Parameter estimation in systems biology models using spline approximation

Background  

Mathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and is still one of the most challenging tasks. Many parameter estimation methods have been developed but none of these methods is effective for all cases and can overwhelm all other approaches. Instead, various methods have their advantages and disadvantages. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints.     

Validation of gene regulatory networks: scientific and inferential

Gene regulatory network models are a major area of study in systems and computational biology and the construction of network models is among the most important problems in these disciplines. The critical epistemological issue concerns validation. Validity can be approached from two different perspectives (i) given a hypothesized network model, its scientific validity relates to the ability to make predictions from the model that can be checked against experimental observations; and (ii) the validity of a network inference procedure must be evaluated relative to its ability to infer a network from sample points generated by the network. This article examines both perspectives in the framework of a distance function between two networks. It considers some of the obstacles to validation and provides examples of both validation paradigms.     

Verification, validation and sensitivity studies in computational biomechanics

Computational techniques and software for the analysis of problems in mechanics have naturally moved from their origins in the traditional engineering disciplines to the study of cell, tissue and organ biomechanics. Increasingly complex models have been developed to describe and predict the mechanical behavior of such biological systems. While the availability of advanced computational tools has led to exciting research advances in the field, the utility of these models is often the subject of criticism due to inadequate model verification and validation (V&V). The objective of this review is to present the concepts of verification, validation and sensitivity studies with regard to the construction, analysis and interpretation of models in computational biomechanics. Specific examples from the field are discussed. It is hoped that this review will serve as a guide to the use of V&V principles in the field of computational biomechanics, thereby improving the peer acceptance of studies that use computational modeling techniques.     

Discriminating between rival biochemical network models: three approaches to optimal experiment design

Background  

The success of molecular systems biology hinges on the ability to use computational models to design predictive experiments, and ultimately unravel underlying biological mechanisms. A problem commonly encountered in the computational modelling of biological networks is that alternative, structurally different models of similar complexity fit a set of experimental data equally well. In this case, more than one molecular mechanism can explain available data. In order to rule out the incorrect mechanisms, one needs to invalidate incorrect models. At this point, new experiments maximizing the difference between the measured values of alternative models should be proposed and conducted. Such experiments should be optimally designed to produce data that are most likely to invalidate incorrect model structures.     

Accounting for robustness in modeling signal transduction responses

Abstract

A classical question in systems biology is to find a Boolean model which is able to predict the observed responses of a signaling network. It has been previously shown that such models can be tailored based on experimental data. While fitting a minimum-size network to the experimentally observed data is a natural assumption, it can potentially result in a network which is not so robust against the noises in the training dataset. Indeed, it is widely accepted now that biological systems are generally evolved to be very robust. Therefore, in the present work, we extended the classical formulation of Boolean network construction in order to put weight on the robustness of the created network. We show that our method results generally in more relevant networks. Consequently, considering robustness as a design principle of biological networks can result in more realistic models.     

Robust detection of periodic time series measured from biological systems

Background  

Periodic phenomena are widespread in biology. The problem of finding periodicity in biological time series can be viewed as a multiple hypothesis testing of the spectral content of a given time series. The exact noise characteristics are unknown in many bioinformatics applications. Furthermore, the observed time series can exhibit other non-idealities, such as outliers, short length and distortion from the original wave form. Hence, the computational methods should preferably be robust against such anomalies in the data.     

Requirements for comparing the performance of finite element models of biological structures

The widespread availability of three-dimensional imaging and computational power has fostered a rapid increase in the number of biologists using finite element analysis (FEA) to investigate the mechanical function of living and extinct organisms. The inevitable rise of studies that compare finite element models brings to the fore two critical questions about how such comparative analyses can and should be conducted: (1) what metrics are appropriate for assessing the performance of biological structures using finite element modeling? and, (2) how can performance be compared such that the effects of size and shape are disentangled? With respect to performance, we argue that energy efficiency is a reasonable optimality criterion for biological structures and we show that the total strain energy (a measure of work expended deforming a structure) is a robust metric for comparing the mechanical efficiency of structures modeled with finite elements. Results of finite element analyses can be interpreted with confidence when model input parameters (muscle forces, detailed material properties) and/or output parameters (reaction forces, strains) are well-documented by studies of living animals. However, many researchers wish to compare species for which these input and validation data are difficult or impossible to acquire. In these cases, researchers can still compare the performance of structures that differ in shape if variation in size is controlled. We offer a theoretical framework and empirical data demonstrating that scaling finite element models to equal force: surface area ratios removes the effects of model size and provides a comparison of stress-strength performance based solely on shape. Further, models scaled to have equal applied force:volume ratios provide the basis for strain energy comparison. Thus, although finite element analyses of biological structures should be validated experimentally whenever possible, this study demonstrates that the relative performance of un-validated models can be compared so long as they are scaled properly.     

Ontology-based instance data validation for high-quality curated biological pathways

Background

Modeling in systems biology is vital for understanding the complexity of biological systems across scales and predicting system-level behaviors. To obtain high-quality pathway databases, it is essential to improve the efficiency of model validation and model update based on appropriate feedback.

