To that end, several detection and quantification methods have been developed to study NO, as well as its redox relatives, nitrite and S-nitrosothiols. While no single technique can offer a complete picture of the nitrogen cycle in a given system in vivo, familiarity with the benefits and limitations of several common tools for NOx determination can assist in the development of new diagnostics and therapeutics.The detection and quantification of nitric oxide and related reactive nitrogen species  S-nitrosothiols, in vivo (summarized in Nitric oxide (NO) is an important bioactive molecule with numerous roles in physiological systems and potential therapeutic applications, many of which are discussed throughout this issue. Understanding the role of NO, particularly in cases where NO homeostasis may be disrupted or NO regulation is intrinsically tied to pathology, relies on the accurate detection and quantification of this molecule. Many techniques exist for both the direct and indirect quantification of NO and related nitrogen species  to oxidize NO to NO+, which results in a small redox current (in the range of picoAmps to nanoAmps). By measuring this redox current in the system of interest and comparing it to the redox current between the electrodes when calibrated using NO standards, nearly real-time (requiring 30–60 s to equilibrate) NO concentrations can be monitored in vivo.Real-time, +. Early electrochemical probes used working electrodes that were either gold-plated or made of pure platinum, though more recently, an alloy of platinum (90%) and iridium (10%) has been suggested due to its improved durability over pure Pt and the electrocatalytic properties of Ir in redox reactions [Working electrodes at a potential of 0.8–0.9 V relative to a silver/silver chloride reference electrode oxidize NO to NO iridium 0% has beeactions .o-phenylenediamine to reduce interaction with cations [Care must be taken with working electrodes to prevent interaction with anions such as nitrite, nitrate, ascorbate or urates; pretreating the electrode with Nafion repels anions. Moreover, oxidation of nonnegative small molecules, such as dopamine and 5-HT, can also result in overestimation of NO levels; this can be partially compensated for by pretreating electrodes in  cations .in vivo, despite extensive calibration against standards. Recent work suggests that this is due in part to electrode size, with larger electrodes underestimating NO due to rapid NO consumption from an unstirred layer; this work suggests that smaller electrodes are preferable not only for decreased invasiveness, but also for increased accuracy [Unfortunately, the extreme variability between different electrodes casts doubt on the utility of such devices for NO quantification. Different working electrodes can vary by as much as six orders of magnitude when attempting to quantify NO accuracy .Electron paramagnetic resonance (EPR) spectroscopy is a technique that can, in theory, detect the paramagnetic species in a sample . However, in practice, several factors may limit the applicability of EPR to any given system. NO is difficult or impossible to detect directly via EPR in most biological systems due to its broad, indistinct EPR signal in aqueous solution. However, it is possible to take advantage of the unique chemical properties of NO in order to create a reaction product, adduct or intermediate with a resolvable EPR spectrum.2, have led to a decrease in the use of NNOs to quantify NO generation in vivo via EPR, except under specific conditions [Conventional diamagnetic spin trapping agents , which are widely used to detect transient free radicals, are often not effective traps for NO. However, nitronyl nitroxides (NNOs), most notably carboxy-PTIO (c-PTIO), have been shown to be extremely effective at scavenging and trapping NO, resulting in a chemical shift that allows real-time EPR observation of the scavenging of NO. The efficacy of this assay is strongly dependent on the use of a proper amount of NNO for the experimental conditions. Moreover, both NNO reactants and products are easily reduced in many biological systems to EPR silent species, limiting their utility in quantification of NO production over time. NNOs can also directly interfere with NO generating pathways, or provide new reactive pathways for the generation of NO. These issues, coupled with the fact that NNOs  have recently been shown to react with other radicals, such as NOnditions .N-methyl-d-glucamine dithiocarbamate (MGD) [S-nitrosothiols.Other families of spin traps exist for the purpose of isolating NO, many of which utilize iron to bind NO and create an adduct that can be detected by EPR. The most common family of synthetic iron-based spin traps are iron-dithiocarbomate-based traps, including diethyldithiocarbamate  and N-mete (MGD) . These s7 M-1 s-1), quantification of metHb formed from oxyHb during a process known to generate NO is often a reliable means of quantifying NO production [-3–10-4 s-1), and has a distinct EPR signal that can be used to quantify hemoglobin-bound NO at concentrations of approximately 0.5 µM and above [in vivo. In addition, EPR can only detect these reaction products at concentrations of a few hundred nanomolar or more.Among the many biological targets for reaction with NO, hemoglobin (Hb) and myoglobin (Mb) are some of the most relevant, and can also be used for the detection and quantification of NO. NO reacts or coordinates with ferrous heme depending on the presence or absence of oxygen. If the ferrous heme is oxygenated , NO reacts to form nitrate and ferric methemoglobin (metHb). MetHb at concentrations aboveapproximately 0.5 µM is easily resolved and quantified by EPR, even in a background with high concentrations of other Hb species, though the NO is consumed in its formation. Because oxyHb reacts very quickly with NO . DAFCs  react quantitatively with NO under aerobic physiological conditions to create fluorescent products with absorption and emission spectra in the visible or near-IR range, allowing for detection and imaging of NO concentrations above 5 nM. DAFCs do not react with nitrite and nitrate, allowing for NO imaging amid a background of nitrogen oxides at much higher concentrations than NO [2O3) and other nitrogen-containing radicals and reducing agents [The first successful fluorescent imaging of NO  than NO , nor do  than NO . Howeverg agents .in vivo. Thus, use of these fluorescent probes has been largely limited to cell cultures, with benzimidazole derivatives having been used in frozen tissue samples.To overcome many limitations of the DAFCs, a new family of copper (II) based fluorescent probes with sensitivity similar to DAFCs (5 nM) was developed  and exteDAFCs and copper-fluoresceins react with NO irreversibly, and may lead to the buildup of a high level of background fluorescence. To create a reversible NO detector, a fluorescent protein with the NO-specific heme domain of soluble guanylate cyclase was created. While both NO-specific and reversible, the threshold of detection for this molecule was only 10 µM. A related protein system with a much better detection limit (0.1 nM) has been developed for use with FRET imaging, but this requires genetic encoding of the detector into the target organism. Future work in this area may lead to a more ubiquitous fluorescent NO detector, but current sGC- and FRET-related detectors, while they have a few unique advantages, are generally less useful than current DAFCs and copper-fluorescein fluorescent probes .in vivo, ranging anywhere from tens of seconds in some tissues to milliseconds or microseconds in the presence of heme-containing proteins such as hemoglobin. With the correspondingly low steady-state concentration of NO, real-time quantification of NO is difficult and at often times, the concentration of the nitrite and nitrate metabolites of NO will serve just as well as (or better than) the concentrations of NO itself [Nitric oxide generally has a relatively short half-life O itself . MoreoveO itself . Due to in vivo quantification of nitrite presents unique challenges. For instance, the typical Griess assay has a detection limit of 1–2 µM, a full order of magnitude above basal nitrite levels in many biological fluids such as plasma. Moreover, the reaction cannot be readily utilized in whole blood due to interference from blood constituents such as hemoglobin and plasma proteins. Thus, various techniques have been developed to improve sensitivity and facilitate blood, plasma and serum sample analysis using techniques based on the Griess reaction, each with advantages and disadvantages. The presence of even trace contaminants, anticoagulants and proteins can all reduce the accuracy of Griess-based assays [For over