Effective knowledge‐based potentials

Empirical or knowledge‐based potentials have many applications in structural biology such as the prediction of protein structure, protein–protein, and protein–ligand interactions and in the evaluation of stability for mutant proteins, the assessment of errors in experimentally solved structures, and the design of new proteins. Here, we describe a simple procedure to derive and use pairwise distance‐dependent potentials that rely on the definition of effective atomic interactions, which attempt to capture interactions that are more likely to be physically relevant. Based on a difficult benchmark test composed of proteins with different secondary structure composition and representing many different folds, we show that the use of effective atomic interactions significantly improves the performance of potentials at discriminating between native and near‐native conformations. We also found that, in agreement with previous reports, the potentials derived from the observed effective atomic interactions in native protein structures contain a larger amount of mutual information. A detailed analysis of the effective energy functions shows that atom connectivity effects, which mostly arise when deriving the potential by the incorporation of those indirect atomic interactions occurring beyond the first atomic shell, are clearly filtered out. The shape of the energy functions for direct atomic interactions representing hydrogen bonding and disulfide and salt bridges formation is almost unaffected when effective interactions are taken into account. On the contrary, the shape of the energy functions for indirect atom interactions (i.e., those describing the interaction between two atoms bound to a direct interacting pair) is clearly different when effective interactions are considered. Effective energy functions for indirect interacting atom pairs are not influenced by the shape or the energy minimum observed for the corresponding direct interacting atom pair. Our results suggest that the dependency between the signals in different energy functions is a key aspect that need to be addressed when empirical energy functions are derived and used, and also highlight the importance of additivity assumptions in the use of potential energy functions.     

Analysis of three- and four-compartment models forin vivo radioligand-neuroreceptor interaction

Currently applied three-copartment models for analyzing kinetic data derived fromin vivo positron emission tomographic (PET) studies of radioligand-neuroreceptor interactions require assumptions which may not be strictly valid. Such assumptions include very rapid kinetics for nonspecific binding and the absence of multiple specific receptors or subtypes. Computer simulations, based on an exact analytical solution of the relevant differential equations, indicate the numerical errors that can arise when the assumptions are invalid. We propose a fourcompartment model which requires fewer assumptions. A simple relationship is derived for expressing the microscopic rate constants of either the three- or four-compartment model as explicit functions of the experimentally-observed macroscopic rate constants. This could eliminate the need for time-consuming, iterative, non-linear, curve-fitting approaches and numerical integration. The usefulness of the four-compartment model is limited, however, by the sensitivity and temporal resolution of current PET imaging devices.     

Models for recovering the energy landscape of conformational transitions from single-molecule pulling experiments

Single-molecule force spectroscopy is a powerful experimental technique for probing intermolecular forces and conformational transitions of individual molecules. This technique involves measuring the mechanical response of a molecule subjected to a constant or time-varying force. Statistical mechanics has played a pivotal role in interpreting force measurements in terms of the underlying kinetics and energy landscape of the molecular transition being studied. Here, we provide a didactic review of various statistical–mechanical models used for analysing these measurements, emphasising the theoretical ideas and assumptions used in deriving these models.     

Nonparametric models and methods for designs with dependent censored data: part I

We consider a nonparametric (NP) approach to the analysis of repeated measures designs with censored data. Using the NP model of Akritas and Arnold (1994, Journal of the American Statistical Association 89, 336-343) for marginal distributions, we present test procedures for the NP hypotheses of no main effects, no interaction, and no simple effects. This extends the existing NP methodology for such designs (Wei and Lachin, 1984, Journal of the American Statistical Association 79, 653-661). The procedures do not require any modeling assumptions and should be useful in cases where the assumptions of proportional hazards or location shift fail to be satisfied. The large-sample distribution of the test statistics is based on an i.i.d. representation for Kaplan-Meier integrals. The testing procedures apply also to ordinal data and to data with ties. Useful small-sample approximations are presented, and their performance is examined in a simulation study. Finally, the methodology is illustrated with two real life examples, one with censored and one with missing data. It is indicated that one of the data sets does not conform to any set of assumptions underlying the available methods and also that the present method provides a useful additional analysis even when data sets conform to modeling assumptions.     

