BACKGROUND
there is evidence from across the phyla that enzymes are often associated with one another into assemblies or metabolons in which metabolites may or may not be channeled directly from one enzyme to the next in the pathway.
investigation of glycolytic metabolons responsible for the metabolism of glucose has a long and controversial history  <cit> , but it seems clear that in eukaryotes several of the glycolytic enzymes can form oligomers  <cit>  and associate with other glycolytic enzymes  <cit> .
in the model prokaryote, escherichia coli, the glycolytic pathway has been isolated as a large equimolar multi-enzyme complex in which metabolites were sequestered  <cit> .
there is also evidence that enzymes may be assembled into much larger hyperstructures  <cit> , as in the case of cellulolytic enzymes in bacteria such as acetivibrio cellulolyticus  <cit>  or compartmentalized into organelles such as glycosomes as in the case of glycolytic enzymes in trypanosomes  <cit> , or associated with the tubulin cytoskeleton, as in the case of many glycolytic enzymes in mammalian cells  <cit> .
the actual advantages – or lack of them – conferred by metabolons and hyperstructures on metabolic efficiency are unclear.
what happens to efficiency when enzymes responsible for import are restricted to a patch of membrane, or when cytoplasmic enzymes are bound to membrane transporters, or when metabolons are brought together in a hyperstructure?
if quantitative answers to these questions could be obtained rapidly and cheaply in silico, it would be of value not only to the understanding of existing systems but also to the construction of engineered systems.
the development of programs that allow genetic engineers to know in advance which constructions are worth making is therefore biotechnology's equivalent of the quest for the holy grail.
simulation with stochastic automata and multi-agent systems is an attractive alternative to differential equations for studying the diffusion and interaction of the many different enzymes and metabolites in cells which may be present in either small or large numbers  <cit> .
a stochastic automaton, hsim , has been developed and an early version used to model the assembly of cytoskeletal filaments in a virtual cell  <cit> .
in extending hsim to the analysis of the assembly, movement and disassembly of large numbers of molecules and macromolecules, we have chosen to base our studies very loosely on two pathways that continue to be intensely studied in e. coli: the phosphoenolpyruvate:sugar phosphotransferase system , which is responsible for sensing and importing sugars such as glucose and which supplies sugar phosphates to a second intensely studied pathway, the glycolytic pathway  <cit> .
here, we use hsim to determine quantitatively the effects of metabolon and hyperstructure formation on a modified version of these systems in which glycolysis is truncated.
RESULTS
equal numbers of enzymes in varying conditions of association
the extent to which the assembly of enzymes into metabolons confers greater efficiency in a modified version of glycolysis and the pts  was the first question we addressed after testing hsim .
glycolysis is modified because the real glycolytic pathway yields two peps per g6p which are converted into pyruvate by pyruvate kinase but it is not known how much of this pep is available for the pts in vivo, let alone how much is available in an individual cell as opposed to a population of cells.
an initial presence of pep is required to prime the system.
in conditions in which only one pep per glucose imported is available for the pts, the maximum rate of functioning is determined by the initial concentration of pep .
this is because each pep is transformed into a pyruvate and donates a phosphate to allow generation of another pep.
the numbers of pyruvate molecules produced are given after  <dig> s simulation when the number of pyruvate molecules is a linear function of time .
consider first conditions in which the number of pep molecules is  <dig> and in which metabolons allow the products of one enzyme to be released in the vicinity of the adjacent one; that is, channeling is not obligatory, and metabolites can escape from the metabolon.
when the glycolytic enzymes are assembled into spatially separate glycolytic metabolons, the quantity of pyruvate made is no greater than when these enzymes are separate, but when the pts enzymes are assembled into pts metabolons, the quantity of pyruvate made is fifteen times greater .
in the latter conditions, glycolysis then becomes limiting as shown by the fact that when all the enzymes are in separate metabolons, the quantity of pyruvate made reaches its maximum and is forty-four times greater.
this pattern is conserved for all initial concentrations of pep over  <dig>  in general, pyruvate production is highest at the highest initial concentrations of pep.
when the pts enzymes are free, and when the initial concentrations of pep are high , the yield of pyruvate is much less than that of the pep.
this is because the flow of phosphate through the pts is too slow, and the enzyme ei is constantly phosphorylated so that it cannot fully exploit the available pool of pep.
