To model or not to model

Summary Self-improving control systems may belong to either of two categories, according to whether or not they embody an explicit model of the part of their environment with which they interact. The two forms of operation are discussed and compared, and it is shown that the two may be mathematically equivalent. The treatment also gives theoretical justification for a particular mode of operation for nonmodel-forming controllers.     

A future of the model organism model

Changes in technology are fundamentally reframing our concept of what constitutes a model organism. Nevertheless, research advances in the more traditional model organisms have enabled fresh and exciting opportunities for young scientists to establish new careers and offer the hope of comprehensive understanding of fundamental processes in life. New advances in translational research can be expected to heighten the importance of basic research in model organisms and expand opportunities. However, researchers must take special care and implement new resources to enable the newest members of the community to engage fully with the remarkable legacy of information in these fields.     

Infinite-allele model and infinite-site model in population genetics

Both the infinite-allele model and infinite-site model have contributed to development of population genetics. Although the former is a model mainly for protein polymorphism and the latter is mainly for DNA polymorphism, these two models are related: the expected heterozygosity and homozygosity can be obtained from the infinite-site model, and the expectation of the amount of DNA polymorphism can be obtained from the infinite-allele model.     

The influence of model parameters on model validation

The study examined the sensitivity of two musculoskeletal models to the parameters describing each model. Two different models were examined: a phenomenological model of human jumping with parameters based on live subject data, and the second a model of the First Dorsal Interosseous with parameters based on cadaveric measurements. Both models were sensitive to the model parameters, with the use of mean group data not producing model outputs reflective of either the performance of any group member or the mean group performance. These results highlight the value of subject specific model parameters, and the problems associated with model validation.     

Antibodies as a model system for comparative model refinement

Predicting the conformations of loops is a critical aspect of protein comparative (homology) modeling. Despite considerable advances in developing loop prediction algorithms, refining loops in homology models remains challenging. In this work, we use antibodies as a model system to investigate strategies for more robustly predicting loop conformations when the protein model contains errors in the conformations of side chains and protein backbone surrounding the loop in question. Specifically, our test system consists of partial models of antibodies in which the “scaffold” (i.e., the portion other than the complementarity determining region, CDR, loops) retains native backbone conformation, whereas the CDR loops are predicted using a combination of knowledge‐based modeling (H1, H2, L1, L2, and L3) and ab initio loop prediction (H3). H3 is the most variable of the CDRs. Using a previously published method, a test set of 10 shorter H3 loops (5–7 residues) are predicted to an average backbone (N? Cα? C? O) RMSD of 2.7 Å while 11 longer loops (8–9 residues) are predicted to 5.1 Å, thus recapitulating the difficulties in refining loops in models. By contrast, in control calculations predicting the same loops in crystal structures, the same method reconstructs the loops to an average of 0.5 and 1.4 Å for the shorter and longer loops, respectively. We modify the loop prediction method to improve the ability to sample near‐native loop conformations in the models, primarily by reducing the sensitivity of the sampling to the loop surroundings, and allowing the other CDR loops to optimize with the H3 loop. The new method improves the average accuracy significantly to 1.3 Å RMSD and 3.1 Å RMSD for the shorter and longer loops, respectively. Finally, we present results predicting 8–10 residue loops within complete comparative models of five nonantibody proteins. While anecdotal, these mixed, full‐model results suggest our approach is a promising step toward more accurately predicting loops in homology models. Furthermore, while significant challenges remain, our method is a potentially useful tool for predicting antibody structures based on a known Fv scaffold. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Timeline: Neurospora: a model of model microbes

In the 1940s, studies with Neurospora pioneered the use of microorganisms in genetic analysis and provided the foundations for biochemical genetics and molecular biology. What has happened since this orange mould was used to show that genes control metabolic reactions? How did it come to be the fungal counterpart of Drosophila? We describe its continued use during the heyday of research with Escherichia coli and yeast, and its emergence as a biological model for higher fungi.     

Tests and model selection for the general growth curve model

The model considered here is a generalized multivariate analysis of variance model useful especially for many types of growth curve problems including biological growth and technology substitution. It is defined as Yp x N = Xp x m tau m x r Ar x N + epsilon p x N, where tau is unknown, and X and A are known design matrices of ranks m less than p and r less than N, respectively. Furthermore, the columns of epsilon are independent p-variate normal with mean vector 0 and common covariance matrix sigma. In general, p is the number of time (or spatial) points observed on each of the N cases, (m - 1) is the degree of polynomial in time, and r is the number of groups. The main focus of this paper is the selection of models for the general growth curve model with regard to the covariance matrix sigma. Likelihood ratio tests and selection procedures based on sample reuse and predictions are proposed. Special emphasis is on the serial covariance structure for sigma, which has been shown to be quite important in the prediction of biological data and technology substitution data. One-population and K-population problems are considered. Some of the results are illustrated with two sets of biological data.     

