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PubMed2005

On the origins of approximations for stochastic chemical kinetics.

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.

Algorithms↗
PubMed1997

Quantitative aspects of evaluating the consequences of pollution for parasite populations and communities.

The utility of parasites as indicators of environmental health depends upon scientists' ability to understand how environmental stress may cause changes in parasite populations and communities. Predicting the changes due to pollution calls for dynamic models and experimentally determined knowledge of the consequences of pollution on the parameters of the model. Through an interplay of modeling, laboratory experiments, and field comparisons scientists can develop a theory of pollution and parasites and perhaps use it to assess the impact of pollution. To develop a theoretical framework for the effects of pollution on host-parasite relationships will require an identification of the appropriate scale and a determination of whether the host and parasite populations should be treated as open and recruitment-driven or closed and reproduction-driven. A theory can then be developed using epidemiology models. Those models are divided into prevalence models that track the prevalence of infection and abundance models that track the number of parasites per host. Whether a deterministic model or a stochastic counterpart should be used depends upon the scale but generally a stochastic model will give a more realistic picture. Mimicking the variability inherent in natural systems is the goal of stochastic models. The models emphasize that field tests of their predictions can only be made by studies designed with extensive replication of samples from reference and stressed sites.

Animals↗
PubMed1996

Secondary-task effects on sequence learning.

With a repeated sequence of stimuli, performance in a serial reaction-time task improves more than with a random sequence. The difference has been taken as a measure of implicit sequence learning. Implicit sequence learning is impaired when a secondary task is added to the serial RT task. In the first experiment, secondary-task effects on different types of sequences were studied to test the hypothesis that the learning of unique sequences (where each sequence element has a unique relation to the following one) is not impaired by the secondary task, while the learning of ambiguous sequences is. The sequences were random up to a certain order of sequential dependencies, where they became deterministic. Contrary to the hypothesis, secondary-task effects on the learning of unique sequences were as strong or stronger than such effects on the learning of ambiguous sequences. In the second experiment a hybrid sequence (with unique as well as ambiguous transitions) was used with different secondary tasks. A visuo-spatial and a verbal memory task did not interfere with the learning of the sequence, but interference was observed with an auditory go/no-go task in which high- and low-pitched tones were presented after each manual response and a foot pedal had to be pressed in response to high-pitched tones. Thus, interference seems to be specific to certain secondary tasks and may be related to memory processes (but most likely not to visuo-spatial and verbal memory) or to the organizations of sequences, consistent with previous suggestions.

Adolescent↗
PubMed2005

Control of arterial branching morphogenesis in embryogenesis: go with the flow.

Formation of a properly branched vascular system during embryogenesis is crucial for embryo survival. Here we review the regulation of the morphogenesis of the arterial and venous system during embryogenesis. We show that in addition to deterministic patterning mechanisms and plasticity of endothelial cells, arterial-venous differentiation and branching morphogenesis involves a prominent role for blood flow. Based on in vivo observations of developing arteries, we identified a novel morphological event crucial for the morphogenesis of the arterial tree, disconnection of small side branches. This disconnection of side branches occurs exactly at the point of bifurcation. The rate of disconnection of side branches depends on flow velocity and branching angle. The balance between disconnection and maintenance of arterial side branches determines the number of side branches connected to a large artery. Based on these observations, we postulate that the number of pre-existing collaterals connected to a large artery is a function of the disconnection process and can be regulated by hemodynamics. We furthermore show that embryonic arteries already adapt their lumen diameter to the amount of flow carried. Taken together, we suggest that hemodynamics plays a pivotal role in shaping the arterial system. We suggest that flow-evoked remodeling processes determine the number of preexisting collaterals during critical periods of embryo-fetal development. Insight into these basic principles of arterial growth and branching during embryogenesis may aid to understanding the observed variability in the capacity to establish a collateral circulation in patients with ischemic diseases and finding new strategies for therapeutic arteriogenesis.

