Unveiling steady-state multiplicity in hybridoma cultures: the cybernetic approach

Mammalian cells grown in suspension produce waste metabolites such as lactate, alanine, and ammonia, which reduce the yield of cell mass and the desired product on the nutrients supplied. Previous studies (Cruz et al., 1999; Europa et al., 2000; Follstad et al., 1999) have shown that the cells can be made to alter their metabolism by starving them on their nutrients in continuous cultures at low dilution rates or starting the culture as a fed-batch. This leads to multiple steady states in continuous reactors, with some states being more favorable than others. Mathematical models that take into account the metabolic regulation that leads to these multiple steady states are invaluable tools for bioreactor control. In this article we present a cybernetic modeling strategy in which Metabolic Flux Analysis (MFA) is used to guide the cybernetic formulation. The hybridoma model presented as a result of this strategy considers the partially substitutable, partially complementary nature of glucose and glutamine. The choice of competitions within the network is guided by MFA and the model is successful in explaining the three multiple steady states observed. The cybernetic model though identified for the hybridoma experiments of Hu and others (Europa et al., 2000) seem generally applicable to mammalian systems as it captures the pathways that are common to mammalian cells grown in suspension. The model presented here could be used for start-up strategies for continuous reactors and model-based feedback control for maintaining high productivity of the reactor.     

Exploration of the intercellular heterogeneity of topotecan uptake into human breast cancer cells through compartmental modelling

A mathematical multi-cell model for the in vitro kinetics of the anti-cancer agent topotecan (TPT) following administration into a culture medium containing a population of human breast cancer cells (MCF-7 cell line) is described. This non-linear compartmental model is an extension of an earlier single-cell type model and has been validated using experimental data obtained using two-photon laser scanning microscopy (TPLSM). A structural identifiability analysis is performed prior to parameter estimation to test whether the unknown parameters within the model are uniquely determined by the model outputs. The full model has 43 compartments, with 107 unknown parameters, and it was found that the structural identifiability result could not be established even when using the latest version of the symbolic computation software Mathematica. However, by assuming that a priori knowledge is available for certain parameters, it was possible to reduce the number of parameters to 81, and it was found that this (Stage Two) model was globally (uniquely) structurally identifiable. The identifiability analysis demonstrated how valuable symbolic computation is in this context, as the analysis is far too lengthy and difficult to be performed by hand.     

A model for neural control of gradation of muscle force

A mathematical muscle model is presented that relates neural control signals linearly to muscle force without violating important known physiological constraints, such as the size-principle (Henneman and Mendell 1981) and non-linear twitch summation (Burke et al. 1976). This linearity implies that the neural control signals (defined as a weighted sum of activities in a nerve bundle) can be interpreted as the internal representation of total muscle force. The model allows for different relative contributions from the two force-grading mechanisms, i.e. the recruitment of motor units and the modulation of their firing frequency. It can therefore be applied to a variety of (distal and proximal) muscles. Furthermore, it permits simple mechanisms for controlling muscle force, e.g. in superposed motor tasks. The model confirms our intuitive notion that a weighted sum of activities in a nerve bundle can directly represent an external controlled variable, which in this case is exerted muscle force.     

Dynamic flux balance analysis of the metabolism of Saccharomyces cerevisiae during the shift from fully respirative or respirofermentative metabolic states to anaerobiosis

Dynamic flux balance analysis was utilized to simulate the metabolic behaviour of initially fully respirative and respirofermentative steady-state cultures of Saccharomyces?cerevisiae during sudden oxygen depletion. The hybrid model for the dynamic flux balance analysis included a stoichiometric genome-scale metabolic model as a static part and dynamic equations for the uptake of glucose and the cessation of respirative metabolism. The yeast consensus genome-scale metabolic model [Herrg?rd MJ et?al. (2008) Nat Biotechnol26, 1155-1160; Dobson PD et?al. (2010) BMC Syst Biol4, 145] was refined with respect to oxygen-dependent energy metabolism and further modified to reflect S.?cerevisiae anabolism in the absence of oxygen. Dynamic flux balance analysis captured well the essential features of the dynamic metabolic behaviour of S.?cerevisiae during adaptation to anaerobiosis. Modelling and simulation enabled the identification of short time-scale flux distribution dynamics under the transition to anaerobic metabolism, during which the specific growth rate was reduced, as well as longer time-scale process dynamics when the specific growth rate recovered. Expression of the metabolic genes was set into the context of the identified dynamics. Metabolic gene expression responses associated with the specific growth rate and with the cessation of respirative metabolism were distinguished.     