at low initial numbers of pep molecules , both glycolytic and pts metabolons are advantageous .
this is because both sets of enzymes are under-employed, and improving the efficiency of either glycolysis or the pts allows the enzymes in the other set to function.
it might be argued that the concentrations of pts and glycolytic enzymes are higher in real cells by an order of magnitude and that this is a very important factor in the efficiency.
however, decreasing the volume of the cell 8-fold while retaining the same numbers of enzymes so as to make concentrations similar to those of the real pts did not result in qualitative changes in the results .
that said, the levels of pyruvate production for the free enzymes are an order of magnitude higher at all initial pep values when these enzymes are concentrated in the smaller volume.
since confining enzymes to complementary metabolons increases efficiency, we asked whether the colocalization of complementary metabolons would increase efficiency still further.
to explore the effects of the colocalization of glycolytic and pts metabolons as individual pairs, we attached the first enzyme in our version of the glycolytic pathway, pgi, to eiia and, in a separate experiment, to hpr .
the attachment of the glycolytic metabolon to the pts metabolon at eiia or hpr improved the yield of pyruvate at the lower initial concentrations of pep by up to 150%  but had no significant effect over  <dig> molecules of initial pep which is when the pts can import sufficient glucose for colocalization of the two metabolons to be no longer of an advantage .
in the above colocalization studies, enolase, the final enzyme in our truncated glycolytic metabolon, could release pep far from ei the first enzyme in the pts.
we therefore tested the effect of attaching enolase to ei in conditions in which pgi was also attached to eiia .
this double attachment gave a slightly lower yield of pyruvate compared with the single attachment cases.
hence colocalization of complementary metabolons can lead to an increase in efficiency in some conditions but this is modest in comparison with the increase conferred by metabolon formation itself.
altering numbers of enzymes in varying conditions of association
it is conceivable that the encounters between the substrate and the enzyme on the end of the metabolon are limiting.
to test this , we increased the number of ei fourfold since this is the increase observed when the synthesis of this enzyme is induced in the presence of glucose .
increased dosage of ei had no effect in the presence of pts metabolons since diffusion of pep to the metabolon is essentially limited by the relatively rapid rate of diffusion of pep itself.
increased dosage did, however, have an effect when the pts enzymes were limiting and, as shown in the column for  <dig> initial molecules of pep, resulted in a 40% increase in the yield of pyruvate.
at the lower concentration of  <dig> initial pep molecules, there was no significant advantage to be gained from the increase in ei in any condition whilst at the higher concentration of  <dig> initial pep molecules, most of the new eis are phosphorylated and again increased the yield of pyruvate 40% when the pts enzymes were limiting.
the fact that the increased ei dosage makes a difference only when the pep concentration is high or when the pts enzymes diffuse freely  makes sense, since in a complex, or when pep is diffusion limiting, there should be little benefit from having extra ei outside the metabolon.
thus, the results conform to expectation if the pts is truly rate limiting for overall glucose metabolism.
these results also help answer the question of how many rate-limiting steps there are.
the fact that the overall rate increases when the glycolytic enzymes are in a metabolon indicates that there can be more than one rate-limiting step.
this might be related to phosphofructokinase being an important allosterically controlled enzyme with a key role in the flux of carbon through glycolysis.
however, increasing the level of phosphofructokinase fourfold had no significant effect.
effects of restricting enzymes to a region of the membrane/cytoplasm
bacteria are now known to be highly structured and it is interesting to investigate the efficacy conferred by the assembly of metabolons into a hyperstructure.
we therefore adapted the program so that only glycolytic enzymes function with the exception of enzyme iibc which imports glucose and converts it into p-glu spontaneously .
in all cases, the enzyme iibc species were restricted to a small patch of membrane while the glycolytic metabolons were positioned  <dig> nm away.
as explained above, direct attachment to eiibc was avoided because this would have hindered the import of glucose in the present version of the program.
it should be noted that pep accumulates in this experiment because it is consumed by neither ei nor pyruvate kinase.
there is no significant gain in efficacy when the enzymes are in a hyperstructure in which there is no channeling versus the case when the enzymes are free .
indeed, at the three rates of glucose import tested, the pep production in a hyperstructure comprising  <dig> metabolons without channeling is similar to that of the same number of freely diffusible enzymes.
