Experimental Design for Parameter Estimation of Gene Regulatory Networks

Both qualitative and quantitative model learning frameworks for biochemical systems have been studied in computational systems biology. In this research, after introducing two forms of pre-defined component patterns to represent biochemical models, we propose an integrative qualitative and quantitative modelling framework for inferring biochemical systems. In the proposed framework, interactions between reactants in the candidate models for a target biochemical system are evolved and eventually identified by the application of a qualitative model learning approach with an evolution strategy. Kinetic rates of the models generated from qualitative model learning are then further optimised by employing a quantitative approach with simulated annealing. Experimental results indicate that our proposed integrative framework is feasible to learn the relationships between biochemical reactants qualitatively and to make the model replicate the behaviours of the target system by optimising the kinetic rates quantitatively. Moreover, potential reactants of a target biochemical system can be discovered by hypothesising complex reactants in the synthetic models. Based on the biochemical models learned from the proposed framework, biologists can further perform experimental study in wet laboratory. In this way, natural biochemical systems can be better understood.

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

Mathematical models in systems biology can use quantitative techniques to study the integrated behaviors of biological systems in macro level. Agent-based modeling provides a qualitative framework, focusing on how each individual molecule behaves in micro level. We are motivated to combine their features together to describe the gene regulatory networks, in particular the emergence of macro phenomena from micro interactions. An agent-based model will be well defined as general as possible, including of many agents of various molecular species interacting in it. The mathematical premises, which are grounded in the micro behaviors of agents, can derive the chemical master equations and the stochastic differential equations for modeling the integrated behaviors of systems in macro level. Combing agent-based models with stochastic differential equations affords a more complete perspective on gent regulatory networks. In addition, the sources and magnitudes of deterministic dynamics and random noises are explicitly characterized.

BackgroundAn accurate understanding of interactions among genes plays a major role in developing therapeutic intervention methods. Gene regulatory networks often contain a significant amount of uncertainty. The process of prioritizing biological experiments to reduce the uncertainty of gene regulatory networks is called experimental design. Under such a strategy, the experiments with high priority are suggested to be conducted first.ResultsThe authors have already proposed an optimal experimental design method based upon the objective for modeling gene regulatory networks, such as deriving therapeutic interventions. The experimental design method utilizes the concept of mean objective cost of uncertainty (MOCU). MOCU quantifies the expected increase of cost resulting from uncertainty. The optimal experiment to be conducted first is the one which leads to the minimum expected remaining MOCU subsequent to the experiment. In the process, one must find the optimal intervention for every gene regulatory network compatible with the prior knowledge, which can be prohibitively expensive when the size of the network is large. In this paper, we propose a computationally efficient experimental design method. This method incorporates a network reduction scheme by introducing a novel cost function that takes into account the disruption in the ranking of potential experiments. We then estimate the approximate expected remaining MOCU at a lower computational cost using the reduced networks.ConclusionsSimulation results based on synthetic and real gene regulatory networks show that the proposed approximate method has close performance to that of the optimal method but at lower computational cost. The proposed approximate method also outperforms the random selection policy significantly. A MATLAB software implementing the proposed experimental design method is available at http://gsp.tamu.edu/Publications/supplementary/roozbeh15a/.

The exploding number of computational models produced by Systems Biologists over the last years is an invitation to structure and exploit this new wealth of information. Researchers would like to trace models relevant to specific scientific questions, to explore their biological content, to align and combine them, and to match them with experimental data. To automate these processes, it is essential to consider semantic annotations, which describe their biological meaning. As a prerequisite for a wide range of computational methods, we propose general and flexible similarity measures for Systems Biology models computed from semantic annotations. By using these measures and a large extensible ontology, we implement a platform that can retrieve, cluster, and align Systems Biology models and experimental data sets. At present, its major application is the search for relevant models in the BioModels Database, starting from initial models, data sets, or lists of biological concepts. Beyond similarity searches, the representation of models by semantic feature vectors may pave the way for visualisation, exploration, and statistical analysis of large collections of models and corresponding data.