How did glycogen structure evolve to satisfy the requirement for rapid mobilization of glucose? A problem of physical constraints in structure building

Optimization of molecular design in cellular metabolism is a necessary condition for guaranteeing a good structure–function relationship. We have studied this feature in the design of glycogen by means of the mathematical model previously presented that describes glycogen structure and its optimization function [Meléndez-Hevia et al. (1993), Biochem J 295: 477–483]. Our results demonstrate that the structure of cellular glycogen is in good agreement with these principles. Because the stored glucose in glycogen must be ready to be used at any phase of its synthesis or degradation, the full optimization of glycogen structure must also imply the optimization of every intermediate stage in its formation. This case can be viewed as a molecular instance of the eye problem, a classical paradigm of natural selection which states that every step in the evolutionary formation of a functional structure must be functional. The glycogen molecule has a highly optimized structure for its metabolic function, but the optimization of the full molecule has meaning and can be understood only by taking into account the optimization of each intermediate stage in its formation. Received: 23 October 1996 / Accepted: 21 April 1997     

Improved statistics for genome-wide interaction analysis

Recently, Wu and colleagues [1] proposed two novel statistics for genome-wide interaction analysis using case/control or case-only data. In computer simulations, their proposed case/control statistic outperformed competing approaches, including the fast-epistasis option in PLINK and logistic regression analysis under the correct model; however, reasons for its superior performance were not fully explored. Here we investigate the theoretical properties and performance of Wu et al.'s proposed statistics and explain why, in some circumstances, they outperform competing approaches. Unfortunately, we find minor errors in the formulae for their statistics, resulting in tests that have higher than nominal type 1 error. We also find minor errors in PLINK's fast-epistasis and case-only statistics, although theory and simulations suggest that these errors have only negligible effect on type 1 error. We propose adjusted versions of all four statistics that, both theoretically and in computer simulations, maintain correct type 1 error rates under the null hypothesis. We also investigate statistics based on correlation coefficients that maintain similar control of type 1 error. Although designed to test specifically for interaction, we show that some of these previously-proposed statistics can, in fact, be sensitive to main effects at one or both loci, particularly in the presence of linkage disequilibrium. We propose two new "joint effects" statistics that, provided the disease is rare, are sensitive only to genuine interaction effects. In computer simulations we find, in most situations considered, that highest power is achieved by analysis under the correct genetic model. Such an analysis is unachievable in practice, as we do not know this model. However, generally high power over a wide range of scenarios is exhibited by our joint effects and adjusted Wu statistics. We recommend use of these alternative or adjusted statistics and urge caution when using Wu et al.'s originally-proposed statistics, on account of the inflated error rate that can result.     

Modeling and E-M estimation of haplotype-specific relative risks from genotype data for a case-control study of unrelated individuals

The US National Cancer Institute has recently sponsored the formation of a Cohort Consortium (http://2002.cancer.gov/scpgenes.htm) to facilitate the pooling of data on very large numbers of people, concerning the effects of genes and environment on cancer incidence. One likely goal of these efforts will be generate a large population-based case-control series for which a number of candidate genes will be investigated using SNP haplotype as well as genotype analysis. The goal of this paper is to outline the issues involved in choosing a method of estimating haplotype-specific risk estimates for such data that is technically appropriate and yet attractive to epidemiologists who are already comfortable with odds ratios and logistic regression. Our interest is to develop and evaluate extensions of methods, based on haplotype imputation, that have been recently described (Schaid et al., Am J Hum Genet, 2002, and Zaykin et al., Hum Hered, 2002) as providing score tests of the null hypothesis of no effect of SNP haplotypes upon risk, which may be used for more complex tasks, such as providing confidence intervals, and tests of equivalence of haplotype-specific risks in two or more separate populations. In order to do so we (1) develop a cohort approach towards odds ratio analysis by expanding the E-M algorithm to provide maximum likelihood estimates of haplotype-specific odds ratios as well as genotype frequencies; (2) show how to correct the cohort approach, to give essentially unbiased estimates for population-based or nested case-control studies by incorporating the probability of selection as a case or control into the likelihood, based on a simplified model of case and control selection, and (3) finally, in an example data set (CYP17 and breast cancer, from the Multiethnic Cohort Study) we compare likelihood-based confidence interval estimates from the two methods with each other, and with the use of the single-imputation approach of Zaykin et al. applied under both null and alternative hypotheses. We conclude that so long as haplotypes are well predicted by SNP genotypes (we use the Rh2 criteria of Stram et al. [1]) the differences between the three methods are very small and in particular that the single imputation method may be expected to work extremely well.     

