Adsorption with biodegradation for decolorization of reactive black 5 by Funalia trogii 200800 on a fly ash-chitosan medium in a fluidized bed bioreactor-kinetic model and reactor performance

A non-steady-state mathematical model system for the kinetics of adsorption and biodegradation of reactive black 5 (RB5) by Funalia trogii (F. trogii) ATCC 200800 biofilm on fly ash-chitosan bead in the fluidized bed process was derived. The mechanisms in the model system included adsorption by fly ash-chitosan beads, biodegradation by F. trogii cells and mass transport diffusion. Batch kinetic tests were independently performed to determine surface diffusivity of RB5, adsorption parameters for RB5 and biokinetic parameters of F. trogii ATCC 200800. A column test was conducted using a continuous-flow fluidized bed reactor with a recycling pump to approximate a completely-mixed flow reactor for model verification. The experimental results indicated that F. trogii biofilm bioregenerated the fly ash-chitosan beads after attached F. trogii has grown significantly. The removal efficiency of RB5 was about 95 % when RB5 concentration in the effluent was approximately 0.34 mg/L at a steady-state condition. The concentration of suspended F. trogii cells reached up to about 1.74 mg/L while the thickness of attached F. trogii cells was estimated to be 80 μm at a steady-state condition by model prediction. The comparisons of experimental data and model prediction show that the model system for adsorption and biodegradation of RB5 can predict the experimental results well. The approaches of experiments and mathematical modeling in this study can be applied to design a full-scale fluidized bed process to treat reactive dye in textile wastewater.     

Application of an extended kalman filter method for monitoring high density cultivation of Escherichia coli

A real-time, on-line extended Kalman filter was used to describe and monitor the growth of Escherichia coli on glycerol. The growth of E. coli showed an inhibition kinetics with μ_max=0.806/h, K_S=0.68 g/l and K_i=87.4 g/l. As a feeding strategy, the conventional DO-stat with a DDC-PID control method, in which the dissolved oxygen concentration is maintained at a desired level by varying the substrate feedrate, was employed. The Kalman filter was based on an unstructured mathematical model and on-line measured data. The mathematical model comprised of mass balances of the biomass and substrate as well as kinetic and stoichiometric data which were measured prior to the process. For biomass concentration up to 50 g dry weight/l, the estimation of the process was rather accurate. At higher biomass concentration, product formation, indicated by an intense brown coloring of the fermentation broth, occured. Since the effect of this product on biomass production was not included in the mathematical model, the estimated data diverged from the experimental data at biomass concentrations greater than 50 g dry weight/l.     

Variation of ADM1 by using temperature-phased anaerobic digestion (TPAD) operation

The objective of the study was to examine the application of the Anaerobic Digestion Model No. 1 (ADM1) developed by the IWA task group for mathematical modelling of anaerobic process. Lab-scale temperature-phased anaerobic digestion (TPAD) process were operated continuously, and were fed with co-substrate composed of dog food and flour. The model platform implemented in the simulation was a derivative of the ADM1. Sensitivity analysis showed that k_m.process (maximum specific uptake rate) and K_S.process (half saturation value) had high sensitivities to model components. Important parameters including maximum uptake rate for propionate utilisers (k_m.pro) and half saturation constant for acetate utilisers (K_S.ac) in the thermophilic digester and maximum uptake rate for acetate utilisers (k_m.ac) in the mesophilic digester were estimated using iterative methods, which optimized the parameters with experimental results. Simulation with estimated parameters showed good agreement with experimental results in the case of methane production, uptake of acetate, soluble chemical oxygen demand (SCOD) and total chemical oxygen demand (TCOD). Under these conditions, the model predicted reasonably well the dynamic behavior of the TPAD process for verifying the model.     

