Identifying unique oligonucleotide (oligo) probe sequences is an important step in PCR and microa... more Identifying unique oligonucleotide (oligo) probe sequences is an important step in PCR and microarray experiments. While there are a growing number of complete and annotated genomes, the largest collection of publicly available genetic sequences are expressed sequence tag (EST) sequences. Furthermore, for many organisms that are important to the society, such as barley, the EST is the major data on the expressed genes in a number of these organisms. For the EST sequences, the unique oligo problem is the selection of oligos each of which appears (exactly) in one EST sequence but does not appear (exactly or approximately, for a given hamming difference d) in any other EST sequence. OligoSpawn, in two phase, has been implemented to efficiently select oligos from ESTs. The notion of a “seed” was used in the construction of OligoSpawn, and its run time is exponential dependent on q (the length of the “seed”). For q = 11, it ran on a previous barley dataset of 28MB for 2 hours and 26 minu...
The kinetics of muscle glycogen synthase in different phosphorylation states can be described wit... more The kinetics of muscle glycogen synthase in different phosphorylation states can be described with the same set of kinetic parameters by an adapted Monod–Wyman–Changeux equation in which covalent modification alters the T/R (taut/relaxed) equilibrium constant, L0. Only L0 depends on the phosphorylation state.
Metabolic control analysis [Kacser and Burns (1973) Symp. Soc. Exp. Biol. 27, 65–104; Heinrich an... more Metabolic control analysis [Kacser and Burns (1973) Symp. Soc. Exp. Biol. 27, 65–104; Heinrich and Rapoport (1974) Eur. J. Biochem. 42, 89–95] leads to a description of the systemic properties of a metabolic system (expressed as control coefficients) in terms of the local kinetic properties of the individual enzyme‐catalyzed reactions (expressed as elasticity coefficients). This paper describes a non‐algebraic diagrammatic method which generates the mathematical expressions for flux or concentration‐control coefficients in terms of elasticity coefficients. According to a set of simple rules, ‘flux‐control patterns’ or ‘concentration‐control patterns’ are drawn on a metabolic diagram. Each control pattern represents a product of elasticity coefficients that occurs as a term in the expression for a control coefficient. The rules also generate the correct sign that precedes each term. The control patterns are then used to build the expressions for control coefficients. The procedure wa...
How do fluxes and metabolite concentrations, the variables of metabolic systems, respond to a cha... more How do fluxes and metabolite concentrations, the variables of metabolic systems, respond to a change in some system parameter, such as an enzyme concentration or the affinity of an enzyme towards one of its effectors? Can such systemic behaviour be explained purely in terms of local enzymic properties? These fundamental questions about metabolic behaviour have been successfully addressed by metabolic control analysis (Kacser & Burns, 1973; Heinrich & Rapoport, 1974; also in numerous chapters of this book) and biochemical systems theory (Savageau, 1969abc, 1976; also in Chapters 4 and 5 of this book by Savageau and Voit respectively). In the language of metabolic control analysis the answer amounts to expressing control coefficients, which quantify global systemic behaviour, in terms of elasticity coefficients, which describe local enzymic behaviour. Similar coefficients are defined in biochemical systems theory. It is immaterial whether one derives these expressions from the summation and connectivity relationships of metabolic control analysis or the power law equations of biochemical systems theory. In metabolic control analysis, several methods of solution involving matrix algebra have been developed (Fell & Sauro, 1985; Sauro et al., 1987; Small & Fell, 1989; Westerhoff & Kell, 1986) and they allow for the analysis of flux and concentration control in metabolic pathways containing linear, branched, looped and moiety-conserved structures. These methods are eminently suitable for numerical control analysis, but can be tedious for obtaining the algebraic solution.
Why is it that many of the classical ideas of metabolic regulation have been so difficult to reco... more Why is it that many of the classical ideas of metabolic regulation have been so difficult to reconcile with metabolic control analysis? A major reason seems to be a difference in the questions asked by the two approaches. Analysis of metabolic control asks how changes in parameters affect variables1,2 (for recent review see Ref. 3). Analysis of metabolic regulation asks how changes in metabolite concentrations or functions of metabolite concentrations affect variables4. Although at first sight there seems to be little difference between these questions, deeper study shows that there is an important difference. From a systems point of view parameters are constant quantities, and some metabolites that act as regulators, e.g. hormones, are often parameters of metabolic systems. Nevertheless, many of the metabolites classically regarded as regulators are themselves variables, so that the question of metabolic regulation often concerns the effect of one variable on another, e.g., of the concentration of a feedback inhibitor on the flux through its pool. The latter type of question has up to now been avoided in control analysis; here we will show how it can be answered.