hence, at least under these conditions, the prediction that a metabolite that escapes from a metabolon could be captured by a neighboring metabolon is false.
not surprisingly, channeling between the glycolytic enzymes in the metabolons gives the highest yield of pep.
it should be noted that at the highest rate of import, more glucose is entering than glycolysis can consume, and a stationary state is not attained.
the concentration of p-glu is another interesting parameter that could be studied.
the association of enzymes into metabolons is a potentially powerful way of generating signals  <cit>  and there may be additional advantages in confining metabolons to a few hyperstructures, for example, in generating gradients of metabolites or signaling molecules.
to illustrate this, we positioned the patch of eiibcs and the glycolytic hyperstructure described above at a cell pole and allowed each molecule to be consumed in a reaction catalyzed by a freely diffusible enzyme.
under these conditions, there is a broad range of values of the coefficients of production, diffusion and consumption that generate an easily observable gradient .
where the receptors of signaling molecules are themselves confined to a region, such gradients may lead to the concentration of the molecule exceeding a threshold and hence be of physiological importance; hsim offers the possibility of investigating these situations.
discussion
there is increasing evidence that in both eukaryotic and prokaryotic cells, enzymes are organized into higher order assemblies.
in metabolism, such assemblies may take the form of metabolons  <cit>  which may themselves be associated into still higher order hyperstructures  <cit> .
in signaling, chemotaxis proteins may be organized into arrays in the poles of certain bacteria  <cit> , while in eukaryotes, signal transduction proteins may be assembled into transducons or signalosomes  <cit> .
exploring and exploiting the consequences of such organization is a major challenge.
what are the advantages, if any, of the colocalization of successive enzymes in a pathway?
can these advantages be quantified?
what are the effects of increasing the number of copies of a particular enzyme or of the efficiency of the reaction that it catalyzes?
what happens when enzymes responsible for import are restricted to a patch of membrane or when cytoplasmic enzymes are bound to membrane enzymes or transporters?
to help provide quantitative answers to such questions, we have developed a stochastic automaton, hsim  <cit> , to simulate realistically the diffusion of metabolites and enzymes in both the membrane and the cytoplasm, the reactions between enzymes and their substrates, and interactions between enzymes leading to their assembly into metabolons and hyperstructures.
for a typical workstation, hsim takes  <dig> minutes to simulate  <dig> minute of real time for a cell, irrespective of its size, containing a total of  <dig> molecules , irrespective of the number of classes of these molecules.
the system that we have investigated with hsim is a simplified one loosely based on the pts and glycolysis in e. coli which, although intensely studied for many years, is still imperfectly understood.
for example, how many rate-limiting steps are there, and how might these be related to the formation of metabolons?
our version of glycolysis has  <dig> enzymes that act successively to produce only one pep from each g6p.
as in the real pts, our version has  <dig> enzymes that pass a phosphate group from one another to the final membrane-bound enzyme, eiicbglc, that imports and phosphorylates glucose to make g6p and completes the loop in the synthesis of one pep from one g6p.
this system has the advantage of avoiding the complication of the rate of pep production being non-linear due to both synthesis of two pep molecules per g6p and consumption of pep also depending on pyruvate kinase .
enolase, the final glycolytic enzyme in our version, catalyzes the production of pyruvate from pep and transfers a phosphate to ei, the first enzyme in the pts.
pyruvate production is used as a measure of the efficacy of the system.
enzymes can either diffuse freely and release their products immediately or be in metabolons.
enzymes in metabolons can either release their products immediately to diffuse away or channel them obligatorily to the next enzyme in the pathway, provided this recipient enzyme is itself in a state to receive the metabolite .
the initial concentrations of pep at which increased efficiency is conferred by assembly of either the pts or the glycolytic enzymes into separate metabolons are readily revealed by hsim.
moreover, descriptions that would otherwise be qualitative can be turned into quantitative ones.
for example, at intermediate initial levels of pep , the pts is limiting while glycolysis is not, and the formation of pts metabolons increases pyruvate production fourfold.
at low levels of pep , both glycolytic and pts metabolons are advantageous, and the formation of both sets of metabolons can increase pyruvate production up to eightfold.
we then tested the prediction that attaching the pts and glycolytic metabolons to form pairs would increase efficiency relative to these metabolons that are not physically associated.
