Executable cell biology

Computational modeling of biological systems is becoming increasingly important in efforts to better understand complex biological behaviors. In this review, we distinguish between two types of biological models--mathematical and computational--which differ in their representations of biological phenomena. We call the approach of constructing computational models of biological systems 'executable biology', as it focuses on the design of executable computer algorithms that mimic biological phenomena. We survey the main modeling efforts in this direction, emphasize the applicability and benefits of executable models in biological research and highlight some of the challenges that executable biology poses for biology and computer science. We claim that for executable biology to reach its full potential as a mainstream biological technique, formal and algorithmic approaches must be integrated into biological research. This will drive biology toward a more precise engineering discipline.     

Insights into the molecular dynamics of plant light-harvesting proteins in vivo

To understand physiological processes at the molecular level, new techniques are needed to determine the details of protein structure and dynamics in intact systems. We describe a specific example of such an approach, involving differential analysis of the carotenoid resonance Raman signal in the plant photosynthetic membrane. Carotenoids play important roles in the photosynthetic membrane and are particularly vital to photoprotective regulatory mechanisms. Our methodology selectively revealed the details of associations between specific carotenoid molecules and specific protein binding sites. Changes in the molecular configuration of these cofactors associated with alterations in the physiological state of the photosynthetic system were observed. This approach can be applied to a wide range of complex biological systems, whenever a protein with a light-absorbing cofactor is involved.     

Guidelines for visualizing and annotating rule-based models

Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme-substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FcεRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.     

Dimensionality Reduction of Bistable Biological Systems

Time hierarchies, arising as a result of interactions between system’s components, represent a ubiquitous property of dynamical biological systems. In addition, biological systems have been attributed switch-like properties modulating the response to various stimuli across different organisms and environmental conditions. Therefore, establishing the interplay between these features of system dynamics renders itself a challenging question of practical interest in biology. Existing methods are suitable for systems with one stable steady state employed as a well-defined reference. In such systems, the characterization of the time hierarchies has already been used for determining the components that contribute to the dynamics of biological systems. However, the application of these methods to bistable nonlinear systems is impeded due to their inherent dependence on the reference state, which in this case is no longer unique. Here, we extend the applicability of the reference-state analysis by proposing, analyzing, and applying a novel method, which allows investigation of the time hierarchies in systems exhibiting bistability. The proposed method is in turn used in identifying the components, other than reactions, which determine the systemic dynamical properties. We demonstrate that in biological systems of varying levels of complexity and spanning different biological levels, the method can be effectively employed for model simplification while ensuring preservation of qualitative dynamical properties (i.e., bistability). Finally, by establishing a connection between techniques from nonlinear dynamics and multivariate statistics, the proposed approach provides the basis for extending reference-based analysis to bistable systems.     

Markov state modeling of membrane transport proteins

The flux of ions and molecules in and out of the cell is vital for maintaining the basis of various biological processes. The permeation of substrates across the cellular membrane is mediated through the function of specialized integral membrane proteins commonly known as membrane transporters. These proteins undergo a series of structural rearrangements that allow a primary substrate binding site to be accessed from either side of the membrane at a given time. Structural insights provided by experimentally resolved structures of membrane transporters have aided in the biophysical characterization of these important molecular drug targets. However, characterizing the transitions between conformational states remains challenging to achieve both experimentally and computationally. Though molecular dynamics simulations are a powerful approach to provide atomistic resolution of protein dynamics, a recurring challenge is its ability to efficiently obtain relevant timescales of large conformational transitions as exhibited in transporters. One approach to overcome this difficulty is to adaptively guide the simulation to favor exploration of the conformational landscape, otherwise known as adaptive sampling. Furthermore, such sampling is greatly benefited by the statistical analysis of Markov state models. Historically, the use of Markov state models has been effective in quantifying slow dynamics or long timescale behaviors such as protein folding. Here, we review recent implementations of adaptive sampling and Markov state models to not only address current limitations of molecular dynamics simulations, but to also highlight how Markov state modeling can be applied to investigate the structure–function mechanisms of large, complex membrane transporters.     

Graphical approach to model reduction for nonlinear biochemical networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a "concentration-clamp" procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β(1)-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal "kinetic biomarkers" of the overall β(1)-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems.     

