Power-law modeling based on least-squares minimization criteria.

The power-law formalism has been successfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a wider range of concentration values than the classical power-law. Although the implications of this alternative approach remain to be established, our results show that the predicted steady-state using the least-squares power-law is closest to the actual steady-state of the target system.     

Multilocus association testing of quantitative traits based on partial least-squares analysis

Because of combining the genetic information of multiple loci, multilocus association studies (MLAS) are expected to be more powerful than single locus association studies (SLAS) in disease genes mapping. However, some researchers found that MLAS had similar or reduced power relative to SLAS, which was partly attributed to the increased degrees of freedom (dfs) in MLAS. Based on partial least-squares (PLS) analysis, we develop a MLAS approach, while avoiding large dfs in MLAS. In this approach, genotypes are first decomposed into the PLS components that not only capture majority of the genetic information of multiple loci, but also are relevant for target traits. The extracted PLS components are then regressed on target traits to detect association under multilinear regression. Simulation study based on real data from the HapMap project were used to assess the performance of our PLS-based MLAS as well as other popular multilinear regression-based MLAS approaches under various scenarios, considering genetic effects and linkage disequilibrium structure of candidate genetic regions. Using PLS-based MLAS approach, we conducted a genome-wide MLAS of lean body mass, and compared it with our previous genome-wide SLAS of lean body mass. Simulations and real data analyses results support the improved power of our PLS-based MLAS in disease genes mapping relative to other three MLAS approaches investigated in this study. We aim to provide an effective and powerful MLAS approach, which may help to overcome the limitations of SLAS in disease genes mapping.     

Adaptive on-line simulation of bioreactors: Fermentation monitoring and modeling system

Summary In order to study and control fermentation processes, indirect on-line measurements and mathematical models can be used. Here an on-line model for fermentation processes is presented. The model is based on atom and partial mass balances as well as on stability equations for the protolytes. The model is given an adaptive form by including transport equations for mass transfer and expressions for the fermentation kinetics. The state of the process can be estimated on-line using the balance component of the model completed with measurement equations for the input and the output flows of the process. Adaptivity is realized by means of on-line estimation of the parameters in the transport and kinetic expressions using recursive regression analysis. On-line estimation of the kinetic and mass transfer parameters makes model-based predictions possible and enables intelligent process control while facilitating testing of the validity of the measurement variables. A practical MS-Windows 3.1 model implementation called FMMS—Fermentation Monitoring and Modeling System is shown. The system makes it easy to configure the operating conditions for a run. It uses Windows dialogs for all set-ups, model configuration parameters, elemental compositions, on-line measurement devices and signal conditioning. Advanced on-line data analysis makes it possible to plot variables against each other for easy comparison. FMMS keeps track of over 100 variables per run. These variables are either measured or estimated by the model. Assay results can also be entered and plotted during fermentation. Thus the model can be verified almost instantly. Historical fermentation runs can be re-analyzed in simulation mode. This makes it possible to examine different signal conditining filters as well as the sensitivity of the model. Combined, the data analysis and the simulation mode make it easy to test and develop model theories and new ideas.     

Reduced order modeling of passive and quasi-active dendrites for nervous system simulation

Accurate neuron models at the level of the single cell are composed of dendrites described by a large number of compartments. The network-level simulation of complex nervous systems requires highly compact yet accurate single neuron models. We present a systematic, numerically efficient and stable model order reduction approach to reduce the complexity of large dendrites by orders of magnitude. The resulting reduced dendrite models match the impedances of the full model within the frequency range of biological signals and reproduce the original action potential output waveforms.     

Individual based modeling and parameter estimation for a Lotka-Volterra system

Stochastic component, inevitable in biological systems, makes problematic the estimation of the model parameters from a single sequence of measurements, despite the complete knowledge of the system. We studied the problem of parameter estimation using individual-based computer simulations of a 'Lotka-Volterra world'. Two kinds (species) of particles--X (preys) and Y (predators)--moved on a sphere according to deterministic rules and at the collision (interaction) of X and Y the particle X was changed to a new particle Y. Birth of preys and death of predators were simulated by addition of X and removal of Y, respectively, according to exponential probability distributions. With this arrangement of the system, the numbers of particles of each kind might be described by the Lotka-Volterra equations. The simulations of the system with low (200-400 particles on average) number of individuals showed unstable oscillations of the population size. In some simulation runs one of the species became extinct. Nevertheless, the oscillations had some generic properties (e.g. mean, in one simulation run, oscillation period, mean ratio of the amplitudes of the consecutive maxima of X and Y numbers, etc.) characteristic for the solutions of the Lotka-Volterra equations. This observation made it possible to estimate the four parameters of the Lotka-Volterra model with high accuracy and good precision. The estimation was performed using the integral form of the Lotka-Volterra equations and two parameter linear regression for each oscillation cycle separately. We conclude that in spite of the irregular time course of the number of individuals in each population due to stochastic intraspecies component, the generic features of the simulated system evolution can provide enough information for quantitative estimation of the system parameters.     

