Commentary: model building, quantitative testing, and model comparison

The final goal is to create mathematical models that are based on our current knowledge of the underlying physiology and that explain all of the experimental data available. To do this, we suggest a consideration of several potential mathematical structures in the formulation of models and the formal comparison of these various structures with other models in the literature. However, when making these comparisons, one must pay careful attention to the systems being modeled and the data sets chosen to represent those systems.     

ChIP-chip: data, model, and analysis

ChIP-chip (or ChIP-on-chip) is a technology for isolation and identification of genomic sites occupied by specific DNA-binding proteins in living cells. The ChIP-chip signals can be obtained over the whole genome by tiling arrays, where a peak shape is generally observed around a protein-binding site. In this article, we describe the ChIP-chip process and present a probability model for ChIP-chip data. We then propose a model-based method for recognizing the peak shapes for the purpose of detecting protein-binding sites. We also investigate the issue of bandwidth in nonparametric kernel smoothing method.     

The reactive scope model — A new model integrating homeostasis, allostasis, and stress

Allostasis, the concept of maintaining stability through change, has been proposed as a term and a model to replace the ambiguous term of stress, the concept of adequately or inadequately coping with threatening or unpredictable environmental stimuli. However, both the term allostasis and its underlying model have generated criticism. Here we propose the Reactive Scope Model, an alternate graphical model that builds on the strengths of allostasis and traditional concepts of stress yet addresses many of the criticisms. The basic model proposes divergent effects in four ranges for the concentrations or levels of various physiological mediators involved in responding to stress. (1) Predictive Homeostasis is the range encompassing circadian and seasonal variation — the concentrations/levels needed to respond to predictable environmental changes. (2) Reactive Homeostasis is the range of the mediator needed to respond to unpredictable or threatening environmental changes. Together, Predictive and Reactive Homeostasis comprise the normal reactive scope of the mediator for that individual. Concentrations/levels above the Reactive Homeostasis range is (3) Homeostatic Overload, and concentrations/levels below the Predictive Homeostasis range is (4) Homeostatic Failure. These two ranges represent concentrations/levels with pathological effects and are not compatible with long-term (Homeostatic Overload) or short-term (Homeostatic Failure) health. Wear and tear is the concept that there is a cost to maintaining physiological systems in the Reactive Homeostasis range, so that over time these systems gradually lose their ability to counteract threatening and unpredictable stimuli. Wear and tear can be modeled by a decrease in the threshold between Reactive Homeostasis and Homeostatic Overload, i.e. a decrease in reactive scope. This basic model can then be modified by altering the threshold between Reactive Homeostasis and Homeostatic Overload to help understand how an individual's response to environmental stressors can differ depending upon factors such as prior stressors, dominance status, and early life experience. We illustrate the benefits of the Reactive Scope Model and contrast it with the traditional model and with allostasis in the context of chronic malnutrition, changes in social status, and changes in stress responses due to early life experiences. The Reactive Scope Model, as an extension of allostasis, should be useful to both biomedical researchers studying laboratory animals and humans, as well as ecologists studying stress in free-living animals.     

Protein model discrimination attempts using mutational sensitivity,predicted secondary structure,and model quality information

Structure prediction methods often generate a large number of models for a target sequence. Even if the correct fold for the target sequence is sampled in this dataset, it is difficult to distinguish it from other decoy structures. An attempt to solve this problem using experimental mutational sensitivity data for the CcdB protein was described previously by exploiting the correlation of residue depth with mutational sensitivity (r ~ 0.6). We now show that such a correlation extends to four other proteins with localized active sites, and for which saturation mutagenesis datasets exist. We also examine whether incorporation of predicted secondary structure information and the DOPE model quality assessment score, in addition to mutational sensitivity, improves the accuracy of model discrimination using a decoy dataset of 163 targets from CASP. Although most CASP models would have been subjected to model quality assessment prior to submission, we find that the DOPE score makes a substantial contribution to the observed improvement. We therefore also applied the approach to CcdB and four other proteins for which reliable experimental mutational data exist and observe that inclusion of experimental mutational data results in a small qualitative improvement in model discrimination relative to that seen with just the DOPE score. This is largely because of our limited ability to quantitatively predict effects of point mutations on in vivo protein activity. Further improvements in the methodology are required to facilitate improved utilization of single mutant data.     

Welch, Sedgwick, and the Hopkins model of hygiene

William H. Welch and William T. Sedgwick, two of the founding fathers of American public health, were both early generation "Hopkins Men." Sedgwick was part of the first group of graduate students to attend Johns Hopkins University, and Welch was part of the initial faculty at the University's medical school. While they never worked together as colleagues at Hopkins, both became interested in the exciting new discoveries of the microbial nature of human disease and developed similar public health programs based on this information. Sedgwick expanded upon these investigations in the new sanitary science program at MIT, where academic public health first emerged in the United States following Sedgwick's appointment in 1883. Welch, who had been exposed to European research in microbiology, promoted microbial research in pathology in Baltimore in 1884. His laboratory-based investigations expanded until they led to the formation of the country's first school of public health in 1916. Thus, a "Hopkins Model" for hygiene and public health emerged from the efforts of both Welch and Sedgwick.     

