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Reproducibility is a foundational standard for validating scientific claims in computational research. Stochastic computational models are employed across diverse fields such as systems biology, financial modelling and environmental sciences. Existing infrastructure and software tools support various aspects of reproducible model development, application, and dissemination, but do not adequately address independently reproducing simulation results that form the basis of scientific conclusions. To bridge this gap, we introduce the Empirical Characteristic Function Equality Convergence Test (EFECT), a data-driven method to quantify the reproducibility of stochastic simulation results. EFECT employs empirical characteristic functions to compare reported results with those independently generated by assessing distributional inequality, termed EFECT error, a metric to quantify the likelihood of equality. Additionally, we establish the EFECT convergence point, a metric for determining the required number of simulation runs to achieve an EFECT error value of a priori statistical significance, setting a reproducibility benchmark. EFECT supports all real-valued and bounded results irrespective of the model or method that produced them, and accommodates stochasticity from intrinsic model variability and random sampling of model inputs. We tested EFECT with stochastic differential equations, agent-based models, and Boolean networks, demonstrating its broad applicability and effectiveness. EFECT standardizes stochastic simulation reproducibility, establishing a workflow that guarantees reliable results, supporting a wide range of stakeholders, and thereby enhancing validation of stochastic simulation studies, across a model's lifecycle. To promote future standardization efforts, we are developing open source software library libSSR in diverse programming languages for easy integration of EFECT., Comment: 25 pages, 4 figures

In this paper, a set of Python methods is described that can be used to compute the frequency response of an arbitrary biochemical network given any input and output. Models can be provided in standard SBML or Antimony format. The code takes into account any conserved moieties so that this software can be used to also study signaling networks where moiety cycles are common. A utility method is also provided to make it easy to plot standard Bode plots from the generated results. The code also takes into account the possibility that the phase shift could exceed 180 degrees which can result in ugly discontinuities in the Bode plot. In the paper, some of the theory behind the method is provided as well as some commentary on the code and several illustrative examples to show the code in operation. Illustrative examples include linear reaction chains of varying lengths and the effect of negative feedback on the frequency response. Software License: MIT Open Source Availability: The code is available from https://github.com/sys-bio/frequencyResponse., Comment: Fixed some minor typos

Antimony is a high-level, human-readable text-based language designed for defining and sharing models in the systems biology community. It enables scientists to describe biochemical networks and systems using a simple and intuitive syntax. It allows users to easily create, modify, and distribute reproducible computational models. By allowing the concise representation of complex biological processes, Antimony enhances collaborative efforts, improves reproducibility, and accelerates the iterative development of models in systems biology. This paper provides an update to the Antimony language since it was introduced in 2009. In particular, we highlight new annotation features, support for flux balance analysis, a new rateOf method, support for probability distributions and uncertainty, named stochiometries, and algebraic rules. Antimony is also now distributed as a C/C++ library, together with python and Julia bindings, as well as a JavaScript version for use within a web browser. Availability: https://github.com/sys-bio/antimony.

This paper explores some basic concepts of Biochemical Systems Theory (BST) and Metabolic Control Analysis (MCA), two frameworks developed to understand the behavior of biochemical networks. Initially introduced by Savageau, BST focuses on system stability and employs power laws in modeling biochemical systems. On the other hand, MCA, pioneered by authors such as Kacser and Burns and Heinrich and Rapoport, emphasizes linearization of the governing equations and describes relationships (known as theorems) between different measures. Despite apparent differences, both frameworks are shown to be equivalent in many respects. Through a simple example of a linear chain, the paper demonstrates how BST and MCA yield identical results when analyzing steady-state behavior and logarithmic gains within biochemical pathways. This comparative analysis highlights the interchangeability of concepts such as kinetic orders, elasticities and other logarithmic gains.