a century, the Griess reaction and its derivatives have been used to quantify nitrite in a variety of situations. However, application of the Griess reaction for d assays ,15.4 to both prevent oxidation of nitrite and precipitate proteins from the solution that could potentially interfere with nitrite detection via nitrosation of cysteine or nitration/nitrosation of carbon or nitrogen under the acidic conditions necessary to conduct the Griess reaction [Numerous sample preparation and storage methods have been used in the analysis of nitrite and nitrate concentrations by the Griess reaction, and some of the procedures used are not clear. Thus, even seemingly similar protocols can differ by an order of magnitude or more in their reported concentrations. Out of the commercially available storage monovettes, serum has been shown to have the lowest levels of nitrite contamination. EDTA and citrate, and to a lesser extent heparin, have been found to have significant levels of nitrite contamination, often greater than the nitrite concentration in the sample itself. Beyond selection of storage media, samples must be properly preserved and prepared for analysis by techniques based on Griess reactions. Nitrite can oxidize forming nitrate, a process that can be inhibited by alkali. Alkali is often combined with ZnSOreaction . Dilutioreaction . Due to reaction .Although the Griess reaction is the most widely cited technique for the quantification of nitrite, it is by no means the only method available, nor does it exclude the concurrent use of other techniques to improve the quality of data collection, detection limits and range of conditions under which data can be gathered. Numerous chromatography-based assays exist for the detection of nitrite (and often nitrate), frequently employing pre- or postcolumn treatments (sometimes based on the Griess reaction) to quantify these anions without interference from contaminants in the initial solution .HPLC techniques can be used to quantify nitrite in conjunction with the Griess reaction described above or other methods of nitrite detection, such as the DAN fluorochrome  described elsewhere . HPLC syx) employ both HPLC and spectrophotometric analysis of the diazo product of the Griess reaction. These specialized systems have the advantage of highly reproducible results that can be obtained with less time-consuming sample preparation procedures. However, as with any commercial assay system, care must be taken to validate the assay in each new situation and to ensure consistent quality of results [Specialized systems designed and marketed for the detection of nitrogen oxides  used for the simultaneous derivatization and quantization of nitrite ,17. Recein vivo NO metabolites such as nitrite and nitrate, and can be used in situations where traditional Griess reaction assays and chromatography fail. This typically requires a specialized chemiluminescent detector, and such detectors designed for the quantification of NO are commercially available and well validated [Ozone-based chemiluminescence is a technique for the detection of NO gas that has been used with great success in a variety of applications. It is particularly useful in the determination of alidated .S-nitrosothiols, as discussed later in this article). Notably, chemiluminescence does not require deproteination prior to analysis, and can be conducted in the presence of hemoglobin and other contaminants, although oxidizing hemoglobin before analysis  has been shown to be useful in the prevention of oxidation of nitrite to nitrate [While the potential applications of chemiluminescence are numerous, it is a particularly valuable tool for the determination of nitrite and nitrate  acidified with acetic acid can be used to reduce the majority of relevant NOx species and is preferred for analysis of nitrite concentration , whereas copper(I)/cysteine is often used for the determination of S-nitrosothiols (discussed later in this issue).Chemiluminescent determination of nitrite or nitrate requires the reduction of the relevant NOChemiluminescence is highly sensitive, with a detection threshold on the order of 1 pmol of total nitrite or 1 nM of nitrite in solution, depending on the quantity of sample used. However, it also has limitations and potential pitfalls. Foaming /cysteine as a reductant) can cause an overflow from the reaction vessel when biological samples (particularly those with high protein levels) are injected into the reaction chamber. There is also a great deal of variability between instruments, and even on the same instrument between uses; thus, care must be taken to calibrate the instruments against a set of known standards before each use .in vivo as a protein modification factor. NO in the presence of oxygen can form S-nitrosothiols (R-S-N=O) (RSNOs). These RSNOs may transport NO activity, and also likely affect cellular NO signaling pathways. Thus, determination of the in vivo concentration of these RSNOs is important for understanding NO transport and signaling within the body. Quantification of small-molecule RSNOs at relatively high concentration in vitro can often be accomplished using UV/Vis spectroscopy, but the relatively low concentrations of these compounds in vivo, coupled with the fact that S-nitrosothiols of interest are often associated with large macromolecules, render spectroscopic techniques untenable. Thus, the most commonly used techniques for quantification of RSNOs generated in vivo rely on detection of liberated NO or the labeling of thiols vacated following the liberation of NO  method, potassium iodide (KI) and iodine (I2) create tri-iodide in the presence of acetic acid. This serves as the reducing agent, simultaneously liberating NO from RSNOs, nitrosamines, iron–nitrosyl complexes and nitrite. Because of the less-specific nature of this assay, and the frequent contamination of materials by nitrite, care must be taken to maintain accurate controls [In the tri-iodide . In this technique, Cu(I) reduces the nitrosothiol, while cysteine both reduces Cu(II) and forms CSNO. CO gas flow prevents any heme present from capturing NO before it can be detected. This method has the significant advantage of being nitrite silent, and thus ignores many otherwise-troublesome sources of contamination . The 3C 3Fe(CN)6, NEM and DTPA. K3Fe(CN)6 (ferricyanide) oxidizes hemoglobin to the non-NO capturing metHb state, while NEM blocks free thiols from becoming S-nitrosated during the treatment, and the metal chelator DTPA protects SNO bonds from free metals. The modified 2C method eliminates the complications of CO flow during the experiment, while preserving many of the 3C method's advantages (particularly nitrite independence). However, this method requires pretreatment of samples and additional care when dealing with some hemoglobin-based samples [To overcome some of the difficulties with the 3C assay, a modified copper/cysteine procedure has been developed, frequently referred to as the modified 2C method. This uses pretreatment with K samples .S-nitrosothiol reduction, it does not provide any insight into the specific location of that NO. For this, other techniques must be used, and can often be used in tandem with chemiluminescence for improved results.Each of these methods has advantages and disadvantages, but all three share certain key features. Perhaps most notably, while chemiluminescence can allow for accurate quantification of NO liberated from S-nitrosothiols in proteins is the biotin switch technique (BST). This technique involves three basic steps. First, the free cysteine thiols must be blocked ; next, RSNOs are reduced ; finally, free thiols are tagged with a biotin label or other compound, such as a fluorescent marker, that facilitates separation of labeled proteins by techniques like western blotting or biotin pull-down. However, there are several concerns surrounding this technique, notably, the possibility that some sites of S-nitrosation are destroyed during the procedure, and the potential lack of specificity and completeness of ascorbate in reducing RSNO, with indications that ascorbate may not reduce RSNOs at all sites, and may also reduce sulfenic acids and some disulfides. Despite these concerns, the BST has been widely used to identify SNO nitrosation sites, with many recent variations offering improved sensitivity and specificity. These various modified versions of the BST are collectively a topic of some length, and have been widely reviewed [The most widely used method for the indirect detection and labeling of reviewed .S-nitrosation by various NO releasing compounds, including those that may be developed for therapeutic applications. Another method, termed the d-Switch technique, has recently been developed