Search

Understanding the large reaction networks found in biological systems is a daunting task. One approach is to divide a network into more manageable smaller modules, thus simplifying the problem. This is a common strategy used in engineering. However, the process of identifying biological modules is still in its infancy and very little is understood about the range and capabilities of motif structures found in biological modules. In order to delineate these modules, a library of functional motifs has been generated via in silico evolution techniques. On the basis of their functional forms, networks were evolved from four broad areas: oscillators, bistable switches, homeostatic systems and frequency filters. Some of these motifs were constructed from simple mass action kinetics, others were based on Michaelis–Menten kinetics as found in protein/protein networks and the remainder were based on Hill equations as found in gene/protein interaction networks. The purpose of the study is to explore the capabilities of different network architectures and the rich variety of functional forms that can be generated. Ultimately, the library may be used to delineate functional motifs in real biological networks. [ABSTRACT FROM AUTHOR]

Modern biological research is increasingly informed by computational simulation experiments, which necessitate the development of methods for annotating, archiving, sharing, and reproducing the conducted experiments. These simulations increasingly require extensive collaboration among modelers, experimentalists, and engineers. The Minimum Information About a Simulation Experiment (MIASE) guidelines outline the information needed to share simulation experiments. SED-ML is a computer-readable format for the information outlined by MIASE, created as a community project and supported by many investigators and software tools. Level 1 Version 5 of SED-ML expands the ability of modelers to define simulations in SED-ML using the Kinetic Simulation Algorithm Onotoloy (KiSAO). While it was possible in Version 4 to define a simulation entirely using KiSAO, Version 5 now allows users to define tasks, model changes, ranges, and outputs using the ontology as well. SED-ML is supported by a growing ecosystem of investigators, model languages, and software tools, including various languages for constraint-based, kinetic, qualitative, rule-based, and spatial models, and many simulation tools, visual editors, model repositories, and validators. Additional information about SED-ML is available at https://sed-ml.org/., (© 2024 the author(s), published by De Gruyter, Berlin/Boston.)

The dogma that cancer is a genetic disease is being questioned. Recent findings suggest that genetic/nongenetic duality is necessary for cancer progression. A think tank organized by the Shraman Foundation's Institute for Theoretical Biology compiled key challenges and opportunities that theoreticians, experimentalists, and clinicians can explore from a systems biology perspective to provide a better understanding of the disease as well as help discover new treatment options and therapeutic strategies., Competing Interests: Declaration of interests No interests are declared., (Copyright © 2022. Published by Elsevier Inc.)

Computational simulation experiments increasingly inform modern biological research, and bring with them the need to provide ways to annotate, archive, share and reproduce the experiments performed. These simulations increasingly require extensive collaboration among modelers, experimentalists, and engineers. The Minimum Information About a Simulation Experiment (MIASE) guidelines outline the information needed to share simulation experiments. SED-ML is a computer-readable format for the information outlined by MIASE, created as a community project and supported by many investigators and software tools. The first versions of SED-ML focused on deterministic and stochastic simulations of models. Level 1 Version 4 of SED-ML substantially expands these capabilities to cover additional types of models, model languages, parameter estimations, simulations and analyses of models, and analyses and visualizations of simulation results. To facilitate consistent practices across the community, Level 1 Version 4 also more clearly describes the use of SED-ML constructs, and includes numerous concrete validation rules. SED-ML is supported by a growing ecosystem of investigators, model languages, and software tools, including eight languages for constraint-based, kinetic, qualitative, rule-based, and spatial models, over 20 simulation tools, visual editors, model repositories, and validators. Additional information about SED-ML is available at https://sed-ml.org/., Competing Interests: Authors state no conflict of interest., (2021 Lucian P. Smith et al.)

People who are engineering biological organisms often find it useful to communicate in diagrams, both about the structure of the nucleic acid sequences that they are engineering and about the functional relationships between sequence features and other molecular species. Some typical practices and conventions have begun to emerge for such diagrams. The Synthetic Biology Open Language Visual (SBOL Visual) has been developed as a standard for organizing and systematizing such conventions in order to produce a coherent language for expressing the structure and function of genetic designs. This document details version 2.3 of SBOL Visual, which builds on the prior SBOL Visual 2.2 in several ways. First, the specification now includes higher-level "interactions with interactions," such as an inducer molecule stimulating a repression interaction. Second, binding with a nucleic acid backbone can be shown by overlapping glyphs, as with other molecular complexes. Finally, a new "unspecified interaction" glyph is added for visualizing interactions whose nature is unknown, the "insulator" glyph is deprecated in favor of a new "inert DNA spacer" glyph, and the polypeptide region glyph is recommended for showing 2A sequences., (© 2021 Hasan Baig et al., published by De Gruyter, Berlin/Boston.)