Probabilistic approach to obtain hit-size effectiveness functions which relate microdosimetry and radiobiology

A probabilistic approach has been developed to relate microdosimetry, biological effects, and radiation quality. It is used to derive, and subsequently apply, microdosimetry-based cellular response functions for different biological end points of relevance for radiological protection. The approach makes use of measurable microdosimetry spectra and avoids assumptions concerning the course of mechanisms of radiation action. Instead, it postulates a response function that is, and behaves like, the cumulative probability that a subcellular target structure will respond to a specific target-averaged ionization density. Statistical distributions are applied and their parameters are evaluated to characterize the randomness involved in the localization of sensitive sites and in the reactivity of the whole sensitive structure. The resulting response functions can be used for prediction of the effects of low-level radiation. Such predictions for some selected effects of a stochastic nature (mutagenesis, chromosome abnormalities, etc.) are presented as relative biological effectiveness values based on low doses of radiations with a wide range of linear energy transfer and compared with various quality factor specifications. Cellular response relationships, termed hit-size effectiveness functions, can also be applied directly in radiation protection metrology by incorporating them into the software used to process the readings of microdosimetric spectrometers. The derivation of the functions, rather than their uses in radiation protection, is the principal subject of this report.     

Biased random walk models for chemotaxis and related diffusion approximations

Summary Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distributions are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.     

A review of global potentially available cropland estimates and their consequences for model‐based assessments

The world's population is growing and demand for food, feed, fiber, and fuel is increasing, placing greater demand on land and its resources for crop production. We review previously published estimates of global scale cropland availability, discuss the underlying assumptions that lead to differences between estimates, and illustrate the consequences of applying different estimates in model‐based assessments of land‐use change. The review estimates a range from 1552 to 5131 Mha, which includes 1550 Mha that is already cropland. Hence, the lowest estimates indicate that there is almost no room for cropland expansion, while the highest estimates indicate that cropland could potentially expand to over three times its current area. Differences can largely be attributed to institutional assumptions, i.e. which land covers/uses (e.g. forests or grasslands) are societally or governmentally allowed to convert to cropland, while there was little variation in biophysical assumptions. Estimates based on comparable assumptions showed a variation of up to 84%, which originated mainly from different underlying data sources. On the basis of this synthesis of the assumptions underlying these estimates, we constructed a high, a medium, and a low estimate of cropland availability that are representative of the range of estimates in the reviewed studies. We apply these estimates in a land‐change model to illustrate the consequences on cropland expansion and intensification as well as deforestation. While uncertainty in cropland availability is hardly addressed in global land‐use change assessments, the results indicate a large range of estimates with important consequences for model‐based assessments.     

Statistical mechanics of protein folding by exhaustive enumeration

It is hard to construct theories for the folding of globular proteins because they are large and complicated molecules having enormous numbers of nonnative conformations and having native states that are complicated to describe. Statistical mechanical theories of protein folding are constructed around major simplifying assumptions about the energy as a function of conformation and/or simplifications of the representation of the polypeptide chain, such as one point per residue on a cubic lattice. It is not clear how the results of these theories are affected by their various simplifications. Here we take a very different simplification approach where the chain is accurately represented and the energy of each conformation is calculated by a not unreasonable empirical function. However, the set of amino acid sequences and allowed conformations is so restricted that it becomes computationally feasible to examine them all. Hence we are able to calculate melting curves for thermal denaturation as well as the detailed kinetic pathway of refolding. Such calculations are based on a novel representation of the conformations as points in an abstract 12-dimensional Euclidean conformation space. Fast folding sequences have relatively high melting temperatures, native structures with relatively low energies, small kinetic barriers between local minima, and relatively many conformations in the global energy minimum's watershed. In contrast to other folding theories, these models show no necessary relationship between fast folding and an overall funnel shape to the energy surface, or a large energy gap between the native and the lowest nonnative structure, or the depth of the native energy minimum compared to the roughness of the energy landscape. Proteins 32:425–437, 1998. © 1998 Wiley-Liss, Inc.     