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology in order to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent properties such as memory, consciousness, and recognition of self and non-self. To understand how these interconnected reactions lead to cellular life characterized by activation, inhibition, regulation, homeostasis, and adaptation, computational analyses and simulations are essential, a fact recognized by the biological communities. At the same time, students struggle to understand and apply binding and kinetic analyses for the simplest reactions such as the irreversible first-order conversion of a single reactant to a product. This likely results from cognitive difficulties in combining structural, chemical, mathematical, and textual descriptions of binding and catalytic reactions. To help students better understand dynamic reactions and their analyses, we have introduced two kinds of interactive graphs and simulations into the online educational resource, Fundamentals of Biochemistry, a multivolume biochemistry textbook that is part of the LibreText collection. One type is available for simple binding and kinetic reactions. The other displays progress curves (concentrations vs time) for both simple reactions and more complex metabolic and signal transduction pathways, including those available through databases using systems biology markup language (SBML) files. Users can move sliders to change dissociation and kinetic constants as well as initial concentrations and see instantaneous changes in the graphs. They can also export data into a spreadsheet for further processing, such as producing derivative Lineweaver-Burk and traditional Michaelis-Menten graphs of initial velocity (v0) vs substrate concentration., Comment: 17 pages, 2 tables, 8 figures. Submitted to Biochemistry and Molecular Biology Education. Funding: MiniSidewinder: NIH/NIGMS (Grant R01-GM123032-04) LibreText: Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot

We describe a web-based tool, MakeSBML (https://sys-bio.github.io/makesbml/), that provides an installation-free application for creating, editing, and searching the Biomodels repository for SBML-based models. MakeSBML is a client-based web application that translates models expressed in human-readable Antimony to the System Biology Markup Language (SBML) and vice-versa. Since MakeSBML is a web-based application it requires no installation on the user's part. Currently, MakeSBML is hosted on a GitHub page where the client-based design makes it trivial to move to other hosts. This model for software deployment also reduces maintenance costs since an active server is not required. The SBML modeling language is often used in systems biology research to describe complex biochemical networks and makes reproducing models much easier. However, SBML is designed to be computer-readable, not human-readable. We therefore employ the human-readable Antimony language to make it easy to create and edit SBML models., Comment: 4 pages, 1 figure. Author roles: Bartholomew E Jardine: Writing - Original draft preparation, Software. Lucian P Smith: Software, Writing. Herbert M Sauro: Conceived, Software design, Writing

SBcoyote is an open-source cross-platform biochemical reaction viewer and editor released under the liberal MIT license. It is written in Python and uses wxPython to implement the GUI and the drawing canvas. It supports the visualization and editing of compartments, species, and reactions. It includes many options to stylize each of these components. For instance, species can be in different colors and shapes. Other core features include the ability to create alias nodes, alignment of groups of nodes, network zooming, as well as an interactive bird-eye view of the network to allow easy navigation on large networks. A unique feature of the tool is the extensive Python plugin API, where third-party developers can include new functionality. To assist third-party plugin developers, we provide a variety of sample plugins, including, random network generation, a simple auto layout tool, export to Antimony, export SBML, import SBML, etc. Of particular interest are the export and import SBML plugins since these support the SBML level 3 layout and render standard, which is exchangeable with other software packages. Plugins are stored in a GitHub repository, and an included plugin manager can retrieve and install new plugins from the repository on demand. Plugins have version metadata associated with them to make it install plugin updates. Availability: https://github.com/sys-bio/SBcoyote.

Computational models are increasingly used in high-impact decision making in science, engineering, and medicine. The National Aeronautics and Space Administration (NASA) uses computational models to perform complex experiments that are otherwise prohibitively expensive or require a microgravity environment. Similarly, the Food and Drug Administration (FDA) and European Medicines Agency (EMA) have began accepting models and simulations as form of evidence for pharmaceutical and medical device approval. It is crucial that computational models meet a standard of credibility when using them in high-stakes decision making. For this reason, institutes including NASA, the FDA, and the EMA have developed standards to promote and assess the credibility of computational models and simulations. However, due to the breadth of models these institutes assess, these credibility standards are mostly qualitative and avoid making specific recommendations. On the other hand, modeling and simulation in systems biology is a narrow domain and several standards are already in place. As systems biology models increase in complexity and influence, the development of a credibility assessment system is crucial. Here we review existing standards in systems biology, credibility standards in other science, engineering, and medical fields, and propose the development of a credibility standard for systems biology models., Comment: 12 pages, 2 figures

