A simple model of radiation action in cells based on a repair saturation mechanism.

This paper describes a new theoretical model for the response of cells to radiation. This model is based on the existence of a lesion interaction mechanism in the cell, along with processes of recovery and repair that are able to repair the damage produced by radiation in the cells. Such a mechanism makes the cells evolve from a sublethal state to a normal one. Repair and recovery are not instantaneous, but are produced over an average period that we suppose is represented by an exponential function. The probability of cellular recovery and repair is also affected by radiation. These mechanisms become less probable as the dose administered to the cell increases (repair saturation mechanism). This model is suitable for instantaneous doses as well as for arbitrary dose rates. Results obtained from the model for normal tissues and low doses are approximately equal to those obtained by the linear-quadratic model or by the incomplete repair model. The model yields a survival curve with an exponential tail for high doses and for long periods of irradiation.     

Does a reduction in the price of rhino horn prevent poaching?

Rhino poaching around the world has increased inordinately, to the extent that concerns exist over the possible survival of the species. An open access rhino poaching model is developed for South African rhino. The model is a hybrid dynamical model, as both a system dynamics model as well as a Bayesian network model are developed. The system dynamics model is used to estimate the unknown parameter values (through optimisation) and also to determine the intervals for the parameters. These intervals are then used in the Bayesian Belief Network model to assess uncertainty. Hybrid approaches improve the ability to validate models compared with conventional modelling. The resultant model indicates that reducing the price of rhino horn would not be effective at curbing poaching, unless poacher costs are also increased. However, increasing poacher costs is not a realistic policy option since these costs are largely beyond the control of decision-makers. The insensitivity of price to poaching effort has implications for methods proposed to reduce the value of rhinos, such as introducing synthetic rhino horn and the de-horning of rhinos.     

A mathematical model and computer simulation study of insulin receptor regulation

A homeomorphic mathematical model of cell surface insulin receptor regulation is developed. The overall structure of the model is based on molecular mechanisms suggested by in vivo and in vitro experimental evidence from many different cell types. Model parameters correspond to cellular processes which are constrained by known boundry value conditions. As an example, computer simulation results are compared with published data from BC3H-1 myocytes in culture. With appropriate parameter choice, this model is able to simulate data from other cell types. Cellular processes which are explicitly represented in the model include: bound and unbound receptor endocytosis, receptor recycling, intracellular receptor degradation, and state-dependent receptor synthesis. Most of these processes are represented as first-order events. Using more complex representations of the model structure with higher order rate constants or saturable pathways does not qualitatively improve simulation results. Simulations are able to reproduce ligand-induced down and up regulation of receptors as well as the initial spontaneous display of surface insulin receptors. To demonstrate the behavior of our model and illustrate its utility for explaining insulin receptor regulation for a variety of conditions, simulations for which experimental data is unavailable for direct comparison are also shown. We believe the structure of our model is sufficient to explain insulin receptor regulation in a wide variety of cell types. In addition our model may aid in understanding the receptor component of insulin resistance (decreased sensitivity or responsiveness to insulin) seen in pathological states such as obesity and diabetes mellitus. Finally, this model may be applicable to the study of the regulation of other polypeptide hormone receptors.     

Generalized Binomial Regression Model

The generalized negative binomial distribution has been found useful in fitting over-dispersed as well as under-dispersed count data. We define and study the generalized binomial regression model which is used to predict a count response variable affected by one or more explanatory variables. The methods of maximum likelihood and moments are given for estimating the model parameters. Approximate tests for the adequacy of the model are considered. The generalized binomial regression model has been applied to two observed data sets to which binomial regression model was applied earlier.     

A data assimilation technique applied to a predator-prey model

A new approach for data assimilation, which is based on the adjoint method, but allows the computer code for the adjoint to be constructed directly from the model computer code, is described. This technique is straightforward and reduces the chance of introducing errors in the construction of the adjoint code. Implementation of the technique is illustrated by applying it to a simple predator-prey model in a model fitting mode. A series of identical twin numerical experiments are used to show that this data assimilation approach can successfully recover model parameters as well as initial conditions. However, the ease with which these values are recovered is dependent on the form of the model equations as well as on the type and amount of data that are available. Additional numerical experiments show that sufficient coefficient and parameter recoveries are possible even when the assimilated data contain significant random noise. Thus, for biological systems that can be described by ecosystem models, the adjoint method represents a powerful approach for estimating values for little-known biological parameters, such as initial conditions, growth rates, and mortality rates.     

The rice field eel as a model system for vertebrate sexual development

Complex developmental mechanisms of vertebrates are unraveled using comparative genomic approaches. Several teleosts, such as zebrafish, medaka and pufferfish, are used as genetic model systems because they are amenable to studies of gene function. The rice field eel, a freshwater fish, is emerging as a specific model system for studies of vertebrate sexual development because of its small genome size and naturally occurring sex reversal. Data presented here support the use of the rice field eel as another important fish model for comparative genome studies, especially in vertebrate sexual development. This model system is complementary rather than redundant.     

Modeling of halorhodopsin and rhodopsin based on bacteriorhodopsin

Bacteriorhodopsin (BR), halorhodopsin (HR), and rhodopsin (Rh) all belong to the class of seven-helix membrane proteins. For BR, a structural model at atomic resolution is available; for HR, diffraction data are available only down to a resolution of 6 Å in the membrane plane, and for Rh, down to 9 Å. BR and HR are closely related proteins with a sequence homology of 34%, while Rh does not share any sequence homology with BR. An atomic model for HR is derived that is based on sequence alignment and the atomic model for BR and is improved by molecular dynamics simulations. The model structure obtained accounts well for the experimentally observed difference between HR and BR in the projection map, where HR exhibits a higher density in the region between helices D and E. The reason for this difference lies partially in the different side chains and partially in slightly different helix tilts. The scattering amplitudes and phases of the model structure are calculated and agree with the experimental data down to a resolution of about 8 Å. If the helix positions are adopted from the projection map for HR and used as input in the model, this number improves to 7 Å. Analogously, an atomic model for Rh is derived based on the atomic model for BR and subjected to molecular dynamics simulations. Optimal agreement with the experimental projection map for Rh is obtained when the entire model structure is rotated slightly about two axes in the membrane plane. The agreement with the experimental projection map is not as satisfactory as for HR, but the results indicate that even for a nonhomologous, but structurally related, protein such as Rh, an acceptable model structure can be derived from the structure of BR. © 1996 Wiley-Liss, Inc.     

A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts

A phenomenological model for the evolution of shape transition of cells is considered. These transitions are determined by the emission of growth-factors, as well as mechanical interaction if cells are subjected to hard impingement. The originality of this model necessitates a formal treatment of the mathematical model, as well as the presentation of elementary cases in order to illustrate the consistence of the model. We will also show some small-scale relevant applications.     

A three plus three parameters mechanistic model for viral filtration

Viral filtration is an expensive regulatory requirement in downstream processing of monoclonal antibodies (mAbs). This process step is typically operated with an overdesigned filter in order to account for any batch to batch variability in the filter, as well as the feed characteristics. Here, we propose a simple, six‐parameter mechanistic model for viral filtration where three parameters are membrane‐specific while the other three depend on feed characteristics and membrane‐feed interactions. Viruses are considered as passive particles which are retained by the membrane on the basis of size exclusion. The model envisages that the viral filter contains two kind of pores: virus‐retentive, small‐sized pores and non‐retentive, large‐sized pores. The small‐sized pores get blocked during filtration resulting in decrease in active membrane area, while the large‐sized pores get constricted during filtration. The length of constricted part increases during filtration and contributes to increase in hydraulic resistance of the filter. Rate of these processes (blocking and constriction) are assumed to be proportional to the instantaneous rate of retention of the viral particles. The general nature of the model is validated with the experimental data on viral filtration for four different commercial membranes used in biotech industries as well as different model viruses. The proposed model has been demonstrated to describe the behavior of filters with very good accuracy. The best‐fit model parameter values indicate about the various phenomena that are responsible for differences in the behavior of the membranes as well as change in retention and flux with feed concentration. The proposed model can be used for improving design of virus filters as well as in appropriate sizing of the filters during processing. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1538–1547, 2017     

A unification of multivariate methods for meta-analysis of genetic association studies

Methods for multivariate meta-analysis of genetic association studies are reviewed, summarized and presented in a unified framework. Modifications of standard models are described in detail in order to be applied in genetic association studies. The model based on summary data is uniformly defined for both discrete and continuous outcomes and analytical expressions for the covariance of the two jointly modeled outcomes are derived for both cases. The models based on the binary nature of the data are fitted using both prospective and retrospective likelihood. Furthermore, formal tests for assessing the genetic model of inheritance are developed based on standard normal theory. The general model is compared to the recently proposed genetic model-free bivariate approach (either using summary or binary data), and it is clearly shown that the estimates provided by this approach are nearly identical to the estimates derived by the general bivariate model using the aforementioned tests for the genetic model. The methods developed here as well as the tests, are easily implemented in all major statistical packages, escaping the need of self written software. The methods are applied in several already published meta-analyses of genetic association studies (with both discrete and continuous outcomes) and the results are compared against the widely used univariate approach as well as against the genetic model free approaches. Illustrative examples of code in Stata are given in the appendix. It is anticipated that the methods developed in this work will be widely applied in the meta-analysis of genetic association studies.     

A Biomechanical Triphasic Approach to the Transport of Nondilute Solutions in Articular Cartilage

Biomechanical models for biological tissues such as articular cartilage generally contain an ideal, dilute solution assumption. In this article, a biomechanical triphasic model of cartilage is described that includes nondilute treatment of concentrated solutions such as those applied in vitrification of biological tissues. The chemical potential equations of the triphasic model are modified and the transport equations are adjusted for the volume fraction and frictional coefficients of the solutes that are not negligible in such solutions. Four transport parameters, i.e., water permeability, solute permeability, diffusion coefficient of solute in solvent within the cartilage, and the cartilage stiffness modulus, are defined as four degrees of freedom for the model. Water and solute transport in cartilage were simulated using the model and predictions of average concentration increase and cartilage weight were fit to experimental data to obtain the values of the four transport parameters. As far as we know, this is the first study to formulate the solvent and solute transport equations of nondilute solutions in the cartilage matrix. It is shown that the values obtained for the transport parameters are within the ranges reported in the available literature, which confirms the proposed model approach.     

Competing Risk Analysis of Censored Survival Data

A competing risk model is developed to accommodate both planned Type I censoring and random withdrawals. MLE's, their properties, confidence regions for parameters and mean lifetimes are obtained for a model regarding random censoring as a competing risk and compared to those obtained for the model in which withdrawals are regarded as random censoring. Estimated net and crude probabilities are calculated and compared for the two models. The model is developed for two competing risks, one following a Weibull distribution and the other a Rayleigh distribution, and random withdrawals following a Weibull distribution.     

A critical analysis of a left-handed double helix model for B-DNA fibers.

A search for a left-handed double helix model for B-DNA fibers has been undertaken. The model has to present good stereochemistry and also to be in agreement with X-ray and infrared data. Dihedral angles as well as atomic coordinates and calculated intensities curves are given for the best model obtained. Comparison with experimental results shows that this model must be rejected as a candidate for the representation of B-DNA fibers.     

Substitution Processes in Molecular Evolution. III. Deleterious Alleles

The substitution processes for various models of deleterious alleles are examined using computer simulations and mathematical analyses. Most of the work focuses on the house-of-cards model, which is a popular model of deleterious allele evolution. The rate of substitution is shown to be a concave function of the strength of selection as measured by α = 2Nσ, where N is the population size and σ is the standard deviation of fitness. For α<1, the house-of-cards model is essentially a neutral model; for α>4, the model ceases to evolve. The stagnation for large α may be understood by appealing to the theory of records. The house-of-cards model evolves to a state where the vast majority of all mutations are deleterious, but precisely one-half of those mutations that fix are deleterious (the other half are advantageous). Thus, the model is not a model of exclusively deleterious evolution as is frequently claimed. It is argued that there are no biologically reasonable models of molecular evolution where the vast majority of all substitutions are deleterious. Other models examined include the exponential and gamma shift models, the Hartl-Dykhuizen-Dean (HDD) model, and the optimum model. Of all those examined, only the optimum and HDD models appear to be reasonable candidates for silent evolution. None of the models are viewed as good candidates for protein evolution, as none are both biologically reasonable and exhibit the variability in substitutions commonly observed in protein sequence data.     

A frailty model for informative censoring

To account for the correlation between failure and censoring, we propose a new frailty model for clustered data. In this model, the risk to be censored is affected by the risk of failure. This model allows flexibility in the direction and degree of dependence between failure and censoring. It includes the traditional frailty model as a special case. It allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative. It can also analyze data for competing risks. To fit the model, the EM algorithm is used with Markov chain Monte Carlo simulations in the E-steps. Simulation studies and analysis of data for kidney disease patients are provided. Consequences of incorrectly assuming noninformative censoring are investigated.     

A statistical method for the analysis of nonlinear temperature time series from compost

Temperature is widely accepted as a critical indicator of aerobic microbial activity during composting but, to date, little effort has been made to devise an appropriate statistical approach for the analysis of temperature time series. Nonlinear, time-correlated effects have not previously been considered in the statistical analysis of temperature data from composting, despite their importance and the ubiquity of such features. A novel mathematical model is proposed here, based on a modified Gompertz function, which includes nonlinear, time-correlated effects. Methods are shown to estimate initial values for the model parameter. Algorithms in SAS are used to fit the model to different sets of temperature data from passively aerated compost. Methods are then shown for testing the goodness-of-fit of the model to data. Next, a method is described to determine, in a statistically rigorous manner, the significance of differences among the time-correlated characteristics of the datasets as described using the proposed model. An extra-sum-of-squares method was selected for this purpose. Finally, the model and methods are used to analyze a sample dataset and are shown to be useful tools for the statistical comparison of temperature data in composting.     

An SEIQR model for childhood diseases

It has been shown that the inclusion of an isolated class in the classical SIR model for childhood diseases can be responsible for self-sustained oscillations. Hence, the recurrent outbreaks of such diseases can be caused by autonomous, deterministic factors. We extend the model to include a latent class (i.e. individuals who are infected with the disease, but are not yet able to pass the disease to others) and study the resulting dynamics. The existence of Hopf bifurcations is shown for the model, as well as a homoclinic bifurcation for a perturbation to the model. For historical data on scarlet fever in England, our model agrees with the epidemiological data much more closely than the model without the latent class. For other childhood diseases, our model suggests that isolation is unlikely to be a major factor in sustained oscillations.      

Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe

We present a sex-structured model for heterosexual transmission of HIV/AIDS in a community. The model is formulated using integro-differential equations, which are shown to be equivalent to delay differential equations with a time delay due to incubation period. The sex-structured HIV/AIDS model divides the population into a two sex-structure consisting of females and males. The threshold and equilibria for the model are determined and stabilities are examined. We extend the model to focus on the effects of condom use as a single-strategy approach in HIV prevention in the absence of any treatment. Initially we model the use of male condoms and further extend the model to incorporate the use of both female and male condoms. The model includes two primary factors in condom use to control HIV that are condom efficacy and compliance. The exposure risk of infection after each intervention is obtained. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. The models are numerically analysed to assess the effectiveness of condom use on the transmission dynamics of HIV/AIDS using demographic and epidemiological parameters for Zimbabwe. The study demonstrates the use of sex-structured HIV/AIDS models in assessing the effectiveness of female and male condom use as a preventative strategy in a heterosexually active population. Z. Mukandavire would like to acknowledge financial support given by the National University of Science and Technology through a Staff Development Scholarship. The authors are grateful to Eagle Insurance Company of Zimbabwe for financial support.     

THE BETA-BINOMIAL MODEL: ACCOUNTING FOR INTER-TRIAL VARIATION IN REPLICATED DIFFERENCE AND PREFERENCE TESTS

Binomial tests are commonly used in sensory difference and preference testing under the assumptions that choices are independent and choice probabilities do not vary from trial to trial. This paper addresses violations of the latter assumption (often referred to as overdispersion) and accounts for variation in inter-trial choice probabilities following the Beta distribution. Such variation could arise as a result of differences in test substrate from trial to trial, differences in sensory acuity among subjects or the existence of latent preference segments. In fact, it is likely that overdispersion occurs ubiquitously in product testing. Using the Binomial model for data in which there is inter-trial variation may lead to seriously misleading conclusions from a sensory difference or preference test. A simulation study in this paper based on product testing experience showed that when using a Binomial model for overdispersed Binomial data, Type I error may be 0.44 for a Binomial test specification corresponding to a level of 0.05. Underestimation of Type I error using the Binomial model may seriously undermine legal claims of product superiority in situations where overdispersion occurs. The Beta-Binomial (BB) model, an extension of the Binomial distribution, was developed to fit overdispersed Binomial data. Procedures for estimating and testing the parameters as well as testing for goodness of fit are discussed. Procedures for determining sample size and for calculating estimate precision and test power based on the BB model are given. Numerical examples and simulation results are also given in the paper. The BB model should improve the validity of sensory difference and preference testing.