Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control

Cybernetic modeling strives to uncover the inbuilt regulatory programs of biological systems and leverage them toward computational prediction of metabolic dynamics. Because of its focus on incorporating the global aims of metabolism, cybernetic modeling provides a systems-oriented approach for describing regulatory inputs and inferring the impact of regulation within biochemical networks. Combining cybernetic control laws with concepts from metabolic pathway analysis has culminated in a systematic strategy for constructing cybernetic models, which was previously lacking. The newly devised framework relies upon the simultaneous application of local controls that maximize the net flux through each elementary flux mode and global controls that modulate the activities of these modes to optimize the overall nutritional state of the cell. The modeling concepts are illustrated using a simple linear pathway and a larger network representing anaerobic E. coli central metabolism. The E. coli model successfully describes the metabolic shift that occurs upon deleting the pta-ackA operon that is responsible for fermentative acetate production. The model also furnishes predictions that are consistent with experimental results obtained from additional knockout strains as well as strains expressing heterologous genes. Because of the stabilizing influence of the included control variables, the resulting cybernetic models are more robust and reliable than their predecessors in simulating the network response to imposed genetic and environmental perturbations.     

Metabolic engineering from a cybernetic perspective: aspartate family of amino acids

Using the modular cybernetic framework developed by Varner and Ramkrishna (Varner and Ramkrishna; 1998a, b) a cybernetic model is formulated that describes the time evolution of the aspartate family of amino acids in Corynebacterium lactofermentum ATCC 21799. The network model formulation is employed in the role of a diagnostic tool for the overproduction of threonine. More precisely, having determined a parameter set that describes the time evolution of a base strain (lysine producer), the model predicted response to genetic perturbations, designed to enhance the level of threonine, are simulated using an appropriately modified cybernetic model and compared with the experimental results of Stephanopoulos and Sinskey (Colón et al., 1995a, Appl. Environ. Microbiol. 61, 74-78) for identical genetic perturbations. It is found that the model predicted response to enzymatic over-expression in the aspartate pathway agrees, for the most part, with experimental observations within the experimental error bounds. This result lends credence to the hypothesis that cybernetic models can be employed to predict the local response of a metabolic network to genetic perturbation, thereby, affording cognizance of the potential pitfalls of a particular genetic alteration strategy a priori.     

Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models

We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least-squares kernel machines (LSKMs). This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model also makes it possible to test for the overall genetic pathway effect. We show that the LSKM semiparametric regression can be formulated using a linear mixed model. Estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the covariate effects and the LSKM estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation. The smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood. A score test is developed to test for the genetic pathway effect. Model/variable selection within the LSKM framework is discussed. The methods are illustrated using a prostate cancer data set and evaluated using simulations.     

A cybernetic view of microbial growth: modeling of cells as optimal strategists

A cybernetic framework is presented which views microbial response in multiple substrate environments as a judicious investment of cellular resources in synthesizing different key proteins according to an optimal regulatory strategy. A mathematical model is developed within the cybernetic framework for the diauxic growth of Klebsiella pneumoniae on a mixture of D-glucose and D-xylose. The "bang-bang" optimal policy describes well the experimental observations obtained using a fermenter coupled to an Apple II microcomputer. Striking variations in respiratory levels are observed experimentally during the switching of the cell's adaptive machinery for the utilization of the less preferred substrate.     

代谢网络定量分析研究进展

综述了代谢工程中代谢控制分析、代谢通量分析、生化系统理论、途径分析、控制论模型等定量分析方法的基本理论,以实例说明了这些方法的应用,并对代谢分析方法的发展进行了展望。     