Moiety-conserved cycles are metabolic structures that interconvert different forms of a chemical ... more Moiety-conserved cycles are metabolic structures that interconvert different forms of a chemical moiety (such as ATP-ADP-AMP, the different forms of adenylate), while the sum of these forms remains constant. Their metabolic behaviour is treated within the framework of control analysis [Kacser, H. & Burns, J.A. (1973) Symp. Soc. Exp. Biol 27, 65-104]. To explain the importance of the conserved sum of cycle metabolites as a parameter of the system, the cycle is first regarded as a 'black box'. The interactions of the cycle with the rest of the system are expressed in terms of 'cycle elasticities' and 'cycle control coefficients' by the usual connectivity properties. The conserved sum is seen to be an 'external' parameter in the sense that its effect is described by a combined response expression. All cycle coefficients can be written in terms of elasticities and concentrations of cycle metabolites. The treatment shows how connectivity expressions should be modified when moiety-conserved cycles are present and establishes new summation and connectivity properties. The analysis is applied to a two-member moiety-conserved cycle and its general application is discussed.
The evaluation of a generic simplified bi-substrate enzyme kinetic equation, whose derivation is ... more The evaluation of a generic simplified bi-substrate enzyme kinetic equation, whose derivation is based on the assumption of equilibrium binding of substrates and products in random order, is described. This equation is much simpler than the mechanistic (ordered and ping-pong) models, in that it contains fewer parameters (that is, no K(i) values for the substrates and products). The generic equation fits data from both the ordered and the ping-pong models well over a wide range of substrate and product concentrations. In the cases where the fit is not perfect, an improved fit can be obtained by considering the rate equation for only a single set of product concentrations. Due to its relative simplicity in comparison to the mechanistic models, this equation will be useful for modelling bi-substrate reactions in computational systems biology.
A core model is presented for protein production in Escherichia coli to address the question whet... more A core model is presented for protein production in Escherichia coli to address the question whether there is an optimal ribosomal concentration for non-ribosome protein production. Analysing the steady-state solution of the model over a range of mRNA concentrations, indicates that such an optimum ribosomal content exists, and that the optimum shifts to higher ribosomal contents at higher specific growth rates.
It is shown that both the reversible Hill equation and a generalised, reversible Monod-Wyman-Chan... more It is shown that both the reversible Hill equation and a generalised, reversible Monod-Wyman-Changeux equation can give analogous regulatory behaviour when embedded in a model metabolic pathway.
Whether an allosteric feedback or feedforward modifier actually has an effect on the steady-state... more Whether an allosteric feedback or feedforward modifier actually has an effect on the steady-state properties of a metabolic pathway depends not only on the allosteric modifier effect itself, but also on the control properties of the affected allosteric enzyme in the pathway of which it is part. Different modification mechanisms are analysed: mixed inhibition, allosteric inhibition and activation of the reversible Monod-Wyman-Changeux and reversible Hill models. In conclusion, it is shown that, whereas a modifier effect on substrate and product binding (specific effects) can be an effective negative feedback mechanism, it is much less effective as a positive feedforward mechanism. The prediction is that catalytic effects that change the apparent limiting velocity would be more effective in feedforward activation.
Metabolic control analysis (MCA) was developed to quantify how system variables are affected by p... more Metabolic control analysis (MCA) was developed to quantify how system variables are affected by parameter variations in a system. In addition, MCA can express the global properties of a system in terms of the individual catalytic steps, using connectivity and summation theorems to link the control coefficients to the elasticity coefficients. MCA was originally developed for steady-state analysis and not all summation theorems have been derived for dynamic systems. A method to determine time-dependent flux and concentration control coefficients for dynamic systems by expressing the time domain as a function of percentage progression through any arbitrary fixed interval of time is reported. Time-dependent flux and concentration control coefficients of dynamic systems, provided that they are evaluated in this novel way, obey the same summation theorems as steady-state flux and concentration control coefficients, respectively.