Data-driven flow-map models for data-efficient discovery of dynamics and fast uncertainty quantification of biological and biochemical systems

Computational models are increasingly used to investigate and predict the complex dynamics of biological and biochemical systems. Nevertheless, governing equations of a biochemical system may not be (fully) known, which would necessitate learning the system dynamics directly from, often limited and noisy, observed data. On the other hand, when expensive models are available, systematic and efficient quantification of the effects of model uncertainties on quantities of interest can be an arduous task. This paper leverages the notion of flow-map (de)compositions to present a framework that can address both of these challenges via learning data-driven models useful for capturing the dynamical behavior of biochemical systems. Data-driven flow-map models seek to directly learn the integration operators of the governing differential equations in a black-box manner, irrespective of structure of the underlying equations. As such, they can serve as a flexible approach for deriving fast-to-evaluate surrogates for expensive computational models of system dynamics, or, alternatively, for reconstructing the long-term system dynamics via experimental observations. We present a data-efficient approach to data-driven flow-map modeling based on polynomial chaos Kriging. The approach is demonstrated for discovery of the dynamics of various benchmark systems and a coculture bioreactor subject to external forcing, as well as for uncertainty quantification of a microbial electrosynthesis reactor. Such data-driven models and analyses of dynamical systems can be paramount in the design and optimization of bioprocesses and integrated biomanufacturing systems.     

Towards building the silicon cell: a modular approach

Systems Biology aims to understand quantitatively how properties of biological systems can be understood as functions of the characteristics of, and interactions between their macromolecular components. Whereas, traditional biochemistry focused on isolation and characterization of cellular components, the challenge for Systems Biology lies in integration of this knowledge and the knowledge about molecular interactions. Computer models play an important role in this integration. We here discuss an approach with which we aim to link kinetic models on small parts of metabolism together, so as to form detailed kinetic models of larger chunks of metabolism, and ultimately of the entire living cell. Specifically, we will discuss techniques that can be used to model a sub-network in isolation of a larger network of which it is a part, while still maintaining the dynamics of the larger complete network. We will start by outlining the JWS online system, the silicon cell project, and the type of models we propose. JWS online is a model repository, which can be used for the storage, simulation and analysis of kinetic models. We advocate to integrate a top-down approach, where measurements on the complete system are used to derive fluxes in a detailed structural model, with a bottom-up approach, consisting of the integration of molecular mechanism-based detailed kinetic models into the structural model.     

Narrative-based computational modelling of the Gp130/JAK/STAT signalling pathway

Background  

Appropriately formulated quantitative computational models can support researchers in understanding the dynamic behaviour of biological pathways and support hypothesis formulation and selection by "in silico" experimentation. An obstacle to widespread adoption of this approach is the requirement to formulate a biological pathway as machine executable computer code. We have recently proposed a novel, biologically intuitive, narrative-style modelling language for biologists to formulate the pathway which is then automatically translated into an executable format and is, thus, usable for analysis via existing simulation techniques.     

Computational Modeling,Formal Analysis,and Tools for Systems Biology

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science.     

Modeling cancer: integration of "omics" information in dynamic systems

The last 10 years have seen the rise of many technologies that produce an unprecedented amount of genome-scale data from many organisms. Although the research community has been successful in exploring these data, many challenges still persist. One of them is the effective integration of such data sets directly into approaches based on mathematical modeling of biological systems. Applications in cancer are a good example. The bridge between information and modeling in cancer can be achieved by two major types of complementary strategies. First, there is a bottom-up approach, in which data generates information about structure and relationship between components of a given system. In addition, there is a top-down approach, where cybernetic and systems-theoretical knowledge are used to create models that describe mechanisms and dynamics of the system. These approaches can also be linked to yield multi-scale models combining detailed mechanism and wide biological scope. Here we give an overall picture of this field and discuss possible strategies to approach the major challenges ahead.     

Organization and dynamics of N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)-labeled lipids: a fluorescence approach

Lipids that are labeled with the NBD (7-nitrobenz-2-oxa-1,3-diazol-4-yl) group are widely used as fluorescent analogues of native lipids in biological and model membranes to monitor a variety of processes. NBD-labeled lipids have previously been used to monitor the organization and dynamics of molecular assemblies such as membranes, micelles and reverse micelles utilizing the wavelength-selective fluorescence approach. In this paper, we have characterized the organization and dynamics of various NBD-labeled lipids using red edge excitation shift (REES) and other fluorescence approaches which include analysis of membrane penetration depths of the NBD group using the parallax method. We show here that the environment and location experienced by the NBD group of the NBD-labeled lipids could depend on the ionization state of the lipid. This could have potentially important implications in future studies involving NBD-labeled lipids as tracers in a cellular context.     

Computational aspects of feedback in neural circuits

It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We demonstrate these computational implications of feedback both theoretically, and through computer simulations of detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike trains over longer periods of time, and to process new information contained in such spike trains in diverse ways according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with feedback provide a new model for working memory that is consistent with a large set of biological constraints. Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks.     