Summary: The Systems Biology Markup Language (SBML) is an extensible standard format for exchanging biochemical models. One of the extensions for SBML is the SBML Layout and Render package. This allows modelers to describe a biochemical model as a pathway diagram. However, up to now there has been little support to help users easily add and retrieve such information from SBML. In this application note, we describe a new Python package called SBMLDiagrams. This package allows a user to add layout and render information or retrieve it using a straightforward Python API. The package uses skia-python to support the rendering of the diagrams, allowing export to commons formats such as PNG or PDF. Availability: SBMLDiagrams is publicly available and licensed under the liberal MIT open-source license. The package is available for all major platforms. The source code has been deposited at GitHub (github.com/sys-bio/SBMLDiagrams). Users can install the package using the standard pip installation mechanism: pip install SBMLDiagrams. Contact: hsauro@uw.edu.

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed through a distinct interface. To help investigators find and use simulation tools, we developed BioSimulators (https://biosimulators.org), a central registry of the capabilities of simulation tools and consistent Python, command-line, and containerized interfaces to each version of each tool. The foundation of BioSimulators is standards, such as CellML, SBML, SED-ML, and the COMBINE archive format, and validation tools for simulation projects and simulation tools that ensure these standards are used consistently. To help modelers find tools for particular projects, we have also used the registry to develop recommendation services. We anticipate that BioSimulators will help modelers exchange, reproduce, and combine simulations., Comment: 6 pages, 2 figures

Motivation: This paper presents libRoadRunner 2.0, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models expressed using Systems Biology Markup Language SBML). Results: libRoadRunner is a self-contained library, able to run both as a component inside other tools via its C++ and C bindings, and interactively through its Python or Julia interface. libRoadRunner uses a custom Just-In-Time JIT compiler built on the widely-used LLVM JIT compiler framework. It compiles SBML-specified models directly into native machine code for a large variety of processors, making it appropriate for solving extremely large models or repeated runs. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and nonlinear algebraic equations) and including several SBML extensions such as composition and distributions. It offers multiple deterministic and stochastic integrators, as well as tools for steady-state, sensitivity, stability analysis, and structural analysis of the stoichiometric matrix. Availability: libRoadRunner binary distributions are available for Mac OS X, Linux, and Windows. The library is licensed under the Apache License Version 2.0. libRoadRunner is also available for ARM-based computers such as the Raspberry Pi and can in principle be compiled on any system supported by LLVM-13. http://sys-bio.github.io/roadrunner/index.html provides online documentation, full build instructions, binaries, and a git source repository.

Motivation: An essential step in developing computational tools for the inference, optimization, and simulation of biochemical reaction networks is gauging tool performance against earlier efforts using an appropriate set of benchmarks. General strategies for the assembly of benchmark models include collection from the literature, creation via subnetwork extraction and de novo generation. However, with respect to biochemical reaction networks, these approaches and their associated tools are either poorly suited to generate models that reflect the wide range of properties found in natural biochemical networks or to do so in numbers that enable rigorous statistical analysis. Results: In this work we present SBbadger, a python-based software tool for the generation of synthetic biochemical reaction or metabolic networks with user-defined degree distributions, multiple available kinetic formalisms, and a host of other definable properties. SBbadger thus enables the creation of benchmark model sets that reflect properties of biological systems and generate the kinetics and model structures typically targeted by computational analysis and inference software. Here we detail the computational and algorithmic workflow of SBbadger, demonstrate its performance under various settings, provide samples outputs, and compare it to currently available biochemical reaction network generation software.