Cybernetic model predictive control of a continuous bioreactor with cell recycle

The control of poly-beta-hydroxybutyrate (PHB) productivity in a continuous bioreactor with cell recycle is studied by simulation. A cybernetic model of PHB synthesis in Alcaligenes eutrophus is developed. Model parameters are identified using experimental data, and simulation results are presented. The model is interfaced to a multirate model predictive control (MPC) algorithm. PHB productivity and concentration are controlled by manipulating dilution rate and recycle ratio. Unmeasured time varying disturbances are imposed to study regulatory control performance, including unreachable setpoints. With proper controller tuning, the nonlinear MPC algorithm can track productivity and concentration setpoints despite a change in the sign of PHB productivity gain with respect to dilution rate. It is shown that the nonlinear MPC algorithm is able to track the maximum achievable productivity for unreachable setpoints under significant process/model mismatch. The impact of model uncertainty upon controller performance is explored. The multirate MPC algorithm is tested using three controllers employing models that vary in complexity of regulation. It is shown that controller performance deteriorates as a function of decreasing biological complexity.     

Application of hybrid cybernetic model in simulating myeloma cell culture co-consuming glucose and glutamine with mixed consumption patterns

A dynamic model called hybrid cybernetic model (HCM) based on structured metabolic network is established for simulating mammalian cell metabolism featured with partially substitutable and partially complementary consumption patterns of two substrates, glucose and glutamine. Benefiting from the application of elementary mode analysis (EMA), the complicated metabolic network is decomposed into elementary modes (EMs) facilitating the employment of the hybrid cybernetic framework to investigate the external and internal flux distribution and the regulation mechanism among them. According to different substrate combination, two groups of EMs are obtained, i.e., EMs associated with glucose uptake and simultaneous uptake of glucose and glutamine. Uptake fluxes through various EMs are coupled together via cybernetic variables to maximize substrate uptake. External fluxes and internal fluxes could be calculated and estimated respectively, by the combination of the stoichiometrics of metabolic networks and fluxes through regulated EMs. The model performance is well validated via three sets of experimental data. Through parameter identification of limited number of experimental data, other external metabolites are precisely predicted. The obtained kinetic parameters of three experimental cultures have similar values, which indicates the robustness of the model. Furthermore, the prediction performance of the model is successfully validated based on identified parameters.     

A Network Flow-Based Method to Predict Anticancer Drug Sensitivity

Predicting anticancer drug sensitivity can enhance the ability to individualize patient treatment, thus making development of cancer therapies more effective and safe. In this paper, we present a new network flow-based method, which utilizes the topological structure of pathways, for predicting anticancer drug sensitivities. Mutations and copy number alterations of cancer-related genes are assumed to change the pathway activity, and pathway activity difference before and after drug treatment is used as a measure of drug response. In our model, Contributions from different genetic alterations are considered as free parameters, which are optimized by the drug response data from the Cancer Genome Project (CGP). 10-fold cross validation on CGP data set showed that our model achieved comparable prediction results with existing elastic net model using much less input features.     

Cybernetic modeling based on pathway analysis for Penicillium chrysogenum fed-batch fermentation

A macrokinetic model employing cybernetic methodology is proposed to describe mycelium growth and penicillin production. Based on the primordial and complete metabolic network of Penicillium chrysogenum found in the literature, the modeling procedure is guided by metabolic flux analysis and cybernetic modeling framework. The abstracted cybernetic model describes the transients of the consumption rates of the substrates, the assimilation rates of intermediates, the biomass growth rate, as well as the penicillin formation rate. Combined with the bioreactor model, these reaction rates are linked with the most important state variables, i.e., mycelium, substrate and product concentrations. Simplex method is used to estimate the sensitive parameters of the model. Finally, validation of the model is carried out with 20 batches of industrial-scale penicillin cultivation.     

