Modeling the effects of strigolactone levels on maize root system architecture.

Maize is the most in-demand staple crop globally. Its production relies strongly on the use of fertilizers for the supply of nitrogen, phosphorus, and potassium, which the plant absorbs through its roots, together with water. The architecture of maize roots is determinant in modulating how the plant interacts with the microbiome and extracts nutrients and water from the soil. As such, attempts to use synthetic biology and modulate that architecture to make the plant more resilient to drought and parasitic plants are underway. These attempts often try to modulate the biosynthesis of hormones that determine root architecture and growth. Experiments are laborious and time-consuming, creating the need for simulation platforms that can integrate metabolic models and 3D root growth models and predict the effects of synthetic biology interventions on both, hormone levels and root system architectures. Here, we present an example of such a platform that is built using Mathematica. First, we develop a root model, and use it to simulate the growth of many unique 3D maize root system architectures (RSAs). Then, we couple this model to a metabolic model that simulates the biosynthesis of strigolactones, hormones that modulate root growth and development. The coupling allows us to simulate the effect of changing strigolactone levels on the architecture of the roots. We then integrate the two models in a simulation platform, where we also add the functionality to analyze the effect of strigolactone levels on root phenotype. Finally, using in silico experiments, we show that our models can reproduce both the phenotype of wild type maize, and the effect that varying strigolactone levels have on changing the architecture of maize roots.

Metabolic engineering of Halomonas elongata: Ectoine secretion is increased by demand and supply driven approaches.

The application of naturally-derived biomolecules in everyday products, replacing conventional synthetic manufacturing, is an ever-increasing market. An example of this is the compatible solute ectoine, which is contained in a plethora of treatment formulations for medicinal products and cosmetics. As of today, ectoine is produced in a scale of tons each year by the natural producer Halomonas elongata. In this work, we explore two complementary approaches to obtain genetically improved producer strains for ectoine production. We explore the effect of increased precursor supply (oxaloacetate) on ectoine production, as well as an implementation of increased ectoine demand through the overexpression of a transporter. Both approaches were implemented on an already genetically modified ectoine-excreting strain H. elongata KB2.13 (ΔteaABC ΔdoeA) and both led to new strains with higher ectoine excretion. The supply driven approach led to a 45% increase in ectoine titers in two different strains. This increase was attributed to the removal of phosphoenolpyruvate carboxykinase (PEPCK), which allowed the conversion of 17.9% of the glucose substrate to ectoine. For the demand driven approach, we investigated the potential of the TeaBC transmembrane proteins from the ectoine-specific Tripartite ATP-Independent Periplasmic (TRAP) transporter as export channels to improve ectoine excretion. In the absence of the substrate-binding protein TeaA, an overexpression of both subunits TeaBC facilitated a three-fold increased excretion rate of ectoine. Individually, the large subunit TeaC showed an approximately five times higher extracellular ectoine concentration per dry weight compared to TeaBC shortly after its expression was induced. However, the detrimental effect on growth and ectoine titer at the end of the process hints toward a negative impact of TeaC overexpression on membrane integrity and possibly leads to cell lysis. By using either strategy, the ectoine synthesis and excretion in H. elongata could be boosted drastically. The inherent complementary nature of these approaches point at a coordinated implementation of both as a promising strategy for future projects in Metabolic Engineering. Moreover, a wide variation of intracelllular ectoine levels was observed between the strains, which points at a major disruption of mechanisms responsible for ectoine regulation in strain KB2.13.

A mathematical model for strigolactone biosynthesis in plants.

Strigolactones mediate plant development, trigger symbiosis with arbuscular mycorrhizal fungi, are abundant in 80% of the plant kingdom and help plants gain resistance to environmental stressors. They also induce germination of parasitic plant seeds that are endemic to various continents, such as Orobanche in Europe or Asia and Striga in Africa. The genes involved in the early stages of strigolactones biosynthesis are known in several plants. The regulatory structure and the latter parts of the pathway, where flux branching occurs to produce alternative strigolactones, are less well-understood. Here we present a computational study that collects the available experimental evidence and proposes alternative biosynthetic pathways that are consistent with that evidence. Then, we test the alternative pathways through in silico simulation experiments and compare those experiments to experimental information. Our results predict the differences in dynamic behavior between alternative pathway designs. Independent of design, the analysis suggests that feedback regulation is unlikely to exist in strigolactone biosynthesis. In addition, our experiments suggest that engineering the pathway to modulate the production of strigolactones could be most easily achieved by increasing the flux of ß-carotenes going into the biosynthetic pathway. Finally, we find that changing the ratio of alternative strigolactones produced by the pathway can be done by changing the activity of the enzymes after the flux branching points.

