In addition to the macroscopic simulation, we analysed the buffering of bursts of high adenosine triphosphate hydrolysis by creatine kinase during cyclical muscle activity at the biochemical pathway level. To investigate the low oxygen to carbohydrate ratio for the brain, which takes up lactate during exercise, we calculated the flux distribution in cerebral energy metabolism. Computational modelling of the human body, describing heat exchange and energy metabolism, makes simulation of endurance sports events feasible.The human physiological system is stressed to its limits during endurance sports competition events. We describe a whole body computational model for energy conversion during bicycle racing. About 23 per cent of the metabolic energy is used for muscle work, the rest is converted to heat. We calculated heat transfer by conduction and blood flow inside the body, and heat transfer from the skin by radiation, convection and sweat evaporation, resulting in temperature changes in 25 body compartments. We simulated a mountain time trial to Alpe d'Huez during the Tour de France. To approach the time realized by Lance Armstrong in 2004, very high oxygen uptake must be sustained by the simulated cyclist. Temperature was predicted to reach 39 By computational modelling of the body during such challenging events, we can investigate adaptation under extreme stress, which is not only useful to understand the physiology of athletes but also of rescue workers, fire fighters and mountaineers, and others who must perform close to maximal capacity. Understanding the body's response under maximal stress may also help to understand disease processes. For instance, tissue hypoxia may be caused by great exertion rather than by ischaemia or tumour growth. Other examples are dehydration, high body temperatures caused by exertion rather than fever, and high blood lactate levels caused by physical exertion rather than hypoxia or shock .Physical exercise affects human physiology at multiple scales. The physical work done by athletes is associated with force exertion, temperature changes in the whole body, sweat excretion and increased uptake of oxygen, water and food, all measurable at the whole body level. At the cellular scale, adenosine triphosphate (ATP) hydrolysis energizes the interaction of actin and myosin molecules in the sarcomeres of the muscle cells. The response of the body involves an extensive interplay between various organs. The heart, for instance, starts to pump more blood to transport oxygen and carbon substrates to the muscle and remove carbon dioxide, lactic acid and heat. The brain participates, among others, by regulating lung ventilation, but is challenged with increased lactic acid levels and higher blood temperature, potentially altering neuronal metabolism. The brain also controls muscle coordination and, importantly, determines the motivation of the athlete to perform maximally despite high brain temperatures, acidification, fatigue and sometimes even pain . To prepHere, we will implement a whole body model for energy conversion and heat transport. The latter is very relevant because almost 80 per cent of the metabolic energy during exercise is converted to heat. We will couple this whole body model to equations for the motion and external power requirements during cycling. At the subcellular scale, we will look at models for intracellular events, which have a much higher biochemical and/or time resolution than the whole body model. We discuss the supply of metabolic fuel for exercise by nutrition. In addition, we introduce a model of metabolic flux distribution to predict how brain metabolism may deal with higher blood lactate levels. Metabolic events in the muscle cells are analysed at high time resolution with a model for the buffering of bursts of high ATP hydrolysis caused by the rhythmic muscle contractions during bicycle racing.To demonstrate the applicability of whole body modelling to world class athletic performance, we simulate a mountain time trial in the Tour de France from Bourg d'Oisans to Alpe d'Huez. As the basis for our virtual cyclist, we use published physiological data  for Lanc2.We will start with the description of a whole body computational model that describes the physiological system of an athlete performing external work at the macroscopic level. Although the model can be applied to various endurance sports, we will apply it to bicycle racing here.The energy conversion relevant to propel the bicycle takes place in muscle. During cycling, less than a quarter of the energy obtained by burning nutrients with oxygen is converted to external work. The remainder of the energy is converted to heat, which is transported from the muscle by thermal conduction and circulatory convection. The blood also delivers oxygen and carbon substrates to the muscle and carries away the breakdown products, such as carbon dioxide and lactic acid, in addition to heat. The heat is distributed through the body by the blood and raises the temperature in all organs, including the brain and skin. The heat transported to the skin can be dissipated for a major part by evaporation of sweat. Which muscle groups are active depends on the type of exercise. Because of the specific localization of muscle activity and the extensive interplay between all organs, it is highly desirable that the whole body model contains multiple segments to represent distinct muscle groups and organs.The whole body model can be viewed conveniently to consist of a controlled system, which contains metabolism and heat transport in blood and tissue, and a controlling system that regulates the response of the controlled system by neural and hormonal signals. Heart rate, cardiac output and lung ventilation increase under control of nerve signals from the brain. Sweat excretion and skin vasodilation are, for an important part, under central neural control. Therefore, the controller part of the model represents the action of the nervous and hormonal system on the heat transport in the controlled system, which consists of heat capacities, thermal conductance, tissue perfusion, etc.A macroscopic model of human whole body physiology was described by Stolwijk & Hardy  and orig(a)th node. The cardiac output representing the total blood flow is partitioned to all the other 24 nodes and exchanges heat with the tissue. To each node, a certain mass, heat capacity and basal metabolic rate are assigned. For the head, for instance, the muscle mass is relatively small (about 0.4 kg), while in the legs, the muscle mass is large (about 10 kg). The core node of the head segment is relatively large (3 kg) because it represents the brain and the skull. The muscle nodes can contribute to external work by energy conversion from nutrients and oxygen. Below, we provide an outline of the model. Detailed equations for the model are given in the electronic supplementary material.The controlled system of the body is divided into six segments in the model. The central segment of the body (the trunk) consists of the thorax and abdomen. Other segments represent the head, arms, hands, legs and feet . Each ofN to node N+1 isN] from a node by blood flow BF is given byCblood the heat capacity of blood. This equation is simple because the temperature in blood flowing through small arteries and arterioles becomes almost equilibrated with tissue, even before it reaches the capillaries  consists of a basal heat production rate QB[N] plus a potentially large additional heat production in muscle during exercise. Cnode is the heat capacity of the node. Even if a node has low Q[N], its temperature may rise considerably because of heat conduction from adjacent nodes and heat transfer from the blood. Heat may, for instance, be transferred from leg muscles to the brain and skin via the blood.The rate of change, dA large quantity of heat is transported to the environment via the skin by radiation, convection and evaporation of water. Water is excreted from the sweat glands under central and local control. The skin also loses heat by convection, which is very much increased by high air velocity. This velocity is not only caused by the wind, but also by the motion of the cyclist. A small fraction of heat is given off to air in the airways and lungs by conduction and evaporation. Detailed equations are given in the electronic supplementary material.(b)The body senses the local temperature in various locations, among others in the brain and in the skin. Signals from the sensors are sent to the brain. If temperature is increased, the central controller sends signals to cause skin vasodilation and sweat production. If body temperature falls, signals are generated to produce heat by shivering and to constrict the blood vessels that control skin blood flow. Relatively little is known about the nervous mechanisms that sense tissue temperature and which form the control system in the brain, generating efferent signals to effector mechanisms that control heat generation and transport in the body . PeripheTherefore, in the computational model, a simple black box approach was chosen: the deviation of node temperatures from a reference temperature constitutes the input to the central controlling mechanism . In partThe equations describing the controller were parametrized based on extensive measurements of the relation between input signals (brain and skin temperatures) and output signals  ,5. There(c)For an athlete who tries to win a race, not only the physical work capacity counts, but also the motivation to go to the limits of performance despite exhaustion and perhaps even pain. The key parameter for the physical capacity is the maximal oxygen uptake of the athlete that can be measured in the laboratory. However, during a long effort, oxygen uptake cannot be sustained at the same level as during a relatively short test in the laboratory. The available mechanical power tends to show a downward trend during a long race . Because(d)The ordinary differential equations were implemented and integrated in R computing language using the lsoda routine, which is based on algorithms by Hindmarsh  and Petz3.The external mechanical power available to increase and maintain the speed of the cyclist–bicycle system is delivered by the muscle nodes in the computational model of the cyclist. Physical power equals the force propelling the bicycle times the velocity. The opposing forces that must be overcome to propel the bicycle are (i) the frictional force of the air (wind drag), (ii) the frictional force of the tyres on the road (rolling resistance), (iii) the component of the force of gravity, which is parallel to the road surface when climbing, and (iv) the force used to accelerate or decelerate. The external power delivered by the cyclist's muscles is balanced by the power of the opposing forces. A voluntary decision to exert more force is associated with more external power and may lead to acceleration.Rr) is a force (in N) given byS is the gradient of the road , M is the mass of the rider and Mb is the mass of the bicycle  concentration reported for this study ranged from 0.89 10−7 M at rest to 1.20 10−7 M at 75 per cent of VO2(max) [Parameter values for Mi-CK reaction, kinetics of ATP production and MOM permeability to metabolites were collected from van Beek . Kineticr and Cr b among og others . The [H+VO2(max) , and wasVO2(max) . Maximal2max of 4.1 l min−1 of the subjects in the bicycling exercise [JATP,hyd, of 628 and 1175 μM s−1 for 40 and 75 per cent of VO2max, respectively. Parameter estimation was done with the downhill simplex algorithm implemented in the SloppyCell modelling environment [a priori information into account yields more robust parameter values [figure 3b. The model predicts