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.     

Structural analysis based on state-space modeling.

A new method has been developed to compute the probability that each amino acid in a protein sequence is in a particular secondary structural element. Each of these probabilities is computed using the entire sequence and a set of predefined structural class models. This set of structural classes is patterned after Jane Richardson''s taxonomy for the domains of globular proteins. For each structural class considered, a mathematical model is constructed to represent constraints on the pattern of secondary structural elements characteristic of that class. These are stochastic models having discrete state spaces (referred to as hidden Markov models by researchers in signal processing and automatic speech recognition). Each model is a mathematical generator of amino acid sequences; the sequence under consideration is modeled as having been generated by one model in the set of candidates. The probability that each model generated the given sequence is computed using a filtering algorithm. The protein is then classified as belonging to the structural class having the most probable model. The secondary structure of the sequence is then analyzed using a "smoothing" algorithm that is optimal for that structural class model. For each residue position in the sequence, the smoother computes the probability that the residue is contained within each of the defined secondary structural elements of the model. This method has two important advantages: (1) the probability of each residue being in each of the modeled secondary structural elements is computed using the totality of the amino acid sequence, and (2) these probabilities are consistent with prior knowledge of realizable domain folds as encoded in each model. As an example of the method''s utility, we present its application to flavodoxin, a prototypical alpha/beta protein having a central beta-sheet, and to thioredoxin, which belongs to a similar structural class but shares no significant sequence similarity.     

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.     

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.     

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.     

Brain functional network modeling and analysis based on fMRI: a systematic review

In recent years, the number of patients with neurodegenerative diseases (i.e., Alzheimer’s disease, Parkinson’s disease, mild cognitive impairment) and mental disorders (i.e., depression, anxiety and schizophrenia) have increased dramatically. Researchers have found that complex network analysis can reveal the topology of brain functional networks, such as small-world, scale-free, etc. In the study of brain diseases, it has been found that these topologies have undergoed abnormal changes in different degrees. Therefore, the research of brain functional networks can not only provide a new perspective for understanding the pathological mechanism of neurological and psychiatric diseases, but also provide assistance for the early diagnosis. Focusing on the study of human brain functional networks, this paper reviews the research results in recent years. First, this paper introduces the background of the study of brain functional networks under complex network theory and the important role of topological properties in the study of brain diseases. Second, the paper describes how to construct a brain functional network using neural image data. Third, the common methods of functional network analysis, including network structure analysis and disease classification, are introduced. Fourth, the role of brain functional networks in pathological study, analysis and diagnosis of brain functional diseases is studied. Finally, the paper summarizes the existing studies of brain functional networks and points out the problems and future research directions.     

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.     

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.     

Rational design of a nitrite reductase based on myoglobin: a molecular modeling and dynamics simulation study

Myoglobin (Mb) is an ideal scaffold protein for rational protein design mimicking native enzymes. We recently designed a nitrite reductase (NiR) based on sperm whale Mb by introducing an additional distal histidine (Leu29 to His29 mutation) and generating a distal tyrosine (Phe43 to Tyr43 mutation) in the heme pocket, namely L29H/F43Y Mb, to mimic the active site of cytochrome cd (1) NiR from Ps. aeruginosa that contains two distal histidines and one distal tyrosine. The molecular modeling and dynamics simulation study herein revealed that L29H/F43Y Mb has the necessary structural features of native cytochrome cd (1) NiR and can provide comparable interactions with nitrite as in native NiRs, which provides rationality for the protein design and guides the protein engineering. Additionally, the present study provides an insight into the relatively low NiR activity of Mb in biological systems.     

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.     

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.     

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.