An Extended Chaotic Maps-Based Three-Party Password-Authenticated Key Agreement with User Anonymity

User anonymity is one of the key security features of an authenticated key agreement especially for communicating messages via an insecure network. Owing to the better properties and higher performance of chaotic theory, the chaotic maps have been introduced into the security schemes, and hence numerous key agreement schemes have been put forward under chaotic-maps. Recently, Xie et al. released an enhanced scheme under Farash et al.’s scheme and claimed their improvements could withstand the security loopholes pointed out in the scheme of Farash et al., i.e., resistance to the off-line password guessing and user impersonation attacks. Nevertheless, through our careful analysis, the improvements were released by Xie et al. still could not solve the problems troubled in Farash et al‥ Besides, Xie et al.’s improvements failed to achieve the user anonymity and the session key security. With the purpose of eliminating the security risks of the scheme of Xie et al., we design an anonymous password-based three-party authenticated key agreement under chaotic maps. Both the formal analysis and the formal security verification using AVISPA are presented. Also, BAN logic is used to show the correctness of the enhancements. Furthermore, we also demonstrate that the design thwarts most of the common attacks. We also make a comparison between the recent chaotic-maps based schemes and our enhancements in terms of performance.     

MathSBML: a package for manipulating SBML-based biological models

MathSBML is a Mathematica package designed for manipulating Systems Biology Markup Language (SBML) models. It converts SBML models into Mathematica data structures and provides a platform for manipulating and evaluating these models. Once a model is read by MathSBML, it is fully compatible with standard Mathematica functions such as NDSolve (a differential-algebraic equations solver). MathSBML also provides an application programming interface for viewing, manipulating, running numerical simulations; exporting SBML models; and converting SBML models in to other formats, such as XPP, HTML and FORTRAN. By accessing the full breadth of Mathematica functionality, MathSBML is fully extensible to SBML models of any size or complexity. AVAILABILITY: Open Source (LGPL) at http://www.sbml.org and http://www.sf.net/projects/sbml     

Theoretical basis for the interpretation of surface permeability data by a transient method

Surface permeability data are frequently required when the system under study consists of a multiple zone membrane. Rotunno et al. (1970) developed a transient method to determine surface permeabilities in which the solute from one compartment is fully absorbed by the membrane without being transferred to the other. The theoretical analysis of the various possible situations is presented here to show that: (1) a linear plot of uptake vs. contact time can be expected for the most simple case (quasi-steady state in the external zone) even in the presence of considerable boundary layer resistance, and (2) a linear display of experimental data is not exclusive for that case, but it can also occur in the more complex situation of a composite resistance of a semi-infinite medium plus boundary layer. On this basis, different alternatives to interpret the data are suggested, according to the physical situation and the equations developed for each case.     

Evaluation of two models for human topoisomerase I interaction with dsDNA and camptothecin derivatives

Human topoisomerase I (Top1) relaxes supercoiled DNA during cell division. Camptothecin stabilizes Top1/dsDNA covalent complexes which ultimately results in cell death, and this makes Top1 an anti-cancer target. There are two current models for how camptothecin and derivatives bind to Top1/dsDNA covalent complexes (Staker, et al., 2002, Proc Natl Acad Sci USA 99: 15387-15392; and Laco, et al., 2004, Bioorg Med Chem 12: 5225-5235). The interaction energies between bound camptothecin, and derivatives, and Top1/dsDNA in the two models were calculated. The published structure-activity-relationships for camptothecin and derivatives correlated with the interaction energies for camptothecin and derivatives in the Laco et al. model, however, this was not the case for several camptothecin derivatives in the Stacker et al. model. By defining the binding orientation of camptothecin and derivatives in the Top1/dsDNA active-site these results allow for the rational design of potentially more efficacious camptothecin derivatives.     

Limits of Data Analysis in Scientific Inference: Reply to Sleep et al.