Logical problems and misunderstandings in “problems with dimensionless measurement models of synchrony in biological systems”

A model for the standardized measurement of synchrony in behavioral or biological states was proposed for use in comparative analyses of synchrony's adaptive significance. A recent critique attempts to discredit dimensionless (unitless) or standardized measures of synchrony in general and the proposed model in particular. Although the critique helps define and sharpen thinking about the measurement of synchrony and makes some well‐taken points, it also arrives at questionable conclusions based upon dubious assumptions. The critique proceeds from a fictional example in which all biological states being considered always have exactly the same durations for all individuals and always start or end for all individuals at exactly the same instants in time. These unreal, biologically meaningless premises, together with other questionable assumptions, are the basis of inappropriate analyses of standardized measures. The critique's arguments reveal a failure to understand the basic underlying principle of the standardized method and are dependent upon faulty logic. A statistical discussion contains both worthy points and arguable comments based not on data or actual probabilities of real events but on irrelevant chance outcomes derived from the biologically meaningless assumptions. The critique's conclusions are not credible, and its basic question probably is not scientifically answerable. Am. J. Primatol. 47:29–42, 1999. © 1999 Wiley‐Liss, Inc.     

Developmental Models for Estimating Ecological Responses to Environmental Variability: Structural,Parametric, and Experimental Issues

Developmental models that account for the metabolic effect of temperature variability on poikilotherms, such as degree-day models, have been widely used to study organism emergence, range and development, particularly in agricultural and vector-borne disease contexts. Though simple and easy to use, structural and parametric issues can influence the outputs of such models, often substantially. Because the underlying assumptions and limitations of these models have rarely been considered, this paper reviews the structural, parametric, and experimental issues that arise when using degree-day models, including the implications of particular structural or parametric choices, as well as assumptions that underlie commonly used models. Linear and non-linear developmental functions are compared, as are common methods used to incorporate temperature thresholds and calculate daily degree-days. Substantial differences in predicted emergence time arose when using linear versus non-linear developmental functions to model the emergence time in a model organism. The optimal method for calculating degree-days depends upon where key temperature threshold parameters fall relative to the daily minimum and maximum temperatures, as well as the shape of the daily temperature curve. No method is shown to be universally superior, though one commonly used method, the daily average method, consistently provides accurate results. The sensitivity of model projections to these methodological issues highlights the need to make structural and parametric selections based on a careful consideration of the specific biological response of the organism under study, and the specific temperature conditions of the geographic regions of interest. When degree-day model limitations are considered and model assumptions met, the models can be a powerful tool for studying temperature-dependent development.     

A model of labelled-ligand displacement assays resulting in logit-log relationships

Equations for ligand displacement asays are derived from Chou's median effect principle in which assumptions on the relative binding kinetics of the ligand and labeled-ligand are not required. Assumptions underlying this approach are (1) that the antiserum and standard ligand reagents are functionally homogeneous, (2) the tracer reagent has two homogeneous populations—one of labeled-ligand and one of nonlabeled-ligand, (3) that the reaction is at or near equilibrium, and (4) that ligand binding reactions can be represented by enzyme kinetic equations with no formed product. Equations found from this approach provide a basis from which the empirical logit-log transform commonly used for radioimmunoassay standard curves can be derived. In addition, they provide some insight into the origins of nonlinearity of the widely used logit-log transform. The logit-log relationship is shown to be equivalent to an arithmetic plot. Finally, procedures are suggested from the model whereby the linearity of the common logit-log transform can be improved and the compliance of the transform and model assumptions with the underlying chemistry can be tested.     