for analysis of cell lysates. This technique uses NEM to block and tag all free thiols, followed by a procedure similar to the BST to reduce S-nitrosothiols and label them with isotope labeled d5-NEM. This technique allows quantification of both total cysteine and S-nitrosated cysteine by LC–MS. Such systems allow for identification of S-nitrosated proteins directly from cell lysate. While this is not an in vivo assay, the ability to identify proteins as candidates for S-nitrosation can provide valuable insights into physiological systems, and contribute to models of biological activity [Examples of notable recent advances in BST-related assays include the development of a microarray-based assay, which uses an antibiotin antibody to facilitate high-throughput analysis with great sensitivity. Although this technique does not cover the entire proteome, and can return a relatively few false positives, it can provide rapid insight into target proteins of activity .in vivo analysis or imaging, promising initial steps in this direction have been taken. For instance, a coumarin-based phosphine was recently developed that fluoresces upon reaction of the phosphine with RSNO [in vitro. However, the potential of such molecules, including the family of triarylphosphines [in vivo may be attainable [S-nitrosothiols based on this phosphine chemistry [RSNOs can also be detected by fluorescent methods. In general, reactive species such as RSNOs may be targets of less-specific fluorescent probes . While fith RSNO . This moosphines , to servtainable . A recenhemistry .S-nitrosothiols in vivo present numerous challenges, which depend largely on the conditions of study and the inherent difficulty in tracking transient species with short lifespans and relatively low physiological concentrations. While by no means an exhaustive list, many of the most useful and most widely used techniques, as well as some promising candidates for future investigation, have been summarized here. The interested researcher is encouraged to seek more details on any methods of interest in the articles referenced here. In the future improvements in fluorescence-based or mass-spectrometry-based techniques may improve in vivo detection. For now, there are many available techniques all of which can provide useful information provided proper controls are incorporated.The accurate detection and monitoring of NO, nitrite and S-nitrosothiols in vivo, but none of them are universally applicable in all situations.There are many ways to investigate nitric oxide, nitrite and in vivo use of electrochemical probes (though these are subject to many limitations), electron paramagnetic resonance spectroscopy and fluorescence imaging.NO can be determined by direct Nitrite can be determined by use of the Griess reaction and its derivatives, chromatography and chemiluminescence.S-nitrosothiols can also be quantified by chemiluminescence; determination of their location on proteins requires tagging the sites of S-nitrosation, such as by the Biotin switch technique or a derivative thereof.


E.coli GFP-tagged enzymes for cells growing exponentially.Although much is understood about the enzymatic cascades that underlie cellular biosynthesis, comparatively little is known about the rules that determine their cellular organization. We performed a detailed analysis of the localization of E.coli’s metabolic network shows that localized enzymes, in contrast to non-localized ones, form a tree-like hierarchical structure, have a higher within-group connectivity, and are traversed by a higher number of feed-forward and feedback loops than their non-localized counterparts. A Gene Ontology analysis of these enzymes reveals an enrichment of terms related to essential metabolic functions in growing cells. Given that these findings suggest a distinct metabolic role for localization, we studied the dynamics of cellular localization of the cell wall synthesizing enzymes in B. subtilis and found that enzymes localize during exponential growth but not during stationary growth.We found that out of 857 globular enzymes, at least 219 have a discrete punctuate localization in the cytoplasm and catalyze the first or the last reaction in 60% of biosynthetic pathways. A graph-theoretic analysis of We conclude that active biochemical pathways inside the cytoplasm are organized spatially following a rule where their first or their last enzymes localize to effectively connect the different active pathways and thus could reflect the activity state of the cell’s metabolic network.The online version of this article (doi:10.1186/s12918-014-0131-1) contains supplementary material, which is available to authorized users. The imain vitro ,6; neverin vitro -9, littlIt is possible that the existence of large multi-enzyme complexes, as opposed to freely diffusing enzymes, could either be determined by constraints limited to highly specialized reactions, or a general mechanism used throughout the cell to achieve a generic metabolic function. Supporting the latter option, the hypothesis of metabolic channeling proposes that reaction products in a metabolic pathway move from one active site to another within tightly associated multi-enzyme complexes. Such organization may possess several kinetic advantages for the cell ,11; for E.coli cells growing exponentially. We found that 25% of known cytoplasmic enzymes show a discrete punctuate localization in the cytoplasm. When the E.coli biosynthetic pathways were organized into Elementary Flux Patterns (EFPs), we observed a significant preference for the first or last enzyme in such EFP-defined pathways to be localized and that localized enzymes form a tree-like hierarchical structure with higher within-group connectivity.In order to determine if enzyme localization is a generic and functionally relevant property of enzymatic reactions in cells, we studied the distribution of genome-wide GFP-tagged enzymes in A complete Set of E.coli K-12 ORF Archive (ASKA) library of GFP-tagged ORF clones [E.coli biosynthetic enzymes. We used the images displayed on GenoBase representing E.coli cultures growing exponentially and expressing each a protein whose C-terminus was fused to a GFP (see Sup. Mat for a complete definition of the list). As the KEGG collection, a set of manually drawn pathway maps indicating molecular interactions and reactions networks, indicates that E.coli K-12 MG1655 has 857 enzymes involved in known metabolic reactions, at least 25% of the enzymes in E.coli cells growing exponentially show a discrete punctuate localization at diverse locations of the cytoplasm .The complex organization of the bacterial cytoplasm suggests that enzymes could, not only freely diffuse, but also show spatial ordering in the cytoplasm. To explore the rules of putative enzymatic organization, we took advantage of the images of F clones  displayeE. coli [Due to the high connectivity of metabolic reactions, it is difficult to uniquely assign pathway positions to enzymes. We decided to analyze the position of localized enzymes organizing biochemical pathways from a genome-scale metabolic network of E. coli  into EleE. coli . EFPs arE. coli . EFPs deE.coli EFPs composed of 3 to 12 reactions per EFP, from 27 different biochemical pathways including nucleotide, amino acid, nitrogen, central and alternate carbon metabolism, as defined in [or the last enzyme localized to the total number of same-length EFPs having at least one enzyme localized  have either the first or the last enzyme localized and 33 EFPs have both enzymes localized. This indicates an important role for the start or end position of pathways that might underlie enzymatic regulatory strategies.E.coli metabolic network . The metabolic network is described by an asymmetric Boolean square matrix Mij of 1214 unique reactions where each reaction is associated to an enzyme and a non-zero matrix value mij = 1 indicates that the reaction i feeds into reaction j by producing a compound used by reaction j  enrichment analysis of the list of localized enzymes. Significantly enriched GO terms related to enzymatic functions that are essential for growth, the top ones being nucleotide, ion, ATP and amino acid binding as well as ubiquinone synthesis Table . UbiquinE.coli cells growing exponentially, we decided to test whether enzyme localization would vary in different growth conditions. We studied the dynamics of cellular organization in exponential and stationary growth in the bacterium B. subtilis. Due to its larger size, B. subtilis has emerged as an excellent model organism for bacterial cytology and in particular to study the very well conserved set of cell wall synthesizing enzymes [E.coli as shown in Additional file B.subtilis and in both organisms only MurA and MurG