Parameterization for In-Silico Modeling of Ion Channel Interactions with Drugs

Since the first Hodgkin and Huxley ion channel model was described in the 1950s, there has been an explosion in mathematical models to describe ion channel function. As experimental data has become richer, models have concomitantly been improved to better represent ion channel kinetic processes, although these improvements have generally resulted in more model complexity and an increase in the number of parameters necessary to populate the models. Models have also been developed to explicitly model drug interactions with ion channels. Recent models of drug-channel interactions account for the discrete kinetics of drug interaction with distinct ion channel state conformations, as it has become clear that such interactions underlie complex emergent kinetics such as use-dependent block. Here, we describe an approach for developing a model for ion channel drug interactions. The method describes the process of extracting rate constants from experimental electrophysiological function data to use as initial conditions for the model parameters. We then describe implementation of a parameter optimization method to refine the model rate constants describing ion channel drug kinetics. The algorithm takes advantage of readily available parallel computing tools to speed up the optimization. Finally, we describe some potential applications of the platform including the potential for gaining fundamental mechanistic insights into ion channel function and applications to in silico drug screening and development.     

Quantitative modeling of inducer transport in fed-batch cultures of Escherichia coli

An unsteady, unstructured, unsegregated and based on first principles mathematical model has been proposed to describe IPTG (isopropyl-β-d-tiogalactopiranoside) transport in induced fed-batch cultures of E. coli M15 ΔglyA [pQEαβrham] [pREP4] producing rhamnulose 1-phosphate aldolase (RhuA). The model predicts extracellular and intracellular IPTG concentration. Experimental extracellular IPTG concentrations under different operational conditions were obtained by HPLC–MS analysis. These experimental data were used to fit the parameters of the model. The model was also able to predict the experimental behavior of two different E. coli strains producing fuculose 1-phosphate aldolase (FucA). IPTG transport to cells was the contribution of three processes: a diffusion process, and two active processes (one non-specific and another specific).     

Mathematical Modelling of the MAP Kinase Pathway Using Proteomic Datasets

The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.     

Lymph Node Colonization Dynamics after Oral Salmonella Typhimurium Infection in Mice

An understanding of how pathogens colonize their hosts is crucial for the rational design of vaccines or therapy. While the molecular factors facilitating the invasion and systemic infection by pathogens are a central focus of research in microbiology, the population biological aspects of colonization are still poorly understood. Here, we investigated the early colonization dynamics of Salmonella enterica subspecies 1 serovar Typhimurium (S. Tm) in the streptomycin mouse model for diarrhea. We focused on the first step on the way to systemic infection — the colonization of the cecal lymph node (cLN) from the gut — and studied roles of inflammation, dendritic cells and innate immune effectors in the colonization process. To this end, we inoculated mice with mixtures of seven wild type isogenic tagged strains (WITS) of S. Tm. The experimental data were analyzed with a newly developed mathematical model describing the stochastic immigration, replication and clearance of bacteria in the cLN. We estimated that in the beginning of infection only 300 bacterial cells arrive in the cLN per day. We further found that inflammation decreases the net replication rate in the cLN by 23%. In mice, in which dendritic cell movement is impaired, the bacterial migration rate was reduced 10-fold. In contrast, mice that cannot generate toxic reactive oxygen species displayed a 4-fold higher migration rate from gut to cLN than wild type mice. Thus, combining infections with mixed inocula of barcoded strains and mathematical analysis represents a powerful method for disentangling immigration into the cLN from replication in this compartment. The estimated parameters provide an important baseline to assess and predict the efficacy of interventions.     

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.     