Predicting climate-induced range shifts: model differences and model reliability

Predicted changes in the global climate are likely to cause large shifts in the geographic ranges of many plant and animal species. To date, predictions of future range shifts have relied on a variety of modeling approaches with different levels of model accuracy. Using a common data set, we investigated the potential implications of alternative modeling approaches for conclusions about future range shifts and extinctions. Our common data set entailed the current ranges of 100 randomly selected mammal species found in the western hemisphere. Using these range maps, we compared six methods for modeling predicted future ranges. Predicted future distributions differed markedly across the alternative modeling approaches, which in turn resulted in estimates of extinction rates that ranged between 0% and 7%, depending on which model was used. Random forest predictors, a model‐averaging approach, consistently outperformed the other techniques (correctly predicting >99% of current absences and 86% of current presences). We conclude that the types of models used in a study can have dramatic effects on predicted range shifts and extinction rates; and that model‐averaging approaches appear to have the greatest potential for predicting range shifts in the face of climate change.     

Forecasting with the age-period-cohort model and the extended chain-ladder model

We consider forecasting from age-period-cohort models, as wellas from the extended chain-ladder model. The parameters of thesemodels are known only to be identified up to linear trends.Forecasts from such models may therefore depend on arbitrarylinear trends. A condition for invariant forecasts is proposed.A number of standard forecast models are analysed.     

The Freter model: A simple model of biofilm formation

A simple, conceptual model of biofilm formation, due to R. Freter et al. (1983), is studied analytically and numerically in both CSTR and PFR. Two steady state regimes are identified, namely, the complete washout of the microbes from the reactor and the successful colonization of both the wall and bulk fluid. One of these is stable for any particular set of parameter values and sharp and explicit conditions are given for the stability of each. The effects of adding an anti-microbial agent to the CSTR are examined.Supported by NSF Grant DMS 0107439 and UTA Grant REP 14748717Supported by NSF Grant DMS 0107160     

Reducing model complexity of the general Markov model of evolution

The selection of an optimal model for data analysis is an important component of model-based molecular phylogenetic studies. Owing to the large number of Markov models that can be used for data analysis, model selection is a combinatorial problem that cannot be solved by performing an exhaustive search of all possible models. Currently, model selection is based on a small subset of the available Markov models, namely those that assume the evolutionary process to be globally stationary, reversible, and homogeneous. This forces the optimal model to be time reversible even though the actual data may not satisfy these assumptions. This problem can be alleviated by including more complex models during the model selection. We present a novel heuristic that evaluates a small fraction of these complex models and identifies the optimal model.     

Statistical model building and model criticism for human circadian data

Mathematical models have played an important role in the analysis of circadian systems. The models include simulation of differential equation systems to assess the dynamic properties of a circadian system and the use of statistical models, primarily harmonic regression methods, to assess the static properties of the system. The dynamical behaviors characterized by the simulation studies are the response of the circadian pacemaker to light, its rate of decay to its limit cycle, and its response to the rest-activity cycle. The static properties are phase, amplitude, and period of the intrinsic oscillator. Formal statistical methods are not routinely employed in simulation studies, and therefore the uncertainty in inferences based on the differential equation models and their sensitivity to model specification and parameter estimation error cannot be evaluated. The harmonic regression models allow formal statistical analysis of static but not dynamical features of the circadian pacemaker. The authors present a paradigm for analyzing circadian data based on the Box iterative scheme for statistical model building. The paradigm unifies the differential equation-based simulations (direct problem) and the model fitting approach using harmonic regression techniques (inverse problem) under a single schema. The framework is illustrated with the analysis of a core-temperature data series collected under a forced desynchrony protocol. The Box iterative paradigm provides a framework for systematically constructing and analyzing models of circadian data.     

Probability screening model

A comparative analysis is given of various types of systems of selecting biologically active substances. A theoretical probability model of tests on chemical compounds for biological activity (screening) has been constructed which permits an evaluation of the efficacy of screening on the basis of fairly reasonable assumptions. It has been shown that this efficacy decreases in time with a fixed number of types of activity taken into consideration and rises sharply with an increase in the number of types of activity of chemical compounds taken into account in the tests.     

The UTCI-clothing model

The Universal Thermal Climate Index (UTCI) was conceived as a thermal index covering the whole climate range from heat to cold. This would be impossible without considering clothing as the interface between the person (here, the physiological model of thermoregulation) and the environment. It was decided to develop a clothing model for this application in which the following three factors were considered: (1) typical dressing behaviour in different temperatures, as observed in the field, resulting in a model of the distribution of clothing over the different body segments in relation to the ambient temperature, (2) the changes in clothing insulation and vapour resistance caused by wind and body movement, and (3) the change in wind speed in relation to the height above ground. The outcome was a clothing model that defines in detail the effective clothing insulation and vapour resistance for each of the thermo-physiological model’s body segments over a wide range of climatic conditions. This paper details this model’s conception and documents its definitions.     

Wagner's canalization model

Wagner (1996, Does evolutionary plasticity evolve? Evolution 50, 1008-1023.) and Siegal and Bergman, 2002 and Azevedo et al., 2006 have studied a simple model of the evolution of a network of N genes, in order to explain the observed phenomenon that systems evolve to be robust. These authors primarily considered the case N=10 and used simulations to reach their conclusions. Here we investigate this model in more detail, considering systems of different sizes with and without recombination, and with selection for convergence instead of to a specified limit. For the simpler evolutionary model lacking recombination, we analyze the system as a neutral network. This allows us to describe the equilibrium distribution networks within genotype space. Our results show that, given a sufficiently large population size, the qualitative observation that systems evolve to be robust, is itself robust, as it does not depend on the details of the model. In simple terms, robust systems have more viable offspring, so the evolution of robustness is merely selection for increased fecundity, an observation that is well known in the theory of neutral networks.