Animals↗
PubMed2004

Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: "quorum" sensing by a single bacterium.

Deterministic and stochastic models describing quorum sensing by Staphylococcus aureus within an endosome, and the subsequent escape via the production of virulence factors, are developed and analysed. Particular attention is given to a biologically-relevant asymptotic limit of the problem, for which the solutions, including the endosome escape time, can be explicitly characterised in terms of the model parameters.

Computer Simulation↗
PubMed1995

EEG predictability: adequacy of non-linear forecasting methods.

The predictive properties of EEG segments were analyzed. The sample included alpha, delta as well as spike and wave EEG activity recordings. Most of these segments are better described with non-linear autoregressive models, and a non-linear forecasting algorithm is routinely required. In terms of their predictive properties, segments can be divided into unpredictable, predictable and very predictable, these three groups being similarly represented among the alpha activity EEG segments. In EEG segments with alpha activity, poor predictability is associated with poor organization of the rhythmic pattern. Concerning dynamic properties, it was found that cyclic skeletons were highly represented among the very predictable segments, which reflect a contribution of the deterministic component of the autoregressive model to the predictability of the segments. Notable contributions of the noise component may explain the properties of unpredictable segments. These results point to a great diversity of predictive patterns among EEG recordings. Other factors besides the existence of chaotic dynamics must be regarded.

Algorithms↗
PubMed2001

Stochastic dynamic population model for northern corn rootworm (Coleoptera: Chrysomelidae).

A stochastic dynamic population model for the complete life cycle of northern corn rootworm, Diabrotica barberi Smith & Lawrence, is described. Adult population dynamics from emergence to oviposition are based on a published single-season model for which temperature-dependent development and age-dependent advancement determine adult population dynamics and oviposition. Randomly generated daily temperatures make this model component stochastic. Stochastic hatch is 50+/-8%. A stochastic nonlinear density-dependent larval survival model is estimated using field data from artificial infestation experiments. A regional model of corn phenology is estimated to incorporate the effect of dispersal on adult mortality. Random daily weather is generated using parameters for Brookings, SD. Model performance is evaluated with deterministic simulations, which show that the population converges to zero unless adult mortality is reduced by the availability of corn pollen from the regional model of corn phenology. Stochastic model performance is evaluated with stochastic daily weather, egg hatch, and larval survival in various combinations. Sensitivity analysis is conducted to evaluate model responsiveness to each parameter. Model results are generally consistent with published data.

Animals↗
PubMed1976

A psychoanalytic model for human freedom and rationality.

The nature and scope of freedom and rationality in man are explored in light of the problems posed by a deterministic framework for understanding and explaining human though, feeling, and behavior. It is argued that the sort of explanation afforded by a psychodynamic theory is fully compatible with attributing freedom and rationality to persons. In particular, psychoanalytic theory is able to account for the existence of causal laws governing all aspects of human behavior, while providing a schema by which we can distinguish rational from irrational behavior, and free acts from those that are unfree.

Behavior↗
PubMed2002

Robustness of circadian rhythms with respect to molecular noise.

We use a core molecular model capable of generating circadian rhythms to assess the robustness of circadian oscillations with respect to molecular noise. The model is based on the negative feedback exerted by a regulatory protein on the expression of its gene. Such a negative regulatory mechanism underlies circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. The model incorporates gene transcription into mRNA, translation of mRNA into protein, reversible phosphorylation leading to degradation of the regulatory protein, transport of the latter into the nucleus, and repression of gene expression by the nuclear form of the protein. To assess the effect of molecular noise, we perform stochastic simulations after decomposing the deterministic model into elementary reaction steps. The oscillations predicted by the stochastic simulations agree with those obtained with the deterministic version of the model. We show that robust circadian oscillations can occur already with a limited number of mRNA and protein molecules, in the range of tens and hundreds, respectively. Entrainment by light/dark cycles and cooperativity in repression enhance the robustness of circadian oscillations with respect to molecular noise.