Qualitative and Quantitative Analyses of the Echolocation Strategies of Bats on the Basis of Mathematical Modelling and Laboratory Experiments

Prey pursuit by an echolocating bat was studied theoretically and experimentally. First, a mathematical model was proposed to describe the flight dynamics of a bat and a single prey. In this model, the flight angle of the bat was affected by angles related to the flight path of the single moving prey, that is, the angle from the bat to the prey and the flight angle of the prey. Numerical simulation showed that the success rate of prey capture was high, when the bat mainly used the angle to the prey to minimize the distance to the prey, and also used the flight angle of the prey to minimize the difference in flight directions of itself and the prey. Second, parameters in the model were estimated according to experimental data obtained from video recordings taken while a Japanese horseshoe bat (Rhinolphus derrumequinum nippon) pursued a moving moth (Goniocraspidum pryeri) in a flight chamber. One of the estimated parameter values, which represents the ratio in the use of the angles, was consistent with the optimal value of the numerical simulation. This agreement between the numerical simulation and parameter estimation suggests that a bat chooses an effective flight path for successful prey capture by using the angles. Finally, the mathematical model was extended to include a bat and prey. Parameter estimation of the extended model based on laboratory experiments revealed the existence of bat’s dynamical attention towards prey, that is, simultaneous pursuit of prey and selective pursuit of respective prey. Thus, our mathematical model contributes not only to quantitative analysis of effective foraging, but also to qualitative evaluation of a bat’s dynamical flight strategy during multiple prey pursuit.     

An unstructured kinetic model for the improvement of triterpenes production by Ganoderma lucidum G0119 based on nitrogen source effect

The kinetics of cell growth and triterpenes production for liquid submerged fermentation of the medicinal mushroom Ganoderma lucidum were investigated. A kinetic model was developed based on the Logistic and Luedeking-Piret equations for cell growth, substrate consumption and triterpene formation. The kinetic parameters of the model were optimized by specifically designed Runge-Kutta genetic algorithms. The mathematical model simulated the experimental data well and was capable of explaining the behavior of triterpenes production. The predictions of the kinetics from this model are very good both for normal fermentation kinetics under nitrogen limitation as well as for predictions of transitions to sluggish fermentations. The resulting model is very useful for scaling up liquid submerged fermentation of the mushroom G. lucidum and its application to the industrial production of triterpene.     

Dynamics and modeling on fermentative production of poly (β-hydroxybutyric acid) from sugars via lactate by a mixed culture of Lactobacillus delbrueckii and Alcaligenes eutrophus

The mixed culture system was considered in the present research where sugars such as glucose were converted to lactate by Lactobacillus delbrueckii and the lactate was converted to poly β-hydroxybutyrate (PHB) by Alcaligenes eutrophus in one fermentor. For the modeling of the effect of NH₃ concentration on the cell growth of A. eutrophus and PHB production rates, metabolic flux distributions were computed at two culture phases of cell growth and PHB production periods. It was found that the NADPH, generated through isocitrate dehydrogenate in TCA cycle, was predominantly utilized for the reaction from α-ketoglutalate to glutamate when NH₃ was abundant, while it tended to be utilized for the PHB production through acetoacetyl CoA reductase as NH₃ concentration decreased. This phenomenon was reflected in the development of mathematical model. In the mixed culture experiments, the two phases were observed, namely the lactate production phase due to L. delbrueckii and the lactate consumption phase due to A. eutrophus. The lactate concentration could be estimated on-line by the amount of NaOH solution and HCl solution supplied to keep the culture pH at constant level. Several mixed culture experiments were conducted to see the dynamics of the system. Finally, a mathematical model which can describe the dynamic behavior of the present mixed culture was developed and the model parameters were tuned for fitting the experimental data. The model may be used for several purposes such as control, optimization, and understanding process dynamics etc.     

