Identifying Optimal Models to Represent Biochemical Systems

Biochemical systems involving a high number of components with intricate interactions often lead to complex models containing a large number of parameters. Although a large model could describe in detail the mechanisms that underlie the system, its very large size may hinder us in understanding the key elements of the system. Also in terms of parameter identification, large models are often problematic. Therefore, a reduced model may be preferred to represent the system. Yet, in order to efficaciously replace the large model, the reduced model should have the same ability as the large model to produce reliable predictions for a broad set of testable experimental conditions. We present a novel method to extract an “optimal” reduced model from a large model to represent biochemical systems by combining a reduction method and a model discrimination method. The former assures that the reduced model contains only those components that are important to produce the dynamics observed in given experiments, whereas the latter ensures that the reduced model gives a good prediction for any feasible experimental conditions that are relevant to answer questions at hand. These two techniques are applied iteratively. The method reveals the biological core of a model mathematically, indicating the processes that are likely to be responsible for certain behavior. We demonstrate the algorithm on two realistic model examples. We show that in both cases the core is substantially smaller than the full model.     

Analysis and Simulation of Division- and Label-Structured Population Models

In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models only consider the size of the overall populations, others take division numbers and labeling of the cells into account. In this work, we present a modeling and computational framework for proliferating cell populations undergoing symmetric cell division, which incorporates both the discrete division number and continuous label dynamics. Thus, it allows for the consideration of division number-dependent parameters as well as the direct comparison of the model prediction with labeling experiments, e.g., performed with Carboxyfluorescein succinimidyl ester (CFSE), and can be shown to be a generalization of most existing models used to describe these data. We prove that under mild assumptions the resulting system of coupled partial differential equations (PDEs) can be decomposed into a system of ordinary differential equations (ODEs) and a set of decoupled PDEs, which drastically reduces the computational effort for simulating the model. Furthermore, the PDEs are solved analytically and the ODE system is truncated, which allows for the prediction of the label distribution of complex systems using a low-dimensional system of ODEs. In addition to modeling the label dynamics, we link the label-induced fluorescence to the measure fluorescence which includes autofluorescence. Furthermore, we provide an analytical approximation for the resulting numerically challenging convolution integral. This is illustrated by modeling and simulating a proliferating population with division number-dependent proliferation rate.     

Accelerating the Gillespie Exact Stochastic Simulation Algorithm Using Hybrid Parallel Execution on Graphics Processing Units

The Gillespie Stochastic Simulation Algorithm (GSSA) and its variants are cornerstone techniques to simulate reaction kinetics in situations where the concentration of the reactant is too low to allow deterministic techniques such as differential equations. The inherent limitations of the GSSA include the time required for executing a single run and the need for multiple runs for parameter sweep exercises due to the stochastic nature of the simulation. Even very efficient variants of GSSA are prohibitively expensive to compute and perform parameter sweeps. Here we present a novel variant of the exact GSSA that is amenable to acceleration by using graphics processing units (GPUs). We parallelize the execution of a single realization across threads in a warp (fine-grained parallelism). A warp is a collection of threads that are executed synchronously on a single multi-processor. Warps executing in parallel on different multi-processors (coarse-grained parallelism) simultaneously generate multiple trajectories. Novel data-structures and algorithms reduce memory traffic, which is the bottleneck in computing the GSSA. Our benchmarks show an 8×−120× performance gain over various state-of-the-art serial algorithms when simulating different types of models.     

Rule-Based Models of the Interplay between Genetic and Environmental Factors in Childhood Allergy

Both genetic and environmental factors are important for the development of allergic diseases. However, a detailed understanding of how such factors act together is lacking. To elucidate the interplay between genetic and environmental factors in allergic diseases, we used a novel bioinformatics approach that combines feature selection and machine learning. In two materials, PARSIFAL (a European cross-sectional study of 3113 children) and BAMSE (a Swedish birth-cohort including 2033 children), genetic variants as well as environmental and lifestyle factors were evaluated for their contribution to allergic phenotypes. Monte Carlo feature selection and rule based models were used to identify and rank rules describing how combinations of genetic and environmental factors affect the risk of allergic diseases. Novel interactions between genes were suggested and replicated, such as between ORMDL3 and RORA, where certain genotype combinations gave odds ratios for current asthma of 2.1 (95% CI 1.2-3.6) and 3.2 (95% CI 2.0-5.0) in the BAMSE and PARSIFAL children, respectively. Several combinations of environmental factors appeared to be important for the development of allergic disease in children. For example, use of baby formula and antibiotics early in life was associated with an odds ratio of 7.4 (95% CI 4.5-12.0) of developing asthma. Furthermore, genetic variants together with environmental factors seemed to play a role for allergic diseases, such as the use of antibiotics early in life and COL29A1 variants for asthma, and farm living and NPSR1 variants for allergic eczema. Overall, combinations of environmental and life style factors appeared more frequently in the models than combinations solely involving genes. In conclusion, a new bioinformatics approach is described for analyzing complex data, including extensive genetic and environmental information. Interactions identified with this approach could provide useful hints for further in-depth studies of etiological mechanisms and may also strengthen the basis for risk assessment and prevention.     