a relatively modest increase of 150% was observed for some pep concentrations below  <dig> per cell, and no increase was observed over that.
hsim can be used to investigate the possibility that a particular enzyme is rate-limiting in a pathway, and that increasing the number of copies of the enzyme will improve efficiency .
to illustrate this, we increased the number of ei fourfold, which corresponds to the increase observed when glucose is added.
this resulted in a 40% increase in pyruvate formation under conditions where the pts enzymes were already limiting.
the association of enzymes into hyperstructures much larger than metabolons either exists already or can be created by genetic engineering by modifying enzymes so that they associate either with themselves into homopolymers or with other enzymes into heteropolymers or with cytoskeletal structures or with membrane domains.
surprisingly, there was little advantage to be gained in terms of efficiency of pyruvate production from a hyperstructure unless channeling was allowed.
this doubled efficiency.
it is, of course, conceivable that the advantage of grouping enzymes into hyperstructures lies elsewhere in, for example, signaling  <cit> .
we therefore positioned a hyperstructure at a pole and explored the consequences on the distribution of pep under conditions in which pep is consumed in a reaction catalyzed by a freely diffusible enzyme.
this showed that a gradient of pep can be generated by a broad range of values of different parameters; in other words, if enzymes are altered so as to assemble into a hyperstructure, it is easy to form a gradient.
CONCLUSIONS
in sum, our results show how hsim may help answer fundamental problems and evaluate biotechnological objectives.
here we have applied hsim to the analysis of a simplified model system in steady state conditions.
however, it may also prove useful where parameters such as numbers of enzymes and substrates fluctuate.
continued development of hsim and other stochastic automata and multi-agent systems should show that the dream of meaningful experiments in silico is not a pipedream.

 there is evidence from across the phyla that enzymes are often associated with one another into assemblies or metabolons in which metabolites may or may not be channeled directly from one enzyme to the next in the pathway. investigation of glycolytic metabolons responsible for the metabolism of glucose has a long and controversial history, but it seems clear that in eukaryotes several of the glycolytic enzymes can form oligomers and associate with other glycolytic enzymes. in the model prokaryote, escherichia coli, the glycolytic pathway has been isolated as a large equimolar multi-enzyme complex in which metabolites were sequestered. there is also evidence that enzymes may be assembled into much larger hyperstructures, as in the case of cellulolytic enzymes in bacteria such as acetivibrio cellulolyticus or compartmentalized into organelles such as glycosomes as in the case of glycolytic enzymes in trypanosomes, or associated with the tubulin cytoskeleton, as in the case of many glycolytic enzymes in mammalian cells. the actual advantages – or lack of them – conferred by metabolons and hyperstructures on metabolic efficiency are unclear. what happens to efficiency when enzymes responsible for import are restricted to a patch of membrane, or when cytoplasmic enzymes are bound to membrane transporters, or when metabolons are brought together in a hyperstructure? if quantitative answers to these questions could be obtained rapidly and cheaply in silico, it would be of value not only to the understanding of existing systems but also to the construction of engineered systems. the development of programs that allow genetic engineers to know in advance which constructions are worth making is therefore biotechnology's equivalent of the quest for the holy grail. simulation with stochastic automata and multi-agent systems is an attractive alternative to differential equations for studying the diffusion and interaction of the many different enzymes and metabolites in cells which may be present in either small or large numbers. a stochastic automaton, hsim, has been developed and an early version used to model the assembly of cytoskeletal filaments in a virtual cell. in extending hsim to the analysis of the assembly, movement and disassembly of large numbers of molecules and macromolecules, we have chosen to base our studies very loosely on two pathways that continue to be intensely studied in e. coli: the phosphoenolpyruvate:sugar phosphotransferase system, which is responsible for sensing and importing sugars such as glucose and which supplies sugar phosphates to a second intensely studied pathway, the glycolytic pathway. here, we use hsim to determine quantitatively the effects of metabolon and hyperstructure formation on a modified version of these systems in which glycolysis is truncated.  