a decline of PCr, the high-energy phosphate store, with increasing workload, while ATP levels stay relatively constant. The model predictions for PCr, Cr and ATP are relatively close to the measured values, despite the fact that the kinetic parameters in the model were kept close to their reported literature values by constraining them with their measurement error using Bayesian priors.To estimate the rate of ATP hydrolysis powering contractile work in leg muscle, we use the average VOexercise , measureexercise , and assexercise . Furtherexercise . From thironment . Becauseironment , we consironment . Taking r values . Results2(max) [b). Because lactate production may change at later stages of exercise, the incorporation of dynamic changes in lactate production and intracellular pH in future modelling work is desirable.A limitation of the present model analysis is the absence of glycolytic ATP formation. Tissue lactate levels were reported to be substantially elevated going from rest to 75 per cent of VO2(max)  at the tc), as used previously for a beating heart [For many professional cyclists, mechanical efficiency is maximized at pedal cadences around 90 r.p.m. . In ordefigure 3ng heart . The legng heart . Given tc). With normally active CK, the amplitude of ATP synthesis is almost fully buffered. Blocking CK by 98 per cent results in a ninefold increase of the amplitude of the ATP synthesis oscillations from 106 to 938 μM s−1. These results demonstrate the importance of the CK system in maintaining cellular ATP homeostasis and buffering of high amplitudes in mitochondrial ATP production in skeletal muscle during cycling.To investigate the effectiveness of CK in buffering these pulses in ATP demand, we simulated conditions of normal and impaired enzyme activity c. With n7.V1, while reactions 2 and 3 consume one and two molecules, respectively, of X at fluxes V2 and V3, the balance equation for metabolite X isEnergy for muscle contraction is derived from the oxidation of carbohydrates and fatty acids derived from the food. The energy is used to synthesize ATP. The pathways for the metabolism of these carbon substrates may be analysed with computational models, which represent the biochemical reaction networks consisting of enzymes and of metabolites. A certain metabolite can be produced by one particular type of enzyme and be used by the next enzyme in the metabolic network. The enzyme content determines the maximal rate at which a reaction can take place. The precise distribution of the flow of carbon in the intracellular metabolic pathways can be predicted by models of interconnected metabolic reactions. The calculation of the flux distribution in the network resembles calculations based on Kirchhoff's law in electrical circuits: the amount of material flowing into a node in the network must equal the amount of material flowing out. For instance, if reaction 1 produces a certain metabolite X at flux is (FBA)  derives (a)Most of the relevant reactions in the cell can be found in databases of metabolic pathways. In order to facilitate the building of metabolic pathway models, we developed the computer package BiGGR, which, among others, downloads the reactions from the Biochemical, Genetic and Genomic (BiGG) knowledgebase of metabolic reconstructions, which contains several thousand manually curated enzymatic reactions for the human system . The namBiGGR facilitates FBA, building on a range of linear optimization routines, which were already available for R . In addi(b)2 uptake/glucose uptake is close to 6 [2 uptake/(glucose+1/2 lactate) uptake), which falls below 3. The fate of carbohydrate in the brain during exercise remains unknown [Glucose is the main substrate for fuelling cerebral metabolism under normal physiological conditions when blood lactate concentration remains low. The ratio of Oose to 6 . During ose to 6 . However unknown . With nu unknown ,44. Imme unknown .et al. [To investigate whether excess carbohydrate uptake can be explained by fatty acid synthesis, we developed a computational model that represents pathways of central metabolism in the brain and simulated the fluxes of glucose and lactate metabolism during rest and maximal exercise. Given the high lipid content of the brain, this is a plausible hypothesis. The reactions in our model comprise central energy metabolism and fatty acid synthesis in their appropriate compartments (cytosol and mitochondria), and metabolite transport across the mitochondrial membranes. The inclusion of the malate-aspartate and glycerol-3-phosphate shuttles allows for transport of reducing equivalents between the cytosol and mitochondria. Amino acid synthesis of alanine and glutamate/gamma-amino butyric acid (GABA) cycling were included. Reactions are taken from the BiGG database, and measurements of substrate uptake in the brain during rest and exercise were taken from Quistorff et al. . We use et al.  linked t−1 glucose in the whole human brain is in agreement with the O2/glucose ratio and yields a maximal mitochondrial ATP synthesis of 9.28 mmol min−1. No flux through the pentose phosphate pathway is predicted (a). During 15 min of exercise, glucose uptake doubles, and, in addition, 0.53 mmol min−1 lactate and 3.2 mmol min−1 oxygen are taken up. We hypothesize that given the low ratio of oxygen to glucose and lactate uptake, the carbon in these carbohydrates may be used to synthesize and store fatty acids. We calculate that 0.14 mmol min−1 of fatty acid  must be synthesized in the brain to balance glucose and lactate uptake with the limited availability of oxygen to oxidize carbon (b). The pentose phosphate pathway is now activated to produce nicotinamide adenine dinucleotide phosphate, which is required for the synthesis of free fatty acid. The result above suggests that fatty acid synthesis, perhaps followed by incorporation into lipids that are abundantly present in the brain, is a possible pathway for the excess carbon. Future experiments to measure storage of cerebral fatty acid, possibly using stable isotope labelling of precursors [At rest with no lactate present, metabolism of 0.4 mmol minredicted a. Duringe carbon b. The peecursors ,46, allo8.The model approaches discussed address various spatial, temporal and biochemical resolutions and are conceptually complementary. However, they were not yet linked in an integrated computational framework and executed simultaneously. For the buffering of the ATP hydrolysis peaks in the CK model, we calculated the amplitude of ATP hydrolysis offline. Yet, it seems feasible to couple the CK model to the whole body model. In that way, the energy turnover in the leg muscles would be coupled directly to the amplitude of ATP hydrolysis during cyclical work on the bicycle. The levels of inorganic phosphate and the maximal ADP concentration during the cycle could be used to indicate the fatigue status of the muscle and might be used to determine the obtainable level of exertion. The minimal concentration of ADP may additionally indicate the risk of oxygen radical formation because of low stimulation of the mitochondria.To develop computational models of endurance sports performance further, it might be very efficient if a framework existed where the modelling approaches at various scales could be seamlessly integrated. In addition, if one builds and links models of metabolic pathways, it is very efficient if one can integrate biochemical reactions available from databases. A prerequisite for such an exchange of reactions is a uniform standard nomenclature and symbols for metabolites, enzymes and other entities in physiological models. For the present work, we used the nomenclature of the BiGG database , but it Given the extensive research literature on sports physiology and the vast knowledge on basic biology, it is timely to start to develop quantitative models of human physiology. Quantitative integration of physiological and biochemical knowledge in computational models may facilitate the understanding of human performance, and may increasingly become a central research tool for integrative physiology. Because professional world class athletes push their performance to the very limits, model analysis of their performance during sports events may provide a unique window on human physiology. By demonstrating the application of virtual physiological modelling to sports or space travel, we may arouse the interest of the general public and young scientists. The benefits for medical applications and enhanced safety surveillance of athletes will no doubt follow.2 value achieved during the race. The result suggests that VO2max explaining the performance during the race is higher than the maximum found in laboratory tests earlier in time. Athletes use all sorts of methods to prepare optimally for the decisive race. Many athletes expose themselves to low oxygen concentrations, for instance, by sojourn at high altitude or by breathing gas mixtures with decreased oxygen content during sleep, to increase natural erythropoietin production. The winner of the 2004 time trial to Alpe d'Huez may have used hypoxic exposure as reported in Coyle [Our model mainly predicts the maximal VOin Coyle . In addiOur model does not yet contain oxygen transport to make it possible to analyse oxygen delivery and uptake. It is, therefore, not yet possible to analyse the effects of illegal (recombinant erythropoietin and autologous blood transfusion) or legal methods (hypoxic exposure) to support increased oxygen uptake with our model, but this may be an interesting future expansion of the model. An important aspect of preparation for a long endurance sports event is optimal nutrition to supply sufficient carbon fuel for long, intense exercise. The effect of nutrition on glycogen and fat stores in the body and the interaction of carbohydrates and fat during exercise are aspects that require extensive model analysis in the future. The glycaemic index or the glycaemic load, which describe the effect of various carbohydrate formulations can be incorporated in the models . The intA mathematical or computational model always represents a simplified reflection of the real complex system. Even if we build increasingly complex models, we will never completely approach reality. However, this poses no problem because we already have the real system. Restricting ourselves to capture only the essential processes in mathematical equations helps us to understand and predict the system's behaviour. Even if models gradually become quite complex, we can still track all interactions and how they synergize to yield the overall result. The easy accessibility of variables in computer models provides an advantage over the real system. Computational modelling is, therefore, a powerful tool to integrate all the knowledge of human scientists gathered in studies that, by themselves, consider only parts and details of the system. By doing this, we also produce powerful tools to predict the performance of the human body and learn how human body function may be improved in health and disease.9.We conclude that simulation of athletic performance with a computational model of energy turnover and heat transport in the whole human body is feasible. The maximal oxygen uptake capacity of the athlete can be estimated based on performance in a race. The temperatures in various parts of the body such as brain and active muscle groups can be predicted. The changes in the phosphocreatine energy buffer status can be predicted, although glycolytic ATP production and pH regulation will have to be added. The model of carbon flux distribution in central metabolism allows us to investigate hypotheses on the apparent dysbalance of glucose and lactate uptake with cerebral metabolic needs.