People who are engineering biological organisms often find it useful to communicate in diagrams, both about the structure of the nucleic acid sequences that they are engineering and about the functional relationships between sequence features and other molecular species. Some typical practices and conventions have begun to emerge for such diagrams. The Synthetic Biology Open Language Visual (SBOL Visual) has been developed as a standard for organizing and systematizing such conventions in order to produce a coherent language for expressing the structure and function of genetic designs. This document details version 2.2 of SBOL Visual, which builds on the prior SBOL Visual 2.1 in several ways. First, the grounding of molecular species glyphs is changed from BioPAX to SBO, aligning with the use of SBO terms for interaction glyphs. Second, new glyphs are added for proteins, introns, and polypeptide regions (e. g., protein domains), the prior recommended macromolecule glyph is deprecated in favor of its alternative, and small polygons are introduced as alternative glyphs for simple chemicals.

Biological engineers often find it useful to communicate using diagrams. These diagrams can include information both about the structure of the nucleic acid sequences they are engineering and about the functional relationships between features of these sequences and/or other molecular species. A number of conventions and practices have begun to emerge within synthetic biology for creating such diagrams, and the Synthetic Biology Open Language Visual (SBOL Visual) has been developed as a standard to organize, systematize, and extend such conventions in order to produce a coherent visual language. Here, we describe SBOL Visual version 2, which expands previous diagram standards to include new functional interactions, categories of molecular species, support for families of glyph variants, and the ability to indicate modular structure and mappings between elements of a system. SBOL Visual 2 also clarifies a number of requirements and best practices, significantly expands the collection of glyphs available to describe genetic features, and can be readily applied using a wide variety of software tools, both general and bespoke.

Synthetic biology builds upon the techniques and successes of genetics, molecular biology, and metabolic engineering by applying engineering principles to the design of biological systems. The field still faces substantial challenges, including long development times, high rates of failure, and poor reproducibility. One method to ameliorate these problems is to improve the exchange of information about designed systems between laboratories. The synthetic biology open language (SBOL) has been developed as a standard to support the specification and exchange of biological design information in synthetic biology, filling a need not satisfied by other pre-existing standards. This document details version 2.3.0 of SBOL, which builds upon version 2.2.0 published in last year's JIB Standards in Systems Biology special issue. In particular, SBOL 2.3.0 includes means of succinctly representing sequence modifications, such as insertion, deletion, and replacement, an extension to support organization and attachment of experimental data derived from designs, and an extension for describing numerical parameters of design elements. The new version also includes specifying types of synthetic biology activities, unambiguous locations for sequences with multiple encodings, refinement of a number of validation rules, improved figures and examples, and clarification on a number of issues related to the use of external ontology terms.

People who are engineering biological organisms often find it useful to communicate in diagrams, both about the structure of the nucleic acid sequences that they are engineering and about the functional relationships between sequence features and other molecular species . Some typical practices and conventions have begun to emerge for such diagrams. The Synthetic Biology Open Language Visual (SBOL Visual) has been developed as a standard for organizing and systematizing such conventions in order to produce a coherent language for expressing the structure and function of genetic designs. This document details version 2.1 of SBOL Visual, which builds on the prior SBOL Visual 2.0 standard by expanding diagram syntax to include methods for showing modular structure and mappings between elements of a system, interactions arrows that can split or join (with the glyph at the split or join indicating either superposition or a chemical process), and adding new glyphs for indicating genomic context (e.g., integration into a plasmid or genome) and for stop codons.

Synthetic biology builds upon the techniques and successes of genetics, molecular biology, and metabolic engineering by applying engineering principles to the design of biological systems. The field still faces substantial challenges, including long development times, high rates of failure, and poor reproducibility. One method to ameliorate these problems would be to improve the exchange of information about designed systems between laboratories. The synthetic biology open language (SBOL) has been developed as a standard to support the specification and exchange of biological design information in synthetic biology, filling a need not satisfied by other pre-existing standards. This document details version 2.2.0 of SBOL that builds upon version 2.1.0 published in last year's JIB special issue. In particular, SBOL 2.2.0 includes improved description and validation rules for genetic design provenance, an extension to support combinatorial genetic designs, a new class to add non-SBOL data as attachments, a new class for genetic design implementations, and a description of a methodology to describe the entire design-build-test-learn cycle within the SBOL data model.