Adaptation to Varying Salinity in Halomonas elongata: Much More Than Ectoine Accumulation.

The halophilic γ-proteobacterium Halomonas elongata DSM 2581 T thrives at salt concentrations well above 10 % NaCl (1.7 M NaCl). A well-known osmoregulatory mechanism is the accumulation of the compatible solute ectoine within the cell in response to osmotic stress. While ectoine accumulation is central to osmoregulation and promotes resistance to high salinity in halophilic bacteria, ectoine has this effect only to a much lesser extent in non-halophiles. We carried out transcriptome analysis of H. elongata grown on two different carbon sources (acetate or glucose), and low (0.17 M NaCl), medium (1 M), and high salinity (2 M) to identify additional mechanisms for adaptation to high saline environments. To avoid a methodological bias, the transcripts were evaluated by applying two methods, DESeq2 and Transcripts Per Million (TPM). The differentially transcribed genes in response to the available carbon sources and salt stress were then compared to the transcriptome profile of Chromohalobacter salexigens, a closely related moderate halophilic bacterium. Transcriptome profiling supports the notion that glucose is degraded via the cytoplasmic Entner-Doudoroff pathway, whereas the Embden-Meyerhoff-Parnas pathway is employed for gluconeogenesis. The machinery of oxidative phosphorylation in H. elongata and C. salexigens differs greatly from that of non-halophilic organisms, and electron flow can occur from quinone to oxygen along four alternative routes. Two of these pathways via cytochrome bo' and cytochrome bd quinol oxidases seem to be upregulated in salt stressed cells. Among the most highly regulated genes in H. elongata and C. salexigens are those encoding chemotaxis and motility proteins, with genes for chemotaxis and flagellar assembly severely downregulated at low salt concentrations. We also compared transcripts at low and high-salt stress (low growth rate) with transcripts at optimal salt concentration and found that the majority of regulated genes were down-regulated in stressed cells, including many genes involved in carbohydrate metabolism, while ribosome synthesis was up-regulated, which is in contrast to what is known from non-halophiles at slow growth. Finally, comparing the acidity of the cytoplasmic proteomes of non-halophiles, extreme halophiles and moderate halophiles suggests adaptation to an increased cytoplasmic ion concentration of H. elongata. Taken together, these results lead us to propose a model for salt tolerance in H. elongata where ion accumulation plays a greater role in salt tolerance than previously assumed.

Anaplerotic Pathways in Halomonas elongata: The Role of the Sodium Gradient.

Salt tolerance in the γ-proteobacterium Halomonas elongata is linked to its ability to produce the compatible solute ectoine. The metabolism of ectoine production is of great interest since it can shed light on the biochemical basis of halotolerance as well as pave the way for the improvement of the biotechnological production of such compatible solute. Ectoine belongs to the biosynthetic family of aspartate-derived amino-acids. Aspartate is formed from oxaloacetate, thereby connecting ectoine production to the anaplerotic reactions that refill carbon into the tricarboxylic acid cycle (TCA cycle). This places a high demand on these reactions and creates the need to regulate them not only in response to growth but also in response to extracellular salt concentration. In this work, we combine modeling and experiments to analyze how these different needs shape the anaplerotic reactions in H. elongata. First, the stoichiometric and thermodynamic factors that condition the flux distributions are analyzed, then the optimal patterns of operation for oxaloacetate production are calculated. Finally, the phenotype of two deletion mutants lacking potentially relevant anaplerotic enzymes: phosphoenolpyruvate carboxylase (Ppc) and oxaloacetate decarboxylase (Oad) are experimentally characterized. The results show that the anaplerotic reactions in H. elongata are indeed subject to evolutionary pressures that differ from those faced by other gram-negative bacteria. Ectoine producing halophiles must meet a higher metabolic demand for oxaloacetate and the reliance of many marine bacteria on the Entner-Doudoroff pathway compromises the anaplerotic efficiency of Ppc, which is usually one of the main enzymes fulfilling this role. The anaplerotic flux in H. elongata is contributed not only by Ppc but also by Oad, an enzyme that has not yet been shown to play this role in vivo. Ppc is necessary for H. elongata to grow normally at low salt concentrations but it is not required to achieve near maximal growth rates as long as there is a steep sodium gradient. On the other hand, the lack of Oad presents serious difficulties to grow at high salt concentrations. This points to a shared role of these two enzymes in guaranteeing the supply of oxaloacetate for biosynthetic reactions.