Animals↗
PubMed2007

Optimization for high-density cultivation of heterotrophic Chlorella based on a hybrid neural network model.

AIMS: The purpose of this study was to develop a reliable hybrid neural network (HNN) model for heterotrophic growth of Chlorella, based on which optimization for fed-batch (FB) cultivation of Chlorella may be successfully realized. METHODS AND RESULTS: Deterministic kinetic model was preliminarily developed for the optimization of FB cultivation of Chlorella. The highest biomass concentration and the maximum productivity were obtained as: 104.9 g l(-1) dry cell weight and 0.613 g l(-1) h(-1), respectively. After several cultivations had been performed, an HNN model was developed. The efficiency of biomass production was further increased by the optimization using this model. The highest biomass concentration and the maximum productivity attained was: 116.2 g l(-1) dry cell weight and 1.020 g l(-1) h(-1), respectively. CONCLUSION: The HNN model agreed well with experimental results in different cultivations. Comparison between the HNN model and the deterministic model showed that the former had better generalization ability, which made it a reliable tool in modelling and optimization. SIGNIFICANCE AND IMPACT OF THE STUDY: The high cell density and productivity of biomass obtained in this study is of significance for the commercial cultivation of Chlorella. The simple and efficient optimization strategy proposed in this paper may be employed in heterotrophic mass culture of Chlorella as well as other similar organisms.

Biomass↗
PubMedDate not supplied

Simulating urban waste compost effects on carbon and nitrogen dynamics using a biochemical index.

Composting has emerged as a valuable route for the disposal of urban waste, with the prospect of applying composts on arable fields as organic amendments. Proper management of urban waste composts (UWCs) requires a capacity to predict their effects on carbon and nitrogen dynamics in the field, an issue in which simulation models are expected to play a prominent role. However, the parameterization of soil organic amendments within such models generally requires laboratory incubation data. Here, we evaluated the benefit of using a biochemical index based on Van Soest organic matter fractions to parameterize a deterministic model of soil C and N dynamics, NCSOIL, as compared with a standard alternative based on laboratory incubation data. The data included C mineralization and inorganic N dynamics in samples of a silt loam soil (Typic Hapludalf) mixed with various types of UWC and farmyard manure. NCSOIL successfully predicted the various nitrogen mineralization-immobilization patterns observed, but underestimated CO(2) release by 10 to 30% with the less stable amendments. The parameterization based on the biochemical index achieved a prediction error significantly larger than the standard parameterization in only 10% of the tested cases, and provided an acceptable fit to experimental data. The decomposition rates and C to N ratios of compost organic matter varied chiefly according to the type of waste processed. However, 62 to 66% of their variance could be explained by the biochemical index. We thus suggest using the latter to parameterize organic amendments in C and N models as a substitute for time-consuming laboratory incubations.

Biodegradation, Environmental↗
PubMed2002

Understanding the persistence of measles: reconciling theory, simulation and observation.

Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'.

Cities↗
PubMed2005

Genetic and economic evaluation of Japanese Black (Wagyu) cattle breeding schemes.