Fission Models of Population Variability

Most models in population genetics are models of allele frequency, making implicit or explicit assumptions of equilibrium or constant population size. In recent papers, we have attempted to develop more appropriate models for the analysis of rare variant data in South American Indian tribes; these are branching process models for the total number of replicates of a variant allele. The spatial distribution of a variant may convey information about its history and characteristics, and this paper extends previous models to take this factor into consideration. A model of fission into subdivisions is superimposed on the previous branching process, and variation between subdivisions is considered. The case where fission is nonrandom and the locations of like alleles are initially positively associated, as would happen were a tribal cluster or village to split on familial lines, is also analyzed. The statistics developed are applied to Yanomama Indian data on rare genetic variants. Due to insufficient time depth, no definitive new inferences can be drawn, but the analysis shows that this model provides results consistent with previous conclusions, and demonstrates the general type of question that may be answered by the approach taken here. In particular, striking confirmation of a higher-than-average growth rate, and hence smaller-than-previously-estimated age, is obtained for the Yan2 serum albumen variant.     

Two Models of Population Growth

Two simple models of the ecology of population growth are described: "exponential" growth with "r -selection," and "logistic" growth, with "K- selection." Various methods for estimating the parameters of these models are presented in detail, along with statistical methods of evaluation and comparison. Also briefly discussed are more complex models of population growth sometimes used by demographers and ecologists. The two simpler models of population growth are then applied, by way of illustration, to two episodes of population growth in protohistoric southwest Iran, dating from 4000–2350 B. C. Interpretation of the results and the implications for future research are then discussed . [population growth, statistical models, exponential growth, logistic growth, early Iran]     

Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model

In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.     

种群数学模型的基本性质

种群数学模型的建立有赖于对生物背景的各种似是而非的假设,然而,在建模过程中,这些假定常常容易得到不当的结合和表达,常常些关于生物背景的清晰而明确的假设被不适当地处理或者甚至被抛开,事实上,即使是某些赫赫有名的种群数学模型也难以完全避免这种缺陷,这一点在我们本文中提及并讨论,要使得所建立的模型在逻辑上可信正确。我们必须确保关于其背景的各种假设得到的始终如一和恰如其分的协调组合。本本文中,我们测试了由Arditi和Michalski在1996年提出的几条建模标准,对于斑块模型,我们在他们的基础上增加了一条模型。我们同时在单种群的其他特殊情形方面的建方面增列了一些重要的标准。按照Arditi和Mchalski的标准以及其他著名的生物建模假定,我们建立了一些有意义的三维捕食－食饵种群模型（比率依赖型）,我们还讨论了种群各种振动现象的建模。     

Robustness Analysis of Stochastic Biochemical Systems

We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.     

Population Genetic Models of Genomic Imprinting

The phenomenon of genomic imprinting has recently excited much interest among experimental biologists. The population genetic consequences of imprinting, however, have remained largely unexplored. Several population genetic models are presented and the following conclusions drawn: (i) systems with genomic imprinting need not behave similarly to otherwise identical systems without imprinting; (ii) nevertheless, many of the models investigated can be shown to be formally equivalent to models without imprinting; (iii) consequently, imprinting often cannot be discovered by following allele frequency changes or examining equilibrium values; (iv) the formal equivalences fail to preserve some well known properties. For example, for populations incorporating genomic imprinting, parameter values exist that cause these populations to behave like populations without imprinting, but with heterozygote advantage, even though no such advantage is present in these imprinting populations. We call this last phenomenon "pseudoheterosis." The imprinting systems that fail to be formally equivalent to nonimprinting systems are those in which males and females are not equivalent, i.e., two-sex viability systems and sex-chromosome inactivation.     