People who are engineering biological organisms often find it useful to communicate in diagrams, both about the structure of the nucleic acid sequences that they are engineering and about the functional relationships between sequence features and other molecular species. Some typical practices and conventions have begun to emerge for such diagrams. The Synthetic Biology Open Language Visual (SBOL Visual) has been developed as a standard for organizing and systematizing such conventions in order to produce a coherent language for expressing the structure and function of genetic designs. This document details version 2.0 of SBOL Visual, which builds on the prior SBOL Visual 1.0 standard by expanding diagram syntax to include functional interactions and molecular species, making the relationship between diagrams and the SBOL data model explicit, supporting families of symbol variants, clarifying a number of requirements and best practices, and significantly expanding the collection of diagram glyphs.

Synthetic biology builds upon the techniques and successes of genetics, molecular biology, and metabolic engineering by applying engineering principles to the design of biological systems. The field still faces substantial challenges, including long development times, high rates of failure, and poor reproducibility. One method to ameliorate these problems would be to improve the exchange of information about designed systems between laboratories. The Synthetic Biology Open Language (SBOL) has been developed as a standard to support the specification and exchange of biological design information in synthetic biology, filling a need not satisfied by other pre-existing standards. This document details version 2.1 of SBOL that builds upon version 2.0 published in last year’s JIB special issue. In particular, SBOL 2.1 includes improved rules for what constitutes a valid SBOL document, new role fields to simplify the expression of sequence features and how components are used in context, and new best practices descriptions to improve the exchange of basic sequence topology information and the description of genetic design provenance, as well as miscellaneous other minor improvements.

One aim of synthetic biologists is to create novel and predictable biological systems from simpler modular parts. This approach is currently hampered by a lack of well-defined and characterized parts and devices. However, there is a wealth of existing biological information, which can be used to identify and characterize biological parts, and their design constraints in the literature and numerous biological databases. However, this information is spread among these databases in many different formats. New computational approaches are required to make this information available in an integrated format that is more amenable to data mining. A tried and tested approach to this problem is to map disparate data sources into a single data set, with common syntax and semantics, to produce a data warehouse or knowledge base. Ontologies have been used extensively in the life sciences, providing this common syntax and semantics as a model for a given biological domain, in a fashion that is amenable to computational analysis and reasoning. Here, we present an ontology for applications in synthetic biology design, SyBiOnt, which facilitates the modeling of information about biological parts and their relationships. SyBiOnt was used to create the SyBiOntKB knowledge base, incorporating and building upon existing life sciences ontologies and standards. The reasoning capabilities of ontologies were then applied to automate the mining of biological parts from this knowledge base. We propose that this approach will be useful to speed up synthetic biology design and ultimately help facilitate the automation of the biological engineering life cycle.

Synthetic biology builds upon the techniques and successes of genetics, molecular biology, and metabolic engineering by applying engineering principles to the design of biological systems. The field still faces substantial challenges, including long development times, high rates of failure, and poor reproducibility. One method to ameliorate these problems would be to improve the exchange of information about designed systems between laboratories. The Synthetic Biology Open Language (SBOL) has been developed as a standard to support the specification and exchange of biological design information in synthetic biology, filling a need not satisfied by other pre-existing standards. This document details version 2.0 of SBOL, introducing a standardized format for the electronic exchange of information on the structural and functional aspects of biological designs. The standard has been designed to support the explicit and unambiguous description of biological designs by means of a well defined data model. The standard also includes rules and best practices on how to use this data model and populate it with relevant design details. The publication of this specification is intended to make these capabilities more widely accessible to potential developers and users in the synthetic biology community and beyond.

While the first version of the Synthetic Biology Open Language (SBOL) has been adopted by several academic and commercial genetic design automation (GDA) software tools, it only covers a limited number of the requirements for a standardized exchange format for synthetic biology. In particular, SBOL Version 1.1 is capable of representing DNA components and their hierarchical composition via sequence annotations. This proposal revises SBOL Version 1.1, enabling the representation of a wider range of components with and without sequences, including RNA components, protein components, small molecules, and molecular complexes. It also introduces modules to instantiate groups of components on the basis of their shared function and assert molecular interactions between components. By increasing the range of structural and functional descriptions in SBOL and allowing for their composition, the proposed improvements enable SBOL to represent and facilitate the exchange of a broader class of genetic designs.