Understanding biochemical design principles with ensembles of canonical non-linear models.

Systems biology applies concepts from engineering in order to understand biological networks. If such an understanding was complete, biologists would be able to design ad hoc biochemical components tailored for different purposes, which is the goal of synthetic biology. Needless to say that we are far away from creating biological subsystems as intricate and precise as those found in nature, but mathematical models and high throughput techniques have brought us a long way in this direction. One of the difficulties that still needs to be overcome is finding the right values for model parameters and dealing with uncertainty, which is proving to be an extremely difficult task. In this work, we take advantage of ensemble modeling techniques, where a large number of models with different parameter values are formulated and then tested according to some performance criteria. By finding features shared by successful models, the role of different components and the synergies between them can be better understood. We will address some of the difficulties often faced by ensemble modeling approaches, such as the need to sample a space whose size grows exponentially with the number of parameters, and establishing useful selection criteria. Some methods will be shown to reduce the predictions from many models into a set of understandable "design principles" that can guide us to improve or manufacture a biochemical network. Our proposed framework formulates models within standard formalisms in order to integrate information from different sources and minimize the dimension of the parameter space. Additionally, the mathematical properties of the formalism enable a partition of the parameter space into independent subspaces. Each of these subspaces can be paired with a set of criteria that depend exclusively on it, thus allowing a separate sampling/screening in spaces of lower dimension. By applying tests in a strict order where computationally cheaper tests are applied first to each subspace and applying computationally expensive tests to the remaining subset thereafter, the use of resources is optimized and a larger number of models can be examined. This can be compared to a complex database query where the order of the requests can make a huge difference in the processing time. The method will be illustrated by analyzing a classical model of a metabolic pathway with end-product inhibition. Even for such a simple model, the method provides novel insight.

Revision and reannotation of the Halomonas elongata DSM 2581T genome.

The genome of the Halomonas elongata type strain DSM 2581, an industrial producer, was reevaluated using the Illumina HiSeq2500 technology. To resolve duplication-associated ambiguities, PCR products were generated and sequenced. Outside of duplications, 72 sequence corrections were required, of which 24 were point mutations and 48 were indels of one or few bases. Most of these were associated with polynucleotide stretches (poly-T stretch overestimated in 19 cases, poly-C underestimated in 15 cases). These problems may be attributed to using 454 technology for original genome sequencing. On average, the original genome sequence had only one error in 56 kb. There were 23 frameshift error corrections in the 29 protein-coding genes affected by sequence revision. The genome has been subjected to major reannotation in order to substantially increase the annotation quality.

Osmoregulation in the Halophilic Bacterium Halomonas elongata: A Case Study for Integrative Systems Biology.

Halophilic bacteria use a variety of osmoregulatory methods, such as the accumulation of one or more compatible solutes. The wide diversity of compounds that can act as compatible solute complicates the task of understanding the different strategies that halophilic bacteria use to cope with salt. This is specially challenging when attempting to go beyond the pathway that produces a certain compatible solute towards an understanding of how the metabolic network as a whole addresses the problem. Metabolic reconstruction based on genomic data together with Flux Balance Analysis (FBA) is a promising tool to gain insight into this problem. However, as more of these reconstructions become available, it becomes clear that processes predicted by genome annotation may not reflect the processes that are active in vivo. As a case in point, E. coli is unable to grow aerobically on citrate in spite of having all the necessary genes to do it. It has also been shown that the realization of this genetic potential into an actual capability to metabolize citrate is an extremely unlikely event under normal evolutionary conditions. Moreover, many marine bacteria seem to have the same pathways to metabolize glucose but each species uses a different one. In this work, a metabolic network inferred from genomic annotation of the halophilic bacterium Halomonas elongata and proteomic profiling experiments are used as a starting point to motivate targeted experiments in order to find out some of the defining features of the osmoregulatory strategies of this bacterium. This new information is then used to refine the network in order to describe the actual capabilities of H. elongata, rather than its genetic potential.

Time Hierarchies and Model Reduction in Canonical Non-linear Models.

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems.

Design Principles as a Guide for Constraint Based and Dynamic Modeling: Towards an Integrative Workflow.