Dielectric Properties of Shape-Distributed Ellipsoidal Particle Systems

Plasmonics - The effective dielectric function of composites consisting of particles dispersed in isotropic or anisotropic media is affected by the composition, size, shape, and orientation of the...     

A Theoretical Graph Method for Search and Analysis of Critical Phenomena in Biochemical Systems. II. Kinetic Models of Biochemical Oscillators Including Two and Three Substances

Four kinetic models of hypothetical complex reactions containing minimal two-substance or three-substance oscillators were constructed on the basis of the graphical rules suggested in the preceding work. The kinetic models are thought to be a part of one of four general biochemical systems: 1) system of mutual protein phosphorylation/dephosphorylation; 2) autophosphorylation of multisubunit protein; 3) association/dissociation of proteins or protein-containing structures during protein–protein or protein–ligand interaction; and 4) two-substrate enzymatic reaction with substrate inhibition by one substrate. Graphical rules of oscillator association with surrounding medium were considered. The graphical criteria of the oscillation generator elimination and criteria of oscillation damping were obtained. Both damped and undamped oscillations of reaction components were obtained by numerical integration of the mathematical models of these reactions. The areas of changes of model parameters and variables, within which the oscillations exist, were found.     

一类总人口在变化的HIV/AIDS传播的动力学模型

建立了HIV/AIDS传播的具有常数移民和指数出生的SI型模型,其中易感人群按照有无不良行为被分为两组.分别对具双线性传染率和具标准传染率的模型讨论了其无病平衡点和地方病平衡点的存在性,并就某些重要的特殊情况进行了平衡点和稳定性的分析.     

The Balance-Scale Task Revisited: A Comparison of Statistical Models for Rule-Based and Information-Integration Theories of Proportional Reasoning

We propose and test three statistical models for the analysis of children’s responses to the balance scale task, a seminal task to study proportional reasoning. We use a latent class modelling approach to formulate a rule-based latent class model (RB LCM) following from a rule-based perspective on proportional reasoning and a new statistical model, the Weighted Sum Model, following from an information-integration approach. Moreover, a hybrid LCM using item covariates is proposed, combining aspects of both a rule-based and information-integration perspective. These models are applied to two different datasets, a standard paper-and-pencil test dataset (N = 779), and a dataset collected within an online learning environment that included direct feedback, time-pressure, and a reward system (N = 808). For the paper-and-pencil dataset the RB LCM resulted in the best fit, whereas for the online dataset the hybrid LCM provided the best fit. The standard paper-and-pencil dataset yielded more evidence for distinct solution rules than the online data set in which quantitative item characteristics are more prominent in determining responses. These results shed new light on the discussion on sequential rule-based and information-integration perspectives of cognitive development.     

On the Exact Measure of Disease Spread in Stochastic Epidemic Models

The basic reproduction number, R ₀, is probably the most important quantity in epidemiology. It is used to measure the transmission potential during the initial phase of an epidemic. In this paper, we are specifically concerned with the quantification of the spread of a disease modeled by a Markov chain. Due to the occurrence of repeated contacts taking place between a typical infective individual and other individuals already infected before, R ₀ overestimates the average number of secondary infections. We present two alternative measures, namely, the exact reproduction number, R _e0, and the population transmission number, R _p , that overcome this difficulty and provide valuable insight. The applicability of R _e0 and R _p to control of disease spread is also examined.     

Advances in Nano Biotic/Abiotic Hybrid Systems: Protein-Based Engineered Devices

Integrative nanobiotechnology utilizes natural ideas and materials for manufacturing nanoscale devices. As living organisms traditionally represent a good model for engineers to learn from, biological components of interest, with optimal functionality, have been used in the creation of biotic/abiotic hybrid devices. As an example, bacteriorhodopsin/F₀F₁-ATP-synthase-incorporated polymer vesicles provide a model of hybrid protein/artificial synthetic membrane system to perform biological functions. Some potential applications are the construction of intervesicular/intravesicular communications, such as excitable vesicles (EVs), for biocomputer and biomolecular motor-powered nanoelectromechanical systems (NEMS) for nanomedicine. Finally, advanced biotic/abiotic hybrid technology is expected to provide an alternative method to conventional fabrication technology to meet the increasing demands by saving enormous engineering efforts.     

Stimulus-dependent Maximum Entropy Models of Neural Population Codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.     

Asymptotic Distribution of Density-Dependent Stage-Grouped Population Dynamics Models

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions of matrix models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana.