Error propagation from prime variables into specific rates and metabolic fluxes for mammalian cells in perfusion culture

Error propagation from prime variables into specific rates and metabolic fluxes was quantified for high‐concentration CHO cell perfusion cultivation. Prime variable errors were first determined from repeated measurements and ranged from 4.8 to 12.2%. Errors in nutrient uptake and metabolite/product formation rates for 5–15% error in prime variables ranged from 8–22%. The specific growth rate, however, was characterized by higher uncertainty as 15% errors in the bioreactor and harvest cell concentration resulted in 37.8% error. Metabolic fluxes were estimated for 12 experimental conditions, each of 10 day duration, during 120‐day perfusion cultivation and were used to determine error propagation from specific rates into metabolic fluxes. Errors of the greater metabolic fluxes (those related to glycolysis, lactate production, TCA cycle and oxidative phosphorylation) were similar in magnitude to those of the related greater specific rates (glucose, lactate, oxygen and CO₂ rates) and were insensitive to errors of the lesser specific rates (amino acid catabolism and biosynthesis rates). Errors of the lesser metabolic fluxes (those related to amino acid metabolism), however, were extremely sensitive to errors of the greater specific rates to the extent that they were no longer representative of cellular metabolism and were much less affected by errors in the lesser specific rates. We show that the relationship between specific rate and metabolic flux error could be accurately described by normalized sensitivity coefficients, which were readily calculated once metabolic fluxes were estimated. Their ease of calculation, along with their ability to accurately describe the specific rate‐metabolic flux error relationship, makes them a necessary component of metabolic flux analysis. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Synchronization of Metabolic Oscillations:Two Cells and Ensembles of Adsorbed Cells

We treat synchronization of metabolic oscillations in two cellsand in ensembles of cells adsorbed at the liquid-solid interface.(i) Synchronization of oscillations in two cells is assumedto occur via perturbation of the metabolite concentration nearone cell due to the metabolite diffusion flux from another cell.This direct channel of synchronization may be important ifthe distance between two cells is comparable with the cell diameter.The corresponding coupling coefficient is found to be proportionalto the metabolite diffusion coefficient and inversely proportionalto the cell radius and the distance between the cells.(ii) In the case of ensembles of adsorbed cells, synchronizationof oscillations is considered to be indirect, i.e., to occur viathe metabolite concentration formed outside the cells nearthe interface due to metabolite diffusion from the cells. We havederived a general integral equation relating the metaboliteconcentration near the interface with concentrations inside the cells.PACS: 82.37.-j, 82.40.Bj     

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.     

Sensitivity analysis of metabolic cascades catalyzed by bifunctional enzymes

Covalent modification/demodification cycles are common in metabolism. When the modification and demodification steps are carried out by two independent enzymes, the degree of modification can be ultrasensitive to the total concentration of either catalyst. We recently showed that the degree of modification of a target molecule cannot exhibit ultrasensitivity to the free concentrations of effectors that decide whether a bifunctional enzyme acts as modifier or demodifier. However, here we can now demonstrate that the degree of modification of a target molecule can display ultrasensitivity to the total, rather than free, concentrations of such effectors. Our results clarify some general aspects of ultrasensitive responses to effectors, including competitive inhibitors, in mono-cyclic cascades.     

Developing the control criterion for a continuous culture of microorganisms

A short survey and a critical analysis of previously proposed criteria for growth control of populations of microorganisms in the chemostat are presented. Based on the analysis of a mathematical model of the steady state of a microbial population in the chemostat, an adequate control criterion is suggested, along with a method to identify the corresponding control factors. The new control criterion is expressed as a product of the factor transformation coefficient and the sensitivity coefficient (SC) of the biomass with respect to the change in the factor at the chemostat inlet (hereinafter, the biomass SC). The control criterion determines the strength of the control exerted by a factor. The method of determining control factors consists in experimental determination of the real SCs for factors and the biomass and calculation on this basis of the corresponding ideal SCs, assuming constant factor transformation coefficients. The ideal SCs are shown to add up to integer values, a constraint that we call quantization relationships. Such relationships are used to test the completeness of the list of control factors. The proposed method was applied to both our own and literature data.Translated from Mikrobiologiya, Vol. 74, No. 1, 2005, pp. 5–16.Original Russian Text Copyright © 2005 by Adamovich, Rogozin, Degermendzhi.     

Biases in the estimation of the demographic parameters of a snowshoe hare population

1. Survival rates and natalities for a population of snowshoe hares in the Yukon were estimated independently of and simultaneously with estimates of population change during the increase phase of a hare cycle.
2. Simple demographic models are used to show that even though the estimated survival rates and natalities were high relative to previously published estimates, the observed demographic parameters are unable to explain the extent of population increase, and we conclude that some of these parameters must be underestimates.
3. A sensitivity analysis is used to examine the potential influence of changes in these demographic parameters on the population growth rate. During most years of the hare cycle the population growth rate is potentially most sensitive to changes in juvenile postweaning survival. Only during crash years is adult survivorship likely to be a more important determinant of the rate of population change.
4. Examination of previously published data sets on two full population cycles suggests that while survival rates are positively correlated with population growth rates, their incorporation into demographic models results in frequent underestimation of the rate of population increase.     

Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

Evaluating the sensitivity of biological models to various model parameters is a critical step towards advancing our understanding of biological systems. In this paper, we investigated sensitivity coefficients for a model simulating transport of tau protein along the axon. This is an important problem due to the relevance of tau transport and agglomeration to Alzheimer’s disease and other tauopathies, such as some forms of parkinsonism. The sensitivity coefficients that we obtained characterize how strongly three observables (the tau concentration, average tau velocity, and the percentage of tau bound to microtubules) depend on model parameters. The fact that the observables strongly depend on a parameter characterizing tau transition from the retrograde to the anterograde kinetic states suggests the importance of motor-driven transport of tau. The observables are sensitive to kinetic constants characterizing tau concentration in the free (cytosolic) state only at small distances from the soma. Cytosolic tau can only be transported by diffusion, suggesting that diffusion-driven transport of tau only plays a role in the proximal axon. Our analysis also shows the location in the axon in which an observable has the greatest sensitivity to a certain parameter. For most parameters, this location is in the proximal axon. This could be useful for designing an experiment aimed at determining the value of this parameter. We also analyzed sensitivity of the average tau velocity, the total tau concentration, and the percentage of microtubule-bound tau to cytosolic diffusivity of tau and diffusivity of bound tau along the MT lattice. The model predicts that at small distances from the soma the effect of these two diffusion processes is comparable.     

Parametric sensitivity of stoichiometric flux balance models applied to wild-type Escherichia coli metabolism

The esterification of lauric acid with geraniol catalyzed by the commercially immobilized lipase preparation from Mucor miehei, Lipozyme(R), was studied in well-stirred flasks. The enzyme support was characterized in terms of its internal and external surface area, protein location, and protein content. It was found that the enzyme was mainly located on the external surface of the support, therefore, internal diffusional limitations were not important. It was also shown that the protein content of the support depends on the size of the particle, with smaller particles containing higher amounts of protein per unit weight. Under the conditions studied, the reaction was not under external mass transfer limitations, and the initial reaction rate depended on the size of the support particles. This was mainly due to the different protein contents on the support as a function of particle size and not to internal or external mass transfer limitations. Also, it was found that the inhibition exerted by water was predominantly a physical effect due to its accumulation around the enzyme. It was also found that the reaction was substrate inhibited by lauric acid, but not by geraniol. (c) 1995 John Wiley & Sons, Inc.     

Application of the transition time of metabolic system as a criterion for optimization of metabolic processes

Transition time of metabolic systems in introduced as a suitable optimization criterion for biotechnological processes in which it is desirable to reduce the lag time and minimize the mass contained within the system. Lag time is the time needed for the system to attain the steady state. Results obtained from the sensitivity analysis of this steady state response are presented within the metabolic control analysis and applied to 3 case studies. In all of them the information provided by the transition time control profile allows the implementation of a strategy for biotechnological manipulations aimed at the improvement of the process. (c) 1994 John Wiley & Sons, Inc.     

代谢工程的发展及其应用

本首先论述了代谢工程的代谢网络理论、代谢分析、节点分析和中心代谢物作用机理等代谢工程理论基础。然后,分析了代谢工程的各种具体设计思路,并以实际例子作了详细说明。另外还对代谢工程的新兴研究方向－逆代谢工程进行了简单说明。