show specific localization.As the significant list of GO terms reflects enzymatic activities necessary for  enzymes . We fluoB.subtilis cell cultures strain JDB2840 expressing MurA-CFP . Genobase Images were generated using the ASKA library and obtained from E.coli cultures growing exponentially and expressing each an enzyme fused C-terminally to a GFP (NO addition of 0.1 mM IPTG). E.coli K-12 W3110 strain has 4364 ORFs, 4351 were tagged with a C-terminal GFP fusion and established as plasmid clones as ASKA library. As indicated in the ASKA website, 516 fusions showed GFP focal distribution, 2874 were shown to be around the whole cell, 390 showed membrane distribution, 103 showed both membrane and focal pattern and 355 showed no GFP signal.Expression of the cloned ORF is under the control of an IPTG-inducible promoter, which is strictly repressed by lacIB.subtilis cultures growing exponentially in DSM medium at 37°C, 100 μl of cells were taken at designated times. To stain membranes, 0.5 μl of FM4-64 (100 mg/ml) was added to samples just before the cells were collected by centrifugation. The pellet was resuspended in 10 μl PBS, and added to a poly-L-lysine pre-treated coverslip. All microscopy was performed on a Nikon Eclipse 90i with a 100X objective using phase contrast and captured by a Hamamatsu Orca-ER camera using Nikon Elements BR software. Exposure for GFP, CFP and TRITC was 400 ms for all pictures taken.For E.coli defined in KEGG and extracted 1214 unique reactions ordered by their R00000 number  and used the list of localized genes from Genobase defined by gene numbers b0000 , given that there are k localized enzymes in that EFP is given by:q the probability that there are k enzymes localized in any position in an EFP of length L, then the probability that the first enzyme is localized isIf we call The same expression holds for the probability that the last reaction is catalyzed by a localized enzyme:The probability that the first and last are localized, given that there are k localized enzymes in an EFP of length L isTherefore the probability that the first and last are localized given that the EFP is of length L isFinally, the probability that the first or the last reaction is localized is equal to:


The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of knowledge on constants, complexity and weak generalization. The basis of the deterministic approach for modelling the physico and bio-chemical reactions occurring in the AD system is the law of mass action, which gives the simple relationship between the reaction rates and the species concentrations. The assumptions made in the deterministic models are not hold true for the reactions involving chemical species of low concentration. The stochastic behaviour of the physicochemical processes can be modeled at mesoscopic level by application of the stochastic algorithms.In this paper a stochastic algorithm (Gillespie Tau Leap Method) developed in MATLAB was applied to predict the concentration of glucose, acids and methane formation at different time intervals. By this the performance of the digester system can be controlled. The processes given by ADM1 (Anaerobic Digestion Model 1) were taken for verification of the model.The proposed model was verified by comparing the results of Gillespie’s algorithms with the deterministic solution for conversion of glucose into methane through degraders. At higher value of ‘τ‘ (timestep), the computational time required for reaching the steady state is more since the number of chosen reactions is less. When the simulation time step is reduced, the results are similar to ODE solver.It was concluded that the stochastic algorithm is a suitable approach for the simulation of complex anaerobic digestion processes. The accuracy of the results depends on the optimum selection of tau value. Anaerobic Digestion (AD) is the process by which the complex form of organic matter such as carbohydrates, fats and proteins are converted into simpler form by the cells of microorganisms in the absence of oxygen. Energy production, high organic loading and low sludge production are major advantages of AD process. The energy produced can replace fossil fuel use, and also has positive effect on reduction of global warming. Modeling is a powerful tool which can be applied to simulate various processes occurring in the digester. Models are applied for parameter estimation also. Using the simulation results it is easy to predict and avoid digester failure. The modeling results give useful guidelines for the design of the digester also. The reaction system in an anaerobic digester is complex with many sequential and parallel steps. The reactions can be Biochemical or Physico – chemical in nature which involves species of higher and lower concentrations. A stochastic approach can be applied to simulate these reactions in exact manner. The complex organic matter which is called substrate is converted into simpler form through various steps by living cells called biomass. These cells grow at suitable environmental conditions of pH, temperature etc. They interact with the environment and substrates in a complicated way. Generally the biochemical processes include acidogenesis, acteogenesis, and anaerobic oxidation of Volatile Fatty acids, methanogenesis and extracellular hydrolysis step. The reaction kinetics of growth and decay of biomass and conversion of substrates from one form to another are detailed in the following sections.Anaerobic digestion modeling was started in the early 1970’s when efficient operation of anaerobic systems was needed. The first developed models were simple with limited number of reaction equations . Importa2 as regulator for VFA production; (c) ammonia inhibition. The growth of methanogenic population is greatly affected by un-dissociated acetic acid, un-ionised VFA and total VFA which cause a drop in pH. Several models have been developed taking the substrate (un-dissociated acetate and VFA) as inhibition factor [2 partial pressure. Due to sudden increase in organic loading, the accumulation of VFA takes place, since acetogens grow at a slower rate than the acidogens. This will increase pH which in turn the H2 partial pressure is increased. This will cause further accumulation of acids and thus methane generation is reduced. Few models have been developed based on the H2 partial pressure as inhibition factor [Various models have been developed based on five major categories: models considering: (a) non-ionised Volatile Fatty Acids and total VFA inhibition; (b) Hn factor ,8. The fn factor –12 and mn factor –15. AmmoIn all the above models, many species are involved in more than one reaction. The reaction kinetics is solved by formulated Ordinary Differential Equations (ODE). To determine the rate of concentration of a particular species in time, all the reactions in which the species is involved are to be included during the formulation of ODEs. The complexity increases with increase in number of reactions and species. To avoid this, Stochastic Algorithm has been applied where the state of the system is updated based on the current state of the system and the transition probability.The complex organic matter which is called substrate is converted into simpler form through various steps by living cells called biomass. These cells grow at suitable environmental conditions of pH, temperature etc. They interact with the environment and substrates in a complicated way. The reaction kinetics of growth and decay of biomass and conversion of substrates from one form to another are detailed in the following sections.max).Once the inoculum is introduced into anaerobic digester, the cells pass through lag phase where they adjust to the new environment. Once they get accustomed to the new environment, they start growing in exponential phase called log phase. During this phase, the specific growth rate remains constant. The specific growth rate is given by dx/dt = µx. When the growth limiting substrate is exhausted, the growth remains stationary and reaches the maintenance mode in the stationary phase. When there is no substrate, the cell population slowly starts decreasing in the death phase. In each growing culture, there is a maximum rate of growth per unit biomass with unlimited substrate in the given environment . This is an empirical formula which can be applied in batch studies. Generally, Monod kinetic model is applied in most of the biological wastewater treatment processes. In this model, when one of the substrate concentrations (S) is Limiting, the biomass growth is represented by µ = µmaxS/(Ks + S). Ks is the value of the limiting nutrient concentration at which the specific growth rate is half its maximum value.A kinetic model represents the