equal numbers of enzymes in varying conditions of association the extent to which the assembly of enzymes into metabolons confers greater efficiency in a modified version of glycolysis and the pts was the first question we addressed after testing hsim. glycolysis is modified because the real glycolytic pathway yields two peps per g6p which are converted into pyruvate by pyruvate kinase but it is not known how much of this pep is available for the pts in vivo, let alone how much is available in an individual cell as opposed to a population of cells. an initial presence of pep is required to prime the system. in conditions in which only one pep per glucose imported is available for the pts, the maximum rate of functioning is determined by the initial concentration of pep. this is because each pep is transformed into a pyruvate and donates a phosphate to allow generation of another pep. the numbers of pyruvate molecules produced are given after s simulation when the number of pyruvate molecules is a linear function of time. consider first conditions in which the number of pep molecules is and in which metabolons allow the products of one enzyme to be released in the vicinity of the adjacent one; that is, channeling is not obligatory, and metabolites can escape from the metabolon. when the glycolytic enzymes are assembled into spatially separate glycolytic metabolons, the quantity of pyruvate made is no greater than when these enzymes are separate, but when the pts enzymes are assembled into pts metabolons, the quantity of pyruvate made is fifteen times greater. in the latter conditions, glycolysis then becomes limiting as shown by the fact that when all the enzymes are in separate metabolons, the quantity of pyruvate made reaches its maximum and is forty-four times greater. this pattern is conserved for all initial concentrations of pep over in general, pyruvate production is highest at the highest initial concentrations of pep. when the pts enzymes are free, and when the initial concentrations of pep are high, the yield of pyruvate is much less than that of the pep. this is because the flow of phosphate through the pts is too slow, and the enzyme ei is constantly phosphorylated so that it cannot fully exploit the available pool of pep. at low initial numbers of pep molecules, both glycolytic and pts metabolons are advantageous. this is because both sets of enzymes are under-employed, and improving the efficiency of either glycolysis or the pts allows the enzymes in the other set to function. it might be argued that the concentrations of pts and glycolytic enzymes are higher in real cells by an order of magnitude and that this is a very important factor in the efficiency. however, decreasing the volume of the cell 8-fold while retaining the same numbers of enzymes so as to make concentrations similar to those of the real pts did not result in qualitative changes in the results. that said, the levels of pyruvate production for the free enzymes are an order of magnitude higher at all initial pep values when these enzymes are concentrated in the smaller volume. since confining enzymes to complementary metabolons increases efficiency, we asked whether the colocalization of complementary metabolons would increase efficiency still further. to explore the effects of the colocalization of glycolytic and pts metabolons as individual pairs, we attached the first enzyme in our version of the glycolytic pathway, pgi, to eiia and, in a separate experiment, to hpr. the attachment of the glycolytic metabolon to the pts metabolon at eiia or hpr improved the yield of pyruvate at the lower initial concentrations of pep by up to 150% but had no significant effect over molecules of initial pep which is when the pts can import sufficient glucose for colocalization of the two metabolons to be no longer of an advantage. in the above colocalization studies, enolase, the final enzyme in our truncated glycolytic metabolon, could release pep far from ei the first enzyme in the pts. we therefore tested the effect of attaching enolase to ei in conditions in which pgi was also attached to eiia. this double attachment gave a slightly lower yield of pyruvate compared with the single attachment cases. hence colocalization of complementary metabolons can lead to an increase in efficiency in some conditions but this is modest in comparison with the increase conferred by metabolon formation itself. altering numbers of enzymes in varying conditions of association it is conceivable that the encounters between the substrate and the enzyme on the end of the metabolon are limiting. to test this, we increased the number of ei fourfold since this is the increase observed when the synthesis of this enzyme is induced in the presence of glucose. increased dosage of ei had no effect in the presence of pts metabolons since diffusion of pep to the metabolon is essentially limited by the relatively rapid rate of diffusion of pep itself. increased dosage did, however, have an effect when the pts enzymes were limiting and, as shown in the column for initial molecules of pep, resulted in a 40% increase in the yield of pyruvate. at the lower concentration of initial pep molecules, there was no significant advantage to be gained from the increase in ei in any condition whilst at the higher concentration of initial pep molecules, most of the new eis are phosphorylated and again increased the yield of pyruvate 40% when the pts enzymes were limiting. the fact that the increased ei dosage makes a difference only when the pep concentration is high or when the pts enzymes diffuse freely makes sense, since in a complex, or when pep is diffusion limiting, there should be little benefit from having extra ei outside the metabolon. thus, the results conform to expectation if the pts is truly rate limiting for overall glucose metabolism. these results also help answer the question of how many rate-limiting steps there are. the fact that the