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.     

Neural system modeling and simulation using Hybrid Functional Petri Net

The Petri net formalism has been proved to be powerful in biological modeling. It not only boasts of a most intuitive graphical presentation but also combines the methods of classical systems biology with the discrete modeling technique. Hybrid Functional Petri Net (HFPN) was proposed specially for biological system modeling. An array of well-constructed biological models using HFPN yielded very interesting results. In this paper, we propose a method to represent neural system behavior, where biochemistry and electrical chemistry are both included using the Petri net formalism. We built a model for the adrenergic system using HFPN and employed quantitative analysis. Our simulation results match the biological data well, showing that the model is very effective. Predictions made on our model further manifest the modeling power of HFPN and improve the understanding of the adrenergic system. The file of our model and more results with their analysis are available in our supplementary material.     

Niche variability and its consequences for species distribution modeling

When species distribution models (SDMs) are used to predict how a species will respond to environmental change, an important assumption is that the environmental niche of the species is conserved over evolutionary time-scales. Empirical studies conducted at ecological time-scales, however, demonstrate that the niche of some species can vary in response to environmental change. We use habitat and locality data of five species of stream fishes collected across seasons to examine the effects of niche variability on the accuracy of projections from Maxent, a popular SDM. We then compare these predictions to those from an alternate method of creating SDM projections in which a transformation of the environmental data to similar scales is applied. The niche of each species varied to some degree in response to seasonal variation in environmental variables, with most species shifting habitat use in response to changes in canopy cover or flow rate. SDMs constructed from the original environmental data accurately predicted the occurrences of one species across all seasons and a subset of seasons for two other species. A similar result was found for SDMs constructed from the transformed environmental data. However, the transformed SDMs produced better models in ten of the 14 total SDMs, as judged by ratios of mean probability values at known presences to mean probability values at all other locations. Niche variability should be an important consideration when using SDMs to predict future distributions of species because of its prevalence among natural populations. The framework we present here may potentially improve these predictions by accounting for such variability.     

RNA structural motif recognition based on least-squares distance

RNA structural motifs are recurrent structural elements occurring in RNA molecules. RNA structural motif recognition aims to find RNA substructures that are similar to a query motif, and it is important for RNA structure analysis and RNA function prediction. In view of this, we propose a new method known as RNA Structural Motif Recognition based on Least-Squares distance (LS-RSMR) to effectively recognize RNA structural motifs. A test set consisting of five types of RNA structural motifs occurring in Escherichia coli ribosomal RNA is compiled by us. Experiments are conducted for recognizing these five types of motifs. The experimental results fully reveal the superiority of the proposed LS-RSMR compared with four other state-of-the-art methods.     

Simulation and modeling of laser-tissue interactions based on a liposome-dye system

This work presents an overview of the use of liposomes for targeted delivery of photosensitizers to tumors for Photodynamic Therapy (PDT). It assesses the results of a quantitative model to explain the interaction of short-pulsed lasers (in the nanosecond and picosecond domains) with a liposome-dye complex in terms of a localized photo-induced thermal mechanism. Incorporation of an organic dye (sulforhodamine) within lipid vesicles has been investigated in conjunction with the effect of laser irradiation on the integrity of the liposome-dye complex. The variation of the absorption coefficient as a function of wavelength for dye-encapsulated liposomes before and after laser-induced release of dye was studied and modeled. The commercial software Mathematica was used to develop a Gaussian model for the energy absorption by the liposome-dye complex. Dye release from 3 microm - liposome encapsulating 25 mM aqueous solution of sulforhodamine dye was studied using 8 ns laser pulses at the second harmonic of the Nd:YAG laser (at 532 nm) and compared with dye release employing 25 ps - laser pulses. In addition, the temperature-dependence of the dye release has been included in the photo-thermal model.     