cell population kinetics. The models can be unstructured, structured unsegregated and segregated. In the unstructured model a single substrate is considered as growth limiting one. Multiple substrates are considered in structured model. In unsegregated model, the average properties of the cell population are considered. In segregated model the discrete and heterogeneity of cell populations are considered. Also various kinetic models such as Maltha’s Law, Slater model and Monod model are used in modeling AD processes. In Maltha’s law the rate of increase of biomass is a function of microbial population only (F(X) = µx). In this model, lag or death phase is not considered. It is assumed that there is unrestricted growth of biomass. In Slater model, final population of biomass is also included. This is represented by logistic equation of biomass growth which relates the specific growth rate μ, biomass concentration X, maximum specific growth rate μmax ,Ks) which describe the microbial processes are able to predict the conditions of maximum growth and when the activity will cease. The main disadvantage of this model is that since the kinetic parameters  vary with substrate, one set of parameters cannot describe biological process at short and longer retention time. To overcome this limitation, first – order models are used [In this model, the kinetic parameters  glucose fermenting acidogens; (ii) propionic acid degrading acetogens; (iii) butyric acid degrading actetogens, acetoclatic methanogens and (iv) hydrogenotrohic methanogens.+/NADH in the cells of biomass depend on the concentration of hydrogen.After hydrolysis of complex substrate into simpler organic compounds such as glucose, short chain fatty organic matter takes place, acidogens degrade glucose into acetic, propionic and butyric acids. Hydrogen is considered as an inhibitor for acidogens according to Embden- Myerhoof pathway since the correlation of NADIn this slowly growing and pH sensitive acteogens oxidize propionic and butyric acids to acetate. At high partial pressure of hydrogen, it acts as an inhibitor in acetogenesis phase. Also acetate inhibition of the propionic and butyric acid degradation step has been considered in numerous studies. So this can be represented by non-competitive type inhibition model.In this step, pH –sensitive and slowly growing acetocalstic methanogens reduce acetate to methane. Here, free ammonia is the inhibitor for the growth of methanogens. The stoichiometric equation and specific growth kinetic reactions are given below:2 in the reaction system due to digestion of propionic and butyric acids by acetogens. So dual substrate form of monod equation can be applied to represent the specific growth rate of Hydrogenotrohic methanogens.There may be growth limitations due to deficiency of COBiochemical reactions and their kinetics in the anaerobic digestion system were assumed to follow first order reactions (hydrolysis), monod type kinetic reactions and inhibition reaction. The complex particulate waste from industries or household is first disintegrated into carbohydrate, protein and lip . During hydrolysis by extra cellular enzymes (hydrolases), monossaccharides, amino acids and Long Chain Fatty Acids (LCFA) are formed. All these bio-chemical extracellular steps were assumed as first order . The firIn the deterministic approach for reaction simulation, the time evolution of the system is considered as continuous which is governed by a set of coupled ODEs. But the stochastic approach regards the time evolution similar to a random walk process which is governed by a single differential equation which is called the master equation. In the deterministic approach, given the initial concentration of various species in a free homogeneous macroscopic environment, the concentration at all future time intervals is determined by averaging random fluctuations to produce a predictable deterministic behaviour . All thekj ,t) , that the reaction event Rμ occurs in time interval [t,t + τ ) is given by a Poisson random variable, P(aj (X (t)),τ ), where j = 1,.. M. The flowchart of Gillespie’s Tau Leap Method is outlined in Figure a0(X (t)) when the number of reactions or the concentration of the reactant species is low. In that case it will be equivalent to Gillespie’s Direct Method where only one reaction is chosen in a time step. In these cases, the algorithm becomes inefficient.Master equation describes the transition of a system from one state to another state using probabilistic formulations. The state of system is determined by incoming and outgoing transitions. Since the state change of a chemical reaction system occurs in a discrete number, the probability to find the current state of the system can be described according to the Master Equation approach. In the Master Equation for reactions, all states are represented by a discrete number of molecules and transition intensities are given by reactions per second. Various Stochastic Simulation Algorithms (SSA) such as Gillespie Direct Method, Tau leap methods, slow reaction method and adaptive tau leap method to generate the trajectories by evolving the reaction type and the time of occurrence of the reaction through the probability distribution –22. It wBased on stoichiometric values, each species is apportioned with theoretical numbers of particles based on the assumed mass. The fluctuations which occur due to stochastic nature of simulation can become less pronounced either by repeating the simulation with less number of particles and computing the mean or by assuming more number of particles. According to the theoretical statistical physics, the fluctuations in the system are inversely proportional to the square root of the number of particles involved in the simulation. So in this work, more number of particles is assigned for a particular species in which the substrate Glucose is assigned with theoretical number of particles proportional to the concentration in the ratio of 1:5. Figure max,glu = 1.25, μmax,bu = 0.833, μmax,pro = 0.542, μmax,ace = 0.333, μmax,hyd = 0.35, Ks = 500, Kb = 200, Kp = 100, Ka = 150, Kh = 150, where μmaxS are maximum uptake rate of various species, K’s are the half saturation value [μ is determined. Then based on the total reaction rate of the system, a reaction is chosen by Poisson random variable. The time step is assumed in such a way that more than one reaction is chosen in a single simulation step. If higher value is chosen, more reactions are chosen where there will be great variation in the propensity function of the chosen reactions. Based on the chosen reactions in a given time step and the stoichiometric constants of products and substrates of the chosen reactions, the number of particles assigned for the reactant and product species involved in the chosen reactions will be modified. So the accuracy of the algorithm depends on the selection of the time step. The simulation results obtained from SBTOOLBOX in Matlab and stochastic algorithm s are shown in Figures The kinetic parameters in this model μon value . The yieWhen simulation time step is more than 1, the number of selections of the chosen reaction is insignificant and the formation of methane is less. Update of sugar takes longer time to reach the steady state. The simulation of formation of acids and formation of methane are rapid. When the tau value is reduced, the simulation results approaches the results of simulation using ODE solver. This is due to the selection of reactions where the propensity function remains constant. At the time step of 0.4, the simulation results get closer to deterministic values. Thus the accuracy of simulation depends on the selection of the optimal value of tau.When more number of reactions are involved in a biochemical processes, the rate of change of concentration of species is determined by evolving a rate equation for each species. As the number of species increases, the number of rate of reactions also increases to evolve the change in the concentration of species. But it is a complex process. The difficulty in formulation of Ordinary Differential Equation (ODE) for reaction simulation can be overcome using Gillespie’s algorithms where the reactions can be represented in the form of matrix which involves the stoichiometric constants and the reaction rate constants. Stochastic Algorithm (SA) has been identified as a better solution where multiscale concentration species are involved in reactions such as sorption, precipitation, degradation, sequential and parallel decay reactions etc. In this paper, the feasibility of applying SA (Gillespie Tauleap Method) in simulation of various bio chemical processes occurring during anaerobic degradation of complex organic matter has been studied.


