A framework for models of biological behaviour

Modelling is most clearly understood as a adjunct in the process of deriving predictions from hypotheses. By representing a hypothesised mechanism in a model we hope by manipulating the model to understand the hypotheses' consequences. Eight dimensions on which models of biological behaviour can vary are described: the degree of realism with which they apply to biology; the level of biology they represent; the generality or range of systems the model is supposed to cover; the abstraction or amount of biological detail represented; the accuracy of representation of the mechanisms; the medium in which the model is built; the match of the model behaviour to biological behaviour; and the utility of the model in providing biological understanding and/or technical insight. It is hoped this framework will help to clarify debates over different approaches to modelling, particularly by pointing out how the above dimensions are relatively independent and should not be conflated.     

Models in biology: form and function

The relationships between physical and biological sciences are important in science education. This is shown in the links between the structure of biological science and the use of models. Although the physical sciences contain many principles of wide application, much of biology consists of very distinct examples. When these examples are used as models of organisms or processes, misunderstanding can occur if the characteristics of the model are used to make inaccurate generalizations. In biological education, stress on the importance of unique features must continually accompany the demonstration of similarities.

Theoretical models are constructed and reconstructed by students learning science, particularly in relation to broadly applicable principles. In biology a student may build a theoretical model of a subject which is itself a model used as an example. Distinct features of biological science may influence a variety of learning situations including problem solving.     

Stochastic Collective Movement of Cells and Fingering Morphology: No Maverick Cells

The classical approach to model collective biological cell movement is through coupled nonlinear reaction-diffusion equations for biological cells and diffusive chemicals that interact with the biological cells. This approach takes into account the diffusion of cells, proliferation, death of cells, and chemotaxis. Whereas the classical approach has many advantages, it fails to consider many factors that affect multicell movement. In this work, a multiscale approach, the Glazier-Graner-Hogeweg model, is used. This model is implemented for biological cells coupled with the finite element method for a diffusive chemical. The Glazier-Graner-Hogeweg model takes the biological cell state as discrete and allows it to include cohesive forces between biological cells, deformation of cells, following the path of a single cell, and stochastic behavior of the cells. Where the continuity of the tissue at the epidermis is violated, biological cells regenerate skin to heal the wound. We assume that the cells secrete a diffusive chemical when they feel a wounded region and that the cells are attracted by the chemical they release (chemotaxis). Under certain parameters, the front encounters a fingering morphology, and two fronts progressing against each other are attracted and correlated. Cell flow exhibits interesting patterns, and a drift effect on the chemical may influence the cells' motion. The effects of a polarized substrate are also discussed.     

A simple criterion for successful biological control on annual crops

Population dynamics of pest insect-natural enemy systems on annual crops is quite different from those seen in classic biological control programes. On an annual crop, for example, the persistence of populations of pest insects is forced to terminate when crops are harvested. Pest control on annual crops aims to suppress the maximum density of the pest below a certain level, and a low level equilibrium is not always the aim. It is important to determine the initial impact just after release of a natural enemy in order to determine the success of a biological control program. Therefore, effectiveness of natural enemies should be evaluated by prediction of such short-term population dynamics. This paper presents a new and simple analytical model for successful biological control on annual crops. A criterion of successful biological control is given as the ratio of the pest and natural enemy populations just when the pest begins to decrease. This ratio is derived from the intrinsic rates of natural increase of both populations and the daily total predation by natural enemies. Using this model, criteria on appropriate number and time of release of natural enemies are obtained. The practical applications of this model are discussed with respect to evaluating the success or failure of natural enemy releases in future biological control programs.     

Stochastic models for X chromosome inactivation

Summary A multivariate Gaussian model for mammalian development is presented with the associated biological and mathematical assumptions. Many biological investigations use the female mammal X chromosome to test hypotheses and to estimate parameters of the developmental system. In particular, Lyon's (1961) hypotheses are used as a basis of the mathematical model. Experimental mouse data and three sets of human experimental data are analyzed using the hypothesized Gaussian model. The estimated biological parameters are consistent with some current biological theories.     