红豆杉细胞悬浮培养结构化数学模型的探讨

用１０Ｌ机械搅拌式生物反应器悬浮培养红豆杉细胞,得到细胞生长、基质消耗和紫杉醇合成动力学曲线。经过代谢动力学分析建立了结构化数学模型。并将模型值与实验值进行比较,结果表明模型预测值与实验值较吻合。     

A simulation support system for solving large physiological models on microcomputers

Although physiological modeling and computer simulation have become useful research tools to test new scientific theories and to design and analyze laboratory experiments, developing a new model can be a tedious process because the investigator must often write very complex and specific routines for data input and output. To facilitate the design of new models (as well as the use of existing models), we have developed MODSIM, a FORTRAN-based simulation support system for the IBM PC computer than can accommodate very large dynamic models having up to several thousand equations. It provides the investigator with utilities for continuous on-line graphical and/or tubular output, as well as facilities for dynamic interaction with the model. The user must only supply a model as a list of mathematical equations written in FORTRAN, along with the initial values of the model variables and parameters. The model is precompiled, compiled, and then linked to the MODSIM utilities. Without further programming, the user can then solve the model, select variables for graphical output, and stop the model at any time to analyze the data or to change a parameter before resuming the simulation. This simulation system makes it very easy to develop new models that actively interact with the experimental research of the investigator.     

Kinetic model for the bioconversion of glucose to 2,5-diketo-D-gluconic acid

Summary A simple unstructured mathematical model for the oxidation of glucose to 2,5-diketo-D-gluconic acid with Erwinia citreus was developed. The kinetic parameters of the model were estimated by the oxygen partial pressure method and directly from the temporal response obtained from the experimental data collected in the batch fermentation. The simple developed model based on the kinetic measurements was able to simulate quite well the dynamic behaviour of the batch fermentation.     

Modeling complex neutrophil dynamics in the grey collie

We have developed a mathematical model for the peripheral regulation of neutrophil production mediated by granulocyte colony-stimulating factor. We have used that model to show that the pattern of neutrophil oscillations in nine grey collies is consistent with the hypothesis that cyclical neutropenia is due to an oscillatory stem cell input to the neutrophil regulatory system, and not due to autonomous oscillations in the peripheral neutrophil regulatory system. In the process of interfacing our model with the laboratory data, we have estimated parameters for the peripheral neutrophil control system consistent with higher than normal apoptotic cell loss within the recognizable neutrophil precursors. This is in agreement with other experimental data. Our estimated model parameters also predict that the peripheral neutrophil production system is globally stable in the grey collies we studied. This further supports our hypothesis that the origin of the oscillatory behavior in cyclical neutropenia is in the stem cell population, consistent with other clinical and experimental evidence.     

Mathematical analysis of the oncornavirus maturation process (virion RNA conversion and morphological condensation)

The rate of the maturation process of avian myeloblastosis virus experimentally estimated on the basis of genomic viral RNA conversion and morphological transition of virions was mathematically analysed. Three mathematical models were suggested and fitted to experimental data. It was found that: (a) model of simple kinetics (Model 1) does not agree with experimental data. Therefore, two hypotheses were considered in further mathematical modelling: (b) virions are identical in time of budding: maturation is dependent on the presence of a virion component which is degraded with time (Model 2). This model agrees with experimental data in all stages of the maturation process. (c) Virions are released from cells at different stages of assembly (Model 3). This model differs from experimental data especially in early stages of maturation. The hypothesis used for the construction of Model 2 seems to be the most plausible to explain the maturation process and is in agreement with data of murine leukemia virus maturation which was found to be accomplished by cleavage of p70 precursor protein.     

Modeling of oleaginous fungal biofilm developed on semi-solid media

An oleaginous fungus, Mortierella isabellina, able to transform efficiently sugar to storage lipid, was used as a model microorganism which develops a biofilm structure during the semi-solid fermentation process for the production of biodiesel from sweet sorghum. A mathematical model was developed to describe the fungal oil production in M. isabellina biofilm. The model describes diffusion and consumption of sugars and nitrogen of sweet sorghum and single cell oil production in a biofilm, which grows according to the kinetics of double-substrate limitation (sugars and nitrogen) with sugar inhibition. Experimental data from a previous experimental study were used to determine the kinetic parameters of the model. Maximum biofilm thickness and the percentage of lipid inside the biofilm were estimated using the model at 1892 μm and 15%, respectively. The proposed mathematical model could prove a useful tool for designing semi-solid fermentation processes.     

