A central goal of synthetic biology is to design sophisticated synthetic cellular circuits that can perform complex computations and information processing tasks in response to specific inputs. The tremendous advances in our ability to understand and manipulate cellular information processing networks raises several fundamental physics questions: How do the molecular components of cellular circuits exploit energy consumption to improve information processing? Can one utilize ideas from thermodynamics to improve the design of synthetic cellular circuits and modules? Here, we summarize recent theoretical work addressing these questions. Energy consumption in cellular circuits serves five basic purposes: (1) increasing specificity, (2) manipulating dynamics, (3) reducing variability, (4) amplifying signal, and (5) erasing memory. We demonstrate these ideas using several simple examples and discuss the implications of these theoretical ideas for the emerging field of synthetic biology. We conclude by discussing how it may be possible to overcome these limitations using "post-translational" synthetic biology that exploits reversible protein modification.
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the…
Many processes in biology, from the regulation of gene expression in bacteria to memory in the brain, involve switches constructed from networks of biochemical reactions. Crucial molecules are present in small numbers, raising questions about noise and stability. Analysis of noise in simple reaction schemes indicates that switches stable for years and switchable in milliseconds can be built from fewer than one hundred molecules. Prospects for direct tests of this prediction, as well as implications, are discussed.
Data tables in the form of spreadsheets or delimited text files are the most utilised data format in Systems Biology. However, they are often not sufficiently structured and lack clear naming conventions that would be required for modelling. We propose the SBtab format as an attempt to establish an easy-to-use table format that is both flexible and clearly structured. It comprises defined table types for different kinds of data; syntax rules for usage of names, shortnames, and database identifiers used for annotation; and standardised formulae for reaction stoichiometries. Predefined table typ…
A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well stirred reactor conditions, for large numbers of molecules, and frequent reactions. This is no longer a robust representation when some molecular species are in small numbers and reactions changing them are infrequent. In this case, discrete stochastic events trigger changes of the smooth deterministic dynamics of the biochemical network. Piecewise-deterministic Markov processes (PDMP) are well adapted for describing such situations. Although PDMP models are now well established in biology, thes…
For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy be…
Living systems operate in a critical dynamical regime -- between order and chaos -- where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the established 'structural theory' of criticality uses automata network connectivity and node bias (to be on or off) as tuning parameters. This parsimony in the number of parameters needed sometimes leads to uncertain predictions about the dynamical regime of both random and systems biology models of biochemical regulation. We derive a more accurate theory of criticality by accounting for canal…
Design of experiments is a branch of statistics that aims to identify efficient procedures for planning experiments in order to optimize knowledge discovery. Network inference is a subfield of systems biology devoted to the identification of biochemical networks from experimental data. Common to both areas of research is their focus on the maximization of information gathered from experimentation. The goal of this paper is to establish a connection between these two areas coming from the common use of polynomial models and techniques from computational algebra.
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experime…
Living cell signaling systems include multistep biochemical signaling reaction cascades (BSCs) comprising modifications of molecular signaling proteins. Substantial data on BSCs have been accumulated in the field of molecular biology and the analysis of signaling systems requires qualitative evaluation. However, quantification of the information and channel capacity of BSCs has not been focused on from the perspective of information theory. In the current study, we aimed to derive basic equations for describing the channel capacity and information density of BSCs using the fluctuation theorem.…
A recent article by Weidner et al. [2021] presents a method to extract graph properties that are predictive of the dynamical behavior of multivariate, discrete models of biochemical regulation. In other words, a method that uses only features from the structure of network interactions to predict which nodes are most involved in automata network dynamics. However, the authors claim that dynamical analysis of large automata network models is "not even feasible." To make sure that others are not discouraged from working on this problem, it is important to clarify that effective dynamical analysis…
We discuss a method of approximate model reduction for networks of biochemical reactions. This method can be applied to networks with polynomial or rational reaction rates and whose parameters are given by their orders of magnitude. In order to obtain reduced models we solve the problem of tropical equilibration that is a system of equations in max-plus algebra. In the case of networks with nonlinear fast cycles we have to solve the problem of tropical equilibration at least twice, once for the initial system and a second time for an extended system obtained by adding to the initial system the…
The linear noise approximation is commonly used to obtain intrinsic noise statistics for biochemical networks. These estimates are accurate for networks with large numbers of molecules. However it is well known that many biochemical networks are characterized by at least one species with a small number of molecules. We here describe version 0.3 of the software intrinsic Noise Analyzer (iNA) which allows for accurate computation of noise statistics over wide ranges of molecule numbers. This is achieved by calculating the next order corrections to the linear noise approximation's estimates of va…
With the completion of human genome mapping, the focus of scientists seeking to explain the biological complexity of living systems is shifting from analyzing the individual components (such as a particular gene or biochemical reaction) to understanding the set of interactions amongst the large number of components that results in the different functions of the organism. To this end, the area of systems biology attempts to achieve a "systems-level" description of biology by focusing on the network of interactions instead of the characteristics of its isolated parts. In this article, we briefly…
Within systems biology there is an increasing interest in the stochastic behavior of genetic and biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous time Markov chain (CTMC). In this paper we consider the stochastic properties of a biochemical circuit, known to control eukaryotic cell cycle and possibly involved in oncogenesis, recently proposed in the literature within a deterministic framework. Due to the inherent stochasticity of biochemical processes and the small number of molecules involved, the s…