A simultaneous saccharification and fermentation model for dynamic growth environments

Many mathematical models by researchers have been formulated for Saccharomyces cerevisiae which is the common yeast strain used in modern distilleries. A cybernetic model that can account for varying concentrations of glucose, ethanol and organic acids on yeast cell growth dynamics does not exist. A cybernetic model, consisting of 4 reactions and 11 metabolites simulating yeast metabolism, was developed. The effects of variables such as temperature, pH, organic acids, initial inoculum levels and initial glucose concentration were incorporated into the model. Further, substrate and product inhibitions were included. The model simulations over a range of variables agreed with hypothesized trends and to observations from other researchers. Simulations converged to expected results and exhibited continuity in predictions for all ranges of variables simulated. The cybernetic model did not exhibit instability under any conditions simulated.     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

A simple structured model describing the growth of Streptomyces lividans

The growth of Streptomyces lividans in defined media was modeled using a simple structured growth model. Conventional unstructured models like Monod kinetics, substrate inhibition kinetics, and the logistic equation were also used in an attempt to fit the data, but the results were all unsatisfactory. The main reason for failure in applying simple unstructured models is that they cannot describe the long lag phases sometimes observed during growth of S. lividans. The simple structured growth model was derived along similar principles to cybernetic growth models. This model quite accurately describes the growth of S. lividans. It assumes that the rate of assimilation of a substrate depends on the concentration of a specific key enzyme. This key enzyme is only produced in the presence of the substrate, and it is broken down at a steady rate. An enzyme synthesis allocation variable, w, similar to the cybernetic variable, u, described in cybernetic growth models, is proposed to control enzyme synthesis. Until the key enzyme concentration approaches its maximum level, very little substrate is consumed. And consequently, the lag phase is sustained.     

Mitochondrial aberrations in mucolipidosis Type IV

Mucolipidosis type IV is a genetic lysosomal storage disease associated with degenerative processes in the brain, eye, and other tissues. Mucolipidosis type IV results from mutations in the gene MCOLN1, which codes for the TRP family ion channel, mucolipin 1. The connection between lysosomal dysfunction and degenerative processes in mucolipidosis type IV is unclear. Here we report that mucolipidosis type IV and several unrelated lysosomal storage diseases are associated with significant mitochondrial fragmentation and decreased mitochondrial Ca2+ buffering efficiency. The mitochondrial alterations observed in these lysosomal storage diseases are reproduced in control cells by treatment with lysosomal inhibitors and with the autophagy inhibitor 3-methyladenine. This suggests that inefficient autophagolysosomal recycling of mitochondria generates fragmented, effete mitochondria in mucolipidosis. Mitochondria accumulate that cannot properly buffer calcium fluxes in the cell. A decrease in mitochondrial Ca2+ buffering capacity in cells affected by these lysosomal storage diseases is associated with increased sensitivity to apoptosis induced by Ca2+-mobilizing agonists and executed via a caspase-8-dependent pathway. Deficient Ca2+ homeostasis may represent a common mechanism of degenerative cell death in several lysosomal storage diseases.     

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

We demonstrate strong experimental support for the cybernetic model based on maximizing carbon uptake rate in describing the microorganism's regulatory behavior by verifying exacting predictions of steady state multiplicity in a chemostat. Experiments with a feed mixture of glucose and pyruvate show multiple steady state behavior as predicted by the cybernetic model. When multiplicity occurs at a dilution (growth) rate, it results in hysteretic behavior following switches in dilution rate from above and below. This phenomenon is caused by transient paths leading to different steady states through dynamic maximization of the carbon uptake rate. Thus steady state multiplicity is a manifestation of the nonlinearity arising from cybernetic mechanisms rather than of the nonlinear kinetics. The predicted metabolic multiplicity would extend to intracellular states such as enzyme levels and fluxes to be verified in future experiments. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Genetic and epigenetic alterations of tumor suppressor and tumor-related genes in gastric cancer