This chapter examines experimental design considerations for a population-based approach for identifying microorganisms involved in specific in situ functions. Although this chapter focuses on a particular population-based approach, many of the experimental design considerations discussed here apply to a wide range of rRNA gene-based population studies and sequence selective PCR assays. This chapter examines an experimental approach that uses the population-based strategy. The approach has the following three phases: (i) identifying populations of rRNA genes whose abundances correlate with the functional parameter, (ii) validating the rRNA gene correlates identified in phase I by using an independent quantitative assay, and (iii) isolating the microorganisms identified by the rRNA gene correlates and reintroducing them into the environment to assess their functions in situ. This approach was recently used to identify microorganisms that suppress the population development of the plant parasitic nematode Heterodera schachtii in southern California soil. Functional gradients are created by manipulating the microbial community with methods such as differential heat treatments, targeted antimicrobial agents, and nutritional amendments. Microbial community composition is examined by rRNA gene analysis. Nucleotide sequence analysis of rRNA gene clone libraries can be used to generate detailed depictions of microbial community composition. PCR assays can be validated by using them to amplify DNAs extracted from different environmental samples and then cloning and sequencing several randomly selected clones from each sample. The assays can be considered selective if they exclusively amplify the target sequence.

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

Calcific aortic valve disease (CAVD) arises from coupled interactions between blood flow, tissue mechanics, and cellular signaling. Hemodynamic forces influence endothelial and interstitial cell behavior, while the resulting tissue remodeling alters valve motion and flow patterns. Capturing this two-way feedback requires models that integrate fluid-structure mechanics with biochemical regulation, yet such multiscale coupling remains technically challenging. Previous computational models have focused on isolated aspects of the disease: fluid-structure interaction (FSI) simulations reproduce valve deformation and flow, and systems biology (SB) models describe molecular signaling that drives fibrosis and calcification. However, without coupling, these approaches cannot predict how mechanical dysfunction initiates biochemical remodeling or how biochemical changes feed back on mechanics. Here, we present a multi-physics computational framework that couples three-dimensional FSI simulations of aortic valve dynamics with a mechanistic SB model of calcification signaling. The FSI module resolves pulsatile blood flow and leaflet deformation, yielding local wall shear stresses and tissue strains throughout the cardiac cycle. These mechanical quantities are used as inputs to the SB module, which represents key biochemical pathways governing inflammation, TGF- β /SMAD signaling, and nitric-oxide (NO)-mediated inhibition within valvular cells. Simulations predict long-term calcification trajectories for valves of varying thickness, showing that fibrosis-induced stiffening lowers shear stress, reduces NO synthesis, and enhances TGF- β activation, thereby accelerating calcification. The framework is modular and extensible, allowing future incorporation of additional pathways, as well as implementation of full two-way coupling between the FSI and SB models. By integrating physics-based hemodynamics with systems-level biochemistry, this study provides a proof-of-principle demonstration of a next-generation, multi-scale modeling platform for studying cardiovascular disease that unites blood flow dynamics and biochemical signaling.

Cellular decision making is the process whereby cells choose one developmental pathway from multiple possible ones, either spontaneously or due to environmental stimuli. Examples in various cell types suggest an almost inexhaustible plethora of underlying molecular mechanisms. In general, cellular decisions rely on the gene regulatory network, which integrates external signals to drive cell fate choice. The search for general principles of such a process benefits from appropriate biological model systems that reveal how and why certain gene regulatory mechanisms drive specific cellular decisions according to ecological context and evolutionary outcomes. In this article, we review the historical and ongoing development of the phage lambda lysis-lysogeny decision as a model system to investigate all aspects of cellular decision making. The unique generality, simplicity, and richness of phage lambda decision making render it a constant source ofmathematical modeling-aided inspiration across all of biology. We discuss the origins and progress of quantitative phage lambda modeling from the 1950s until today, as well as its possible future directions. We provide examples of how modeling enabled methods and theory development, leading to new biological insights by revealing gaps in the theory and pinpointing areas requiring further experimental investigation. Overall, we highlight the utility of theoretical approaches both as predictive tools, to forecast the outcome of novel experiments, and as explanatory tools, to elucidate the natural processes underlying experimental data.