Recent studies have shown that the majority of published computational models in systems biology and physiology are not repeatable or reproducible. There are a variety of reasons for this. One of the most likely reasons is that given how busy modern researchers are and the fact that no credit is given to authors for publishing repeatable work, it is inevitable that this will be the case. The situation can only be rectified when government agencies, universities and other research institutions change policies and that journals begin to insist that published work is in fact at least repeatable if not reproducible. In this chapter guidelines are described that can be used by researchers to help make sure their work is repeatable. A scoring system is suggested that authors can use to determine how well they are doing., Comment: # figures

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Summary: More sophisticated models are needed to address problems in bioscience, synthetic biology, and precision medicine. To help facilitate the collaboration needed for such models, the community developed the Simulation Experiment Description Markup Language (SED-ML), a common format for describing simulations. However, the utility of SED-ML has been hampered by limited support for SED-ML among modeling software tools and by different interpretations of SED-ML among the tools that support the format. To help modelers debug their simulations and to push the community to use SED-ML consistently, we developed a tool for validating SED-ML files. We have used the validator to correct the official SED-ML example files. We plan to use the validator to correct the files in the BioModels database so that they can be simulated. We anticipate that the validator will be a valuable tool for developing more predictive simulations and that the validator will help increase the adoption and interoperability of SED-ML. Availability: The validator is freely available as a webform, HTTP API, command-line program, and Python package at https://run.biosimulations.org/utils/validate and https://pypi.org/project/biosimulators-utils. The validator is also embedded into interfaces to 11 simulation tools. The source code is openly available as described in the Supplementary data. Contact: karr@mssm.edu, Comment: 6 pages, 1 figure

Modeling and simulation (M&S) has revolutionized the way modern engineered products are designed, tested and evaluated. Yet modeling and simulation is much less frequently applied in the study of natural biological and active matter systems. Two of the greatest challenges in applying M\&S approaches to natural biological systems are (1) difficulty in specifying a model, and developing a simulation from it, and (2) tuning and optimizing parameters. Here we address the first challenge directly, and develop a software library that can lead to progress in the second.

Although reproducibility is a core tenet of the scientific method, it remains challenging to reproduce many results. Surprisingly, this also holds true for computational results in domains such as systems biology where there have been extensive standardization efforts. For example, Tiwari et al. recently found that they could only repeat 50% of published simulation results in systems biology. Toward improving the reproducibility of computational systems research, we identified several resources that investigators can leverage to make their research more accessible, executable, and comprehensible by others. In particular, we identified several domain standards and curation services, as well as powerful approaches pioneered by the software engineering industry that we believe many investigators could adopt. Together, we believe these approaches could substantially enhance the reproducibility of systems biology research. In turn, we believe enhanced reproducibility would accelerate the development of more sophisticated models that could inform precision medicine and synthetic biology., Comment: 11 pages, 1 figure

In this technical report, we describe a new version of SimpleSBML which provides an easier to use interface to python-libSBML allowing users of Python to more easily construct, edit, and inspect SBML based models. The most commonly used package for constructing SBML models in Python is python-libSBML based on the C/C++ library libSBML. python-libSBML is a comprehensive library with a large range of options but can be difficult for new users to learn and requires long scripts to create even the simplest models. Inspecting existing SBML models can also be difficult due to the complexity of the underlying object model. Instead, we present SimpleSBML, a package that allows users to add and inspect species, parameters, reactions, events, and rules to a libSBML model with only one command for each. Models can be exported to SBML format, and SBML files can be imported and converted to SimpleSBML commands making it very easy to edit the original SBML model. In the new version, a range of `get' methods is provided that allows users to inspect existing SBML models without having to understand the underlying object model used by libSBML., Comment: Corrections to the original preprint. No change to the software

Linear time-invariant (LTI) systems appear frequently in natural sciences and engineering contexts. Many LTI systems are described by ordinary differential equations (ODEs). For example, biological gene regulation, analog filter circuits, and simple mechanical, electrical, and hydraulic systems can all be described with varying approximations as LTI systems using ODEs. While linearity and time-invariance are straightforward to demonstrate for closed-form system definitions, determining whether an ODE describes a system with LTI properties is less obvious and rarely discussed in depth in the literature. Complications arise due to slightly different definitions of linearity in different contexts. This commentary is intended to provide clarity on this subtle point, and act as an instructional aid or educational supplement.

In systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit. PyBioNetFit is designed for parameterization, and also supports uncertainty quantification, checking models against known system properties, and solving design problems. PyBioNetFit introduces the Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data for parameterization model checking, and design. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms (differential evolution, particle swarm optimization, scatter search) that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving 31 example problems, including the challenging problem of parameterizing a model of cell cycle control in yeast. We benchmark PyBioNetFit's parallelization efficiency on computer clusters, using up to 288 cores. Finally, we demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of therapeutic interventions in autophagy signaling., Comment: 31 pages, 6 figures. Supplementary information available at the link provided in the manuscript

This paper presents libRoadRunner, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models \ expressed using Systems Biology Markup Language (SBML). SBML is the most widely used standard for representing dynamic networks, especially biochemical networks. libRoadRunner supports solution of both large models and multiple replicas of a single model on desktop, mobile and cluster computers. libRoadRunner is a self-contained library, able to run both as a component inside other tools via its C++ and C bindings andnteractively through its Python interface. The Python Application Programming Interface (API) is similar to the APIs of Matlab and SciPy, making it fast and easy to learn, even for new users. libRoadRunner uses a custom Just-In-Time (JIT) compiler built on the widely-used LLVM JIT compiler framework to compile SBML-specified models directly into very fast native machine code for a variety of processors, making it appropriate for solving very large models or multiple replicas of smaller models. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and nonlinear algebraic equations) and several of its extensions. It offers multiple deterministic and stochastic integrators, as well as tools for steady-state, stability analyses and flux balance analysis. We regularly update libRoadRunner binary distributions for Mac OS X, Linux and Windows and license them under Apache License Version 2.0. http://www.libroadrunner.org provides online documentation, full build instructions, binaries and a git source repository.

Background: With the ever increasing use of computational models in the biosciences, the need to share models and reproduce the results of published studies efficiently and easily is becoming more important. To this end, various standards have been proposed that can be used to describe models, simulations, data or other essential information in a consistent fashion. These constitute various separate components required to reproduce a given published scientific result. Results: We describe the Open Modeling EXchange format (OMEX). Together with the use of other standard formats from the Computational Modeling in Biology Network (COMBINE), OMEX is the basis of the COMBINE Archive, a single file that supports the exchange of all the information necessary for a modeling and simulation experiment in biology. An OMEX file is a ZIP container that includes a manifest file, listing the content of the archive, an optional metadata file adding information about the archive and its content, and the files describing the model. The content of a COMBINE Archive consists of files encoded in COMBINE standards whenever possible, but may include additional files defined by an Internet Media Type. Several tools that support the COMBINE Archive are available, either as independent libraries or embedded in modeling software. Conclusions: The COMBINE Archive facilitates the reproduction of modeling and simulation experiments in biology by embedding all the relevant information in one file. Having all the information stored and exchanged at once also helps in building activity logs and audit trails. We anticipate that the COMBINE Archive will become a significant help for modellers, as the domain moves to larger, more complex experiments such as multi-scale models of organs, digital organisms, and bioengineering., Comment: 3 figures, 1 table

Single-cell studies often show significant phenotypic variability due to the stochastic nature of intra-cellular biochemical reactions. When the numbers of molecules, e.g., transcription factors and regulatory enzymes, are in low abundance, fluctuations in biochemical activities become significant and such "noise" can propagate through regulatory cascades in terms of biochemical reaction networks. Here we develop an intuitive, yet fully quantitative method for analyzing how noise affects cellular phenotypes based on identifying a system's nonlinearities and noise propagations. We observe that such noise can simultaneously enhance sensitivities in one behavioral region while reducing sensitivities in another. Employing this novel phenomenon we designed three biochemical signal processing modules: (a) A gene regulatory network that acts as a concentration detector with both enhanced amplitude and sensitivity. (b) A non-cooperative positive feedback system, with a graded dose-response in the deterministic case, that serves as a bistable switch due to noise-induced bimodality. (c) A noise-induced linear amplifier for gene regulation that requires no feedback. The methods developed in the present work allow one to understand and engineer nonlinear biochemical signal processors based on fluctuation-induced phenotypes., Comment: 23 pages, 5 figures, Accepted by Journal of Chemical Physics