Synthesis, characterization, and spectroscopy of model molybdopterin complexes

The preparation and characterization of new model complexes for the molybdenum cofactor are reported. The new models are distinctive for the inclusion of pterin-substituted dithiolene chelates and have the formulation Tp(*)MoX(pterin-R-dithiolene) (Tp(*)=tris(3,5,-dimethylpyrazolyl)borate), X=O, S, R=aryl. Syntheses of Mo(4+) and (5+) complexes of two pterin-dithiolene derivatives as both oxo and sulfido compounds, and improved syntheses for pterinyl alkynes and [Et(4)N][Tp(*)Mo(IV)(S)S(4)] reagents are described. Characterization methods include electrospray ionization mass spectrometry, electrochemistry, infrared spectroscopy, electron paramagnetic resonance and magnetic circular dichroism. Cyclic voltammetry reveals that the Mo(5+/4+) reduction potential is intermediate between that for dithiolenes with electron-withdrawing substituents and simple dithiolates chelates. Electron paramagnetic resonance and magnetic circular dichroism of Mo(5+) complexes where X=O, R=aryl indicates that the molybdenum environment in the new models is electronically similar to that in Tp(*)MoO(benzenedithiolate).     

Psychosomatic symptoms,stress, and modernization: A model

The quantity of research on the effects of stress on disease has increased substantially in recent years, but little effort has been devoted to examining the effects of cultural influences in the stress process. A model is proposed in this paper in which cultural context exerts a modifying influence on the relationship between sociocultural stressors and psychosomatic symptoms, specifically in the context of modernization. In change situations involving increasing modernization there is increased differentiation in systems of social stratification within a community, due to increased potential for upward social mobility. The individuals who are upwardly mobile adopt a particular style of life, involving the acquisition of western consumer goods, as symbolic of their success. Lower class individuals strive to attain this same style of life as a claim to a higher status social identity, but their lower economic condition results in stressful incongruities and higher psychosomatic symptoms. Individuals who are successful in upward mobility are confronted by a different set of stressors that are primarily intrapsychic in nature. Events and circumstances perceived as threats to their self-identity are related to more psychosomatic symptoms. Thus, the meaning of specific stressors changes depending on the sociocultural context of the individual, and this meaning serves as a bridge between environmental circumstances and physiological outcomes. This model receives substantial empirical support in two field studies. Limitations of the model and implications for future research are discussed.Research in St. Lucia was supported by the Connecticut Research Foundation and the University of Connecticut Health Center. Research in the U.S. was supported by Research Grant MH 33943 from the Center for the Study of Minority Group Mental Health, National Institute of Mental Health. Drs. Arthur Kleinman, Lee Badger, H. B. M. Murphy, James Bindon, and Laurence Watkins kindly commented on previous drafts of this paper. Dr. Michael Murphy deserves a special note of gratitude for reading several drafts of the paper and for patiently sitting through several lengthy discussions of it. I alone am responsible for the errors and shortcomings.     

Comparative protein structure modeling by iterative alignment,model building and model assessment

Comparative or homology protein structure modeling is severely limited by errors in the alignment of a modeled sequence with related proteins of known three-dimensional structure. To ameliorate this problem, we have developed an automated method that optimizes both the alignment and the model implied by it. This task is achieved by a genetic algorithm protocol that starts with a set of initial alignments and then iterates through re-alignment, model building and model assessment to optimize a model assessment score. During this iterative process: (i) new alignments are constructed by application of a number of operators, such as alignment mutations and cross-overs; (ii) comparative models corresponding to these alignments are built by satisfaction of spatial restraints, as implemented in our program MODELLER; (iii) the models are assessed by a variety of criteria, partly depending on an atomic statistical potential. When testing the procedure on a very difficult set of 19 modeling targets sharing only 4–27% sequence identity with their template structures, the average final alignment accuracy increased from 37 to 45% relative to the initial alignment (the alignment accuracy was measured as the percentage of positions in the tested alignment that were identical to the reference structure-based alignment). Correspondingly, the average model accuracy increased from 43 to 54% (the model accuracy was measured as the percentage of the Cα atoms of the model that were within 5 Å of the corresponding Cα atoms in the superposed native structure). The present method also compares favorably with two of the most successful previously described methods, PSI-BLAST and SAM. The accuracy of the final models would be increased further if a better method for ranking of the models were available.     

生物地球化学过程模型DNDC的研究进展及其应用

脱氮-分解(denitrification-decomposition,DNDC)模型通过耦合土壤环境驱动的反硝化和分解过程来估计土壤中二氧化碳(CO2)、甲烷(CH4)和氧化亚氮(N2O)等痕量气体的排放量,是目前国际上最成功的模拟陆地生物地球化学循环的模型之一.本文主要阐述了DNDC模型的发展过程及其结构,以及模型的验证和敏感因子分析,并总结了当前DNDC模型应用的热点领域.     