overall rate increases when the glycolytic enzymes are in a metabolon indicates that there can be more than one rate-limiting step. this might be related to phosphofructokinase being an important allosterically controlled enzyme with a key role in the flux of carbon through glycolysis. however, increasing the level of phosphofructokinase fourfold had no significant effect. effects of restricting enzymes to a region of the membrane/cytoplasm bacteria are now known to be highly structured and it is interesting to investigate the efficacy conferred by the assembly of metabolons into a hyperstructure. we therefore adapted the program so that only glycolytic enzymes function with the exception of enzyme iibc which imports glucose and converts it into p-glu spontaneously. in all cases, the enzyme iibc species were restricted to a small patch of membrane while the glycolytic metabolons were positioned nm away. as explained above, direct attachment to eiibc was avoided because this would have hindered the import of glucose in the present version of the program. it should be noted that pep accumulates in this experiment because it is consumed by neither ei nor pyruvate kinase. there is no significant gain in efficacy when the enzymes are in a hyperstructure in which there is no channeling versus the case when the enzymes are free. indeed, at the three rates of glucose import tested, the pep production in a hyperstructure comprising metabolons without channeling is similar to that of the same number of freely diffusible enzymes. hence, at least under these conditions, the prediction that a metabolite that escapes from a metabolon could be captured by a neighboring metabolon is false. not surprisingly, channeling between the glycolytic enzymes in the metabolons gives the highest yield of pep. it should be noted that at the highest rate of import, more glucose is entering than glycolysis can consume, and a stationary state is not attained. the concentration of p-glu is another interesting parameter that could be studied. the association of enzymes into metabolons is a potentially powerful way of generating signals and there may be additional advantages in confining metabolons to a few hyperstructures, for example, in generating gradients of metabolites or signaling molecules. to illustrate this, we positioned the patch of eiibcs and the glycolytic hyperstructure described above at a cell pole and allowed each molecule to be consumed in a reaction catalyzed by a freely diffusible enzyme. under these conditions, there is a broad range of values of the coefficients of production, diffusion and consumption that generate an easily observable gradient. where the receptors of signaling molecules are themselves confined to a region, such gradients may lead to the concentration of the molecule exceeding a threshold and hence be of physiological importance; hsim offers the possibility of investigating these situations. discussion there is increasing evidence that in both eukaryotic and prokaryotic cells, enzymes are organized into higher order assemblies. in metabolism, such assemblies may take the form of metabolons which may themselves be associated into still higher order hyperstructures. in signaling, chemotaxis proteins may be organized into arrays in the poles of certain bacteria, while in eukaryotes, signal transduction proteins may be assembled into transducons or signalosomes. exploring and exploiting the consequences of such organization is a major challenge. what are the advantages, if any, of the colocalization of successive enzymes in a pathway? can these advantages be quantified? what are the effects of increasing the number of copies of a particular enzyme or of the efficiency of the reaction that it catalyzes? what happens when enzymes responsible for import are restricted to a patch of membrane or when cytoplasmic enzymes are bound to membrane enzymes or transporters? to help provide quantitative answers to such questions, we have developed a stochastic automaton, hsim, to simulate realistically the diffusion of metabolites and enzymes in both the membrane and the cytoplasm, the reactions between enzymes and their substrates, and interactions between enzymes leading to their assembly into metabolons and hyperstructures. for a typical workstation, hsim takes minutes to simulate minute of real time for a cell, irrespective of its size, containing a total of molecules, irrespective of the number of classes of these molecules. the system that we have investigated with hsim is a simplified one loosely based on the pts and glycolysis in e. coli which, although intensely studied for many years, is still imperfectly understood. for example, how many rate-limiting steps are there, and how might these be related to the formation of metabolons? our version of glycolysis has enzymes that act successively to produce only one pep from each g6p. as in the real pts, our version has enzymes that pass a phosphate group from one another to the final membrane-bound enzyme, eiicbglc, that imports and phosphorylates glucose to make g6p and completes the loop in the synthesis of one pep from one g6p. this system has the advantage of avoiding the complication of the rate of pep production being non-linear due to both synthesis of two pep molecules per g6p and consumption of pep also depending on pyruvate kinase. enolase, the final glycolytic enzyme in our version, catalyzes the production of pyruvate