The results demonstrate that L. amylophilus is a homofermentative bacterium. In synthetic medium, 60.6% of the glucose entered the Embden–Meyerhof–Parnas (EMP) to produce lactic acid, whereas 36.4% of the glucose entered the pentose phosphate metabolic pathway (HMP). After solid–liquid separation of the KWSS, the addition of Fe3+ during fermentation enhanced the NADPH production efficiency and increased the NADH content. The flux to the EMP was also effectively increased. Compared with the control (60.6% flux to EMP without Fe3+ addition), the flux to the EMP with the addition of Fe3+ (74.3%) increased by 23.8%. In the subsequent pyruvate metabolism, Fe3+ also increased lactate dehydrogenase activity, and inhibited alcohol dehydrogenase, pyruvate dehydrogenase and pyruvate carboxylase, thereby increasing the lactic acid production to 9.03 g l−1, an increase of 8% compared with the control. All other organic acid by-products were lower than in the control. However, the addition of Zn2+ showed an opposite effect, decreasing the lactic acid production. In conclusion it is feasible and effective means using GC-MS, isotope experiment and MATLAB software to integrate research the metabolic flux distribution of lactic acid bacteria, and the results provide the theoretical foundation for similar metabolic flux distribution.The  The composition of kitchen waste is very complex and it mainly consists of organic matter such as starch, dietary fibre, animal fats and so on. Kitchen waste has high moisture content, as well as a high fat, high salt and high starch content. Kitchen waste is mainly disposed through incineration and composting. Considering kitchen waste is not readily combustible, other fuels need to be mixed in. However, kitchen waste hinder the increase in incinerator temperature and the presence of chlorinated compounds corrodes the fireplace and produces dioxins. In addition, the long-term application of high-salt-content fertilizers made from kitchen waste causes adverse effects on the soil and on plant growth, which restricts the development of kitchen waste composting. Lactic acid is an organic acid that is popularly employed in many fields and is in huge demand. Polylactic acid plastics synthesized from lactic acid are biodegradable, environmentally benign, and have broad applications in the market  in synthetic medium containing only six essential amino acids and glucose as the sole carbon source  were added to possibly change the metabolic flux distribution and determine the flow of glucose as a carbon source in lactic acid formation  to produce lactic acid using 13C-MFA. Trace elements were added to the system to optimize the metabolic flux distribution of the Embden–Meyerhof–Parnas  pathway during fermentation, thus providing a theoretical basis for the efficient use of food waste.The current study aims to determine the metabolic flux of Lactobacillus amylophilus was subjected to a metabolic experiment on labelled 13C MRS medium (glucose as the carbon source) to determine the pathway it used in fermentation and to establish a foundation for its flux calculation. The results are shown in 13C-labelled MRS medium resulted in the rapid growth of L. amylophilus. Lactate production gradually increased and reached a steady conversion rate after 12 h. Although very small amounts of formic acid, acetic acid and tartaric acid were formed as fermentation products, the conversion rate of glucose to lactic acid was still much higher than the other pathways, reaching (1.85–1.95) mol mol−1 of glucose  were mainly lactic acid, formic acid, tartaric acid and acetic acid. The most abundant product of the fermentation was lactic acid at 8.34 g l−1, which accounted for 90.5% of the total organic acids. The formic acid, acetic acid and tartaric acid content were relatively much lower; all were less than 0.5 g l−1 and accounted for 4.56%, 3.04% and 1.95% of the total organic acids respectively. The content of the other organic acids were even lower, and negligible. Meanwhile, the concentration of amino acids on the synthetic medium was analysed. The 12 kinds of amino acids obtained were Thr, Ser, Pro, Gly, Ala, Val, Ile, Leu, Tyr, Phe, Lys and His, and their concentrations were (mmol l−1): 0.27, 0.48, 0.12, 0.25, 0.28, 0.38, 0.51, 1.18, 0.24, 1.24, 1.08 and 1.21 respectively.Considering the amylase produced by L. amylophilus was obtained using the matrix in MATLAB based on the extracellular flow and amino acid data. As shown in L. amylophilus through the pentose phosphate pathway (HMP) and the glycolytic pathway (EMP). In the KWSS, 36.7% of the metabolic flux entered the HMP pathway, whereas 60.6% entered the EMP pathway. The conversion rate of glucose to lactic acid through the EMP pathway was 86.6% (1.732 mol mol−1). The conversion rate with KWSS was slightly lower than that in MRS medium (1.85 mol mol−1 to 1.95 mol mol−1), but it was still greater than 80%; thus, the bacteria underwent homofermentation. These results indicate the feasibility of using L. amylophilus to produce lactic acid from KWSS.The intracellular metabolic flux of 3+ is related to an inefficient glucose utilization pathway, whereas Zn2+ is a common factor that naturally exists in cellular proteins, nucleic acids, carbohydrates and lipids, and its presence directly affects cellular reaction. The change in metabolic flux distribution after the control experiment , the addition of trace elements and the nitrogen source is shown in On account of Fe3+ to KWSS leads to the highest possible lactic acid conversion rate 70.36% (94.7% proportion of pyruvate way). Compared with the systems supplied with Zn2+ and NaNO3 and with the control, the conversion rate in the system with Fe3+ was higher by 17.8%, 5.64% and 9.32% respectively. The addition of NaNO3 also increased the conversion rate, but the change was not as obvious as with Fe3+. After the addition of Zn2+, the metabolic flux into HMP pathway increased by 38.9%, whereas the flux into the EMP pathway decreased, thus decreasing the lactic acid flux. Comparison of the organic acid conversion rates in the fermentation broth under four different conditions revealed that the addition of Fe3+ effectively inhibits the generation of by-products. Acetic and propionic acid production reached their minimum and the flux to the HMP pathway was minimal. The lactic acid production is 9.03 g l−1, and conversion rate compared with the contrast increase by 8.3% to 90.3%. In contrast, the addition of Zn2+ inhibited lactic acid generation and increased the production of the undesired products (propionic and tartaric acids). The addition of the trace element Zn2+ did not produce the expected increase in lactic acid flux. The possible reasons for the changes in the key enzymes and coenzymes of L. amylophilus caused by the addition of Fe3+ and Zn2+ are discussed in subsequent sections.As shown in L. amylophilus, NADPH is needed to provide the reducing power for biosynthesis and promote pyruvate production to synthesize cellular component material  using glucose and intermediates, thereby providing raw materials for further lactic acid production. Two pathways in L. amylophilus produce NADPH, glucose-6-phosphate acid dehydrogenation in the HMP pathway and isocitrate dehydrogenation in TCA cycle. The amounts of coenzyme NADH generated and consumed are shown in 3+ was 26.6% higher than the control. On the other hand, the HMP/TCA ratio was 10.8% lower than the control even though the flux of pyruvate into TCA cycle (r8) changed little compared with the control. This demonstrates that the addition of Fe3+ activates the TCA and produces more NADPH. This further increase in NADPH production is probably because Fe3+ enhances the ability of the cells to adjust the NADPH production automatically to satisfy its needs for biosynthesis. The results indicate that Fe3+ promotes the flux to pyruvate synthesis (EMP pathway) and NADPH yield, consequently optimizing the metabolic flux distribution.In lactic acid bacteria, the key coenzyme reduced form of nicotinamide-adenine dinucleotid (NADH) and nicotinamide adenine dinucleotide phosphate (NADPH), greatly affects the decomposition of carbon source and the direction of metabolic synthesis. In 3+ to the KWSS, the flux from node GA3P to glycerol (r4) decreased. The flux to PG (r5), the NADH-generating reaction in the EMP pathway, increased. Consequently, the amount of NADH generated from EMP increased, which accounted for 73.2% of the total NADH, 40.5% higher than that of the control. The flux to pyruvate in the TCA cycle (r8) decreased slightly compared with the control after the addition of Fe3+, which indicates that NADH consumption in the TCA cycle decreased. Given that lactic acid production from pyruvate needs to consume a large amount of NADH and the addition of Fe3+ increases the NADH generation and decreases NADH consumption in the TCA cycle, the increase in NADH promotes lactic acid production. This confirms that Fe3+ optimizes the sugar metabolic pathways by increasing the amount of available coenzyme, and that intracellular NADH plays an important role in metabolism of L. amylophilus to produce lactic acid from pyruvate.As shown in 3+ was higher than that of the control  increased. Therefore, although the flux to glycerol from GA3P node (r4) decreased, the flux to PG (r5) but declined. Despite the increase in the NADH flux through the EMP pathway, its actual content did not increase. NADH formation through TCA cycle significantly decreased. This change was because the flux to TCA cycle decreased significantly and the addition of Zn2+ inhibited the activity of this cycle, thereby reducing NADH generation. The inhibition was also the reason why Zn2+ inhibited lactic acid production in L. amylophilus.Although the percentage of NADPH flux in the HMP pathway increased after the addition of Zn control . Thus, t3+, the LDH activity in the system supplied with Zn2+ was lower than the control, and the activity of PDC, PC and PDHc were higher  was obtained from the Beijing Aoboxing Bio-Tech, whereas industrial-grade cellulose (270 U g−1) was bought from the Beijing Donghua Qiangsheng Bio-Tech.Glucoamylase . Lactobacillus amylophilus was inoculated into MRS medium at a final concentration of 2 g l−1. Anaerobic fermentation was carried out by filling the system with nitrogen gas.The isotope experiment was performed on de Man–Rogosa–Sharpe (MRS) medium  content was 9.2 g l−1. Then, 0.8 g l−1 labelled glucose was added to the diluted saccharified solution to a final 13C glucose ratio of 8.0%. The solution obtained was designated as kitchen waste saccharified solution (KWSS). Lactobacillus amylophilus was inoculated into the KWSS at 2 g l−1. Anaerobic fermentation was conducted by filling the system with nitrogen gas.Kitchen waste saccharification and fermentation was performed as follows: 1.5 g of glucoamylase and 12 g of cellulose enzyme were added to 100 g of food waste samples. The pH was adjusted to 5.0 and hydrolysis was performed at 50°C for 60 min. The glucose concentration reached 28.46 g l13C-MFA is a method to quantify the intracellular flux by measuring the extracellular flux and intracellular labelling information (i.e. intracellular fluxes = extracellular fluxes + labelling data). In 13C labelling experiments, 13C-labelled substrates  are introduced to the biological reaction system, and 13C atoms are distributed in extracellular and intracellular metabolites as well as biomass components via chemical rearrangement, rupture of chemical bonds and formation of new bonds