Inferring transcriptional gene regulatory networks from transcriptomic datasets is a key challenge of systems biology, with potential impacts ranging from medicine to agronomy. There are several techniques used presently to experimentally assay transcription factors to target relationships, defining important information about real gene regulatory networks connections. These techniques include classical ChIP-seq, yeast one-hybrid, or more recently, DAP-seq or target technologies. These techniques are usually used to validate algorithm predictions. Here, we developed a reverse engineering approach based on mathematical and computer simulation to evaluate the impact that this prior knowledge on gene regulatory networks may have on training machine learning algorithms. First, we developed a gene regulatory networks-simulating engine called FRANK (Fast Randomizing Algorithm for Network Knowledge) that is able to simulate large gene regulatory networks (containing 104 genes) with characteristics of gene regulatory networks observed in vivo. FRANK also generates stable or oscillatory gene expression directly produced by the simulated gene regulatory networks. The development of FRANK leads to important general conclusions concerning the design of large and stable gene regulatory networks harboring scale free properties (built ex nihilo). In combination with supervised (accepting prior knowledge) support vector machine algorithm we (i) address biologically oriented questions concerning our capacity to accurately reconstruct gene regulatory networks and in particular we demonstrate that prior-knowledge structure is crucial for accurate learning, and (ii) draw conclusions to inform experimental design to performed learning able to solve gene regulatory networks in the future. By demonstrating that our predictions concerning the influence of the prior-knowledge structure on support vector machine learning capacity holds true on real data (Escherichia coli K14 network reconstruction using network and transcriptomic data), we show that the formalism used to build FRANK can to some extent be a reasonable model for gene regulatory networks in real cells.

The instructional lab setting has been found to be dominated by prescribed tasks and pre-prepared lab kits. This was explained by teachers’ need to guide students to simultaneously progress through a lab curriculum, which prompts them to standardize the lab experience. Nevertheless, prominent professional associations have persistently called to better represent experimental research practices in the lab, and to grant students more agency in the experimental process by orienting them towards more open-ended lab experiences. This paper reports a lab activity designed to advance students’ agency in the practice of experimental design, in a setting governed by a high-stakes national matriculation exam. Three hundred teachers of advanced level high-school physics experienced the lab activity in a national network of professional learning communities (PLCs). The activity was anchored in an experiment to determine the relationship between the current through a battery and its terminal voltage. It was designed to problematize students’ considerations underlying the choices of the location of the voltmeter and the measuring scale of the ammeter, and the possible implications for the validity of the experimental results; e.g. control of the variables, as well as the range and the accuracy of measurements. Teachers first performed the lab activity as learners, discussed it in the PLC meeting, and finally reflected on their experience. Individual responses to the lab worksheets and the reflections were analyzed. Initially, teachers’ considerations did not portray key aspects related to the validity of the experimental results, such as how design choices related to the location of the voltmeter and the ammeter measuring scale impacted the accuracy and range of the measurements and the control of variables. The teachers were highly engaged in the peer discussion in the PLC and found the lab activity valuable in raising students’ awareness of important considerations in experimental design.