Identifying unique oligonucleotide (oligo) probe sequences is an important step in PCR and microa... more Identifying unique oligonucleotide (oligo) probe sequences is an important step in PCR and microarray experiments. While there are a growing number of complete and annotated genomes, the largest collection of publicly available genetic sequences are expressed sequence tag (EST) sequences. Furthermore, for many organisms that are important to the society, such as barley, the EST is the major data on the expressed genes in a number of these organisms. For the EST sequences, the unique oligo problem is the selection of oligos each of which appears (exactly) in one EST sequence but does not appear (exactly or approximately, for a given hamming difference d) in any other EST sequence. OligoSpawn, in two phase, has been implemented to efficiently select oligos from ESTs. The notion of a “seed” was used in the construction of OligoSpawn, and its run time is exponential dependent on q (the length of the “seed”). For q = 11, it ran on a previous barley dataset of 28MB for 2 hours and 26 minu...
The kinetics of muscle glycogen synthase in different phosphorylation states can be described wit... more The kinetics of muscle glycogen synthase in different phosphorylation states can be described with the same set of kinetic parameters by an adapted Monod–Wyman–Changeux equation in which covalent modification alters the T/R (taut/relaxed) equilibrium constant, L0. Only L0 depends on the phosphorylation state.
Metabolic control analysis [Kacser and Burns (1973) Symp. Soc. Exp. Biol. 27, 65–104; Heinrich an... more Metabolic control analysis [Kacser and Burns (1973) Symp. Soc. Exp. Biol. 27, 65–104; Heinrich and Rapoport (1974) Eur. J. Biochem. 42, 89–95] leads to a description of the systemic properties of a metabolic system (expressed as control coefficients) in terms of the local kinetic properties of the individual enzyme‐catalyzed reactions (expressed as elasticity coefficients). This paper describes a non‐algebraic diagrammatic method which generates the mathematical expressions for flux or concentration‐control coefficients in terms of elasticity coefficients. According to a set of simple rules, ‘flux‐control patterns’ or ‘concentration‐control patterns’ are drawn on a metabolic diagram. Each control pattern represents a product of elasticity coefficients that occurs as a term in the expression for a control coefficient. The rules also generate the correct sign that precedes each term. The control patterns are then used to build the expressions for control coefficients. The procedure wa...
How do fluxes and metabolite concentrations, the variables of metabolic systems, respond to a cha... more How do fluxes and metabolite concentrations, the variables of metabolic systems, respond to a change in some system parameter, such as an enzyme concentration or the affinity of an enzyme towards one of its effectors? Can such systemic behaviour be explained purely in terms of local enzymic properties? These fundamental questions about metabolic behaviour have been successfully addressed by metabolic control analysis (Kacser & Burns, 1973; Heinrich & Rapoport, 1974; also in numerous chapters of this book) and biochemical systems theory (Savageau, 1969abc, 1976; also in Chapters 4 and 5 of this book by Savageau and Voit respectively). In the language of metabolic control analysis the answer amounts to expressing control coefficients, which quantify global systemic behaviour, in terms of elasticity coefficients, which describe local enzymic behaviour. Similar coefficients are defined in biochemical systems theory. It is immaterial whether one derives these expressions from the summation and connectivity relationships of metabolic control analysis or the power law equations of biochemical systems theory. In metabolic control analysis, several methods of solution involving matrix algebra have been developed (Fell & Sauro, 1985; Sauro et al., 1987; Small & Fell, 1989; Westerhoff & Kell, 1986) and they allow for the analysis of flux and concentration control in metabolic pathways containing linear, branched, looped and moiety-conserved structures. These methods are eminently suitable for numerical control analysis, but can be tedious for obtaining the algebraic solution.
Why is it that many of the classical ideas of metabolic regulation have been so difficult to reco... more Why is it that many of the classical ideas of metabolic regulation have been so difficult to reconcile with metabolic control analysis? A major reason seems to be a difference in the questions asked by the two approaches. Analysis of metabolic control asks how changes in parameters affect variables1,2 (for recent review see Ref. 3). Analysis of metabolic regulation asks how changes in metabolite concentrations or functions of metabolite concentrations affect variables4. Although at first sight there seems to be little difference between these questions, deeper study shows that there is an important difference. From a systems point of view parameters are constant quantities, and some metabolites that act as regulators, e.g. hormones, are often parameters of metabolic systems. Nevertheless, many of the metabolites classically regarded as regulators are themselves variables, so that the question of metabolic regulation often concerns the effect of one variable on another, e.g., of the concentration of a feedback inhibitor on the flux through its pool. The latter type of question has up to now been avoided in control analysis; here we will show how it can be answered.