Currently, computational techniques used to gap-fill a reaction network compute the minimum set of reactions using Mixed-Integer Linear Programming (MILP). Depending on the number of candidate reactions used to complete the model, MILP can be computationally demanding.Flux Balance Analysis (FBA) is a genome-scale computational technique for modeling the steady-state fluxes of an organism’s reaction network. When the organism’s reaction network needs to be completed to obtain growth using FBA, without relying on the genome, the completion process is called E. coli and yeast models with, in some cases, a three orders of magnitude execution speedup compared with MILP. We have implemented FastGapFilling in MetaFlux as part of Pathway Tools (version 17.5), which is freely available to academic users, and for a fee to commercial users. Download from: biocyc.org/download.shtml.We present a computational technique, called FastGapFilling, that efficiently completes a reaction network by using only Linear Programming, not MILP. FastGapFilling creates a linear program with all candidate reactions, an objective function based on their weighted fluxes, and a variable weight on the biomass reaction: no integer variable is used. A binary search is performed by modifying the weight applied to the flux of the biomass reaction, and solving each corresponding linear program, to try reducing the number of candidate reactions to add to the network to generate a working model. We show that this method has proved effective on a series of incomplete The computational technique presented is very efficient allowing interactive completion of reaction networks of FBA models. Computational techniques based on MILP cannot offer such fast and interactive completion. Gap-filling is a computational technique to complete a reaction network based on FBA without referring to the genome. Indeed, a complete knowledge of the functionality of the genome provides a complete reaction network and no gap-filling would be needed. Essentially, given a set of candidate reactions, gap-filling suggests to add some of these reactions to the model so that the FBA model grows, but without guaranteeing that the enzymes for the added reactions exist in the organism. This computational approach to complete a network is viable if it is unknown how to complete the reaction network based on the genome.Flux Balance Analysis (FBA) is a method for analyzing genome-scale steady-state models of metabolic networks ,2. ConstTo the best of our knowledge, all the current approaches to gap-fill -8 use MiC. neoformans. GapFind/GapFill uses MILP to find metabolites that cannot be produced and gap-fill the network of reactions of the model to produce them.For another example,  reports Although MILP can find a minimum number of reactions, those reactions are still only plausible suggestions to complete a reaction network. The reactions still need to be analyzed to confirm their validity for the organism. This analysis can be done by searching the scientific literature for references to pathways based on the suggested reactions to add. FastGapFilling also needs such an analysis, but it also provides several sets of reactions from which a broader analysis can be done.Moreover, these MILP computational techniques focus on finding the smallest set of candidate reactions to complete a model, but that set is not necessarily the most appropriate solution. For example, if only one reaction is needed to produce an essential compound, it might be the case that there is a solution with two reactions that better correspond to the taxonomy of the organism. Knowing the existence of this other non minimum solution might help discover the right missing reactions, which is a solution that might be given by FastGapFilling.In this paper we present a computational technique using linear programming (LP), avoiding MILP, for reaction gap-filling. Solving a linear program with thousands and even tens of thousands of variables is typically about 1 second. Therefore, LP is a much faster computational technique, compared to MILP, that can give almost immediate feedback on what is needed to complete a reaction network. The gap-filling solutions found by FastGapFilling can be the same or different from those with the MILP approach, as the applications presented in Section “Results” demonstrate. In fact, several sets of candidate reactions are suggested by FastGapFilling, all offering positive growth condition, which may add more insight to complete a reaction network.The next section presents the FastGapFilling algorithm based on LP.try-sets and numerical value parameters, called weights, provided by the user. A try-set is a set of candidates to fill the incomplete model. For example, the try-set of reactions is a set, typically large, of candidate reactions for completing the reaction network. A try-set of nutrients would be a set of candidate compounds that could be transported into the organism to enable growth. Each type of candidates  has its own weight. For each candidate added to the model, its corresponding weight is added to a global objective function and MILP maximizes that objective. Therefore, a positive weight indicates a desire to include as many candidates as possible in the model, and a negative weight indicates a desire to include a minimum number. A typical scenario is assigning a large positive weight for the biomass metabolites and assigning relatively smaller negative weights to all other try-sets. Such a scenario includes as many as possible candidate biomass metabolites by adding a minimum number of reactions, secretions, and nutrients. In MILP, the inclusion/exclusion of each candidate is controlled by an integer variable taking only one of two values, 0 (do not include) or 1 (include). Thousands of such binary variables can exist because — besides the nutrients, secretions, and biomass metabolites — thousands of candidate reactions are typical.To the best of our knowledge, all computational techniques published to date for gap-filling a reaction network are based on MILP, including the one used by MetaFlux . MetaFluLP and MILP differ in one main respect: all variables in LP can take only fractional values, whereas some variables in MILP must have integer values (for example the binary variables). This difference alone makes MILP computationally more demanding. Indeed, a typical MILP solver must iteratively apply a series of LP problems to find the right integer values to satisfy all constraints. This process can be demanding when thousands or even hundred of thousands of LP cases need solving. In contrast, our technique typically requires solving only a few LP problems.The FastGapFilling algorithm is presented in Figure M are included with the actual reactions N of the model to complete.1. When creating the LP formulation, all candidate reactions 2. All biomass metabolites are combined as one biomass reaction as if the FBA model were solved. However, the objective function to maximize is the flux of the biomass reaction, multiplied by a weight, minus the sum of the fluxes of candidate reactions multiplied by the weights provided by the user (See Section “Results” for a discussion about these weights).3. A binary search is performed based on the weight of the biomass reaction: the weight of the biomass flux is changed using a binary search between 0 and the number of candidate reactions. Each time the biomass reaction has a non-zero flux, the set of candidate reactions that are active is kept as one possible solution.The algorithm does not try to gap-fill nutrients or secretions, because the model is assumed to have the correct growth environment specified before attempting to complete the reaction networks. Accordingly, our description of the algorithm does not discuss the growth environment.M is a database of reactions such as MetaCyc, which includes approximately 12,000 reactions.The FastGapFilling algorithm accurately represents the model, because the entire biomass reaction is used as if solving the FBA model. The algorithm’s primary use is finding a small set of candidate reactions for adding to the model to produce greater biomass. In particular, if the biomass is zero , the algorithm tries to obtain growth by activating candidate reactions. That particular case implements reaction gap-filling. Typically, The generic reactions of MetaCyc are instantiated. That is, reactions that operate on classes of compounds are transformed to one or several reactions, where the classes are replaced by specific compounds that exist in the model. Any reversible reaction is transformed into two reactions, one for each direction, a standard practice in constructing FBA models. This transformation simplifies the mathematical modeling as the flux values of all reactions become non-negative.The algorithm’s output is a list of reactions sets. An implementation may output only the smallest set that would suggest the reactions for model completion. But other implementations may present all sets found and let the user select the most biologically appropriate set. The algorithm does not necessarily find the smallest possible set of candidate reactions to complete the given model. It does try to reduce the size of that set, but it does not compute the absolute minimum set of candidate reactions to complete the model. In other words, FastGapFilling uses an heuristic searching for the smallest set of candidate reactions to complete a model, but it may not find the smallest set.δ in the objective function. At each iteration of the search, that weight is adjusted either to help the solver increase the biomass flux fb or to reduce the number of candidate reactions added. The number of iterations done is bounded by ⌈log2|M|⌉.The search for a small set of candidate reactions to add to the model is based on one weight cr given as input to the algorithm are typically based on the kind  or taxonomic range  of the reactions. The cost of a reaction is proportional to its probability of occurring in a model. For example, a reaction that is not known to occur in the taxonomic range of the model  should have a higher cost than a reaction known to occur in the taxonomic range of the model. Examples of costs are presented in Section “Results”.The costs N and M” in the algorithm assumes that sets of nutrients and secretions are given. Actually, the implementation guides the details of this generation, as it may include many other parameters, such as lower and upper bounds on the flux of some reactions, constraints to avoid ineffective high fluxes, and so on. Essentially, the generated LP must be solvable, must satisfy the steady-state constraints, and must restrict the fluxes to non-negative values for all reactions of N and M, including the biomass reaction.The mathematical formulation of the LP problem of this algorithm follows the standard approach of solving an FBA model, except for the objective function described below and specified in Figure δ is a calculated weight by the binary search, fb is the flux of the biomass reaction, and the summation of the terms crfr is done over all candidate reactions of M. This function tends to increase the flux of the biomass, as a maximization is applied and the δfb is the only positive term in it. This function also tends to decrease the number of candidate reactions that have a non-zero flux  because the term fr and cost cr are non-negative values). Indeed, this is the objective of the algorithm: increasing the flux of the biomass while decreasing the number of candidate reactions to add to do so. The essential point is to find the right value for δ such that fb is non-zero . This is the objective of the binary search done by modifying δ such that growth is maintained and the number of active candidate reactions is reduced. Note that the initial value of δ is |M| . This value enables many candidate reactions to be active simultaneously at the beginning of the binary search.The main novelty of the LP formulation is the objective function that changes at each iteration of the binary search. The objective function to maximize is Note that, in general, this algorithm actually suggests adding candidate reactions to the model to increase the biomass. It could also be used for engineering more efficient metabolic pathways, although this aspect is not covered in this paper.The main shortcoming of the algorithm is that it does not find a solution when no set of candidate reactions can be found to produce the entire set of biomass metabolites. In such cases, we recommend reducing the number of metabolites in the biomass reaction.E. coli and yeast models.The following section demonstrates the application of FastGapFilling on an E. coli models and to one incomplete yeast model. We started with a working E. coli model for which no added reaction are needed to obtain growth and then removed from 1 to 14 reactions in order to prohibit growth. A similar procedure was done to create the incomplete yeast model. See the following subsections for more details on the creation of these incomplete models.We have applied the FastGapFilling algorithm to four incomplete E. coli model is based on the EcoCyc database (version 17.5). The model has 1,763 enzymatic reactions, including the instantiated generic enzymatic reactions. The biomass reaction has 69 metabolites. The growth media is composed of glucose, oxygen, ammonium, phosphate, diphosphate, sulfate, and iron. The secretions are carbon-dioxide, acetate, and water. An upper bound of 16 mmol/g/h was constraining the intake of glucose.The original For each incomplete model, we also ran MetaFlux  in develcosts if their values are negative and gains if their values are positive. Costs are applied to reactions, and a gain, to the biomass metabolites. The gain is not user specified when using FastGapFilling, because the weight to the biomass reaction is controlled by the algorithm, but only for MILP. The following costs and gain were used for all cases presented in this paper. In the MILP development mode, weights are user specified to control the candidate reactions to include in the model. They are called 1. A cost of 1 for one candidate spontaneous  reaction2. A cost of 5 for one candidate reaction inside the taxonomic range of the organism3. A cost of 10 for one candidate reaction of unknown taxonomic range4. A cost of 15 for one candidate reaction outside the taxonomic range of the organism5. A gain of 500 for one candidate biomass metaboliteThe relative values of these weights (costs and gain), as opposed to their absolute values, are important. For example, the cost of a spontaneous reaction is smaller than the cost of an enzymatic reaction, because a reaction that does not require an enzyme can occur in any organism. Similarly, the cost of a reaction that is outside the taxonomic range of the organism is set higher than the cost of a reaction in the taxonomic range of the organism because we prefer reactions in the taxonomic range of the organism selected. The candidate reactions are all coming from the MetaCyc database, and their taxonomic ranges are based on the curated pathways of that database.Notice that the gain of one biomass metabolite is high compared to the cost of any reactions. For example, the ratio between the gain and the cost of a reaction in the taxonomic range of the organism is 100. This means that up to 100 such reactions could be added to the model if one more biomass metabolite can be produced. The intention is to produce a maximum number of biomass metabolites even if a large, but still bounded, number of candidate reactions is needed to produce them. As shown in the following subsections, this general result was obtained for all cases presented because a few reactions produced all metabolites.Table E. coli model, we removed the following reaction from the original