from pep and transfers a phosphate to ei, the first enzyme in the pts. pyruvate production is used as a measure of the efficacy of the system. enzymes can either diffuse freely and release their products immediately or be in metabolons. enzymes in metabolons can either release their products immediately to diffuse away or channel them obligatorily to the next enzyme in the pathway, provided this recipient enzyme is itself in a state to receive the metabolite. the initial concentrations of pep at which increased efficiency is conferred by assembly of either the pts or the glycolytic enzymes into separate metabolons are readily revealed by hsim. moreover, descriptions that would otherwise be qualitative can be turned into quantitative ones. for example, at intermediate initial levels of pep, the pts is limiting while glycolysis is not, and the formation of pts metabolons increases pyruvate production fourfold. at low levels of pep, both glycolytic and pts metabolons are advantageous, and the formation of both sets of metabolons can increase pyruvate production up to eightfold. we then tested the prediction that attaching the pts and glycolytic metabolons to form pairs would increase efficiency relative to these metabolons that are not physically associated. a relatively modest increase of 150% was observed for some pep concentrations below per cell, and no increase was observed over that. hsim can be used to investigate the possibility that a particular enzyme is rate-limiting in a pathway, and that increasing the number of copies of the enzyme will improve efficiency. to illustrate this, we increased the number of ei fourfold, which corresponds to the increase observed when glucose is added. this resulted in a 40% increase in pyruvate formation under conditions where the pts enzymes were already limiting. the association of enzymes into hyperstructures much larger than metabolons either exists already or can be created by genetic engineering by modifying enzymes so that they associate either with themselves into homopolymers or with other enzymes into heteropolymers or with cytoskeletal structures or with membrane domains. surprisingly, there was little advantage to be gained in terms of efficiency of pyruvate production from a hyperstructure unless channeling was allowed. this doubled efficiency. it is, of course, conceivable that the advantage of grouping enzymes into hyperstructures lies elsewhere in, for example, signaling. we therefore positioned a hyperstructure at a pole and explored the consequences on the distribution of pep under conditions in which pep is consumed in a reaction catalyzed by a freely diffusible enzyme. this showed that a gradient of pep can be generated by a broad range of values of different parameters; in other words, if enzymes are altered so as to assemble into a hyperstructure, it is easy to form a gradient.  in sum, our results show how hsim may help answer fundamental problems and evaluate biotechnological objectives. here we have applied hsim to the analysis of a simplified model system in steady state conditions. however, it may also prove useful where parameters such as numbers of enzymes and substrates fluctuate. continued development of hsim and other stochastic automata and multi-agent systems should show that the dream of meaningful experiments in silico is not a pipedream. 
we have investigated the general case of transport and metabolism as inspired by the phosphoenolpyruvate:sugar phosphotransferase system for glucose importation and by glycolysis. in silico experiments may be performed successfully using stochastic automata such as hsim to help answer fundamental questions in metabolism about the properties of molecular assemblies and to devise strategies to modify such assemblies for biotechnological ends. a fourfold increase in the numbers of enzyme ei led to a 40% increase in pyruvate production, similar to that observed in vivo in the presence of glucose. we show that pts and glycolytic metabolons can increase production of pyruvate eightfold at low concentrations of phosphoenolpyruvate. to quantify these advantages, we have developed a stochastic automaton that allows experiments to be performed in a virtual bacterium with both a membrane and a cytoplasm.
 the advantages of grouping enzymes into metabolons and into higher order structures have long been debated. to quantify these advantages, we have developed a stochastic automaton that allows experiments to be performed in a virtual bacterium with both a membrane and a cytoplasm. we have investigated the general case of transport and metabolism as inspired by the phosphoenolpyruvate:sugar phosphotransferase system for glucose importation and by glycolysis.  we show that pts and glycolytic metabolons can increase production of pyruvate eightfold at low concentrations of phosphoenolpyruvate. a fourfold increase in the numbers of enzyme ei led to a 40% increase in pyruvate production, similar to that observed in vivo in the presence of glucose. although little improvement resulted from the assembly of metabolons into a hyperstructure, such assembly can generate gradients of metabolites and signaling molecules.  in silico experiments may be performed successfully using stochastic automata such as hsim to help answer fundamental questions in metabolism about the properties of molecular assemblies and to devise strategies to modify such assemblies for biotechnological ends. 