in biological chemical reactions. Furthermore, along with the consumption of glucose, the isotopic abundance of labelled carbon atoms in the metabolites increases continuously. Once their abundance can be detected by nuclear magnetic resonance (NMR) or mass spectrometry (MS), samples are taken and analysed , Zn2+ (1.748 mg l−1) and NaNO3 (0.75 mg l−1)  . These wLactobacillus amylophilus, one kind of homolactics, was used in this study, and its metabolic network is expected to have some similarities with that obtained in former research. Therefore, in this study, the thorough metabolic network of L. amylophilus was obtained on this basis by analysing the extracellular and intracellular substances. The metabolic flux of this network is calculated according to the principle of mass conservation. The material balance of intermediate metabolites was obtained using quasi-steady assumption  was calculated as (J − n). By this means, the overall flux distribution could be determined by measuring F uncorrelated rates.The metabolic network of lactic acid bacteria has been researched thoroughly so far, and themetabolic network distribution of homolactic acid bacteria has also been obtained (i (ix) in the metabolic network was quantified using the following equation:The accumulation rate of metabolite jr is the production flux of metabolite i in reaction j; kr is the consumption flux of metabolite i in reaction k; ja and ka are the stoichiometric coefficients; ix, jr and kr are the specific rates.where Based on the metabolic network model already known, metabolic reaction equations of corresponding number of reaction steps and equations with an equal number of unknown data can be designed. Under the known experimental conditions, the parameters that can be detected are the concentrations of glucose, organic acids, amino acids and biomass. The release rate of carbon dioxide can be obtained according to carbon balance. By using MATLAB software program, the metabolic reaction equations can be solved, and thus the network and flux distribution of glucose and lactic acid metabolism of lactic acid bacteria during kitchen waste fermentation can be constructed.The fermentation broth was centrifuged at 4000 r.p.m. for 15 min. The supernatant liquid was collected and diluted tenfold, and filtered with a 0.45 μm mixed-fibre resin membrane. After ultrasonic degassing for 20 min, the sugar, amino acids and organic acids were measured.2+ (8%), 300 mm × 7.8 mm] with a refractive index detector. The mobile phase was a mixture of acetonitrile and ultrapure water at a ratio of 75:25 , and a flow rate of 0.6 ml min−1. The operation temperature of the column was maintained at 80°C.Twenty microlitres of the sample after pre-treatment was injected into an LC-20A liquid chromatograph [Rezex RCM-Monosaccharide of Ca−1 and split ratio of 50:1; EI power with an ionization voltage of 70 eV; scan range of (10–550) amu; temperatures of the injector, transfer line, ion source and quadrupole were 280°C, 280°C, 230°C and 150°C respectively. The temperature of the column was maintained at 80°C for 2 min, increased to 280°C at a rate of 10°C min−1 and sustained for 40 min. The amino acid components and yields in the fermentation products were then analysed (One microlitre of the sample after pre-treatment was injected into the QP2010 GC-MS instrument. The GC column used was HP5 MS (30 m × 0.25 mm × 0.25 μm). The GC conditions were as follows: carrier gas (helium) at a flow rate of 1.0 ml minAn SBA-40C biosensor was used to measure the ethanol content of the fermentation liquid.−1; the detector wavelength was UV210 nm; the injection volume was 20 μl; and the column temperature was 30°C (A liquid chromatography LC-20A with Inertsil ODS-SP column (5 μm × 250 mm × 6.0 mm) was used under the following conditions. The mobile phase was ultrapure water (pH was adjusted to 2.5 with phosphoric acid) at a flow rate of 0.8 ml min−1 potassium phosphate buffer (pH 6.5). The cells were then resuspended in buffer and oscillated with glass beads at 4°C for 5 min to homogenize the cells. Subsequently, the cells were lysed through ultrasonication (KS-250) for 5 min in an ice bath. The work intensity of the instrument was at 30% for 1 s at an interval of 0.5 s. Finally, the liquid was centrifuged at 8000 r.p.m. for 15 min at 4°C. The resulting supernatant liquid was the crude enzyme solution.The fermentation broth was centrifuged at 8500 r.p.m. for 15 min, and the cells were collected and centrifugally washed three times with 0.1 mol lFour enzymes that are closely related to lactic acid synthesis in glucose metabolism were selected, namely, lactate dehydrogenase (LDH), pyruvate decarboxylase (PDC), pyruvate carboxylase (PC) and pyruvate dehydrogenase complex (PDHc). One unit (U) of enzyme activity for LDH and for PDC is defined as the amount of enzyme needed to oxidize (or reduce) 1 μmol of NADH per minute under optimal temperature and pH. On the other hand, one unit (U) of enzyme activity for PC and for PDH is defined as the amount of enzyme needed to generate 1 μmol of oxaloacetate per minute under optimal temperature and pH. Specific activity was expressed as the unit of enzyme activity per milligram of protein.


We used this model to predict nitrifier diversity, ammonia (NH3) oxidation rates, and nitrous oxide (N2O) production across pH, temperature, and substrate gradients. Predicted nitrifier diversity was predominantly determined by temperature and substrate availability, the latter was strongly influenced by pH. The model predicted that transient N2O production rates are maximized by a decoupling of the AOB and NOB communities, resulting in an accumulation and detoxification of nitrite to N2O by AOB. However, cumulative N2O production (over 6 month simulations) is maximized in a system where the relationship between AOB and NOB is maintained. When the reactions uncouple, the AOB become unstable and biomass declines rapidly, resulting in decreased NH3 oxidation and N2O production. We evaluated this model against site level chemical datasets from the interior of Alaska and accurately simulated NH3 oxidation rates and the relative ratio of AOA:AOB biomass. The predicted community structure and activity indicate (a) parameterization of a small number of traits may be sufficient to broadly characterize nitrifying community structure and (b) changing decadal trends in climate and edaphic conditions could impact nitrification rates in ways that are not captured by extant biogeochemical models.Trait-based microbial models show clear promise as tools to represent the diversity and activity of microorganisms across ecosystem gradients. These models parameterize specific traits that determine the relative fitness of an “organism” in a given environment, and represent the complexity of biological systems across temporal and spatial scales. In this study we introduce a  Understanding the interaction between ecology and biogeochemistry is an important frontier in environmental microbiology. Temporal separation between cellular activity and trace gas flux measurement has hampered efforts to connect, in field studies, the composition, structure, and activity of microbial communities to the biogeochemical processes they catalyze. Given the importance of prokaryotic diversity for ecosystem function  decomposition to its loss as N2O or N2 gas via denitrification. In addition, nitrification is closely linked to the carbon cycle as nitrifier activity determines the relative concentration of two major plant and microbial nitrogen sources: ammonia and nitrate. The availability of these two nutrients in turn affects N mineralization rates, soil OM decomposition, denitrification, plant-productivity, and N-loss through leaching or gas efflux.In the current study we expand the trait-based approach to study a critical component of the nitrogen cycle, nitrification. Nitrification, the oxidation of ammonia to nitrite and then nitrate, is a rate-limiting step in the microbially mediated N cycle Ward, . Nitrifi3 → NO2) is catalyzed by a phylogenetically restricted group of beta- and gammaproteobacteria  concentration . Few NOB have been isolated from soil and the extent of ecophysiological kinetic data for NOB significantly lags that of AOB. Additionally, PCR primers targeting the functional gene involved in nitrite oxidation (nitrite oxidoreductase) have only recently become available  is well known  belonging to five genera  catalyze the second major step of nitrification  and substrate use efficiency (number of moles of substrate required to fix one mole of CO2). Several decades of ecophysiological studies using different nitrifiers have produced a wealth of data that can be used to mathematically characterize different nitrifier guilds. While heterotrophic organisms can also carry out nitrification  to simulate the physiology and ecology of autotrophic nitrifiers (MicroTrait-N), including an explicit representation of the rates of NH3 and NO2 oxidation, N2O production, and nitrogen pool transformations. We apply MicroTrait-N to examine predicted patterns in nitrifier community diversity and activity across several geochemical gradients.Nitrifiers are ideal candidates for building and refining trait-based models. They are autotrophic with a simple metabolism largely defined by central physiological processes, such as substrate acquisition , and temperature. Our approach is general enough that it can be applied to nitrifier populations in freshwater and aquatic environments and flexible enough to be used within soil pores. The model is written in Matlab .MicroTrait-N resolves intra-functional group diversity of the nitrifier populations  by parameterizing multiple guilds spanning a range in the trait-space Figure . Althoug3 inputs, by: (1) using the mean value of each trait; (2) performing Monte Carlo (MC) simulations to account for intra-guild diversity; and (3) running the model in equilibrium and dynamic steady state cycle modes to characterize the impact of temporal forcing variation on predicted emergent microbial community structure.Our guild approach simulates seven lineages of Betaproteobacterial AOB as individual guilds, three NOB guilds, and one AOA guild. The smaller number of NOB and AOA guilds reflects the lack of relevant ecophysiological studies of these groups. Intra-guild diversity is parameterized by allowing a range of values for each trait Table , based oBT, which may represent the ammonia-oxidizing organism  as BTA or the NOB, BTN); (2) carbon biomass (BC); (3) nitrogen biomass (BN); (4) Cellular quotas for carbon (QC); and (5) cellular quotas for nitrogen (QN). The latter two are defined relative to total biomass . Carbon biomass increases by fixing CO2 through the ribulose-bisphosphate enzyme using energy produced during the oxidation of either NH3 or NO2  total cell biomass  of the ith guild for the jth element. Here j represents either C or N. The minimum quota for carbon is 1 and for nitrogen is 1/13.2 (according to the Redfield Ratio). The carbon and nitrogen constraints are then applied to regulate the cell division rate (DB) with Liebig’s law of the minimum  uptake rate, KM is the half saturation constant for NH3 or O2 . CO2 uptake follows Michaelis–Menten kinetics:Here, 2 fixed relative to NH3 oxidized:where 3 oxidized per mole of CO2 fixed, Table where ith AOB biomass over time is calculated as:Growth of the −1) is the first order microbial mortality rate and DA is biomass loss (M s−1) attributable to the detoxification of NO2 following the uncoupling of AOB and NOB mediated reactions (see below). Total biomass loss is the sum of that required to convert NO2 → NO and NO → N2O, and the 1/4 represents the stoichiometric relationship between biomass and NO2 detoxification .Here, Δ (s2 to biomass via the oxidation of NO2 → NO3. NO2 uptake rate is modeled by:The NOB gains energy to fix CO2 occurs via the same pathway as for AOO (Eqs ith NOB guild varies as:where the different terms in Eq.  