E. coli model: To create the first incomplete branched-chainaminotransferleu-rxn, which can be used as an unambiguous keyword to search for more information about that reaction at BioCyc.org.Note: in this subsection and the following subsections, the MetaCyc reaction unique identifier is shown between parentheses. In the reaction just shown, that identifier is That reaction, going right to left, is the last step in the biosynthesis pathway of the amino acid L-leucine and, going left to right, the first step in the L-leucine degradation pathway. No other reaction in the model produces L-leucine. Because L-leucine is part of the biomass reaction of the model, we expect that adding this reaction will be suggested when gap-filling is done. Indeed, the MetaFlux gap-filling MILP solution suggested adding the same reaction, in the right to left direction. MetaFlux could give the relevant direction as part of the solution because all reversible candidate reactions are split into two reactions, one for each direction. MetaFlux did not suggest adding the reaction in the opposite direction because the reaction was not essential for growth given the nutrients. SCIP required 125 seconds to obtain this optimal MILP solution.When the FastGapFilling algorithm was run on the same incomplete model, adding the same reaction, in the same direction, was suggested. Four iterations  were needed before that solution was found; the first three iterations found solutions with three reactions. The total solver running time of these four iterations was 6 seconds.This first simple example shows that FastGapFilling can find the exact same solution as the MILP technique in much less time.E. coli model is derived by removing, additionally to the reaction removed in the first incomplete E. coli model, three reactions that produce the compound tetrahydrofolate, which is part of the biomass. These additional reactions are: The second incomplete Notice that the reaction of the previous incomplete model and these three reactions are in different metabolic pathways.The MILP development mode of MetaFlux suggested adding three of the reactions that were removed: the first two reactions above, and the reaction removed in the first incomplete model. That is, the third removed reaction above was not suggested. The SCIP solver required 7,794 seconds or about 2:10 hours to find this optimal solution.We ran the FastGapFilling algorithm on the same incomplete model. The smallest set of suggestd reactions included the same three reactions. Other solutions proposed included four reactions. FastGapFilling performed 12 LP solving iterations, with a solver total execution time of 16 seconds.This second example shows that FastGapFilling can find the same solution as the MILP technique in substantially less time — in this case, well over 2 orders of magnitude faster.E. coli model tricarboxylic acid cycle (TCA cycle) pathway: For this third example, we selected four reactions to remove from the original E. coli: The MILP solution suggested adding two reactions, both in the taxonomic range of Although, these two reactions were not among the four reactions removed, the second reaction does produce the compound 2-oxoglutarate, one of the compounds produced by one of the reactions removed. Notice that the development mode of MetaFlux produces only one of the possible optimal solutions. Other different minimal cost solutions may provide the same value, but MetaFlux outputs only one of them. In this example, an optimal solution might include two of the four reactions removed, but we cannot confirm it. SCIP required 9,729 seconds or about 2:42 hours to find this solution.However, FastGapFilling found a solution of three reactions after 12 iterations lasting 13 seconds, the first two reactions being the same as the MILP solution plus the following reaction: The third reaction appears to be redundant because its flux, as given by FastGapFilling, is 0.00056, whereas the fluxes of the other two reactions are the same at 0.110394. The flux of the third reaction is much lower than those of the first two reactions.Indeed, the low-flux reactions suggested by FastGapFilling might simply be a way to increase the biomass and might not be reactions essential for growth. In general, this possibility can be verified by only adding the suggested reactions with relatively high fluxes and solving the resulting network. If the biomass can be generated, the low-flux reactions would be nonessential.E. coli model with 14 reactions removed. These reactions were selected because they produced at least one of the following metabolites: L-lysine, L-leucine, L-isoleucine, and L-histidine. All these metabolites participate in the biomass reaction. Essentially, this is an example where many biosynthesis pathways have been disturbed. The following reactions were removed. The fourth incomplete model is the original branched-chainaminotransferileu-rxn, diaminopimdecarb-rxn, and histaldehyd-rxn. These three reactions are among the 14 reactions that were removed.The SCIP solver could not find an optimal solution to the MILP problem after running for 24 hours. However, FastGapFilling produced the following solution, after 12 iterations that took 14 seconds by the SCIP solver, by suggesting three reactions: This example shows that FastGapFilling can be very useful in practice: no optimal or near optimal solution could be found after 24 hours using the MILP approach, whereas FastGapFilling quickly found a gap-filling solution.E. coli model, the original yeast model can grow. The original yeast model is based on the YeastCyc database (version 17.5). The model includes 1,454 enzymatic reactions, including the instantiated generic enzymatic reactions. The biomass reaction is composed of 41 metabolites. The growth media is composed of glucose, oxygen, ammonium, phosphate, sulfate, and iron. The secretions are carbon-dioxide, carbon-monoxide, formate, hydrogen-peroxide, glycolaldehyde, and water. An upper bound of 12 mmol/g/h was constraining the intake of glucose.As a last example of applying the FastGapFilling algorithm, we used a yeast model. As with the To generate an incomplete model, four reactions responsible for the biosynthesis of five lipids  were removed. These five lipids are part of the biomass. The reactions removed are: The first reaction (GPPSYN-RXN) appears in three different pathways , whereas each of the other reactions occurs separately in three other pathways.The optimal MILP solution for gap-filling this incomplete yeast model, required 21,027 seconds or about 5:50 hours, and suggested adding the four reactions above. This set is the least number of reactions expected because MetaCyc (version 17.5) includes no other reactions to produce these lipids.FastGapFilling found the same solution, after 12 iterations lasting 14 seconds using the SCIP solver — a much faster execution time when compared to MILP. The binary search of FastGapFilling also found other solution sets with up to 34 candidate reactions, but the smallest set included the exact four reactions that were removed.FastGapFilling is an efficient technique to gap-fill reaction networks allowing interactive completion of reaction networks of FBA models, whereas MILP fails to offer such an efficiency.The FastGapFilling algorithm increases the biomass flux by minimizing a weighted minimum sum of fluxes from new reactions, whereas the gap-filling approach using MILP is based on adding a minimum number of new reactions to obtain a non-zero biomass flux.Using concrete examples, we show that the FastGapFilling algorithm is efficient for performing reaction gapfilling requiring much less computation time than MILP-based approaches. This result is not surprising because MILP may have to solve hundreds or even thousands of LP problems, whereas the FastGapFilling approach requires solving only a few LP problems.The author declares that he has no competing interests.