A more efficient search strategy for aging genes based on connectivity

MOTIVATION: Many aging genes have been found from unbiased screens in model organisms. Genetic interventions promoting longevity are usually quantitative, while in many other biological fields (e.g. development) null mutations alone have been very informative. Therefore, in the case of aging the task is larger and the need for a more efficient genetic search strategy is especially strong. RESULTS: The topology of genetic and metabolic networks is organized according to a scale-free distribution, in which hubs with large numbers of links are present. We have developed a computational model of aging genes as the hubs of biological networks. The computational model shows that, after generalized damage, the function of a network with scale-free topology can be significantly restored by a limited intervention on the hubs. Analyses of data on aging genes and biological networks support the applicability of the model to biological aging. The model also might explain several of the properties of aging genes, including the high degree of conservation across different species. The model suggests that aging genes tend to have a higher number of connections and therefore supports a strategy, based on connectivity, for prioritizing what might otherwise be a random search for aging genes.     

Neural system modeling and simulation using Hybrid Functional Petri Net

The Petri net formalism has been proved to be powerful in biological modeling. It not only boasts of a most intuitive graphical presentation but also combines the methods of classical systems biology with the discrete modeling technique. Hybrid Functional Petri Net (HFPN) was proposed specially for biological system modeling. An array of well-constructed biological models using HFPN yielded very interesting results. In this paper, we propose a method to represent neural system behavior, where biochemistry and electrical chemistry are both included using the Petri net formalism. We built a model for the adrenergic system using HFPN and employed quantitative analysis. Our simulation results match the biological data well, showing that the model is very effective. Predictions made on our model further manifest the modeling power of HFPN and improve the understanding of the adrenergic system. The file of our model and more results with their analysis are available in our supplementary material.     

The biological age of the respiratory system]

A model of the biological age of the respiratory system is described. The following biological age determinants are used: vital lung capacity, maximal breathing capacity, mid-expiratory flow rate, oxygen consumption. They commonly meet the requirements of the biological age measurement tests as well as reflect main symptoms of the respiratory system ageing. The proposed model has been used to study the peculiarities of the respiratory system ageing in the Abkhasian population and to assess the effect of smoking on this process.     

Branching,blending, and the evolution of cultural similarities and differences among human populations

It has been claimed that blending processes such as trade and exchange have always been more important in the evolution of cultural similarities and differences among human populations than the branching process of population fissioning. In this paper, we report the results of a novel comparative study designed to shed light on this claim. We fitted the bifurcating tree model that biologists use to represent the relationships of species to 21 biological data sets that have been used to reconstruct the relationships of species and/or higher level taxa and to 21 cultural data sets. We then compared the average fit between the biological data sets and the model with the average fit between the cultural data sets and the model. Given that the biological data sets can be confidently assumed to have been structured by speciation, which is a branching process, our assumption was that, if cultural evolution is dominated by blending processes, the fit between the bifurcating tree model and the cultural data sets should be significantly worse than the fit between the bifurcating tree model and the biological data sets. Conversely, if cultural evolution is dominated by branching processes, the fit between the bifurcating tree model and the cultural data sets should be no worse than the fit between the bifurcating tree model and the biological data sets. We found that the average fit between the cultural data sets and the bifurcating tree model was not significantly different from the fit between the biological data sets and the bifurcating tree model. This indicates that the cultural data sets are not less tree-like than are the biological data sets. As such, our analysis does not support the suggestion that blending processes have always been more important than branching processes in cultural evolution. We conclude from this that, rather than deciding how cultural evolution has proceeded a priori, researchers need to ascertain which model or combination of models is relevant in a particular case and why.     

Model for the positional differentiation of the cap in Acetabularia.

A late stage during the biological cycle of the unicellular alga Acetabularia is the differentiation of a cap at the apical end of the stalk. A minimal model of the spatio-temporal regulation of this event is proposed on the basis of biological data available and current hypotheses. This involves the interaction between a diffusing inhibitor specific to the translation of cap mRNAs and a graded distribution of these messengers. The model accounts for delayed protein synthesis which occurs preferably at the apex and is likely to initiate the formation of the cap. The biological and theoretical implications are discussed.     

Varieties of mutualistic interaction in population models

A Lotka-Volterra model of mutalism indicates eight possible cases, of which two lead to survival of both populations, two indicate inevitable extinction, and four are indeterminate, the result depending on the initial population sizes. Conventional neighborhood stability analysis is a poor indicator of the biological result expected. Modification of the Lotka-Volterra model to give non-linear isoclines is necessary to obtain a minimum of biological realism; this modified model is illustrated with an analysis of a legume-Rhizobium mutualism.     