AOO Eqs  and 5 an2O is produced by AOO via two distinct pathways: (1) decomposition of the hydroxylamine intermediate and (2) the likely more significant mechanism of NO2 detoxification , the two reactions may become spatially or temporally uncoupled. NO2 toxicity stimulates a detoxification pathway converting NO2 to N2O via NO. This detoxification pathway is potentially the more significant mechanism by which AOB produce N2O. AOA have recently been shown to produce N2O  of either NO2 or NO. Energy for detoxification is assumed to come from the degradation of microbial biomass resulting in the output of CO2.where 3 concentration ([NH3] (M) depends on a balance between losses from oxidation nA) and NOB guilds (nN):The dynamic aqueous NH2 concentration depends on uptake by NOB to generate energy and losses via detoxification by AOB:where the 1/4 represents the stoichiometry of the detoxification reaction using biomass for energy. The dynamic NO3)], and temperature and compared predictions of this diversity against published studies. Accuracy of modeled communities was gaged by relating the steady state modeled nitrifier diversity to its likely phylogeny based on literature sources of the derived trait values. In addition, an evenness statistic (iJ) is ascribed to each community;We tested MicroTrait-N by examining how nitrifier diversity varies across geochemical gradients in pH, substrate concentration  encouraged the growth of oligotrophic ammonia oxidizers. Both baseline  also declined with decreasing pH from a maximum NH3 oxidation rate of 1.9 M N day−1 to less than 0.1 M N day−1. Predicted N2O production was linearly related to NH3 oxidation  indicating the AOB and NOB reactions were coupled regardless of the pH and N2O was primarily by hydroxylamine decomposition.We simulated a pH gradient from approximately neutral (pH = 7.8) to acidic (pH = 4.5) conditions and recorded diversity and activity  lower than when NOB were present  resulting in a rapid crash in AOO community biomass (data not shown).We simulated Nt Figure B due to 3 are drawn down more quickly as the biomass of AOB increases. However, the second pulse of NH3 results in its most rapid drawdown due to a high cumulative biomass and greater diversity of AOO , a four-fold increase in AOB(5), and a small response in AOB(1). As NH3 is drawn down to lower concentrations (<1 × 10−6 M) AOA briefly become the dominant nitrifiers. While AOA biomass peak when substrate concentrations are low, they are inhibited by subsequent substrate pulses.We simulated the response of our imposed simple community  to pulsed input of substrate over a 9-month period Figure . Over ti Figures A,B. As Nd Figure C. In theO Figure D, nevert−3 to 0.1 M NH3) and low pH (4.3–4.8). These observations therefore provide a comparison to our earlier examination of a pH gradient with a fixed substrate concentration. The model predicted that, in contrast to our previous predictions at low pH and NH3 substrate levels . The highest oxidation rates were associated with the highest NH3 concentrations at the Emergent Fen site (4.9 × 10−4 M N day−1) and with the lowest rates at the Black Spruce and Bog Birch sites (9 × 10−5 and 9 × 10−6 M N day−1 respectively). MicroTrait-N predictions of N2O production also correlated with NH3 concentrations and oxidation rates , and were 85 times higher at the Emergent Fen site (3.6 × 10−6 M N day−1) than the Black Spruce (4.3 × 10−8 M N day−1).Predicted trends in NHs Figure B correla3 to NO3 is an important process that couples N-inputs and losses via denitrification and influences the availability of N in terrestrial and marine environments . Several of the results across gradients showed plausible representation of the dominant nitrifiers guilds emerging on the basis of environmental conditions (discussed below). Our guild characterization recognizes several guilds of the Nitrosomonas [AOB(1-6)], one guild of the Nitrosospira [AOB(7)] and the AOA, and three guilds of the NOB. The guilds resolve broadly into oligotrophic and copiotrophic groups  guild (for which kinetic parameters were derived from the Nitrosospira) with decreasing pH.Few studies offer an experimental analog to the simulations presented here, however, Nicol et al.  examinedThe dominance of the AOA guild at low pH is supported by several studies . This result might suggest that NO2 detoxification substantially increased N2O production by ammonia oxidizers upon uncoupling of the nitrification reactions. However, the toxic effect of NO2 reduces AOO biomass to the point where the populations crash and NH3 oxidation declines. This biomass change is reflected in the cumulative N2O production data over the 6 month simulation, which is approximately 5 times lower than that formed during full nitrification .In the current model, we simulated N2 in a chemostat experiment. Furthermore, Frame and Casciotti  was responsible for the majority of N2O production at low oxygen  and low pH (4.8–4.3). These sites therefore present a contrast to the earlier pH gradient analysis under a lower substrate concentration. In our pH gradient simulation the AOA dominated the low pH possibly due to low substrate availability. Conversely, at higher substrate concentrations Petersen et al. . At the present time, two competing hypotheses describe the relationship between community structure and ecosystem processes: The “diversity” hypothesis and the “mass-ratio” hypothesis Grime, .The “diversity hypothesis” postulates that the richness of functional groups determines the rate of ecosystem processes by a complementary association between different functional groups , the diversity of the community becomes more important, as guilds more suited to the new conditions become numerically prominent and dominate nitrification. At the present time, we are unaware of any field studies in microbial ecology that exclusively test these theories 3 oxidation, and test hypotheses centered around the ecology of NH3-oxidizers and N2O production, issues that temporal and financial restrictions on field studies are often unable to address. An important avenue for future research is to focus on whether the integration of these microbiological diversity modules into ecosystem models can improve site, regional and global predictions of carbon and nutrient cycling.Trait-based microbial ecology can potentially link the observations of experimental environmental microbiology, theoretical energy, and mass exchange considerations, and quantitative modeling with an emphasis on depicting microbial diversity across spatial and temporal scales. Previous applications of the microbial trait-based approach have been successful in predicting rates of primary productivity (Follows et al., The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Mycobacterium tuberculosis metabolism using generic rate equations. M. tuberculosis causes tuberculosis which remains one of the largest killer infectious diseases. Using a genetic algorithm, we estimated kinetic parameters for a genome-scale metabolic model of M. tuberculosis based on flux distributions derived from Flux Balance Analysis. Our results show that an excellent agreement with flux values is obtained under several growth conditions, although kinetic parameters may vary in different conditions. Parameter variability analysis indicates that a high degree of redundancy remains present in model parameters, which suggests that the integration of other types of high-throughput datasets will enable the development of better constrained models accounting for a variety of in vivo phenotypes.The study of biological systems at the genome scale helps us understand fundamental biological processes that govern the activity of living organisms and regulate their interactions with the environment. Genome-scale metabolic models are usually analysed using constraint-based methods, since detailed rate equations and kinetic parameters are often missing. However, constraint-based analysis is limited in capturing the dynamics of cellular processes. In this paper, we present an approach to build a genome-scale kinetic model of  The annotation and sequencing of genomes has made it possible to reconstruct genome-scale metabolic networks for a growing number of organisms [in silico simulation, the phenotypic functions of metabolic systems can be analysed under various environmental or physico-chemical conditions [Genome-scale metabolic models are essential to bridge the gap between metabolic phenotypes and genome-derived biochemical information, as they provide a platform for the interpretation of experimental data related to metabolic states and enable the rganisms . Using cnditions . Applicanditions . Genome-nditions . Other tnditions .in silico by examining the dynamics of cellular processes [The availability of genome-scale metabolic networks has accelerated the development of methods to analyse system-wide metabolic properties. A fundamental aim of systems biology is to predict cellular behaviours rocesses . As a rerocesses . Howeverrocesses ,9, generrocesses , parametrocesses  and convrocesses .H. pylori and E. coli respectively in gene deletion studies [et al. [Reverse engineering is often used in systems biology to reconstruct biological interactions and constrain kinetic parameter values from experimental data . It is o studies . As kine [et al.  the authet al. [Mycobacterium tuberculosis metabolism developed by Beste et al. [M. tuberculosis, no new drug to treat tuberculosis has been developed in the last 30 years, making this organism an important subject for systems biology studies [The model building approach presented in Adiamah et al.  showed te et al. , which we et al. ,17, and  studies ,19. Our M. tuberculosis. Rate equations for all reactions in the model are automatically generated by GRaPe based on the stoichiometry of the reaction. Reactions in the model assume a random-order mechanism as the sequential order of binding and releasing of substrates is often unknown. A key advantage of GRaPe over other tools is its ability to automatically generate rate equations for reactions, making it less error-prone and more time-efficient in building large-scale models. The King-Altman method [We used the GRaPe software  to buildn method  was useda =  and the concentrations of products are represented by a vector b = . The flux v is defined as:The generic rate equations provided in  were use      (1) i is the substrate index, j is the product index, AiK represents the parameter (substrate constants) of the ith substrate and BjK that of the jth product of the reaction, e0 is the concentration of enzyme, +V is the substrate turnover rate and -V is the product turnover rate.where et al. [in vitro measurements of kinetic constants may not necessarily be representative of their numerical values in vivo. Currently, there are various software tools capable of performing parameter estimation: COPASI [M. tuberculosis. Other data sets can also be introduced into the parameter estimation process for constraining purposes, however the availability of comprehensive datasets on a