Circuit diagrams and Unified Modeling Language diagrams are just two examples of standard visual languages that help accelerate work by promoting regularity, removing ambiguity and enabling software tool support for communication of complex information. Ironically, despite having one of the highest ratios of graphical to textual information, biology still lacks standard graphical notations. The recent deluge of biological knowledge makes addressing this deficit a pressing concern. Toward this goal, we present the Systems Biology Graphical Notation (SBGN), a visual language developed by a community of biochemists, modelers and computer scientists. SBGN consists of three complementary languages: process diagram, entity relationship diagram and activity flow diagram. Together they enable scientists to represent networks of biochemical interactions in a standard, unambiguous way. We believe that SBGN will foster efficient and accurate representation, visualization, storage, exchange and reuse of information on all kinds of biological knowledge, from gene regulation, to metabolism, to cellular signaling.

Synthetic biology is an engineering discipline that builds on our mechanistic understanding of molecular biology to program microbes to carry out new functions. Such predictable manipulation of a cell requires modeling and experimental techniques to work together. The modeling component of synthetic biology allows one to design biological circuits and analyze its expected behavior. The experimental component merges models with real systems by providing quantitative data and sets of available biological 'parts' that can be used to construct circuits. Sufficient progress has been made in the combined use of modeling and experimental methods, which reinforces the idea of being able to use engineered microbes as a technological platform.

BioModels Database (http://www.ebi.ac.uk/biomodels/), part of the international initiative BioModels.net, provides access to published, peer-reviewed, quantitative models of biochemical and cellular systems. Each model is carefully curated to verify that it corresponds to the reference publication and gives the proper numerical results. Curators also annotate the components of the models with terms from controlled vocabularies and links to other relevant data resources. This allows the users to search accurately for the models they need. The models can currently be retrieved in the SBML format, and import/export facilities are being developed to extend the spectrum of formats supported by the resource.

Most of the published quantitative models in biology are lost for the community because they are either not made available or they are insufficiently characterized to allow them to be reused. The lack of a standard description format, lack of stringent reviewing and authors' carelessness are the main causes for incomplete model descriptions. With today's increased interest in detailed biochemical models, it is necessary to define a minimum quality standard for the encoding of those models. We propose a set of rules for curating quantitative models of biological systems. These rules define procedures for encoding and annotating models represented in machine-readable form. We believe their application will enable users to (i) have confidence that curated models are an accurate reflection of their associated reference descriptions, (ii) search collections of curated models with precision, (iii) quickly identify the biological phenomena that a given curated model or model constituent represents and (iv) facilitate model reuse and composition into large subcellular models.

Researchers in computational biology today make use of a large number of different software packages for modeling, analysis, and data manipulation and visualization. In this paper, we describe the ERATO Systems Biology Workbench (SBW), a software framework that allows these heterogeneous application components--written in diverse programming languages and running on different platforms--to communicate and use each others' data and algorithmic capabilities. Our goal is to create a simple, open-source software infrastructure which is effective, easy to implement and easy to understand. SBW uses a broker-based architecture and enables applications (potentially running on separate, distributed computers) to communicate via a simple network protocol. The interfaces to the system are encapsulated in client-side libraries that we provide for different programming languages. We describe the SBW architecture and the current set of modules, as well as alternative implementation technologies.

Motivation: Metabolic Control Analysis is one of many disciplines that make use of scaled derivatives. In particular, 'elasticities' are used to quantify the effect of an effector or substrate concentration on an enzyme rate under locally specified conditions. Normally an algebraic expression for the elasticity of an enzyme is obtained by differentiating its rate law, multiplying by the effector concentration and dividing by the rate law itself: this results in considerable expression expansion, and when the results are subsequently simplified it is often at the expense of biological comprehensibility., Results: We present a novel algorithm which not only circumvents the expression expansion, but preserves an elegant separation of the components in enzyme behaviour. Easily implemented, and producing gains in both performance and numerical precision, the algorithm is potentially applicable to a number of existing packages. It also greatly assists the manual derivation and evaluation of elasticities, allowing the elasticity of even quite complex enzyme systems to be written by inspection.