Both genetic and epigenetic alterations of tumor suppressor and tumor-related genes involved in the pathogenesis of gastric cancer are reviewed here, and molecular pathways of gastric carcinogenesis are proposed. Gastric carcinomas are believed to evolve from native gastric mucosa or intestinal metaplastic mucosa that undergoes genetic and epigenetic alterations involving either the suppressor pathway (defects in tumor suppressor genes) or mutator pathway (defects in DNA mismatch repair genes). Methylation of E-cadherin in native gastric mucosa results in undifferentiated carcinomas (suppressor pathway), while methylation of hMLHI results in differentiated foveolar-type carcinomas (mutator pathway). The majority of differentiated gastric carcinomas however, arise from intestinal metaplastic mucosa and exhibit structural alterations of tumor suppressor genes, especially p53. They appear to be related to chronic injury, perhaps due to Helicobacter pylori infection. Approximately 20% of differentiated carcinomas (ordinary-type) have evidence of mutator pathway tumorigenesis. Mutations of E-cadherin are mainly involved in the progression of differentiated carcinomas to undifferentiated tumors. The molecular pathways of gastric carcinogenesis depend on the histological background, and gastric carcinomas show distinct biological behaviors as a result of discernible cellular genetic and epigenetic alterations.     

Genetic differences in seed longevity of various Arabidopsis mutants

Seeds gradually lose their viability during dry storage. The damage that occurs at the biochemical level can alter the seed physiological status and is affected by the storage conditions of the seeds. Although these environmental conditions controlling loss of viability have been investigated frequently, little information is available on the genetics of seed longevity. Using Arabidopsis mutants in defined developmental or biochemical pathways such as those affected in seed coat composition, seed dormancy, hormone function and control of oxidative stress, we tried to gain insight into the genes and mechanisms controlling viability of stored seeds. Mutations like abscisic acid insensitive3 ( abi3 ) as well as abscisic acid deficient1 ( aba1 ) show reduced longevity, which may be partially related to the seed dormancy phenotype of these mutants. Mutants with seed coat alterations, especially aberrant tests shape ( ats ), showed a stronger reduction in germination percentage after storage, indicating the importance of a 'functional' seed coat for seed longevity. A specific emphasis was placed on mutants affected in dealing with Reactive Oxygen Species (ROS). Because several pathways are involved in protection against ROS and because gene redundancy is a common feature in Arabidopsis , 'double' mutants were generated. These 'double' mutants and the corresponding single mutants were subjected to a controlled deterioration test (CDT) and a germination assay on hydrogen peroxide (H₂O₂) after prolonged storage at two relative humidities. CDT and germination on H₂O₂ affected all genotypes, although it appears that other effects like genetic background are more important than the deficiencies in the ROS scavenging pathway. Explanations for this limited effect of mutations affecting ROS scavenging are discussed.     

A cybernetic model of growth correlation in young apple trees

Growth correlations among lateral shoots of one-year-old apple treesMalus Mill., were described. The existence of a mechanism was postulated through which small original differences between buds or young shoots are quickly augmented, thus leading to differentiation of long shoots and short shoots. Existing hypotheses do not seem sufficient for explaining correlative phenomena of this type; a cybernetic approach was therefore applied. Studying growth correlations in terms of cybernetic revealed that previous hypotheses concerning correlations do not contradict each other as often thought, but depict different links in a more general chain of events. A cybernetic model points out the importance of root influences in interaction among shoots. It also shows that synergism between auxin, gibberellin and cytokinin in xylem and phloem differentiation and in starch metabolism is very important for understanding correlations in apple trees.     

Effect of root tip amputation on spiral oscillations of the growing hypocotyl with radicle of the pea (Pisum sativum L.)

In order to interpret the mechanism of elongation growth of the hypocotyl with radicle in the first stages of germination of the pea seed (Pisum sativum L.) a cybernetic model utilizing feed-back as a mechanism of correcting the wrong direction of growth was proposed (Spurný 1966, 1967). In the present study, the effect of amputation of the root tip as the control centre on the trajectory of the growing radicle was investigated. The results have shown that the hypocotyl grows, elongates—the rate of growth being slightly lower than that of the standard, but that no spiral oscillations at all are executed by the organ after amputation of the root tip. This finding appears to confirm the applicability of the proposed cybernetic model, for amputation of the root tip means that not only the control block is eliminated, but also that the channel of feed-back impulses to zone of elongation is interrupted.