large-scale is often lacking.Kinetic models have been shown to produce accurate and testable results , but dueet al.  that in : COPASI  provides: COPASI  uses a s: COPASI . GRaPe ua and b, are part of an equation in the form of a + b or a * b; if only their sum or product is known it is impossible to identify the value of a and b individually; if both the sum and product are known, then the value of a and b can be calculated. This example illustrates that the level of redundancy is dependent on the amount of experimental data used to constrain the estimation. When there is redundancy, the parameter values found in several runs of the estimation algorithm are likely to be different. In this article, we analysed the redundancy or ‘sloppiness’ in parameter estimation using parameter variability analysis (PVA). PVA allowed us to measure the range of changes in a set of parameter values when the estimation is repeated multiple times.One of the issues relating to parameter estimation is that of mathematical redundancy. The redundancy results in multiple sets of parameter values that can fit equally well to an experimental data set. A simple example of redundancy is when two parameters, Figure 1. After each run of estimation, the objective function, which is a measure of the fit of the estimation to the original data, and kinetic parameter values are stored in a data file in a tabbed-delimited format. The results of PVA can then be exported to spreadsheet software and statistically analysed. The PVA function has now been fully integrated into the GRaPe software.Once a model has been constructed or uploaded in GRaPe, PVA can be performed using the same data required to estimate parameter values for the model. The PVA algorithm works by repeating the estimation of kinetic parameters for the model multiple times using a genetic algorithm (GA). The GA works by populating a set of random initial parameter values; this is why results may differ after each run of the algorithm when there is redundancy. These estimated values are then optimised in an iterative manner until the maximum number of iterations is reached or a suitable solution is found. In GRaPe, GA uses flux and metabolic data to constrain parameters as illustrated in M. tuberculosis [M. tuberculosis using a reconstruction of Streptomyces coelicolor as a starting point. Genes were mapped between the two species using gene orthology clusters from the Kyoto Encyclopaedia of Genes and Genomes (KEGG) [M. tuberculosis includes reactions needed for the synthesis of the cell membrane, complex lipids and carbohydrates, which are important for both growth and pathogenesis. Other metabolic pathways such as respiratory pathways and synthesis of biomolecules, which are specific to mycobacteria, were also modelled manually, as well as iron metabolism and transport reactions responsible for the import of carbon, nitrogen, minerals and compounds of high molecular weight. The final stoichiometric model reconstructed by the Beste group consists of 739 metabolites, 849 reactions and 726 genes; they calibrated their model by growing Mycobacterium bovis bacilli Calmette Guérin in a continuous culture and measuring parameters for steady-state growth. FBA was used to calculate substrate consumption rates. Their results showed a close agreement with experimentally determined values. The model was made available as a web-based interactive tool.There are now several genome-scale metabolic reconstructions of rculosis ,19,26 whrculosis  the auths (KEGG) . Using tM. tuberculosis based on the stoichiometric model developed by Beste et al. [M. tuberculosis genome-scale network. The type of rate equation generated for each reaction was based on the stoichiometry of the reaction, as described in the Methods section. The resulting genome-scale model of M. tuberculosis contains 739 metabolites, 856 metabolic reactions and 856 enzyme species.Using GRaPe , we creae et al. . GRaPe aet al. [We obtained flux distributions for three steady-states with glycerol being the only carbon source using the interactive web-based tool developed by Beste et al. . The tooet al. ; as a coWe performed three separate parameter estimations for each of the three glycerol consumption rates. The kinetic parameters for each reaction in the model were estimated using GRaPe’s genetic algorithm. Model 1, with a glycerol consumption rate at 0 mmol/gDW/h, had 2297 kinetic parameters after parameter estimation; Model 2 had 2537 parameters with a glycerol consumption rate at 0.5 mmol/gDW/h, and Model 3 had 2931 parameters after parameter estimation with a glycerol consumption rate at 1 mmol/gDW/h. The difference in the number of parameters after each estimation was due to different numbers of reactions having a zero flux in each case. Furthermore, reactions with negative fluxes had their substrates and products swapped around to prevent having negative kinetic parameter values. The three models are provided in SBML format in We performed a steady-state analysis for Model 1, 2 and 3 using COPASI. The results were then compared with the FBA flux distribution obtained from the Beste model under the same experimental conditions. Our verification analysis showed a near-perfect agreement between the results obtained from our models and the respective FBA simulation. We identified reactions that showed the greatest change in flux with respect to change in glycerol consumption rate . We calcTo determine the degree of redundancy in the values of our estimated kinetic parameters, we performed PVA by repeating our estimation algorithm 100 times for Model 2. It is well known that different sets of parameters values can fit to experimental time-series data resulting in mathematical redundancy ,29. ThisfV, the velocity of the forward reaction, is the most constrained parameter having the smallest standard deviation (fV is directly related to the amount of enzyme and the expression level of the corresponding gene(s), it is expected to be more tightly linked to a particular condition, thus more constrained by a given flux distribution.In order to facilitate their interpretation, the results of PVA were split into five different categories based on the stoichiometry of the reaction . The results of PVA show that many parameters are not strongly constrained . Separateviation . Since VThe high degree of redundancy in the parameter values as indicated by PVA comes in support of our underlying assumption that accurate rate equations and kinetic parameters are not necessarily crucial in constraining the behaviour of the biological system. Nevertheless, the integration of genomic and proteomic data, together with metabolic and flux data, is expected to reduce mathematical redundancy as shown by previous studies ,29.-4 and limiting the data points to three decimal places in the input dataset. The objective function is the summed squared mean distance measured between the simulated data and input data. Reducing the objective function increased computing time but improves the quality of the parameter fit to input data. We performed an experiment to determine the relationship between the value of the objective function and the time taken to compute PVA for one reaction with two substrates, two products, one enzyme and six kinetic parameters .The computation of 100 sets of parameters for each reaction in Model 2  for PVA took over 5 hours and 40 minutes. The relatively fast computing time was a result of reducing the objective function to 10rameters . The resAnother variable that can increase computing time in parameter estimation is the number of data points in the experimental dataset. To examine how the number of data points influences computing time, we performed parameter estimation for a single reaction with two substrates, two products, one enzyme and six kinetic parameters . The resM. tuberculosis model and kinetic parameters by determining whether different conditions could be predicted without re-estimating kinetic parameters. To calibrate the model over a range of glycerol uptakes, we created a virtual time series containing ten repeats of each of the steady-state flux distributions obtained from input conditions with glycerol at 0, 0.5 and 1 mmol/gDW/h, respectively. The flux vector under each experiment was replicated ten times to create a data file with ten data points; we then merged the three individual files to create a data set with 30 time points, which was used as an input file for parameter estimation. Performing parameter estimation with this dataset took 125,022 seconds to complete with the objective function set at 10-4. The range of objective functions observed for individual reactions was between 10-8 and 10‑20. After parameter estimation, three steady-state analyses were performed with glycerol uptake at 0, 0.5 and 1 mmol/gDW/h using COPASI.We tested the predictive capability of our fV and rV), which can vary with different expression of the corresponding enzymes, should be allowed to vary in different conditions, whereas other parameters should remain the same. It is not currently possible to specify different levels of parameter constraints for different conditions in GRaPe, but this possibility may be added in the future.The resulting model was only able to predict the steady-state when glycerol update was at 0.5 mmol/gDW/h. Changing the glycerol level in this model resulted in simulation errors. A possible explanation for this unexpected observation is that combining three separate steady states is a fundamentally different experiment from having a dynamic change in glycerol level. Input flux distributions obtained from separate FBA simulations may be inappropriate to reproduce the dynamics of metabolic adjustment. To create a suitable training data set for dynamic modelling, intermediate data points covering the transition between steady states would be needed, but these data points cannot be obtained by FBA and require detailed experimental measurements. Another possible approach is that forward and backward reaction velocities (Mycobacterium tuberculosis based on generic kinetic equations. In recent years, there has been considerable progress in genome-scale data collection technologies, leading to ever increasing amounts of data in many organisms. However, the exploitation of such large datasets is proving challenging. For example, Ishii et al. [E. coli. Castrillo et al. [S. cerevisiae. Yus et al. [Mycoplasma pneumoniae. While each of these studies provided considerable new knowledge about the biology and cellular functions of their respective organism, a comprehensive model that is able to explain, and thus predict, such a large breadth of properties is still lacking for each of them. The main reason is that the construction of large kinetic models is arduous and challenging, and there are no established tools and techniques enabling the estimation of numerous kinetic parameters from large sets of heterogeneous data. Our aim is to show that, as an initial step, the construction of such genome-scale models given a comprehensive set of flux data can be achieved. The GRaPe tool assigns rate equations to all the reactions in the model based on the stoichiometry of the reaction. We successfully applied our methodology to the M. tuberculosis genome-scale metabolic network, resulting in a kinetic model with 739 metabolites, 856 metabolic reactions and 856 enzymes.In this paper, we present the first genome-scale kinetic model of i et al.  measuredo et al.  carried s et al.  presentein silico by examining the