In this paper we describe a flow-through system for reconstituting parts of metabolism from purified enzymes. This involves pumping continuously into a reaction chamber, fresh enzymes and reagents so that metabolic reactions occur in the chamber. The waste products leave the chamber via the outflow so that a steady state can be setup. The system we chose consisted of a single enzyme, lactate dehydrogenase. This enzyme was chosen because it consumes NADH in the chamber which could be monitored spectrophotometrically. The aim of the work was to investigate whether a steady state could be achieved in the flow system and whether a metabolic control analysis could be done. We measured two control coefficients, CLDH and Cpump for the enzyme flux and NADH concentration and confirmed that the summation theorem applied to this system. The advantage of a flow-through system is that the titrations necessary to estimate the control coefficients can be easily and precisely controlled; this means that accurate estimates for the control coefficients can be obtained. In the paper, we discuss some statistical aspects of the data analysis and some possible applications of the technique, including a method to determine the presence of metabolic channelling between two different enzymes.

Metabolic control analysis allows one to express the elasticity coefficients (which describe the "local" kinetic features of enzymes) in terms of the control coefficients (quantitative indicators of the "global" control properties). However, when coenzymes (or metabolites linked by conservation constraints) are present in the pathway this procedure yields the "apparent" values of elasticity coefficients that correspond to the kinetic responses of the enzymes to such a simultaneous change of the coenzyme forms which leaves the total concentration of these forms unchanged (e.g., NAD+ + NADH in the glycolysis). We show that a generalised connectivity theorem (Kholodenko et al, Eur. J. Biochem. (1994) 225, 179-186) makes it possible to express the elasticity coefficients with respect to every coenzyme form separately. Such expressions include (i) the control coefficients and (ii) the responses to changes in the total concentrations of the coenzymes.

The control and regulation of metabolic systems are determined by their responses to changes in the internal metabolites (the internal state) and parameters of the system. In many cases, the concentrations of the intermediates are constrained by moiety conservations, for example those requiring that all intermediate forms of any enzyme sum to the conserved total concentration of that enzyme. In this study, we show how responses to changes in the internal state are related to responses to changes in the total amounts of conserved moieties. The relationship between these two different measures of control leads to a generalisation of the connectivity theorems. The results have important implications for the study of a variety of phenomena such as metabolite (coenzyme) sequestration, group-transfer and channelling. The relationships we derive make it possible to determine the control features of these pathways. As an illustration, two examples are chosen. The first shows the effect of sequestration of substrate moiety while the second deals with the sequestration of the enzyme moieties and enzyme/enzyme interactions.

SCAMP is a general-purpose simulator of metabolic and chemical networks. The program is written in C and is portable to all computer systems that support an ANSI C compiler. SCAMP accepts metabolic models described in a biochemical language, and this enables novice as well as experienced users rapidly to build and simulate metabolic systems. The language is sufficiently flexible to enable other types of model to be built, e.g. chemostat or ecological models. The language offers many facilities, including: the ability to describe metabolic pathways of any structure and possessing any kinetics using normal chemical notation; optionally build models directly from the differential equations; differing compartment volumes; access to flux, concentration and rate of change information; detection of conserved cycles; access to all coefficients and elasticities of metabolic control analysis; user-defined forcing functions at the model boundaries; user-defined monitoring functions; user-configurable output of any quantity. From the model description SCAMP can either generate C code for later compilation to produce fast executable stand-alone models or run-time code for input to a run-time interpreter for immediate execution. The simulator also incorporates an inbuilt symbolic differentiator for evaluating the Jacobian and elasticity matrices.

Differing views have been given in the literature as to whether the presence in a pathway of an enzyme at a concentration comparable to that of its substrate affects the values of control coefficients and the theorems of metabolic control analysis. Here we argue in favour of one of those views: that there is no effect unless the enzyme sequesters a substrate that contains a conserved moiety. In this particular case, we derive both a general criterion for estimating whether such an effect will be of a significant magnitude, and equations for determining the changes in the flux control coefficients. The nature of the phenomenom and the application of the equations are illustrated with a numerical simulation.