Results

We have developed a new method to guide creating novel high-quality biological pathways, using a rule-based validation. Rules are defined to correct models against biological semantics and improve models for dynamic simulation. In this work, we have defined 40 rules which constrain event-specific participants and the related features and adding missing processes based on biological events. This approach is applied to data in Cell System Ontology which is a comprehensive ontology that represents complex biological pathways with dynamics and visualization. The experimental results show that the relatively simple rules can efficiently detect errors made during curation, such as misassignment and misuse of ontology concepts and terms in curated models.

Conclusions

A new rule-based approach has been developed to facilitate model validation and model complementation. Our rule-based validation embedding biological semantics enables us to provide high-quality curated biological pathways. This approach can serve as a preprocessing step for model integration, exchange and extraction data, and simulation.

     

Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology

Computational models in physiology often integrate functional and structural information from a large range of spatiotemporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and skepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace, and refine animal experiments. A fundamental requirement to fulfill these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations among experiments, models, and simulations in cardiac electrophysiology. We describe the processes, data, and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. We argue that validation is part of the whole MSE system and is contingent upon 1) understanding and coping with sources of biovariability; 2) testing and developing robust techniques and tools as a prerequisite to conducting physiological investigations; 3) defining and adopting standards to facilitate the interoperability of experiments, models, and simulations; 4) and understanding physiological validation as an iterative process that contributes to defining the specific aspects of cardiac electrophysiology the MSE system targets, rather than being only an external test, and that this is driven by advances in experimental and computational methods and the combination of both.     

Modularity analysis based on predicted protein-protein interactions provides new insights into pathogenicity and cellular process of Escherichia coli O157:H7

We review grounding issues that influence the scientific usefulness of any biomedical multiscale model (MSM). Groundings are the collection of units, dimensions, and/or objects to which a variable or model constituent refers. To date, models that primarily use continuous mathematics rely heavily on absolute grounding, whereas those that primarily use discrete software paradigms (e.g., object-oriented, agent-based, actor) typically employ relational grounding. We review grounding issues and identify strategies to address them. We maintain that grounding issues should be addressed at the start of any MSM project and should be reevaluated throughout the model development process. We make the following points. Grounding decisions influence model flexibility, adaptability, and thus reusability. Grounding choices should be influenced by measures, uncertainty, system information, and the nature of available validation data. Absolute grounding complicates the process of combining models to form larger models unless all are grounded absolutely. Relational grounding facilitates referent knowledge embodiment within computational mechanisms but requires separate model-to-referent mappings. Absolute grounding can simplify integration by forcing common units and, hence, a common integration target, but context change may require model reengineering. Relational grounding enables synthesis of large, composite (multi-module) models that can be robust to context changes. Because biological components have varying degrees of autonomy, corresponding components in MSMs need to do the same. Relational grounding facilitates achieving such autonomy. Biomimetic analogues designed to facilitate translational research and development must have long lifecycles. Exploring mechanisms of normal-to-disease transition requires model components that are grounded relationally. Multi-paradigm modeling requires both hyperspatial and relational grounding.     

Rationalization and design of the complementarity determining region sequences in an antibody-antigen recognition interface

Protein-protein interactions are critical determinants in biological systems. Engineered proteins binding to specific areas on protein surfaces could lead to therapeutics or diagnostics for treating diseases in humans. But designing epitope-specific protein-protein interactions with computational atomistic interaction free energy remains a difficult challenge. Here we show that, with the antibody-VEGF (vascular endothelial growth factor) interaction as a model system, the experimentally observed amino acid preferences in the antibody-antigen interface can be rationalized with 3-dimensional distributions of interacting atoms derived from the database of protein structures. Machine learning models established on the rationalization can be generalized to design amino acid preferences in antibody-antigen interfaces, for which the experimental validations are tractable with current high throughput synthetic antibody display technologies. Leave-one-out cross validation on the benchmark system yielded the accuracy, precision, recall (sensitivity) and specificity of the overall binary predictions to be 0.69, 0.45, 0.63, and 0.71 respectively, and the overall Matthews correlation coefficient of the 20 amino acid types in the 24 interface CDR positions was 0.312. The structure-based computational antibody design methodology was further tested with other antibodies binding to VEGF. The results indicate that the methodology could provide alternatives to the current antibody technologies based on animal immune systems in engineering therapeutic and diagnostic antibodies against predetermined antigen epitopes.     

Mapping parameter spaces of biological switches

Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection in Drosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches.     