Moiety-conserved cycles are metabolic structures that interconvert different forms of a chemical ... more Moiety-conserved cycles are metabolic structures that interconvert different forms of a chemical moiety (such as ATP-ADP-AMP, the different forms of adenylate), while the sum of these forms remains constant. Their metabolic behaviour is treated within the framework of control analysis [Kacser, H. & Burns, J.A. (1973) Symp. Soc. Exp. Biol 27, 65-104]. To explain the importance of the conserved sum of cycle metabolites as a parameter of the system, the cycle is first regarded as a 'black box'. The interactions of the cycle with the rest of the system are expressed in terms of 'cycle elasticities' and 'cycle control coefficients' by the usual connectivity properties. The conserved sum is seen to be an 'external' parameter in the sense that its effect is described by a combined response expression. All cycle coefficients can be written in terms of elasticities and concentrations of cycle metabolites. The treatment shows how connectivity expressions should be modified when moiety-conserved cycles are present and establishes new summation and connectivity properties. The analysis is applied to a two-member moiety-conserved cycle and its general application is discussed.
The evaluation of a generic simplified bi-substrate enzyme kinetic equation, whose derivation is ... more The evaluation of a generic simplified bi-substrate enzyme kinetic equation, whose derivation is based on the assumption of equilibrium binding of substrates and products in random order, is described. This equation is much simpler than the mechanistic (ordered and ping-pong) models, in that it contains fewer parameters (that is, no K(i) values for the substrates and products). The generic equation fits data from both the ordered and the ping-pong models well over a wide range of substrate and product concentrations. In the cases where the fit is not perfect, an improved fit can be obtained by considering the rate equation for only a single set of product concentrations. Due to its relative simplicity in comparison to the mechanistic models, this equation will be useful for modelling bi-substrate reactions in computational systems biology.
A core model is presented for protein production in Escherichia coli to address the question whet... more A core model is presented for protein production in Escherichia coli to address the question whether there is an optimal ribosomal concentration for non-ribosome protein production. Analysing the steady-state solution of the model over a range of mRNA concentrations, indicates that such an optimum ribosomal content exists, and that the optimum shifts to higher ribosomal contents at higher specific growth rates.
It is shown that both the reversible Hill equation and a generalised, reversible Monod-Wyman-Chan... more It is shown that both the reversible Hill equation and a generalised, reversible Monod-Wyman-Changeux equation can give analogous regulatory behaviour when embedded in a model metabolic pathway.
Whether an allosteric feedback or feedforward modifier actually has an effect on the steady-state... more Whether an allosteric feedback or feedforward modifier actually has an effect on the steady-state properties of a metabolic pathway depends not only on the allosteric modifier effect itself, but also on the control properties of the affected allosteric enzyme in the pathway of which it is part. Different modification mechanisms are analysed: mixed inhibition, allosteric inhibition and activation of the reversible Monod-Wyman-Changeux and reversible Hill models. In conclusion, it is shown that, whereas a modifier effect on substrate and product binding (specific effects) can be an effective negative feedback mechanism, it is much less effective as a positive feedforward mechanism. The prediction is that catalytic effects that change the apparent limiting velocity would be more effective in feedforward activation.
Metabolic control analysis (MCA) was developed to quantify how system variables are affected by p... more Metabolic control analysis (MCA) was developed to quantify how system variables are affected by parameter variations in a system. In addition, MCA can express the global properties of a system in terms of the individual catalytic steps, using connectivity and summation theorems to link the control coefficients to the elasticity coefficients. MCA was originally developed for steady-state analysis and not all summation theorems have been derived for dynamic systems. A method to determine time-dependent flux and concentration control coefficients for dynamic systems by expressing the time domain as a function of percentage progression through any arbitrary fixed interval of time is reported. Time-dependent flux and concentration control coefficients of dynamic systems, provided that they are evaluated in this novel way, obey the same summation theorems as steady-state flux and concentration control coefficients, respectively.
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Papers by Jannie Hofmeyr