Two usual assumptions of the treatment of metabolism are: (a) the rates of isolated enzyme reactions are additive, i.e., that rate is proportional to enzyme concentration; (b) in a system, the rates of individual enzyme reactions are not influenced by interactions with other enzymes, i.e. that they are acting independently, except by being coupled through shared metabolites. On this basis, control analysis has established theorems and experimental methods for studying the distribution of control. These assumptions are not universally true and it is shown that the theorems can be modified to take account of such deviations. This is achieved by defining additional elasticity coefficients, designated by the symbol pi, which quantify the effects of homologous and heterologous enzyme interactions. Here we show that for the case of non-proportionality of rate with enzyme concentration, (pi ii not equal to 1), the summation theorems are given by (Formula: see text). The example of monomer-oligomer equilibria is used to illustrate non-additive behaviour and experimental methods for their study are suggested.

The association of different enzymes into a complex may induce changes in the kinetic parameters of its component enzymes. This implies that they cannot be treated as independent catalysts. It will affect the formulations and theorems of control analysis and necessitates the introduction of additional elasticities reflecting the effect of one enzyme on the rate of another. We show how this is achieved as an extension of the classical treatment. We present modified summation and connectivity theorems incorporating both homologous and heterologous interactions. The case of channelling of metabolites in such complexes is considered and an experimental method for its detection is suggested.

In metabolic control analysis, the set of rules called the matrix method simplifies writing the matrix equation that relates the control coefficients to elasticities of enzymes, and a subset of the velocities and substrate concentrations in a metabolic system. However, since the process of writing and solving these equations can be clearly defined, a computer program is being produced that will write the equations for the control coefficients given only the reactions of the metabolic system. In this way, the results of metabolic control analysis can be made available to all those who can use them, even if they do not know the theory in detail. The computational strategies underlying such a program, and the similarities to a biochemical simulation program developed previously are described.

Existing theorems from the analysis of metabolic control have been taken and embedded in a simple matrix algebra procedure for calculating the flux control coefficients of enzymes (formerly known as sensitivities) in a metabolic pathway from their kinetic properties (their elasticities). New theorems governing the flux control coefficients of branched pathways and substrate cycles have been derived to allow the procedure to be applied to complex pathway configurations. Modifications to the elasticity terms used in the equations have been theoretically justified so that the method remains valid for pathways with conserved metabolites (for example, the adenine nucleotide pool or the intermediates of a catalytic cycle such as the tricarboxylic acid cycle) or with pools of metabolites kept very near to equilibrium by very rapid reactions. The matrix equations generated using these theorems and relationships may be solved algebraically or numerically. Algebraic solutions have been used to determine the factors responsible for the degree of amplification of flux control coefficients by substrate cycles and to show that it is possible to derive expressions for the elasticities of a group of enzymes.

The matrix algebra procedure for determining the flux control coefficients of enzymes in metabolic pathways has been extended to allow determination of the concentration control coefficients. Although it is shown that the procedure is essentially unchanged in most cases, the presence of moiety-conserved cycles in a pathway places additional limitations on the form of the equations that can be used in the matrix formulation for concentration control coefficients. In the case of branched pathways, a new coefficient has been defined, the branch distribution control coefficient, which can be obtained via the matrix procedure. Thus a single matrix equation permits calculation or algebraic evaluation of the control coefficients for flux, concentration and distribution of flux at branches, so that the complete response of a pathway to alteration of enzyme content, or to modulation by an effector, can be determined. The relationships have been determined between flux control coefficients in isolated sections of metabolic pathways and the coefficients for the same enzymes when part of a larger metabolic system. It is shown that the control analysis of the isolated system provides useful information towards determining the control properties of the extended system.

Metabolic Control Analysis is extended to time dependent systems. It is assumed that the time derivative of the metabolite concentrations can be written as a linear combination of rate laws, each one of first order with respect to the corresponding enzyme concentration. The definitions of the control and elasticity coefficients are extended, and a new type of coefficient ("time coefficient", "T") is defined. First, we prove that simultaneous changes in all enzyme concentrations by the same arbitrary factor, is equivalent to a change in the time scale. When infinitesimal changes are considered, these arguments lead to the derivation of general summation theorems that link control and time coefficients. The comparison of two systems with identical rates, that only differ in one metabolite concentration, leads to a method for the construction of general connectivity theorems, that relate control and elasticity coefficients. A mathematical proof in matrix form, of the summation and connectivity relationships, for time dependent systems is given. Those relationships allow one to express the control coefficients in terms of the elasticity and time coefficients for the case of unbranched pathway.