Comparison and content of the Wright-Fisher model of random genetic drift, the diffusion approximation, and an intermediate model

We investigate the detailed connection between the Wright-Fisher model of random genetic drift and the diffusion approximation, under the assumption that selection and drift are weak and so cause small changes over a single generation. A representation of the mathematics underlying the Wright-Fisher model is introduced which allows the connection to be made with the corresponding mathematics underlying the diffusion approximation. Two ‘hybrid’ models are also introduced which lie ‘between’ the Wright-Fisher model and the diffusion approximation. In model 1 the relative allele frequency takes discrete values while time is continuous; in model 2 time is discrete and relative allele frequency is continuous. While both hybrid models appear to have a similar status and the same level of plausibility, the different nature of time and frequency in the two models leads to significant mathematical differences. Model 2 is mathematically inconsistent and has to be ruled out as being meaningful. Model 1 is used to clarify the content of Kimura's solution of the diffusion equation, which is shown to have the natural interpretation as describing only those populations where alleles are segregating. By contrast the Wright-Fisher model and the solution of the diffusion equation of McKane and Waxman cover populations of all categories, namely populations where alleles segregate, are lost, or fix.     

Differential equation modeling of HIV viral fitness experiments: model identification, model selection, and multimodel inference

Summary .  Many biological processes and systems can be described by a set of differential equation (DE) models. However, literature in statistical inference for DE models is very sparse. We propose statistical estimation, model selection, and multimodel averaging methods for HIV viral fitness experiments in vitro that can be described by a set of nonlinear ordinary differential equations (ODE). The parameter identifiability of the ODE models is also addressed. We apply the proposed methods and techniques to experimental data of viral fitness for HIV-1 mutant 103N. We expect that the proposed modeling and inference approaches for the DE models can be widely used for a variety of biomedical studies.     

Andaman Islanders,Pygmies, and an extension of Horn's model

Horn's model is generalized to state that the optimal pattern of distribution for foragers will correlate with the degree of resource patchiness; in particular (1) where resource attributes are less patchy, the optimal distribution for foragers is to be dispersed, and (2) where resource attributes are more patchy, the optimal distribution for foragers is to be aggregated. Optimality is assessed as the minimum round-trip distance from the forager's home base to a resource item. Patchiness is assessed according to the state taken by any of four resource attributes: dispersion (in space), supply (in time), particle size, and lasting properties. Horn's original contrast between (1) stable and evenly dispersed resources, and (2) mobile and clumped resources is shown to have been internally contradictory; that is, the optimal distribution for foragers would have been the same in both cases.     

FARSITE火行为模型的原理、结构及其应用

应用空间直观火行为模型模拟大的时空尺度上的林火蔓延过程成为林火管理、规划和科学分析的有效工具。FARSITE(Fire Area Simulator)是一个基于热物理、燃烧学和试验理论为一体的空间直观火行为模型,它集成了现有的地表火、树冠火、飞火和火加速等子模型。FARSITE能够利用GIS和RS提供的空间数据,模拟大时空尺度的林火蔓延,模拟结果能够以地图形式输出,反映林火行为的瞬时状态。本文介绍了FARSITE模型的基本原理、结构和运行机制,并将其应用到丰林自然保护区林火蔓延模拟,以期为国内林火管理和火行为模型的开发提供参考。     

A dynamical model of muscle activation, fatigue, and recovery

A dynamical model is presented as a framework for muscle activation, fatigue, and recovery. By describing the effects of muscle fatigue and recovery in terms of two phenomenological parameters (F, R), we develop a set of dynamical equations to describe the behavior of muscles as a group of motor units activated by voluntary effort. This model provides a macroscopic view for understanding biophysical mechanisms of voluntary drive, fatigue effect, and recovery in stimulating, limiting, and modulating the force output from muscles. The model is investigated under the condition in which brain effort is assumed to be constant. Experimental validation of the model is performed by fitting force data measured from healthy human subjects during a 3-min sustained maximal voluntary handgrip contraction. The experimental results confirm a theoretical inference from the model regarding the possibility of maximal muscle force production, and suggest that only 97% of the true maximal force can be reached under maximal voluntary effort, assuming that all motor units can be recruited voluntarily. The effects of different motor unit types, time-dependent brain effort, sources of artifacts, and other factors that could affect the model are discussed. The applications of the model are also discussed.     

A one locus, biased mutation model and its equivalence to an unbiased model

Experimental data suggests that for some continuously-varying characters under stabilising selection, mutation may cause a mean change in the value of the character. A one locus, mathematical model of a continuously-varying biological character with this property of biased mutation is investigated. Via a mathematical transformation, the equilibrium equation describing a large population of individuals is reduced to the equilibrium equation describing a mutationally unbiased problem. Knowledge of an unbiased problem is thus sufficient to determine all equilibrium properties of the corresponding biased problem. In the biased mutation problem, the dependence of the mean equilibrium value of the character, as a function of the mutational bias, is non-monotonic and remains small, for all levels of mutational bias. The analysis presented in this work sheds new light on Turelli's House of Cards Approximation.