水土流失治理新范式:基于流域过程模拟和情景分析的方法

随着土壤侵蚀问题的日益突出,水土流失治理逐渐成为实现区域可持续发展的当务之急.通过在试验小流域实施治理措施并评价其效益是水土流失治理的传统范式,但这种范式存在试验周期长、可重复性差、资金和人工技术投入大、推广性差等局限性,已不能适应当前水土流失治理的需要.近年来兴起的基于流域过程模拟的情景分析方法在定量模拟流域过程对地理变量响应的基础上,通过评价不同治理措施的环境、生态和经济效益,探索能够协调经济发展与环境保护关系的水土流失治理措施.该方法能够在无需大范围工程实施和实地观测的情况下对各种治理措施的效益进行评价,花费少,灵活性强,在水土流失治理措施的决策制定中具有较大优势.本文详细阐述以情景分析方式作为水土流失治理新范式的基本思路,通过实例分析,演示新范式在治理流域水土流失中的应用,并展望新范式在流域治理中的未来发展趋势.     

Structural modeling and analysis of signaling pathways based on Petri nets

The purpose of this paper is to discuss how to model and analyze signaling pathways by using Petri net. Firstly, we propose a modeling method based on Petri net by paying attention to the molecular interactions and mechanisms. Then, we introduce a new notion "activation transduction component" in order to describe an enzymic activation process of reactions in signaling pathways and shows its correspondence to a so-called elementary T-invariant in the Petri net models. Further, we design an algorithm to effectively find basic enzymic activation processes by obtaining a series of elementary T-invariants in the Petri net models. Finally, we demonstrate how our method is practically used in modeling and analyzing signaling pathway mediated by thrombopoietin as an example.     

MRI-based modeling for radiocarpal joint mechanics: validation criteria and results for four specimen-specific models

The objective of this study was to validate the MRI-based joint contact modeling methodology in the radiocarpal joints by comparison of model results with invasive specimen-specific radiocarpal contact measurements from four cadaver experiments. We used a single validation criterion for multiple outcome measures to characterize the utility and overall validity of the modeling approach. For each experiment, a Pressurex film and a Tekscan sensor were sequentially placed into the radiocarpal joints during simulated grasp. Computer models were constructed based on MRI visualization of the cadaver specimens without load. Images were also acquired during the loaded configuration used with the direct experimental measurements. Geometric surface models of the radius, scaphoid and lunate (including cartilage) were constructed from the images acquired without the load. The carpal bone motions from the unloaded state to the loaded state were determined using a series of 3D image registrations. Cartilage thickness was assumed uniform at 1.0 mm with an effective compressive modulus of 4 MPa. Validation was based on experimental versus model contact area, contact force, average contact pressure and peak contact pressure for the radioscaphoid and radiolunate articulations. Contact area was also measured directly from images acquired under load and compared to the experimental and model data. Qualitatively, there was good correspondence between the MRI-based model data and experimental data, with consistent relative size, shape and location of radioscaphoid and radiolunate contact regions. Quantitative data from the model generally compared well with the experimental data for all specimens. Contact area from the MRI-based model was very similar to the contact area measured directly from the images. For all outcome measures except average and peak pressures, at least two specimen models met the validation criteria with respect to experimental measurements for both articulations. Only the model for one specimen met the validation criteria for average and peak pressure of both articulations; however the experimental measures for peak pressure also exhibited high variability. MRI-based modeling can reliably be used for evaluating the contact area and contact force with similar confidence as in currently available experimental techniques. Average contact pressure, and peak contact pressure were more variable from all measurement techniques, and these measures from MRI-based modeling should be used with some caution.     

Free and centrosome-attached microtubules: Quantitative analysis and modeling of two-component system

In cultivated in vitro interphase animal cells, microtubules form a network whose density is highest in the central cell area, in the region of centrosome, and decreases towards the cell periphery. Since identification of individual microtubules in the central cell area is significantly difficult and more often is impossible, there are several approaches to studying microtubules in the internal cell cytoplasm. These approaches are based on a decrease of microtubule density—both real, due to their partial depolymerization (by the action of cold temperatures or cytostatics), or apparent, due to a decrease of cell thickness (by photobleaching of preexisting microtubules and analysis of newly formed ones). In the present work, we propose a method based on the determination of optical density which allows evaluation of the state of the cytoplasmic microtubule system as a whole. The method consists of a comparison of the dependences describing changes of the microtubule optical density from the cell center to the periphery in controls and in experiments. Analysis of living cells by the proposed method has shown that the character of curves describing the decrease of optical density from the cell center to its periphery is different for various cell types; the dependence can be described both as an exponential regression (the CHO cell line) and as a linear regression (the NIH-3T3 and REF cell lines). Our previous studies have allowed the suggestion that the character of the dependence is determined by the ratio of free and centrosome-attached microtubules and by the position of their ends in the cell cytoplasm. To test this hypothesis, we considered model systems with all microtubules assumed to be in a straight orientation and divergent radially from the centrosome, but with different arrangements of plus-and minus-ends. In the model system, in which all the microtubule minus-ends are attached to the centrosome while the plus-ends are at different distances from it, the microtubule density is described by the exponential (f(x) = ae ^?bx ). Introduction of free microtubules into the system leads to a change of the character of this dependence, and the system in which the concentration of free microtubules with minus ends located at different distances from the cytoplasm is 5 times higher than that of the centrosome-attached microtubules is described by the linear regression equation (f(x) = k ^* x + b), which corresponds to the experimentally obtained dependences for 3T3 and REF cells. Thus, we believe that even in cells with a radial microtubule system, free microtubules may constitute the majority.     