BackgroundSignal transduction is the major mechanism through which cells transmit external stimuli to evoke intracellular biochemical responses. Diverse cellular stimuli create a wide variety of transcription factor activities through signal transduction pathways, resulting in different gene expression patterns. Understanding the relationship between external stimuli and the corresponding cellular responses, as well as the subsequent effects on downstream genes, is a major challenge in systems biology. Thus, a systematic approach is needed to integrate experimental data and theoretical hypotheses to identify the physiological consequences of environmental stimuli.ResultsWe proposed a systematic approach that combines forward and reverse engineering to link the signal transduction cascade with the gene responses. To demonstrate the feasibility of our strategy, we focused on linking the NF-κB signaling pathway with the inflammatory gene regulatory responses because NF-κB has long been recognized to play a crucial role in inflammation. We first utilized forward engineering (Hybrid Functional Petri Nets) to construct the NF-κB signaling pathway and reverse engineering (Network Components Analysis) to build a gene regulatory network (GRN). Then, we demonstrated that the corresponding IKK profiles can be identified in the GRN and are consistent with the experimental validation of the IKK kinase assay. We found that the time-lapse gene expression of several cytokines and chemokines (TNF-α, IL-1, IL-6, CXCL1, CXCL2 and CCL3) is concordant with the NF-κB activity profile, and these genes have stronger influence strength within the GRN. Such regulatory effects have highlighted the crucial roles of NF-κB signaling in the acute inflammatory response and enhance our understanding of the systemic inflammatory response syndrome.ConclusionWe successfully identified and distinguished the corresponding signaling profiles among three microarray datasets with different stimuli strengths. In our model, the crucial genes of the NF-κB regulatory network were also identified to reflect the biological consequences of inflammation. With the experimental validation, our strategy is thus an effective solution to decipher cross-talk effects when attempting to integrate new kinetic parameters from other signal transduction pathways. The strategy also provides new insight for systems biology modeling to link any signal transduction pathways with the responses of downstream genes of interest.

Inferring gene regulatory networks (GRNs) from microarray expression data are an important but challenging issue in systems biology. In this study, the authors propose a Bayesian information criterion (BIC)-guided sparse regression approach for GRN reconstruction. This approach can adaptively model GRNs by optimising the l1-norm regularisation of sparse regression based on a modified version of BIC. The use of the regularisation strategy ensures the inferred GRNs to be as sparse as natural, while the modified BIC allows incorporating prior knowledge on expression regulation and thus avoids the overestimation of expression regulators as usual. Especially, the proposed method provides a clear interpretation of combinatorial regulations of gene expression by optimally extracting regulation coordination for a given target gene. Experimental results on both simulation data and real-world microarray data demonstrate the competent performance of discovering regulatory relationships in GRN reconstruction.

BackgroundInference of Gene Regulatory Networks (GRNs) is a difficult and long-standing question in Systems Biology. Numerous approaches have been proposed with the latest methods exploring the richness of single-cell data. One of the current difficulties lies in the fact that many methods of GRN inference do not result in one proposed GRN but in a collection of plausible networks that need to be further refined. In this work, we present a Design of Experiment strategy to use as a second stage after the inference process. It is specifically fitted for identifying the next most informative experiment to perform for deciding between multiple network topologies, in the case where proposed GRNs are executable models. This strategy first performs a topological analysis to reduce the number of perturbations that need to be tested, then predicts the outcome of the retained perturbations by simulation of the GRNs and finally compares predictions with novel experimental data.ResultsWe apply this method to the results of our divide-and-conquer algorithm called WASABI, adapt its gene expression model to produce perturbations and compare our predictions with experimental results. We show that our networks were able to produce in silico predictions on the outcome of a gene knock-out, which were qualitatively validated for 48 out of 49 genes. Finally, we eliminate as many as two thirds of the candidate networks for which we could identify an incorrect topology, thus greatly improving the accuracy of our predictions.ConclusionThese results both confirm the inference accuracy of WASABI and show how executable gene expression models can be leveraged to further refine the topology of inferred GRNs. We hope this strategy will help systems biologists further explore their data and encourage the development of more executable GRN models.

Application of system theory in biology has led to development of computer languages for mathematical modeling which are in open source and apply common standards for model trans-platform exchangeability and integration with extensive model banks, databases, numerical and statistical methods and graphical tools. Standardization has led to Systems Biology Markup Language (SBML) based on XML format, while open source policy enables integration of computer resources and provides synergistic integration of scientific results and methodologies from various scientific fields. Different software projects have been initiated resulting in software such as: SBToolbox, JDesigner, SBWorkbench (SBW), and CellDesigner. The main use of the systems biology software is to investigate biochemical networks, gene regulatory networks, signal transduction, cell communication, dynamical complex behavior, and most importantly to lead to understanding of life regulation. In this work is presented use of Systems Biology Markup Language and modeling tools applied for analysis of signal transduction in T-cell as a part of a human immune system.