ABSTRACT Statistical inference is an important element of science, but these inferences are constrained within the framework established by the objectives and design of a study. The choice of approach to data analysis, while important, has far less consequence on scientific inference than claimed by Sleep et al. (2007). Their principal assertion—that when model selection is used as the approach to data analysis, all studies provide a reliable foundation for distinguishing among mechanistic explanatory hypotheses—is incorrect and encourages faulty inferences. Sleep et al. (2007) overlook the critical distinction between inferences that result from studies designed a priori to discriminate among a set of candidate explanations versus inferences that result from exploring data post hoc from studies designed originally to meet pattern-based objectives. No approach to data analysis, including model selection, has the power to overcome fundamental limitations on inferences imposed by study design. The comments by Sleep et al. (2007) reinforce the need for scientists to understand clearly the inferential basis for their scientific claims, including the roles and limitations of data analysis.     

A combined cell-cycle and metabolic model for the growth of hybridoma cells in steady-state continuous culture

The Model presented in this work demonstrates the combination of cell-cycle model with a model describing the growth and conversion kinetics of hybridoma cells in a steady-state continuous culture. The cell-cycle model is based upon a population balance model as described by Cazzador et al. and assumes the existence of a cycling-and apoptotic-cell population, which together form the viable-cell population. In this part the fraction of apoptotic cells, the age distribution of the cycling and apoptotic-cell population, the mean volume and biomass content per cell of the cycling, apoptotic, and viable cells, and the specific growth and death rates of the cells are calculated. The metabolic part consists of a Monod-type growth equation, four elemental balances, an equation assuming a constant yield of ammonia on glutamine, an equation for product formation, and the relation of Glacken for energy production. Furthermore, a maintenance-energy model for the consumption of glucose and glutamine is introduced, which combines the approaches of Herbert and Pirt into one model in a way similar to Beeftink et al. For energy consumption a Pirt model is assumed. The model is capable of predicting trends in steady-state vaues of a large number of variables of interest like specific growth rate, specific death rate, viability, cell numbers, mean viable-cell volume, and concentrations and conversion rates of product, glucose, glutamine, lactate, and ammonia. Also the concentrations and conversion rates of oxygen and carbon dioxide are qualitatively predicted. The values of the model predictions are generally close to experimental data obtained from literature. (c) 1995 John Wiley & Sons, Inc.     

RAD in the realm of next-generation sequencing technologies

The first North American RAD Sequencing and Genomics Symposium, sponsored by Floragenex (http://www.floragenex.com/radmeeting/), took place in Portland, Oregon (USA) on 19 April 2011. This symposium was convened to promote and discuss the use of restriction-site-associated DNA (RAD) sequencing technologies. RAD sequencing is one of several strategies recently developed to increase the power of data generated via short-read sequencing technologies by reducing their complexity (Baird et al. 2008; Huang et al. 2009; Andolfatto et al. 2011; Elshire et al. 2011). RAD sequencing, as a form of genotyping by sequencing, has been effectively applied in genetic mapping and quantitative trait loci (QTL) analyses in a range of organisms including nonmodel, genetically highly heterogeneous organisms (Table 1; Baird et al. 2008; Baxter et al. 2011; Chutimanitsakun et al. 2011; Pfender et al. 2011). RAD sequencing has recently found applications in phylogeography (Emerson et al. 2010) and population genomics (Hohenlohe et al. 2010). Considering the diversity of talks presented during this meeting, more developments are to be expected in the very near future.     

Modeling of the pyruvate production with Escherichia coli: comparison of mechanistic and neural networks-based models

Three different models: the unstructured mechanistic black-box model, the input–output neural network-based model and the externally recurrent neural network model were used to describe the pyruvate production process from glucose and acetate using the genetically modified Escherichia coli YYC202 ldhA::Kan strain. The experimental data were used from the recently described batch and fed-batch experiments [ Zelić B, Study of the process development for Escherichia coli-based pyruvate production. PhD Thesis, University of Zagreb, Faculty of Chemical Engineering and Technology, Zagreb, Croatia, July 2003. (In English); Zelić et al. Bioproc Biosyst Eng 26:249–258 (2004); Zelić et al. Eng Life Sci 3:299–305 (2003); Zelić et al Biotechnol Bioeng 85:638–646 (2004)]. The neural networks were built out of the experimental data obtained in the fed-batch pyruvate production experiments with the constant glucose feed rate. The model validation was performed using the experimental results obtained from the batch and fed-batch pyruvate production experiments with the constant acetate feed rate. Dynamics of the substrate and product concentration changes was estimated using two neural network-based models for biomass and pyruvate. It was shown that neural networks could be used for the modeling of complex microbial fermentation processes, even in conditions in which mechanistic unstructured models cannot be applied.