In synthetic biology, gene regulatory circuits are often constructed by combining smaller circuit components. Connections between components are achieved by transcription factors acting on promoters. If the individual components behave as true modules and certain module interface conditions are satisfied, the function of the composite circuits can in principle be predicted. In this paper, we investigate one of the interface conditions: fan-out. We quantify the fan-out, a concept widely used in electric engineering, to indicate the maximum number of the downstream inputs that an upstream output transcription factor can regulate. We show that the fan-out is closely related to retroactivity studied by Del Vecchio, et al. We propose an efficient operational method for measuring the fan-out that can be applied to various types of module interfaces. We also show that the fan-out can be enhanced by self-inhibitory regulation on the output. We discuss the potential role of the inhibitory regulations found in gene regulatory networks and protein signal pathways. The proposed estimation method for fanout not only provides an experimentally efficient way for quantifying the level of modularity in gene regulatory circuits but also helps characterize and design module interfaces, enabling the modular construction of gene circuits., Comment: 28 pages, 5 figures

Simulated evolution of biological networks can be used to generate functional networks as well as investigate hypotheses regarding natural evolution. A handful of studies have shown how simulated evolution can be used for studying the functional space spanned by biochemical networks, studying natural evolution, or designing new synthetic networks. If there was a method for easily performing such studies, it can allow the community to further experiment with simulated evolution and explore all of its uses. As a result, we have developed a library written in the C language that performs all the basic functions needed to carry out simulated evolution of biological networks. The library comes with a generic genetic algorithm as well as genetic algorithms for specifically evolving genetic networks, protein networks, or mass-action networks. The library also comes with functions for simulating these networks. A user needs to specify a desired function. A GUI is provided for users to become oriented with all the options available in the library. The library is free and open source under the BSD lisence and can be obtained at evolvenetworks.sourceforge.net. It can be built on all major platforms. The code can be most conveniently compiled using cross-platform make (CMake)., Comment: 10 pages, 3 figures

Gene regulatory circuits show significant stochastic fluctuations in their circuit signals due to the low copy number of transcription factors. When a gene circuit component is connected to an existing circuit, the dynamic properties of the existing circuit can be affected by the connected component. In this paper, we investigate modularity in the dynamics of the gene circuit based on stochastic fluctuations in the circuit signals. We show that the noise in the output signal of the existing circuit can be affected significantly when the output is connected to the input of another circuit component. More specifically, the output signal noise can show significantly longer correlations when the two components are connected. This equivalently means that the noise power spectral density becomes narrower. We define the relative change in the correlation time or the spectrum bandwidth by stochastic retroactivity, which is shown to be directly related to the retroactivity defined in the deterministic framework by del Vecchio et al. This provides an insight on how to measure retroactivity, by investigating stochastic fluctuations in gene expression levels, more specifically, by obtaining an autocorrelation function of the fluctuations. We also provide an interesting aspect of the frequency response of the circuit. We show that depending on the magnitude of operating frequencies, different kinds of signals need to be preferably chosen for circuit description in a modular fashion: at low enough frequency, expression level of transcription factor that are not bound to their specific promoter region needs to be chosen, and at high enough frequency, that of the total transcription factor, both bound and unbound, does., Comment: 18 pages, 9 figures

Synthetic biology brings together concepts and techniques from engineering and biology. In this field, computer-aided design (CAD) is necessary in order to bridge the gap between computational modeling and biological data. An application named TinkerCell has been created in order to serve as a CAD tool for synthetic biology. TinkerCell is a visual modeling tool that supports a hierarchy of biological parts. Each part in this hierarchy consists of a set of attributes that define the part, such as sequence or rate constants. Models that are constructed using these parts can be analyzed using various C and Python programs that are hosted by TinkerCell via an extensive C and Python API. TinkerCell supports the notion of a module, which are networks with interfaces. Such modules can be connected to each other, forming larger modular networks. Because TinkerCell associates parameters and equations in a model with their respective part, parts can be loaded from databases along with their parameters and rate equations. The modular network design can be used to exchange modules as well as test the concept of modularity in biological systems. The flexible modeling framework along with the C and Python API allows TinkerCell to serve as a host to numerous third-party algorithms. TinkerCell is a free and open-source project under the Berkeley Software Distribution license. Downloads, documentation, and tutorials are available at www.tinkercell.com., Comment: 23 pages, 20 figures

Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a network are desirable. In this work, we are particular interested in the question of whether a given pathway can potentially harbor multiple stable steady states. In other words, the challenge is to find the set of parameters such that the dynamical system defined by a set of ordinary differential equations will contain multiple stable steady states. Being able to find parameters that cause a network to be bistable may also be benefitial for engineering synthetic bistable systems where the engineer needs to know a working set of parameters. Result: We have developed an algorithm that optimizes the parameters of a dynamical system so that the system will contain at least one saddle or unstable point. The algorithm then looks at trajectories around this saddle or unstable point to see whether the different trajectories converge to different stable points. The algorithm returns the parameters that causes the system to exhibit multiple stable points. Since this is an optimization algorithm, it is not quaranteed to find a solution. Repeated runs are often required to find a solution for systems where only a narrow set of parameters exhibit bistability. Availability: The C code for the algorithm is available at http://tinkercell.googlecode.com, Comment: 5 pages, 4 figures

In this paper, we investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances are shown to depend on the size of the measurement time window ($\epsilon$), within which reaction events are counted for measuring a single flux. The degree of the $\epsilon$-dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time scale separation. This $\epsilon$-dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks. We propose a systematic way to control fluctuations of reactant concentrations while minimizing changes in mean concentration levels. Such orthogonal control is obtained by introducing a control vector indicating the strength and direction of parameter perturbations leading to a sensitive control. We also propose a possible implication in the control of flux fluctuation: The control distribution for flux fluctuations changes with the measurement time window size, $\epsilon$. When a control engineer applies a specific control operation on a reaction system, the system can respond contrary to what is expected, depending on the time window size $\epsilon$., Comment: 34 pages, 11 figures

Synthetic biology is the engineering of cellular networks. It combines principles of engineering and the knowledge of biological networks to program the behavior of cells. Computational modeling techniques in conjunction with molecular biology techniques have been successful in constructing biological devices such as switches, oscillators, and gates. The ambition of synthetic biology is to construct complex systems from such fundamental devices, much in the same way electronic circuits are built from basic parts. As this ambition becomes a reality, engineering concepts such as interchangeable parts and encapsulation will find their way into biology. We realize that there is a need for computational tools that would support such engineering concepts in biology. As a solution, we have developed the software Athena that allows biological models to be constructed as modules. Modules can be connected to one another without altering the modules themselves. In addition, Athena houses various tools useful for designing synthetic networks including tools to perform simulations, automatically derive transcription rate expressions, and view and edit synthetic DNA sequences. New tools can be incorporated into Athena without modifying existing program via a plugin interface, IronPython scripts, Systems Biology Workbench interfacing and the R statistical language. The program is currently for Windows operating systems, and the source code for Athena is made freely available through CodePlex, www.codeplex.com/athena., Comment: 17 pages, 7 figures

The aim of this work is to make available to the community a large collection of mass-action reaction networks of a given size for further research. The set is limited to what can be computed on a modern multi-core desktop in reasonable time (< 20 days). We have currently generated over 47 million unique reaction networks. All currently generated sets of networks are available and as new sets are completed they will also be made available. Also provided are programs for translating them into different formats, along with documentation and examples. Source code and binaries for all the programs are included. These can be downloaded from (http://www.sys-bio.org/networkenumeration). This library of networks will allow for thorough studies of the reaction network space. Additionally, these methods serve as an example for future work on enumerating other types of biological networks, such as genetic regulatory networks and mass-action networks that include regulation., Comment: 17 pages, 6 figures