Construction of a large scale integrated map of macrophage pathogen recognition and effector systems

Background

Mathematical models provide abstract representations of the information gained from experimental observations on the structure and function of a particular biological system. Conferring a predictive character on a given mathematical formulation often relies on determining a number of non-measurable parameters that largely condition the model's response. These parameters can be identified by fitting the model to experimental data. However, this fit can only be accomplished when identifiability can be guaranteed.

Results

We propose a novel iterative identification procedure for detecting and dealing with the lack of identifiability. The procedure involves the following steps: 1) performing a structural identifiability analysis to detect identifiable parameters; 2) globally ranking the parameters to assist in the selection of the most relevant parameters; 3) calibrating the model using global optimization methods; 4) conducting a practical identifiability analysis consisting of two (a priori and a posteriori) phases aimed at evaluating the quality of given experimental designs and of the parameter estimates, respectively and 5) optimal experimental design so as to compute the scheme of experiments that maximizes the quality and quantity of information for fitting the model.

Conclusions

The presented procedure was used to iteratively identify a mathematical model that describes the NF-κB regulatory module involving several unknown parameters. We demonstrated the lack of identifiability of the model under typical experimental conditions and computed optimal dynamic experiments that largely improved identifiability properties.     

Evaluation of HIV-1 kinetic models using quantitative discrimination analysis

MOTIVATION: Since the identification of human immunodeficiency virus (HIV) over twenty years ago, many mathematical models of HIV dynamics have been proposed. The purpose of this study was to evaluate intracellular and intercellular scale HIV models that best described the dynamics of viral and cell titers of a person, where parameters were determined using typically available patient data. In this case, 'best' was defined as the model most capable of describing experimental patient data and was determined by Bayesian-based model discrimination analysis and the ability to provide realistic results. RESULTS: Twenty models of HIV-1 viral dynamics were initially evaluated to determine whether parameters could be obtained from readily available clinical data from established HIV-1 patients with stable disease. Based on this analysis, three models were chosen for further examination and comparison. Parameters were estimated using experimental data from a cohort of 338 people monitored for up to 2484 days. The models were evaluated using a Bayesian technique to determine which model was most probable. The model ultimately selected as most probable was overwhelmingly favored relative to the remaining two models, and it accounted for uninfected cells, infected cells and cytotoxic T lymphocyte dynamics. The authors developed a fourth model for comparison purposes by combining the features of the original three models. Parameters were estimated for the new model and the statistical analysis was repeated for all four models. The model that was initially favored was selected again upon model discrimination analysis. CONTACT: srivasta@engr.uconn.edu.     

Growth models of cultures with two liquid phases. VI. Parameter estimation and statistical analysis

Parameter estimation studies have been conducted employing mathematical models developed previously by the investigators and experimental data collected by the last author. A batch fermentation process in which Candida lipolytica were cultured on n-hexadecane dissolved in dewaxed gas oil was employed to obtain the experimental data. The kinetic data from a number of batch experiments conducted at different initial substrate concentrations and different dispersed phase volume fractions were analyzed assuming that, the basic model parameters (maximum specific growth rate, saturation constant, substrate phase equilibrium constant, adsorption constant, desorption constant, etc.) did not change from experiment to experiment. The Gauss-Newton method with modification by Greenstadt, Eisenpress, Bard, and Carroll was used to minimize the conventional sum of squares criterion on the IBM 300/50 computer. The individual confidence intervals were obtained for each individual parameter. Tin- models were compared employing the F-test for equality of variances and an analysis of residuals. For the two best models, the estimated parameter values were compared with available experimental information. The results showed good agreement between the experimental data and the values predicted by the mathematical models. The results presented in this work did suggest that growth on small segregated drops may be more important than continuous phase growth on dissolved substrate.