Comparison of Gene Regulatory Networks via Steady-State Trajectories

The modeling of genetic regulatory networks is becoming increasingly widespread in the study of biological systems. In the abstract, one would prefer quantitatively comprehensive models, such as a differential-equation model, to coarse models; however, in practice, detailed models require more accurate measurements for inference and more computational power to analyze than coarse-scale models. It is crucial to address the issue of model complexity in the framework of a basic scientific paradigm: the model should be of minimal complexity to provide the necessary predictive power. Addressing this issue requires a metric by which to compare networks. This paper proposes the use of a classical measure of difference between amplitude distributions for periodic signals to compare two networks according to the differences of their trajectories in the steady state. The metric is applicable to networks with both continuous and discrete values for both time and state, and it possesses the critical property that it allows the comparison of networks of different natures. We demonstrate application of the metric by comparing a continuous-valued reference network against simplified versions obtained via quantization.     

Computational cell biology in the post-genomic era

Rapid accumulation of biological data from novel high throughput technologies characteristic of genomic and proteomic research as well as advances in more traditional biological disciplines are leading to wider use of detailed and complex computational models of cell behavior. These models address a variety of dynamic intracellular processes ranging from interactions within a gene regulation network to intracellular and intercellular signal transduction. This review focuses on the current trends in computation cell biology, particularly emphasizing the role of experimental validation. The recent successes and future challenges facing computational cell biology are also discussed.     

Predictive models in ecology: Comparison of performances and assessment of applicability

Ecological systems are governed by complex interactions which are mainly nonlinear. In order to capture the inherent complexity and nonlinearity of ecological, and in general biological systems, empirical models recently gained popularity. However, although these models, particularly connectionist approaches such as multilayered backpropagation networks, are commonly applied as predictive models in ecology to a wide variety of ecosystems and questions, there are no studies to date aiming to assess the performance, both in terms of data fitting and generalizability, and applicability of empirical models in ecology. Our aim is hence to provide an overview for nature of the wide range of the data sets and predictive variables, from both aquatic and terrestrial ecosystems with different scales of time-dependent dynamics, and the applicability and robustness of predictive modeling methods on such data sets by comparing different empirical modeling approaches. The models used in this study range from predicting the occurrence of submerged plants in shallow lakes to predicting nest occurrence of bird species from environmental variables and satellite images. The methods considered include k-nearest neighbor (k-NN), linear and quadratic discriminant analysis (LDA and QDA), generalized linear models (GLM) feedforward multilayer backpropagation networks and pseudo-supervised network ARTMAP.Our results show that the predictive performances of the models on training data could be misleading, and one should consider the predictive performance of a given model on an independent test set for assessing its predictive power. Moreover, our results suggest that for ecosystems involving time-dependent dynamics and periodicities whose frequency are possibly less than the time scale of the data considered, GLM and connectionist neural network models appear to be most suitable and robust, provided that a predictive variable reflecting these time-dependent dynamics included in the model either implicitly or explicitly. For spatial data, which does not include any time-dependence comparable to the time scale covered by the data, on the other hand, neighborhood based methods such as k-NN and ARTMAP proved to be more robust than other methods considered in this study. In addition, for predictive modeling purposes, first a suitable, computationally inexpensive method should be applied to the problem at hand a good predictive performance of which would render the computational cost and efforts associated with complex variants unnecessary.     

Algorithms in nature: the convergence of systems biology and computational thinking

Computer science and biology have enjoyed a long and fruitful relationship for decades. Biologists rely on computational methods to analyze and integrate large data sets, while several computational methods were inspired by the high‐level design principles of biological systems. Recently, these two directions have been converging. In this review, we argue that thinking computationally about biological processes may lead to more accurate models, which in turn can be used to improve the design of algorithms. We discuss the similar mechanisms and requirements shared by computational and biological processes and then present several recent studies that apply this joint analysis strategy to problems related to coordination, network analysis, and tracking and vision. We also discuss additional biological processes that can be studied in a similar manner and link them to potential computational problems. With the rapid accumulation of data detailing the inner workings of biological systems, we expect this direction of coupling biological and computational studies to greatly expand in the future.     

Numerical Parameter Space Compression and Its Application to Biophysical Models

Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e., are sensitive to) only a subset of those parameters. This phenomenon is due to parameter space compression (PSC), in which a subset of parameters emerges as “stiff” as a function of time or space. PSC has only been used to explain analytically solvable physics models. We have generalized this result by developing a numerical approach to PSC that can be applied to any computational model. We validated our method against analytically solvable models of a random walk with drift and protein production and degradation. We then applied our method to a simple computational model of microtubule dynamic instability. We propose that numerical PSC has the potential to identify the low-dimensional structure of many computational models in biophysics. The low-dimensional structure of a model is easier to interpret and identifies the mechanisms and experiments that best characterize the system.     

A modified Ising model of Barabási–Albert network with gene-type spins

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

     

Ranked retrieval of Computational Biology models

Background  

The study of biological systems demands computational support. If targeting a biological problem, the reuse of existing computational models can save time and effort. Deciding for potentially suitable models, however, becomes more challenging with the increasing number of computational models available, and even more when considering the models' growing complexity. Firstly, among a set of potential model candidates it is difficult to decide for the model that best suits ones needs. Secondly, it is hard to grasp the nature of an unknown model listed in a search result set, and to judge how well it fits for the particular problem one has in mind.