1H NMR-based metabolic profiling reveals inherent biological variation in yeast and nematode model systems

The application of metabolomics to human and animal model systems is poised to provide great insight into our understanding of disease etiology and the metabolic changes that are associated with these conditions. However, metabolomic studies have also revealed that there is significant, inherent biological variation in human samples and even in samples from animal model systems where the animals are housed under carefully controlled conditions. This inherent biological variability is an important consideration for all metabolomics analyses. In this study, we examined the biological variation in (1)H NMR-based metabolic profiling of two model systems, the yeast Saccharomyces cerevisiae and the nematode Caenorhabditis elegans. Using relative standard deviations (RSD) as a measure of variability, our results reveal that both model systems have significant amounts of biological variation. The C. elegans metabolome possesses greater metabolic variance with average RSD values of 29 and 39%, depending on the food source that was used. The S. cerevisiae exometabolome RSD values ranged from 8% to 12% for the four strains examined. We also determined whether biological variation occurs between pairs of phenotypically identical yeast strains. Multivariate statistical analysis allowed us to discriminate between pair members based on their metabolic phenotypes. Our results highlight the variability of the metabolome that exists even for less complex model systems cultured under defined conditions. We also highlight the efficacy of metabolic profiling for defining these subtle metabolic alterations.     

The impact of flucycloxuron on eggs weight kinetic and hematological parameters of chicken (Gallus domesticus)

The struggle against the harmful bugs of culture is intensified, and several products are appeared every year without the knowledge how to control their effects on environment and especially on being life. The introduced chemical products in nature are generally, the synthesis products witch are the pesticides. Our study consist the impact mechanism of a pesticides (FCX) on other biological model than harmful bugs, this biological model is a vertebrate model witch is the domestic chicken eggs (Gaollus domesticus). The toxicity of Flucycloxuron reviewed across the eggs weight kinetic accompanied with embryonic hematological parameters, in ovo and after hatching. The tested concentrations of pesticide are 1, 10 and 20 microg/egg injected at first day of incubation. Eggs treatment by three concentrations of pesticides, disturbs the studied parameters, where we observe that the pesticide inhibit the nutriment transformation, translated by eggs decreased weight kinetic according to the control, also the FCX affect the shell weight and cause the alteration of shell integrity. Hematological parameters show a clear impact of the pesticide at the lowest concentration (1 microg/egg). The obtained results confirm that the chosen biological model is good bio-indicator for eventual pollution and they are not far from pesticides toxicity.     

生物网络研究进展述评

生物网络是一类典型的复杂适应性系统,包含了许多个体的多层次的各种相互作用和关系,在过去的十年里,利用复杂网络理论对生物网络进行研究引起了人们的注意并获得了快速发展.本文首先从从度分布、聚类系数及鲁棒性等角度对现阶段生物网络性质的研究进行了简要介绍,后进一步对生物网络的聚类算法及主要建模理论做出了概括.今后的研究趋势在于如何建立合理的生物网络模型,以深入研究生物网络的各种性质.     

Interpreting the evolutionary regression: the interplay between observational and biological errors in phylogenetic comparative studies

Regressions of biological variables across species are rarely perfect. Usually, there are residual deviations from the estimated model relationship, and such deviations commonly show a pattern of phylogenetic correlations indicating that they have biological causes. We discuss the origins and effects of phylogenetically correlated biological variation in regression studies. In particular, we discuss the interplay of biological deviations with deviations due to observational or measurement errors, which are also important in comparative studies based on estimated species means. We show how bias in estimated evolutionary regressions can arise from several sources, including phylogenetic inertia and either observational or biological error in the predictor variables. We show how all these biases can be estimated and corrected for in the presence of phylogenetic correlations. We present general formulas for incorporating measurement error in linear models with correlated data. We also show how alternative regression models, such as major axis and reduced major axis regression, which are often recommended when there is error in predictor variables, are strongly biased when there is biological variation in any part of the model. We argue that such methods should never be used to estimate evolutionary or allometric regression slopes.     