HIERARCHICAL SELECTION THEORY AND SEX RATIOS. II. ON APPLYING THE THEORY,AND A TEST WITH FIG WASPS

Predictions from the theory of sex ratios in subdivided populations are tested by studying fig wasps (Agaonidae). Observations strongly support the qualitative prediction that fig wasp sex ratios (males/total) decrease with increasing amounts of both inbreeding and competition among male relatives for access to mates (local mate competition). However, the observed sex ratio is consistently lower than predicted by previous quantitative models. Many assumptions underlying these models are unrealistic. Each unrealistic assumption is discussed as it applies to fig wasps, and where appropriate, new quantitative predictions are derived based on more realistic assumptions. New predictions are compared to the data in an a posteriori fashion and are found to be much closer to the observations than previous models from the literature, but further work will be required before a close match between theory and observation can be claimed.     

A New Statistical Goodness-of-Fit Test Based on Graphical Representation

A statistical goodness-of-fit test, based on representing the sample observations by linked vectors, is developed. The direction and the length of the linked vectors are defined as functions of the expected values of the order statistics and sample order statistics, respectively. The underlying method can be used to test distributional assumptions for any location-scale family. A test statistic Q_n is introduced and some of its properties are studied. It is shown that the proposed test can be generalized to test if two or more independent samples come from the same distribution. The test procedure provides a graphical method of identifying the true distribution when the null hypothesis is rejected.     

L’éclairage biologique des activités mentales: réduction ou mise en perspective ?

The relationship between the human psychological faculties and their underlying biological foundation is traditionally addressed within the mind-matter philosophical framework and its ethical extension regarding freedom and determinism. Neurobiology represents a new method, reflective of our times, to articulate the relationships between biological and psychological phenomena. The various points of view in this field are often based on implicit ontological presuppositions and, at least sometimes, unconscious epistemological assumptions: monism vs dualism, functionalism, reductionism, eliminativism, type identity and other more or less sophisticated variations. Bearing in mind the pitfalls these create, we can try to determine structural analogies across the different levels of the living being and the mind: the energy imbalance maintained for cell survival; the dynamic and complementary relationship between homeostatic and allostatic functions in living organisms; the tension between essential and complementary cognitive brain processes, such as the processes used to represent an object and those used to locate an object in space. Those phenomena all bear structural analogies, even though they work at different levels.     

Correlation of RNA Secondary Structure Statistics with Thermodynamic Stability and Applications to Folding

The accurate prediction of the secondary and tertiary structure of an RNA with different folding algorithms is dependent on several factors, including the energy functions. However, an RNA higher-order structure cannot be predicted accurately from its sequence based on a limited set of energy parameters. The inter- and intramolecular forces between this RNA and other small molecules and macromolecules, in addition to other factors in the cell such as pH, ionic strength, and temperature, influence the complex dynamics associated with transition of a single stranded RNA to its secondary and tertiary structure. Since all of the factors that affect the formation of an RNAs 3D structure cannot be determined experimentally, statistically derived potential energy has been used in the prediction of protein structure. In the current work, we evaluate the statistical free energy of various secondary structure motifs, including base-pair stacks, hairpin loops, and internal loops, using their statistical frequency obtained from the comparative analysis of more than 50,000 RNA sequences stored in the RNA Comparative Analysis Database (rCAD) at the Comparative RNA Web (CRW) Site. Statistical energy was computed from the structural statistics for several datasets. While the statistical energy for a base-pair stack correlates with experimentally derived free energy values, suggesting a Boltzmann-like distribution, variation is observed between different molecules and their location on the phylogenetic tree of life. Our statistical energy values calculated for several structural elements were utilized in the Mfold RNA-folding algorithm. The combined statistical energy values for base-pair stacks, hairpins and internal loop flanks result in a significant improvement in the accuracy of secondary structure prediction; the hairpin flanks contribute the most.     