dynamics and properties of cellular processes has the potential to increase our understanding of biological systems. This makes it necessary to advance towards kinetic modelling in our drive to understand the detailed dynamics of cellular functions and their regulation. However, it is time-consuming and costly to experimentally measure all metabolite concentrations, reaction fluxes and kinetic parameters at the genome scale. Additionally, many kinetic equations are unknown and thus, standard rate laws have been used to describe metabolism. Liebermeister et al. [et al. [et al. [Predicting cellular behaviours r et al. , Adiamah [et al.  and Ao e [et al.  have allet al. [M. tuberculosis which was capable of predicting different growth conditions using FBA. The phenotype growth of 78% of mutant strains was correctly predicted by the Beste model. We built a genome-scale kinetic model of M. tuberculosis based on this stoichiometric model and showed that our model accurately reproduced genome-scale flux distributions under different growth conditions. The kinetic parameters used in our model were estimated using only flux values, therefore there remains a degree of redundancy in parameter values as illustrated by PVA. The results from PVA indicate that fV, the velocity of the forward reaction, is the most constrained parameter. The rest of the parameters in our model exhibit a high degree of redundancy. Banga [-8. The compromise between computing time and more precise parameter values must always be considered when performing parameter estimation. Furthermore, our results also show that computing time increases non-linearly with the number of data points in the parameter estimation training data. When parameter estimation is being carried out for a system in steady-state, the number of data points can be reduced to lower the computing time.Beste et al.  producedy. Banga  suggestsy. Banga . Reducinet al [An attempt was also made to constrain our kinetic parameters by training them with data based on three distinct experimental conditions. However, our model was able to predict only one state revealing the limits of using FBA steady states to constrain a dynamic model. Optimisation techniques can be used to estimate kinetic parameters based on simulated or experimental data ,35. Howeet al  where thMycobacterium tuberculosis based on generic kinetic equations. The model has 739 metabolites, 856 metabolic reactions and 856 enzymes. All kinetic parameters were estimated using a genetic algorithm based on the stoichiometry of reactions and flux distributions in the network. Our results show a near-perfect agreement with flux distributions under different growth conditions. The kinetic parameters used in our model were estimated using only fluxes, therefore there remains a degree of redundancy in parameter values. To further improve the predictive power of genome-scale dynamic models, the integration of more experimental data types including gene expression, proteomics and metabolomics, as well as the use of dynamic training data sets, will be needed. Nevertheless, our method for constructing a genome-scale kinetic model of M. tuberculosis represents a platform for further model development and analysis.In this article, we developed a genome-scale kinetic model of


In addition, our model provides excellent predictions of whether a medium will produce more or less growth than another  a nutrient's structure and function, ii) the presence of a small number of enzymes in the organism, and iii) the carbon flow in pathways that catabolize nutrients. When applied to test organisms, our model allows us to predict whether a nutrient can be a carbon source with an accuracy of about 90% with respect to  in silico organisms to systematically explore whether an arbitrary nutrient can stimulate growth as a single source of carbon, and how effectively it can be used by the organism. We find that we can predict whether a nutrient is a source of carbon and the biomass yield of that nutrient with a simple model that transcends the diversity of species and their environments. Our model for catabolic potential can therefore be used as a baseline model for any microbe for which we lack a metabolic reconstruction.The ability of microbial species to consume compounds found in the environment to generate commercially-valuable products has long been exploited by humanity. The vast untapped diversity of microbial species offers a wealth of potential resources. However, little is known about most microbial species. While the metabolic network of an organism can be studied to find its nutritional requirements, we lack a reliable metabolic reconstruction for most species. We use  The biomass production predictions of our model depend exclusively on the characteristics of the available carbon sources and the set of metabolic pathways that can catabolize them. Our model is able to match the predictions of flux balance analysis with no significant computational effort and providing insight into the determinants of catabolic efficiency.In order to formalize the intuition used to build and fine-tune the constraints used to predict growth rates using metabolic reconstructions, we present here a systems-level Our phenomenological model expresses the impact that different carbon sources (or nutrients) have on a microbe's ability to grow using only information on the chemical structure of these carbon sources and on the ability of a microbe to catabolize these nutrients. Our model is built to reproduce the predictions of flux balance analysis calculations (FBA) on metabolic reconstructions, thus it will suffer from the same limitations. Indeed, while FBA is a powerful tool to investigate microbial metabolism and microbial growth in particular, it has a number of limitations when estimating growth rates and the effect of media and environmental conditions on growth.It is well-known that microbes need a minimal medium and a carbon source in order to grow. Minimal media have been described for a number of species and contain essential chemical species without which the species would not be able to grow FBA is a linear optimization method that predicts the maximal conversion of a set of carbon sources into biomass with a fixed minimal medium. In order for FBA conversion rates to reproduce empirical growth rates, one needs to consider an additional ATP maintenance flux which is obtained by fitting FBA results to empirical growth rates obtained for a certain temperature, minimal medium, and carbon source uptake. While ATP maintenance rates obtained for a specific minimal medium have been shown to give accurate predictions of growth rates in different minimal media for some organisms Additionally, because metabolic reconstructions do not consider regulatory constraints, FBA will predict that a microbe is capable of uptaking two different sugars simultaneously, while it is well-known that if there is more than one sugar carbon source at high enough concentrations, the organism will exhaust the preferred one before consuming the others E. coliB.subtilisSaccharomyces cerevisiaeMethanosarcina barkeriHelicobacter pylori, a gram-negative bacterium Staphylococcus aureus, a gram-positive bacterium Mycobacterium tuberculosis, an acid-fast gram-positive bacterium To develop a phenomenological model that is able to reproduce maximal biomass conversion rates per carbon source under aerobic conditions, we investigate the maximum amount of biomass that can be produced by an organism in the presence of a minimal medium, oxygen and one or more carbon sources including at most one sugar. To this end, we run FBA on metabolic reconstructions in which we remove ATP maintenance The rationale for choosing a small number of species for model building and validation is that lower quality reconstructions are likely to have significant gaps that could incorrectly bias the determination of the model. Additionally, the aggregate set of nutrients available for these reconstructions is of 352 nutrients, which cover all nutrient types and 90 out of 97 pathways available in KEGG We believe that the development of a systems-level model of microbial metabolism is not only complementary to current approaches but offers some advantages with respect to them. Specifically, while FBA run on metabolic reconstructions already has the capability of predicting maximum biomass yield, our model has the advantage that since it does not consider microscopic details of the metabolism of a species it is directly applicable to any other organism growing under the conditions of our analysis. In fact, we show that solving over a thousand linear equations under constraints can be well approximated by a simpler model whose principles are easier to understand. As such, our model offers the possibility of uncovering universal features of the metabolism of organisms that other computational approaches are not capable of. The mathematical model we develop is thus a valuable tool from both fundamental and applied perspectives, since it can help understand the metabolism of organisms for which a metabolic reconstruction is not available, or guide the process of validating metabolic reconstructions.In order to develop a mathematical model that relates nutrient (carbon source) uptake in complex media to biomass production, we need to address three different questions see . The firThen, we need to assess what is the maximum amount of biomass a nutrient can produce when acting as the sole source of carbon. Our specific aim will be to find a mathematical relationship between nutrient composition  and the biomass produced per unit of nutrient uptaken.In third place, we need to assess how maximal biomass production is affected when several nutrients are present in a medium. That is to say, we need to determine the relationship between biomass produced and the characteristics of the nutrients available in the medium. Finally, to prompt and aid experimental studies, we use our model to predict which nutrients can be a source of carbon for four species lacking a metabolic reconstruction, and predict the biomass production of these species in complex media. We show that the carbons available in the 20 natural amino acids in a medium provide the best boost to biomass production regardless of the species.The first step is to build a model that predicts whether an individual nutrient ies  see . If it cTo establish whether a given nutrient is a source of carbon for a given organism, we first need to determine whether the nutrient can be transported into the cell from the extracellular medium . This quM. barkeri does not uptake nutrients that we classify as sugars, sugar derivatives, cell boundary, fatty acids, purines, or pyrimidines. However, experiments with M. barkeri may have deliberately been focused on small organic compounds, so one may question the range of nutrients that M. barkeri is truly capable of uptaking. Note that we will have to ask this question for every new in silico organism, an infeasible task given the large number of experiments that one would need to perform.The number of nutrients that are actively transported by a species varies greatly with nutrient class  can be labeled  belongs .not to be sources of carbon: cell boundary nutrients and cofactors. Nutrients in the cell boundary class form the cell wall or the cell membrane and are composed of distinct metabolites that could, in principle, serve as carbon sources on their own. For example, lipid A contains several fatty acid chains that can be