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.     

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.     

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.     

A model of the plant-to-plant movement of aphids I. Description of the model

The plant-to-plant movement of insects in one of the factors determining the distribution of individuals in insect populations. In this report the movement of barley aphids was analyzed by a statistical model. The model is represented as the convolution of three probability functions:

1. The probability that s individuals are found on a plant at time t₀:Q(s);
2. The probability that i individuals leave the plant and remain on the ground from time t₀ to t₁:_sC_ipⁱq^s−i and p+q=1, where p and q are the proportions of individuals which do not leave a plant and which leave it once or more, respectively;
3. The probability that j individuals climb a plant between time t₀ to t₁ and stay there at time t₁:e^−λλ^j/λ^!, where λ is the mean of the individuals.

The probability that l individuals are located on a plant at time t₁ is represented by the following equation It was shown by simple experiments that the experimental populations were well fitted to the model.     

Implicit solvent model estimates of the stability of model structures of the alamethicin channel

Alamethicin is a hydrophobic helical peptide of 20 residues, which oligomerizes to form ion-conducting channels in membranes. The behavior of an intact alamethicin channel in POPC bilayers was recently studied, using 2 ns molecular dynamics (MD) simulations of a model hexameric channel. These simulations produced numerous conformations of the channel. In the present study, we used 11 of these channel conformations and carried out continuum-solvent model calculations, similar to those used for the monomers in our previous studies, to investigate the energetics of the channel inside the lipid bilayer. Our results suggest that, out of the 11 channel conformations produced by the MD simulations, only four are stable inside the lipid bilayer, with water-to-membrane free energies of transfer ranging from ~–6 to ~–10 kcal/mol. Analysis of the results suggests two causes for the apparent instability of the remainder of the structures inside the lipid bilayer, both resulting from the desolvation of channel polar groups (i.e. their transfer from the aqueous phase into the bilayer). The first is specific, uncompensated backbone hydrogen bonds, which exist in the region of the channel exposed to the hydrocarbon of the lipid bilayer. The second is exposure of intra-pore water molecules to the surrounding lipid. Thus, the association of these structures with the membrane involves a large electrostatic desolvation free-energy penalty. The apparent conflict between continuum-solvent and MD calculations, and its significance for the interpretation of membrane proteins simulations, are discussed.     

Eggbox model of the alveoli

An attractive and informative visual aid for teaching about gaseous exchange     

Mutation-absorption model of the enzyme

Gradual changes in function of proteins in response to single changes in primary structure are often observed to occur and are a necessary condition for evolution by variation and natural selection at the protein level. A probabilistic (entropy theory_ analysis of the effect of changes in primary structure on three-dimensional shape and function shows that such gradualism is based on the presence of a control system in the molecule involving a definite general form of structure-function degeneracy. The assumptions of the analysis are that primary structure determines tertiary structure (or a thermal distribution of tertiary configurations and allosteric forms), tertiary structure determines function (characterized by rate and other parameters), and that certain features of tertiary structure may be specialized for particular functions. The main conclusion is that embodied in the molecule is a subsystem which serves as a buffer, absorbing mutation or other forms of genetic variation and expressing these as graceful variations in features of the shape critical for function. This buffer system may be realized by numerical redundancy of amino acids or other mechanisms which increase the redundancy of weak interactions responsible for folding, utilization of amino acids having a greater number of analogs with redundant features, or local and global structural formats which allow for more effective utilization of redundancy. The mutation-absorption model has implications for the interpretation of structure-function relations in biology, the topology of the adaptive landscape, the interpretation of isoenzymes and allozymes, the relationship between selection and neutralism in evolution, and the relation between the complexity of and energy required by biological systems and the effectiveness of evolutionary optimization.     

Tests of the heterosis model

Summary An alternative to the classical model of self-incompatibility indicates that genetic control of self-incompatibility could involve more than one locus and function through passive failure of incompatible pollen tubes rather than through their active inhibition. Both aspects of the alternative model have been tested and, in each case, the data support the classical single-locus oppositional interpretation rather than the alternative. On the basis of these data, and others now available, we conclude that, in the Solanaceae, and presumably also in some others, self-incompatibility is better explained by the classical interpretation. Several points, however, remain to be resolved.     

The relationship between the transition matrix model and the diffusion model

The diffusion equation model and the Lefkovitch matrix model have been employed independently in plant population ecology in order to analyze the dynamics of growth and size structure. The two models describe the dynamics of size structure in biological populations, and thus there must be some relationship between them. In the present paper, we examine the theoretical relationship between these two models. We demonstrate, on a certain assumption, that the one-step Lefkovitch matrix model corresponds to a difference equation of the diffusion equation and that the two- and three-step Lefkovitch matrix model correspond to difference equations of the 4th- and 6th-order Kramers-Moyal expansions, respectively. It is also shown that 2n moments (the first to the 2n-th moments) of growth rate are necessary and sufficient to rewrite uniquely the n-step Lefkovitch matrix model in terms of the linear combination of the moments. We finally discuss the relationship between the species characteristics of census data and the appropriate types of the Lefkovitch matrix.     

K-Na transport: the Brewer model replaces the active transport model

In the 1940's several experimental observations were made regarding the K+ and Na+ content of chilled and restored red blood cells. As a consequence, the concept of active transport was developed. Brewer, a physicist, developed a model for membrane transport based on the electrical properties of double bonds in the ground and excited states. Of particular importance is the membrane double bond P = O. This model was largely formulated from isotope concentration studies using mass spectroscopy, photospectrometry and the nature of malignant cells. In this study, it is shown that the Brewer model completely explains the experimental results which led to the concept of active transport. In addition, it also explains the results of some adjunct experiments.     

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.     

Three-dimensional model of the feline hindlimb

This article describes a three-dimensional musculoskeletal model of the feline hindlimb based on digitized musculoskeletal anatomy. The model consists of seven degrees of freedom: three at the hip and two each at the knee and ankle. Lines of action and via points for 32 major muscles of the limb are described. Interspecimen variability of muscle paths was surprisingly low; most via points displayed a scatter of only a few millimeters. Joint axes identified by mechanical techniques as noncoincident and nonorthogonal were further honed to yield moment arms consistent with previous reports. Interspecimen variability in joint axes was greater than that of muscle paths and highlights the importance of joint axes in kinematic models. The contribution of specific muscles to the direction of endpoint force generation is discussed.     

A mathematical model of the urethra

Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.     

Stationary states of the Hartline-Ratliff model

For the Hartline-Ratliff model the exact conditions for the uniqueness of the stationary state are determined. Also sufficient conditions for dynamic stability are derived.