Viral ion channels: molecular modeling and simulation

In a number of membrane-bound viruses, ion channels are formed by integral membrane proteins. These channel proteins include M2 from influenza A, NB from influenza B, and, possibly, Vpu from HIV-1. M2 is important in facilitating uncoating of the influenza A viral genome and is the target of amantadine, an anti-influenza drug. The biological roles of NB and Vpu are less certain. In all cases, the protein contains a single transmembrane alpha-helix close to its N-terminus. Channels can be formed by homo-oligomerization of these proteins, yielding bundles of transmembrane helices that span the membrane and surround a central ion-permeable pore. Molecular modeling may be used to integrate and interpret available experimental data concerning the structure of such transmembrane pores. This has proved successful for the M2 channel domain, where two independently derived models are in agreement with one another, and with solid-state nuclear magnetic resonance (NMR) data. Simulations based on channel models may yield insights into possible ion conduction and selectivity mechanisms.     

A comparative analysis based on different strength criteria for evaluation of risk factor for dental implants

A numerical analysis is developed to study the interaction phenomena between endousseus titanium dental implants and surrounding jawbone tissue. The interest is focused on the most appropriate evaluation of the stress state arising in the tissue because of the implant under physiological loading. The problem is considered with regard to linear elastic response of the one and to short time effect. Different configurations of bone-implant system are described, using axial-symmetrical and three-dimensional models, by means of finite and geometric element method. The investigation attains to the stress states induced in bone that lead to a limit condition near the effective failure surface. The parameter commonly adopted in literature, such as the Von Mises stress, represents an excessive simplification of problem formulation, leading to an incorrect evaluation of the real failure risk for the implant, due to the assumption of the isotropic and deviatoric nature of the adopted stress measure. More suitable criterion can be assumed, such as the Tsai-Wu criterion, to take into account the anisotropy that characterises the response of bone, as well as the influence of a hydrostatic stress state. The analysis developed offers a comparison of results by using different criteria, leading to an evaluation of reliability of the procedure to be followed and addressing also to an evaluation of a risk factor for the implant investigated.     

Experimental analysis of a neural system: Two modeling approaches

The retinal neural system in the catfish which transforms light intensity temporal variations into the horizontal cell potential is experimentally analyzed and modeled by two distinct methods. The first method involves testing the system with gaussian white-noisemodulated light intensity and the subsequent derivation of a mathematical model in terms of a Wiener functional series. The second method involves testing of the system by step and sinewave stimuli and the postulation of a set of nonlinear differential equations which are designed to fit these stimulus-response data. In this latter approach, the differential equations describe the usually assumed dynamic behavior of the component subsystems, such as photoreceptor and horizontal cell membranes in terms of properties of membrance resistance and capacitance. The system behavior is found to exhibit certain small signal nonlinearities such as dynamic asymmetry in the response as well as certain large signal nonlinearities. The two modeling approaches and the resulting models are compared and it is found that the functional model derived from the white-noise experiment, while it does not attempt to describe the underlying system structure as the differential equation does, produced, in general, more satisfactory results as far as the input-output behavior of the system is concerned. It is suggested that combination of the two approaches could be very fruitful in modeling a particular system.     

Prey capture tactics of spiders: An analysis based on a simulation model for spider's growth

The prey capture tactics of spiders was analyzed, considering the energy gained by the capture of prey and that required for it. For the purpose of it, a growth model of spiders was constructed, expressing the flow rate of prey biomass to the spider's body by differential equations. Solving these equations under the differing values of three parameters, growth curves of spiders was obtained. These three parameters are the amount of prey biomass supplied daily to spiders, x₀, the rate of prey capture of spiders, α, and a coefficient of the respiration rate required for the capture of prey, k. When the value of k increased, spiders could grow only at high value of x₀. These results suggest that habitats with small prey biomass are preferred by spiders adopting a sit-and-wait tactics for prey capture, which requires small values of k. Wolf spiders are one of these spiders showing that tactics. On the other hand, web-builders which require large amount of energy for spinning webs (namely, take large value of k), are able to grow only in the habitats with large prey biomass. Each species of spiders are considered to locate in a certain point between both extremes of these tactics for the capture of prey.