Analysis of the connectional organization of neural systems associated with the hippocampus in rats

The hippocampus of the rat enjoys a central significance for researchers interested in the neural mechanisms of memory and spatial information processing. Many of the theoretical models advanced to explain function in this system, however, do not reflect the wealth of information on the connectivity of these structures, and employ greatly simplified treatments of its complex connectivity. We were interested in whether a more analytical approach, which begins with analysis of the connectivity of the system, might provide insights complementary to those derived by synthetic models. Accordingly, we collated detailed neuroanatomical information about the connectivity of the hippocampal system in the rat, and analysed the resulting data. Analyses of connectivity based on a variety of different analytical techniques have recently been used to elucidate the global organization of other systems in the macaque and cat, and have given rise to successful predictions. We applied non-metric multidimensional scaling and non-parametric cluster analysis to our summary matrix of connection data. The analyses produced organizational schemes that were consistent with known physiological properties and provided the basis for making tentative predictions of the further structures that may contain 'place' and 'head-direction' cells, which structures we identify. The consistency between the analyses of connectivity and the distribution of physiological properties across the system suggests that functional relationships are constrained by the organization of the connectivity of the system, and so that structure and function are linked at the systems level.     

An Information-Based Approach to Change-Point Analysis with Applications to Biophysics and Cell Biology

This article describes the application of a change-point algorithm to the analysis of stochastic signals in biological systems whose underlying state dynamics consist of transitions between discrete states. Applications of this analysis include molecular-motor stepping, fluorophore bleaching, electrophysiology, particle and cell tracking, detection of copy number variation by sequencing, tethered-particle motion, etc. We present a unified approach to the analysis of processes whose noise can be modeled by Gaussian, Wiener, or Ornstein-Uhlenbeck processes. To fit the model, we exploit explicit, closed-form algebraic expressions for maximum-likelihood estimators of model parameters and estimated information loss of the generalized noise model, which can be computed extremely efficiently. We implement change-point detection using the frequentist information criterion (which, to our knowledge, is a new information criterion). The frequentist information criterion specifies a single, information-based statistical test that is free from ad hoc parameters and requires no prior probability distribution. We demonstrate this information-based approach in the analysis of simulated and experimental tethered-particle-motion data.     

Attractor analysis of asynchronous Boolean models of signal transduction networks

Prior work on the dynamics of Boolean networks, including analysis of the state space attractors and the basin of attraction of each attractor, has mainly focused on synchronous update of the nodes’ states. Although the simplicity of synchronous updating makes it very attractive, it fails to take into account the variety of time scales associated with different types of biological processes. Several different asynchronous update methods have been proposed to overcome this limitation, but there have not been any systematic comparisons of the dynamic behaviors displayed by the same system under different update methods. Here we fill this gap by combining theoretical analysis such as solution of scalar equations and Markov chain techniques, as well as numerical simulations to carry out a thorough comparative study on the dynamic behavior of a previously proposed Boolean model of a signal transduction network in plants. Prior evidence suggests that this network admits oscillations, but it is not known whether these oscillations are sustained. We perform an attractor analysis of this system using synchronous and three different asynchronous updating schemes both in the case of the unperturbed (wild-type) and perturbed (node-disrupted) systems. This analysis reveals that while the wild-type system possesses an update-independent fixed point, any oscillations eventually disappear unless strict constraints regarding the timing of certain processes and the initial state of the system are satisfied. Interestingly, in the case of disruption of a particular node all models lead to an extended attractor. Overall, our work provides a roadmap on how Boolean network modeling can be used as a predictive tool to uncover the dynamic patterns of a biological system under various internal and environmental perturbations.     

Integrated Modeling Framework for Manufacturing Systems: A Unified Representation of the Physical Process and Information System

The task of process modeling in a manufacturing environment centers around controlling and improving the flow of materials. This flow comprises a complicated web of control and physical systems. Despite a variety of manufacturing system modeling approaches, more rigorous process modeling is required. This paper presents an integrated modeling framework for manufacturing systems (IMF-M). Conceptual modeling of physical materials flow supported by a graphical representation facilitates improvement of operations in manufacturing environments. A declarative and executable representation of control information systems helps to improve information management by managing a variety of information models with improved readability and reusability. A unified representation of the physical process and information system provides a common modeling milieu in which efforts can be coordinated among several groups working in the different domains of scheduling, shop floor and logistics control, and information system. Since the framework helps adapt to the changes of the physical process and information system affecting each other in a consistent manner, the modeling output enhances integration of the manufacturing system.