catabolized in E. coli. However, as in this particular example, these complex nutrients do not have enzymes available to decompose them, and they are instead used directly in the formation of the cell boundary. Cofactors have several metabolic functions , but nearly none of them is catabolized by the species we study. Functional classes highlight that if a compound has a function in the cell other than being a source of carbon, then there will be selective pressure against the occurrence of enzymes that breakdown these nutrients.Based on the predicted biological function of the nutrients, we identify two classes whose nutrients are consistently found When considering the chemical structure of nutrients, we find four nutrient classes whose components are consistent in whether they were sources of carbon or not: inorganic compounds, pyrimidines, sugars, and sugar derivatives. We label inorganic compounds and pyrimidines as E. coli and B. subtilis, but E. coli and B. subtilis, purines are catabolized via the degradation of urate into glyoxylate; we find a well-characterized enzyme in this pathway that is present in these species, but is not present in the other two: 5-hydoxyisourate hydrolase (EC: 3.5.2.17). Therefore, if an organism contains genes encoding for this enzyme we label all purines uptaken by that organism as  We find mixed results outside of the four structural classes discussed above. Purines .The next step is to determine for those nutrients that produce growth what is the maximal production of biomass when that nutrient is the only source of carbon. In fact, if a nutrient is the carbon-limiting source in a given medium, the biomass yield of the nutrient must be related to the number of carbons in the nutrient. In effectively catabolized.It is visually apparent from ir yield . We consWe find two sets of nutrients for which the number of carbons that is effectively catabolized is not the actual number of carbons available in the nutrient Very often, catabolism of complex nutrients starts by breaking them down into a number of simpler nutrients, which are then catabolized according to their respective pathways. Tryptophan, lipids and nucleotides are examples of such complex nutrients: tryptophan is broken down into three separate metabolites ; lipids are broken into fatty acids, glycerol and a functional group such as choline; nucleotides are broken into a phosphorylated ribose and a nucleobase. Each of these simple compounds can act as nutrients on their own.Complex nutrients display some of the largest variation in biomass yield, as highlighted in An additional consideration is the fact that some nutrients “leak” carbons during catabolism. Purines are an example of this; they are reduced to glyoxylate, but in doing so, they “leak” three carbons as carbon dioxide and urea, which cannot be catabolized for the carbon. Therefore For some classes, such as amino acids and sugar derivatives, the variance of the biomass yield for nutrients within the classes is also reduced. This reduction supports the use of the effective number of carbons as the predictor of biomass yield of a single nutrient. We thus modify Finally, we want to model the maximal biomass production when there is more than a single source of carbon present in the medium, or in other words when organisms grow in a complex medium. We consider complex media in which nutrients are restricted to five classes: sugars, fatty acids, amino acids, purines, and pyrimidines, partly because they are commonly used in growth rate/biomass yield experiments, and partly because it simplifies the analysis of the results. In addition, complex purines and pyrimidines are a mixture of sugars and nucleobases, and as we are already considering sugars, we only use the simple nucleobases.independent contribution to the biomass production. For each species The simplest plausible model for the contribution of nutrients to the biomass production is one in which each nutrient in silico biomass production of the organism on the complex media S. aureus, for whose reconstruction it is not clear what units were used for the biomass production).To test this model, we randomly generate ensembles of complex media as described in the Data and in silico experimental results for training set species  and test set species (H. pylori and M. tuberculosis). This indicates that the model accurately captures which media will result in faster/slower production of biomass. For each species, however, the model systematically under or over-predicts growth. A regression of the predicted biomass production versus experimental in silico production indicates that E. coli, B. subtilis, S. cerevisiae, H. pylori, and M. tuberculosis.We find a very strong correlation , L. monocytogenes (a gram-positive bacterium), D. discoideum (an eukaryote), and T. acidophilum (an archaeon).Our model sheds light on several questions related to the impact of nutrients on the biomass production of microbes. Our approach treats microbial metabolism as a “black box” that uses nutrients to reach optimal biomass production. Because the model does not take species-specific details into consideration, it is useful for generating predictions for any microbe, something that would be impossible with any existing modeling approach. To illustrate how one would proceed to extrapolate to “new” organisms and to show what kind of insights one could obtain, we generate predictions for four organisms that lack a metabolic reconstruction: We find that, overall, these species are predicted to take up fewer nutrients than the species in the test set . This isD. discoideum contains the enzymes for We then use the model of catabolic potential to predict whether each of these nutrients could be a source of carbon. In Finally, we combine our models of biomass yield of ex media . We chooNote that these predictions for biomass production are based on the biomass yield per carbon available in the nutrients present in the medium. Biomass yield is a time independent quantity that cannot be directly associated to growth rate. However, because biomass yield gives an upper limit for growth rate Microbes use nutrients found in their environments to grow. Understanding and developing quantitative models of this process is of fundamental importance in cell biology, physiology, medicine, evolution, synthetic biology and bioengineering, not to mention of practical importance to those that need to grow microbes in laboratories. Given the diversity of the microbial world and the number of combinations of nutrients available in their environments, this seems too difficult a problem. In this study, we focused on how microbes might catabolize nutrients to obtain carbon for biomass production.will be catabolized. The second level concerns whether all of the carbon in a catabolized nutrient is available for biomass production. The final level incorporates the biomass yield for selected classes of nutrients and enables us to make a prediction on the biomass production of a microbe in a complex medium. To validate our approach, we compare the predictions of the complete model with in silico predictions of growth in complex media of species that are not part of the training set. Our results on these species are excellent predictions of which media will produce more/less growth.Our model comprises three levels, with each level building up on the results from the previous one. The first level concerns whether a nutrient in silico microbial biomass production was Finally, we looked at the biomass yield of sugars, amino acids, purines, pyrimidines, and fatty acids. We found little variation in the yield of these nutrients amongst different species, and were able to postulate a model for the biomass production of a microbe on a complex medium containing any number of these important nutrients. All of these nutrients have separate catabolic pathways, with the exception of some groups of amino acids which share a catabolic pathway. The fact that the The ability of our model to predict biomass production on complex media must be balanced by an understanding of its limitations. First, we model microbial metabolism as a black box, and therefore we do not account for absent pathways that biosynthesize some biomass components. The absence of such pathways would require that the corresponding biomass components be made available in the medium used, but our model cannot be used to predict which of these are indeed required. This means we cannot use the model in its current form to predict the minimal medium that is needed for a microbe to grow.Second, microbial species are sometimes identified by the nutrients they take up and excrete. The ability of a microbe to transport such compounds in and out of the cell is largely dependent on the specific protein transporters available. A separate body of work exists, largely in the form of TransportDB Third, the stoichiometric method we describe for generating the biomass data cannot be used to predict the growth rate of a microbe because kinetic information is not included. However, our model provides a baseline to which one can add kinetic information. For example, the rate-limiting step in poor growth media is likely to be the rate at which a microbe takes up nutrients. Therefore one can use the kinetics of nutrient transport with our prediction of biomass yield to predict growth rate.All this notwithstanding, we believe that our approach and models open the door to significant advances in the quantitative modeling of microbial metabolism, and eventually of the metabolism of more complex organisms. In particular, our models could be extended to consider whether a nutrient acts, not only as a source of carbon, but also as a source of nitrogen or energy, or directly as a component of the biomass. Our models could also be extended to include more detailed information about pathways, or to consider functional metabolic modules E. coliB.subtilisSaccharomyces cerevisiaeMethanosarcina barkeriHelicobacter pylori, a gram-negative bacterium Staphylococcus aureus, a gram-positive bacterium Mycobacterium tuberculosis, an acid-fast gram-positive bacterium http://gcrg.ucsd.edu/ in SBML format (accessed 03/27/2009). There are in silico organisms in the training set. According to the reconstructions, out of these We first consider a training set of four species for which there are high quality metabolic reconstructions available, and which cover a wide range of microbial phylogeny: a gram-negative bacterium E. coli, a gram-in silico organism We use the available reconstructions and the literature to define a fully minimal medium for each Rhodopseudomonas palustris (a gram-negative bacterium), Listeria monocytogenes (a gram-positive bacterium), Dictyostelium discoideum (an eukaryote), and Thermoplasma acidophilum (an archaeon). We identified the nutrients that these organisms take up  the redundancy in pathway membership; S2) the model selection process. Tables describing: S1) the minimal media used for each species; S2) the prediction of our model for each nutrient separated by nutrient type; S3) the reassignment of KEGG IDs and pathways for compounds lacking that information; S4) the composition of complex nutrients; S5) the classification of nutrients in different classes; S6) the uptake of fatty acids and sugars by the different species; S7) the prediction of the logistic regression pathway model for each nutrient; S8) coefficients for the different terms in the logistic regression model.(PDF)Click here for additional data file.