inference suggests avenues for future methods development and provides simple considerations for genomic experimental design. Our code is publicly available at http://err.bio.nyu.edu/inferelator/.

The future of toxicity testing

In 2007, the U.S. National Research Council (NRC) released a report, "Toxicity Testing in the 21st Century: A Vision and a Strategy," that proposes a paradigm shift for toxicity testing of environmental agents. The vision is based on the notion that exposure to environmental agents leads to adverse health outcomes through the perturbation of toxicity pathways that are operative in humans. Implementation of the NRC vision will involve a fundamental change in the assessment of toxicity of environmental agents, moving away from adverse health outcomes observed in experimental animals to the identification of critical perturbations of toxicity pathways. Pathway perturbations will be identified using in vitro assays and quantified for dose response using methods in computational toxicology and other recent scientific advances in basic biology. Implementation of the NRC vision will require a major research effort, not unlike that required to successfully map the human genome, extending over 10 to 20 years, involving the broad scientific community to map important toxicity pathways operative in humans. This article provides an overview of the scientific tools and technologies that will form the core of the NRC vision for toxicity testing. Of particular importance will be the development of rapidly performed in vitro screening assays using human cells and cell lines or human tissue surrogates to efficiently identify environmental agents producing critical pathway perturbations. In addition to the overview of the NRC vision, this study documents the reaction by a number of stakeholder groups since 2007, including the scientific, risk assessment, regulatory, and animal welfare communities.