Limit cycles in periodically perturbed population systems

A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.     

Weighted next reaction method and parameter selection for efficient simulation of rare events in biochemical reaction systems

The weighted stochastic simulation algorithm (wSSA) recently developed by Kuwahara and Mura and the refined wSSA proposed by Gillespie et al. based on the importance sampling technique open the door for efficient estimation of the probability of rare events in biochemical reaction systems. In this paper, we first apply the importance sampling technique to the next reaction method (NRM) of the stochastic simulation algorithm and develop a weighted NRM (wNRM). We then develop a systematic method for selecting the values of importance sampling parameters, which can be applied to both the wSSA and the wNRM. Numerical results demonstrate that our parameter selection method can substantially improve the performance of the wSSA and the wNRM in terms of simulation efficiency and accuracy.     

Isotopic method for estimating microbial cell volumes

Reid, Della F. (University of Hawaii, Honolulu), and Hilmer A. Frank. Isotopic method for estimating microbial cell volumes. J. Bacteriol. 92:639-644. 1966.-A sensitive isotopic method was developed for estimating the mean cell volume in small numbers of bacterial spores by measuring directly the extracellular fluid volume when cells are present in a saturated inulin solution containing inulin-C(14) at low specific activity. The method minimizes errors due to solute adsorption to the cells and avoids errors arising from differences in cell packing. The effects of these sources of error on cell volume and intercellular space estimations made with nonpenetrating solutes are discussed.     

Calculations of protein volumes: sensitivity analysis and parameter database

MOTIVATION: The precise sizes of protein atoms in terms of occupied packing volume are of great importance. We have previously presented standard volumes for protein residues based on calculations with Voronoi-like polyhedra. To understand the applicability and limitations of our set, we investigated, in detail, the sensitivity of the volume calculations to a number of factors: (i) the van der Waals radii set, (ii) the criteria for including buried atoms in the calculations or atom selection, (iii) the method of positioning the dividing plane in polyhedra construction, and (iv) the set of structures used in the averaging. RESULTS: We find that different radii sets have only moderate affects to the distribution and mean of volumes. Atom selection and dividing plane methods cause larger changes in protein atoms volumes. More significantly, we show how the variation in volumes appears to be clearly related to the quality of the structures analyzed, with higher quality structures giving consistently smaller average volumes with less variance.     

Urease activity and its Michaelis constant for soil systems

Summary Urea hydrolysis was measured in two separate sets of experiments. (1) Nine soil (0–15 cm) samples were treated with 200 g of urea-N g^–1 dry soil and incubated (at 37°C) at 50 per cent of the water holding capacity. Samples were periodically analysed for the remaining urea-N. The urease activity (time in hoursrequired to hydrolyse half the applied urea-N) was determined to be 5.8 to 15.2 hours in the various soils, which appeared to associate principally with the organic carbon content of the soils (r=–0.80^**). (2) Three soils were treated with 25 to 2000 g urea-N g^–1 dry soil amounting to 0.9 to 72.0 mM urea in 11 soil: solution. The system was buffered at pH 7.2 and agitated for 5h when the remaining urea-N was determined. The values of Km and Vmax were computed by two methods (i) from the integrated form of the Michaelis-Menten equation based on the results of the first study, and (ii) from the Michaelis-Menton equation based on urea hydrolysis in the second study. The integrated method appeared to be more suitable for enzyme kinetic studies in soil systems where the Km and V_max values bore close relationship (r=–0.88^**).     

Exploring uncertainty of Amazon dieback in a perturbed parameter Earth system ensemble

The future of the Amazon rainforest is unknown due to uncertainties in projected climate change and the response of the forest to this change (forest resiliency). Here, we explore the effect of some uncertainties in climate and land surface processes on the future of the forest, using a perturbed physics ensemble of HadCM3C. This is the first time Amazon forest changes are presented using an ensemble exploring both land vegetation processes and physical climate feedbacks in a fully coupled modelling framework. Under three different emissions scenarios, we measure the change in the forest coverage by the end of the 21st century (the transient response) and make a novel adaptation to a previously used method known as “dry‐season resilience” to predict the long‐term committed response of the forest, should the state of the climate remain constant past 2100. Our analysis of this ensemble suggests that there will be a high chance of greater forest loss on longer timescales than is realized by 2100, especially for mid‐range and low emissions scenarios. In both the transient and predicted committed responses, there is an increasing uncertainty in the outcome of the forest as the strength of the emissions scenarios increases. It is important to note however, that very few of the simulations produce future forest loss of the magnitude previously shown under the standard model configuration. We find that low optimum temperatures for photosynthesis and a high minimum leaf area index needed for the forest to compete for space appear to be precursors for dieback. We then decompose the uncertainty into that associated with future climate change and that associated with forest resiliency, finding that it is important to reduce the uncertainty in both of these if we are to better determine the Amazon's outcome.     

A perturbed two-level model for exciton trapping in small photosynthetic systems.

The study of exciton trapping in photosynthetic systems provides significant information about migration kinetics within the light harvesting antenna (LHA) and the reaction center (RC). We discuss two random walk models for systems with weakly coupled pigments, with a focus on the application to small systems (10-40 pigments/RC). Details of the exciton transfer to and from the RC are taken into consideration, as well as migration within the LHA and quenching in the RC. The first model is obtained by adapting earlier local trap models for application to small systems. The exciton lifetime is approximated by the sum of three contributions related to migration in the LHA, trapping by the RC, and quenching within the RC. The second model is more suitable for small systems and regards the finite rate of migration within the LHA as a perturbation of the simplified model, where the LHA and the RC are each represented by a single pigment level. In this approximation, the exciton lifetime is the sum of a migration component and a single nonlinear expression for the trapping and quenching of the excitons. Numerical simulations demonstrate that both models provide accurate estimates of the exciton lifetime in the intermediate range of 20-50 sites/RC. In combination, they cover the entire range of very small to very large photosynthetic systems. Although initially intended for regular LHA lattices, the models can also be applied to less regular systems. This becomes essential as more details of the structure of these systems become available. Analysis with these models indicates that the excited state decay in LH1 is limited by the average rate at which excitons transfer to the RC from neighboring sites in the LHA. By comparing this to the average rate of transfer within the LHA, various structural models that have been proposed for the LH1 core antenna are discussed.     

Analysis and parameter resolution in highly cooperative systems

We have examined common methods of analysis of highly cooperative systems such as oxygen binding by hemoglobin and thermal denaturation. Through extensive simulation of ligand-binding data for a tetrameric macromolecule we show that careful attention must be paid to the formulation of the fitting function and to proper assessment of the number of parameters involved. We conclude that the partition function should be formulated in terms of overall reaction parameters as opposed to stepwise reaction parameters and that bias is introduced by fixing physical parameters such as extrapolated end points.     

Global parameter estimation methods for stochastic biochemical systems

Background  

The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.     

A general method for biological parameter estimation

Summary A general observer-based estimator method is developed and applied for process modelling and monitoring. This parameter estimation technique was successfully applied to a L-lysine fermentation process. It was a useful tool to detect the effect of major culture conditions on cell growth and product synthesis. It can also be used for the development of adaptive optimal control schemes.     

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

Background  

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.     

A new method for determining the Michaelis constant

A new method is described for evaluating the parameters K(m) and V in the Michaelis-Menten equation, and is illustrated with experimental data from the literature.