During the last 10 years, systems biology has matured from a fuzzy concept combining omics, mathematical modeling and computers into a scientific field on its own right. In spite of its incredible potential, the multilevel complexity of its objects of study makes it very difficult to establish a reliable connection between data and models. The great number of degrees of freedom often results in situations, where many different models can explain/fit all available datasets. This has resulted in a shift of paradigm from the initially dominant, maybe naive, idea of inferring the system out of a number of datasets to the application of different techniques that reduce the degrees of freedom before any data set is analyzed. There is a wide variety of techniques available, each of them can contribute a piece of the puzzle and include different kinds of experimental information. But the challenge that remains is their meaningful integration. Here we show some theoretical results that enable some of the main modeling approaches to be applied sequentially in a complementary manner, and how this workflow can benefit from evolutionary reasoning to keep the complexity of the problem in check. As a proof of concept, we show how the synergies between these modeling techniques can provide insight into some well studied problems: Ammonia assimilation in bacteria and an unbranched linear pathway with end-product inhibition.

Chemical reaction network approaches to Biochemical Systems Theory.

This paper provides a framework to represent a Biochemical Systems Theory (BST) model (in either GMA or S-system form) as a chemical reaction network with power law kinetics. Using this representation, some basic properties and the application of recent results of Chemical Reaction Network Theory regarding steady states of such systems are shown. In particular, Injectivity Theory, including network concordance [36] and the Jacobian Determinant Criterion [43], a "Lifting Theorem" for steady states [26] and the comprehensive results of Müller and Regensburger [31] on complex balanced equilibria are discussed. A partial extension of a recent Emulation Theorem of Cardelli for mass action systems [3] is derived for a subclass of power law kinetic systems. However, it is also shown that the GMA and S-system models of human purine metabolism [10] do not display the reactant-determined kinetics assumed by Müller and Regensburger and hence only a subset of BST models can be handled with their approach. Moreover, since the reaction networks underlying many BST models are not weakly reversible, results for non-complex balanced equilibria are also needed.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models.

BACKGROUND: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. RESULTS: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. CONCLUSIONS: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

A blueprint of ectoine metabolism from the genome of the industrial producer Halomonas elongata DSM 2581 T.

The halophilic γ-proteobacterium Halomonas elongata DSM 2581(T) thrives at high salinity by synthesizing and accumulating the compatible solute ectoine. Ectoine levels are highly regulated according to external salt levels but the overall picture of its metabolism and control is not well understood. Apart from its critical role in cell adaptation to halophilic environments, ectoine can be used as a stabilizer for enzymes and as a cell protectant in skin and health care applications and is thus produced annually on a scale of tons in an industrial process using H. elongata as producer strain. This paper presents the complete genome sequence of H. elongata (4,061,296 bp) and includes experiments and analysis identifying and characterizing the entire ectoine metabolism, including a newly discovered pathway for ectoine degradation and its cyclic connection to ectoine synthesis. The degradation of ectoine (doe) proceeds via hydrolysis of ectoine (DoeA) to Nα-acetyl-L-2,4-diaminobutyric acid, followed by deacetylation to diaminobutyric acid (DoeB). In H. elongata, diaminobutyric acid can either flow off to aspartate or re-enter the ectoine synthesis pathway, forming a cycle of ectoine synthesis and degradation. Genome comparison revealed that the ectoine degradation pathway exists predominantly in non-halophilic bacteria unable to synthesize ectoine. Based on the resulting genetic and biochemical data, a metabolic flux model of ectoine metabolism was derived that can be used to understand the way H. elongata survives under varying salt stresses and that provides a basis for a model-driven improvement of industrial ectoine production.

Biochemical pathway modeling tools for drug target detection in cancer and other complex diseases.

In the near future, computational tools and methods based on the mathematical modeling of biomedically relevant networks and pathways will be necessary for the design of therapeutic strategies that fight complex multifactorial diseases. Beyond the use of pharmacokinetic and pharmacodynamic approaches, we propose here the use of dynamic modeling as a tool for describing and analyzing the structure and responses of signaling, genetic and metabolic networks involved in such diseases. Specifically, we discuss the design and construction of meaningful models of biochemical networks, as well as tools, concepts, and strategies for using these models in the search of potential drug targets. We describe three different families of computational tools: predictive model simulations as tools for designing optimal drug profiles and doses; sensitivity analysis as a method to detect key interactions that affect critical outcomes and other characteristics of the network; and other tools integrating mathematical modeling with advanced computation and optimization for detecting potential drug targets. Furthermore, we show how potential drug targets detected with these approaches can be used in a computer-aided context to design or select new drug molecules. All concepts are illustrated with simplified examples and with actual case studies extracted from the recent literature.

Flux duality in nonlinear GMA systems: implications for metabolic engineering.