Synthetic biology is an interdisciplinary field aiming to design biochemical systems with desired behaviors. To this end, molecular controllers have been developed which, when embedded into a pre-existing ambient biochemical network, control the dynamics of the underlying target molecular species. When integrated into smaller compartments, such as biological cells in vivo, or vesicles in vitro, controllers have to be calibrated to factor in the intrinsic noise. In this context, molecular controllers put forward in the literature have focused on manipulating the mean (first moment), and reducin…
Analyzing qualitative behaviors of biochemical reactions using its associated network structure has proven useful in diverse branches of biology. As an extension of our previous work, we introduce a graph-based framework to calculate steady state solutions of biochemical reaction networks with synthesis and degradation. Our approach is based on a labeled directed graph $G$ and the associated system of linear non-homogeneous differential equations with first order degradation and zeroth order synthesis. We also present a theorem which provides necessary and sufficient conditions for the dynamic…
Robustness of biochemical systems has become one of the central questions in Systems Biology, although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the stoichiometry of the underlying interrelated components, but also on a multitude of kinetic parameters. For given parameter values, recent findings have aimed at characterizing the property of the system components to exhibit same concentrations in the resulting steady states, termed absolute concentration robustness (ACR). However, the existing method for det…
The relationship between components of biochemical network and the resulting dynamics of the overall system is a key focus of computational biology. However, as these networks and resulting mathematical models are inherently complex and non-linear, the understanding of this relationship becomes challenging. Among many approaches, model reduction methods provide an avenue to extract components responsible for the key dynamical features of the system. Unfortunately, these approaches often require intuition to apply. In this manuscript we propose a practical algorithm for the reduction of biochem…
Innovation in synthetic biology often still depends on large-scale experimental trial-and-error, domain expertise, and ingenuity. The application of rational design engineering methods promise to make this more efficient, faster, cheaper and safer. But this requires mathematical models of cellular systems. And for these models we then have to determine if they can meet our intended target behaviour. Here we develop two complementary approaches that allow us to determine whether a given molecular circuit, represented by a mathematical model, is capable of fulfilling our design objectives. We di…
A mathematical framework to study organising principles in graphical representations of biochemical processes
University of Rostock（罗斯托克大学）；Christian-Albrechts-University（克里斯蒂安-阿尔布莱希特大学）；Leibniz-Institute for Food Systems Biology（莱布尼茨食品系统生物研究所）；Technical University of Munich（慕尼黑工业大学）；Stellenbosch Institute for Advanced Study（斯泰伦博斯高等研究院）
The stochastic simulation of large-scale biochemical reaction networks is of great importance for systems biology since it enables the study of inherently stochastic biological mechanisms at the whole cell scale. Stochastic Simulation Algorithms (SSA) allow us to simulate the dynamic behavior of complex kinetic models, but their high computational cost makes them very slow for many realistic size problems. We present a pilot service, named WebStoch, developed in the context of our StochSoCs research project, allowing life scientists with no high-performance computing expertise to perform over …
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species responsible for pattern formation. Meanwhile, synthetic biologists have designed Turing systems for implementation in cell colonies, but none have yet led to visible patterns in the laboratory. In both cases, the relationship between underlying chemistry and emergent biology remains mysterious. To help resolve the mystery, this article asks the question: what kinds of…
Information transmission in biological signaling circuits has often been described using the metaphor of a noise filter. Cellular systems need accurate, real-time data about their environmental conditions, but the biochemical reaction networks that propagate, amplify, and process signals work with noisy representations of that data. Biology must implement strategies that not only filter the noise, but also predict the current state of the environment based on information delayed due to the finite speed of chemical signaling. The idea of a biochemical noise filter is actually more than just a m…
Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement of strand-displacement DNA computing, a large class of abstract biochemical networks may be physically realized using DNA molecules. Methods for systematic design of the abstract systems with prescribed behaviors have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochem…
The major biochemical networks of the living cell, the network of interacting genes and the network of biochemical reactions, are highly interdependent, however, they have been studied mostly as separate systems so far. In the last years an appropriate theoretical framework for studying interdependent networks has been developed in the context of statistical physics. Here we study the interdependent network of gene regulation and metabolism of the model organism Escherichia coli using the theoretical framework of interdependent networks. In particular we aim at understanding how the biological…
Computing the projected reachable set of switched affine systems: an application to systems biology
Laboratory for Information and Decision Systems, MIT（麻省理工学院信息与决策系统实验室）；Department of Information Engineering, University of Padova（帕多瓦大学信息工程系）；Automatic Control Laboratory, ETH（苏黎世联邦理工学院自动控制实验室）
Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space (associated with different biochemical functions). Switching is often realized by a bistable system (i.e. a dynamical system allowing two stable steady state solutions) and, in the majority of cases, bistability is established numerically. In our point of view this approach is too restrictive, as, one the one hand, due to predominant parameter uncertainty numerical …
Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated t…
Systems biology and whole-cell modelling are demanding increasingly comprehensive mathematical models of cellular biochemistry. These models require the development of simplified models of specific processes which capture essential biophysical features but without unnecessarily complexity. Recently there has been renewed interest in thermodynamically-based modelling of cellular processes. Here we present an approach to developing of simplified yet thermodynamically consistent (hence physically plausible) models which can readily be incorporated into large scale biochemical descriptions but whi…
The connection between optimal biological function and energy use, measured for example by the rate of metabolite consumption, is a current topic of interest in the systems biology literature which has been explored in several different contexts. In [J. P. Barton and E. D. Sontag, Biophys. J. 104, 6 (2013)], we related the metabolic cost of enzymatic futile cycles with their capacity to act as insulators which facilitate modular interconnections in biochemical networks. There we analyzed a simple model system in which a signal molecule regulates the transcription of one or more target proteins…
Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems we know that behavioral changes in the individual constituents of a collectively-behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here we apply such an approach to the emergence …