Clarification and application of an ion parametric resonance model for magnetic field interactions with biological systems

Theoretical models proposed to date have been unable to clearly predict biological results from exposure to low-intensity electric and magnetic fields (EMF). Recently a predictive ionic resonance model was proposed by Lednev, based on an earlier atomic spectroscopy theory described by Podgoretskii and Podgoretskii and Khrustalev. The ion parametric resonance (IPR) model developed in this paper corrects mathematical errors in the earlier Lednev model and extends that model to give explicit predictions of biological responses to parallel AC and DC magnetic fields caused by field-induced changes in combinations of ions within the biological system. Distinct response forms predicted by the IPR model depend explicitly on the experimentally controlled variables: magnetic flux densities of the AC and DC magnetic fields (B_ac and B_dc, respectively); AC frequency (f_ac); and, implicitly, charge to mass ratio of target ions. After clarifying the IPR model and extending it to combinations of different resonant ions, this paper proposes a basic set of experiments to test the IPR model directly which do not rely on the choice of a particular specimen or endpoint. While the fundamental bases of the model are supported by a variety of other studies, the IPR model is necessarily heuristic when applied to biological systems, because it is based on the premise that the magnitude and form of magnetic field interactions with unhydrated resonant ions in critical biological structures alter ion-associated biological activities that may in turn be correlated with observable effects in living systems. © 1994 Wiley-Liss, Inc.     

Variance-based sensitivity analysis of biological uncertainties in carbon ion therapy

PurposeBiological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2) are needed for treatment planning and plan evaluation in carbon ion therapy. We present a model-independent, Monte Carlo based sensitivity analysis (SA) approach to quantify the impact of different uncertainties on the biological models.Methods and materialsThe Monte Carlo based SA is used for the evaluation of variations in biological parameters. The key property of this SA is the high number of simulation runs, each with randomized input parameters, allowing for a statistical variance-based ranking of the input variations. The potential of this SA is shown in a simplified one-dimensional treatment plan optimization. Physical properties of carbon ion beams (e.g. fragmentation) are simulated using the Monte Carlo code FLUKA. To estimate biological effects of ion beams compared to X-rays, we use the Local Effect Model (LEM) in the framework of the linear-quadratic (LQ) model. Currently, only uncertainties in the output of the biological models are taken into account.Results/conclusionsThe presented SA is suitable for evaluation of the impact of variations in biological parameters. Major advantages are the possibility to access and display the sensitivity of the evaluated quantity on several parameter variations at the same time. Main challenges for later use in three-dimensional treatment plan evaluation are computational time and memory usage. The presented SA can be performed with any analytical or numerical function and hence be applied to any biological model used in carbon ion therapy.     

Parameter Estimation and Model Selection in Computational Biology

A central challenge in computational modeling of biological systems is the determination of the model parameters. Typically, only a fraction of the parameters (such as kinetic rate constants) are experimentally measured, while the rest are often fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The measurements, which can come from immunoblotting assays, fluorescent markers, etc., tend to be very noisy and taken at a limited number of time points. In this work we present a new approach to the problem of parameter selection of biological models. We show how one can use a dynamic recursive estimator, known as extended Kalman filter, to arrive at estimates of the model parameters. The proposed method follows. First, we use a variation of the Kalman filter that is particularly well suited to biological applications to obtain a first guess for the unknown parameters. Secondly, we employ an a posteriori identifiability test to check the reliability of the estimates. Finally, we solve an optimization problem to refine the first guess in case it should not be accurate enough. The final estimates are guaranteed to be statistically consistent with the measurements. Furthermore, we show how the same tools can be used to discriminate among alternate models of the same biological process. We demonstrate these ideas by applying our methods to two examples, namely a model of the heat shock response in E. coli, and a model of a synthetic gene regulation system. The methods presented are quite general and may be applied to a wide class of biological systems where noisy measurements are used for parameter estimation or model selection.     

Melanoblast proliferation dynamics during mouse embryonic development. Modeling and validation

In this paper, we are looking for mathematical modeling of mouse embryonic melanoblast proliferation dynamics, taking into account, the expression level of β‐catenin. This protein plays an important role into the whole signal pathway process. Different assumptions on some unobservable features lead to different candidate models. From real data measured, from biological experiments and from a priori biological knowledge, it was able to validate or invalidate some of the candidate models. Data assimilation and parameter identification allowed us to derive a mathematical model that is in very good agreement with biological data. As a result, the produced model can give tracks for biologists into their biological investigations and experimental evidence. Another interest is the use of this model for robust hidden parameter identification like double times or number of founder melanoblasts.