Pathway models in biotechnology are customarily designed with metabolite concentrations as the primary, dependent variables, whereas fluxes are derived quantities that are secondarily computed from the primary variables. In other fields of mathematics, such as graph theory and linear systems analysis, it has proven useful to complement primal network model designs in terms of vertices (pools) and edges (processes) with dual designs, where the roles of the primary and secondary quantities are interchanged. The conversion from primal to dual systems is fairly easy in linear systems, but it is unclear to what degree it is possible in nonlinear systems. In this article, we present a method to transform nonlinear primal models of pathways or other biotechnological processes that conform to the Generalized Mass Action (GMA) structure within the formalism of Biochemical Systems Theory (BST) into dual models that focus on fluxes, rather than pools. Interestingly, this transformation is relatively straightforward, once some notational issues are streamlined, and the resulting dual system is again in the format of a GMA system. The transformation is illustrated with the example of glycolysis in Saccharomyces cerevisiae, a well known organism in the food industry. The results suggest how rewriting a model in terms of its fluxes helps bridge the gap between flux balance and dynamic models and also offers a view of the investigated system that is complementary to that of the original model. This dual view is important, because fluxes are sometimes more relevant for the behavior of a biotechnological system than (metabolite) pools. The dual system furthermore offers a systematic approach toward understanding the dynamical constraints under which the system operates.

Metabolic Engineering with power-law and linear-logarithmic systems.

Metabolic Engineering aims to improve the performance of biotechnological processes through rational manipulation rather than random mutagenesis of the organisms involved. Such a strategy can only succeed when a mathematical model of the target process is available. Simplifying assumptions are often needed to cope with the complexity of such models in an efficient way, and the choice of such assumptions often leads to models that fall within a certain structural template or formalism. The most popular formalisms can be grouped in two categories: power-law and linear-logarithmic. As optimization and analysis of a model strongly depends on its structure, most methods in Metabolic Engineering have been defined within a given formalism and never used in any other. In this work, the four most commonly used formalisms (two power-law and two linear-logarithmic) are placed in a common framework defined within Biochemical Systems Theory. This framework defines every model as matrix equations in terms of the same parameters, enabling the formulation of a common steady state analysis and providing means for translating models and methods from one formalism to another. Several Metabolic Engineering methods are analysed here and shown to be variants of a single equation. Particularly, two problem solving philosophies are compared: the application of the design equation and the solution of constrained optimization problems. Generalizing the design equation to all the formalisms shows it to be interchangeable with the direct solution of the rate law in matrix form. Furthermore, optimization approaches are concluded to be preferable since they speed the exploration of the feasible space, implement a better specification of the problem and exclude unrealistic results. Beyond consolidating existing knowledge and enabling comparison, the systematic approach adopted here can fill the gaps between the different methods and combine their strengths.

Optimization of biotechnological systems through geometric programming.

BACKGROUND: In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. RESULTS: A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. CONCLUSION: GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus, efficient methods for optimizing GMA systems have multifold appeal.

Optimization of biochemical systems by linear programming and general mass action model representations.

A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.

Modelling, steady state analysis and optimization of the catalytic efficiency of the triosephosphate isomerase.

In the present work we have modelled and optimized the reaction mechanism of the triose phosphate isomerase (TIM) enzyme (E.C. 5.3.1.1). For this purpose we have used an approach that combines the S-system representation within the power law formalism and linear programming techniques. By this means we have explored those rate constants whose alterations are likely to improve the catalytic efficiency of the enzyme and investigated the available room for optimization in different metabolic conditions. The role and plausibility of the different types of mutations on the evolution of this enzyme have also been considered. Steady state sensitivity analysis was carried out and a new set of aggregated logarithmic gains was defined in order to quantify the responses of the system to changes in groups of rate constants that could be explained in terms of mutations affecting the catalytic properties of the enzyme. Evaluation of these logarithmic gains at different levels of saturation and disequilibrium ratios enabled us to reach conclusions about the meaning and role of the diffusion limitation terms. The catalytic efficiency of the monoenzymatic system was optimized through changes in the kinetic rate constants within different sets of restrictions ranging from thermodynamic or kinetic to evolutionary ones. Results showed that, at very different conditions, there is still room for improvement in the TIM enzyme. Thus, in a wide range of metabolically significant values of the disequilibrium ratio there is a minimal variation in the optimal profile that yields 2.1 times the velocity of the basal states. Though most of this increase is accounted for by the increase of the second order constants (that could have already reached a theoretical maximum) significant increases (20%) in catalytic efficiencies are obtained by changes of the internal steps only. Besides these new findings our optimization approach has been able to reproduce results obtained with other approaches.