A generalized formulation of dual radiation action

Dual radiation action is a process in which cellular lesions are produced as a result of the interaction of pairs of sublesions that are molecular alterations produced by ionizing radiation. Previous formulations of this process have employed a number of simplifying assumptions that limit the accuracy and the range of application of theoretical analysis. The formulation presented here removes some of these restrictions by introducing three functions that describe the geometry of the sensitive material in the cell, the geometry of the pattern of energy deposition, and the interaction probability of sublesions as a function of their separation. The relation derived is similar to that obtained previously, in that lesion production is found to depend on two terms that are proportional to the first and the second power of the absorbed dose. However, the coefficients of these terms are now derived on the basis of a more realistic treatment.     

Dehouck-Gilis-Rooman 统计势能函数的简化

统计有效能函数(Statisticaleffectiveenergyfunction(SEEF))又称统计势能函数,来源于对已知蛋白质结构数据库进行的统计分析。近年来Dehouck-Gilis-Rooman(DGR)小组通过将蛋白质结构的总体统计势能分解成低阶的势能项之和,提出了一种新型的统计势能函数,这种势能函数由有限个可加和的项组成。我们试图对这种势能函数进行简化,即通过诱导蛋白质数据库选择尽可能少的势能项,而且这些势能项的加和可满足一定的性能要求。结果我们得出了六组势能项组合,其性能可和DGR小组得出的势能项组合相媲美,但其势能项数目却大大减少,完全可用于蛋白质结构预测。     

Empirical Protein Energy Maps

WORK by several groups^1–5 has led to the calculation of energy maps for the peptide unit, which is the dependence of the conformational energy E_?,ψ on the torsional angles around the N-C^α bond (?) and the C^α-C bond (ψ)⁶ (Fig. 1) by using a standard set of bond lengths, valence angles and potential functions derived from small molecules. Although calculated maps are improved by refining the potential functions and increasing the number of parameters, there are differences according to the particular assumptions made. The most probable conformation of a peptide unit in proteins, using the available experimental information, is given by the following approach.     

Thermodynamics of protein folding: a microscopic view

Statistical thermodynamics provides a powerful theoretical framework for analyzing, understanding and predicting the conformational properties of biomolecules. The central quantity is the potential of mean force or effective energy as a function of conformation, which consists of the intramolecular energy and the solvation free energy. The intramolecular energy can be reasonably described by molecular mechanics-type functions. While the solvation free energy is more difficult to model, useful results can be obtained with simple approximations. Such functions have been used to estimate the intramolecular energy contribution to protein stability and obtain insights into the origin of thermodynamic functions of protein folding, such as the heat capacity. With reasonable decompositions of the various energy terms, one can obtain meaningful values for the contribution of one type of interaction or one chemical group to stability. Future developments will allow the thermodynamic characterization of ever more complex biological processes.     

Abundance-body size relationships: the roles of metabolism and population dynamics

1. Species' abundance scales approximately as an inverse power of body mass. This property has been explained on the basis of metabolic rates of organisms of different sizes. 2. This paper considers the additional effect of population dynamics on the abundance-body size relationship, on the grounds that mass flow through food webs also depends on interactions between predators and their prey. To do this, an analysis of simple dynamical food-chain models was carried out, using rate parameters which scaled with body mass according to empirically based rules. 3. The analysis shows that a function for the abundance-body size relationship derived from metabolic theory is a good first approximation to a function derived for food chains at dynamic equilibrium, although the mechanistic interpretation of terms in the functions is not the same. 4. The results are sensitive to assumptions about the scaling of the self-limitation of basal species with respect to body size. Depending on the assumption made, the abundance-body size relationship may have a power parameter -1 at all trophic levels, or be described by different functions at different trophic levels.