Deterministic simulation was used to evaluate 10 breeding schemes for genetic gain and profitability and in the context of maximizing returns from investment in Japanese Black cattle breeding. A breeding objective that integrated the cow-calf and feedlot segments was considered. Ten breeding schemes that differed in the records available for use as selection criteria were defined. The schemes ranged from one that used carcass traits currently available to Japanese Black cattle breeders (Scheme 1) to one that also included linear measurements and male and female reproduction traits (Scheme 10). The latter scheme represented the highest level of performance recording. In all breeding schemes, sires were chosen from the proportion selected during the first selection stage (performance testing), modeling a two-stage selection process. The effect on genetic gain and profitability of varying test capacity and number of progeny per sire and of ultrasound scanning of live animals was examined for all breeding schemes. Breeding schemes that selected young bulls during performance testing based on additional individual traits and information on carcass traits from their relatives generated additional genetic gain and profitability. Increasing test capacity resulted in an increase in genetic gain in all schemes. Profitability was optimal in Scheme 2 (a scheme similar to Scheme 1, but selection of young bulls also was based on information on carcass traits from their relatives) to 10 when 900 to 1,000 places were available for performance testing. Similarly, as the number of progeny used in the selection of sires increased, genetic gain first increased sharply and then gradually in all schemes. Profit was optimal across all breeding schemes when sires were selected based on information from 150 to 200 progeny. Additional genetic gain and profitability were generated in each breeding scheme with ultrasound scanning of live animals for carcass traits. Ultrasound scanning of live animals was more important than the addition of any other traits in the selection criteria. These results may be used to provide guidance to Japanese Black cattle breeders.

Animals↗
PubMedDate not supplied

[Causality in urologic research].

Clinical-epidemiological research may orient us about the causes of disease, the relationships among them, and the relative magnitudes of their effects. The objective of this article is to link the notion of cause with the basic clinical-epidemiological parameters. There are different models explaining causality. All of them present the possible etiologic explanations for the diseases, taking into consideration the current knowledge at the time they have been posed. We start from a purely determinist conception, understanding causality as a constant connection between two factors x and y, unique, and perfectly predictable. Currently, this model is inadequate to be applied to many diseases. Many researchers have modified the determinist model to explain the multiple causality of disease, posing the existence of associations of causal factors, more than single factors, being these associations treated as sufficient cause (i.e. as a group of minimal conditions and events that inevitably produce the disease). That determinist concept of causality is supplemented with the probabilistic concept. The theory of probability is used in it, as well as the related statistical, methods, to empirically evaluate a possible association that is believed causal. As a consequence of the lack of certainty of the prediction at the individual level, the theoretical notion of cause is replaced by the empirical concept of risk factor, referring to a variable which is considered to be related to the probability that one individual develops the disease. Causal inference in epidemiology is the logic development of a theory, based on observations and arguments that attribute the presence (association) of a disease to one or more risk factors. We will follow the principles posed by B. Hill for the complex process called scientific generalization. To correctly perform this relationship between our ideas and are observations it is absolutely important to start from a correct election of the study design with which the research is undertaken.

Biomedical Research↗
PubMedDate not supplied

Incorporating phenotype-dependent growth rates into the color-shift model for preneoplastic hepatocellular lesions.

Multi-stage models occupy a central position in modeling the carcinogenesis process. These models formalize the hypothesis that cells have to undergo several transformations on their way to malignancy. This hypothesis assumes that a preneoplastic cell of a later stage arises through a mutational event of a single cell of a previous stage and that preneoplastic cells proliferate clonally. However, there is some evidence that multi-stage models cannot adequately describe the formation and the progression of preneoplastic lesions at least in certain organs [Math. Biosci. 168 (2000) 167]. An alternative model assuming that all cells in a colony of altered hepatocytes change their phenotype more or less simultaneously rather than by mutation of single cells has already been introduced [Math. Biosci. 148 (1998) 181] and is called color-shift model (CSM). This model assumed deterministic phenotype-independent growth for the foci once they are generated. An expansion of the CSM allowing for variability between deterministic growth behaviour of phenotypically different colonies is presented (modCSM) and the model is applied to focal lesion data from a rat hepatocarcinogenesis experiment. The fit of the originally proposed and the modCSM are compared with respect to their ability to predict numbers and radii of preneoplastic cell foci.

Animals↗
PubMedDate not supplied

Density functions of residence times for deterministic and stochastic compartmental systems.

A significant consideration in modeling systems with stages is to obtain models for the individual stages that have probability density functions (pdfs) of residence times that are close to those of the real system. Consequently, the theory of residence time distributions is important for modeling. Here I show first that linear deterministic compartmental systems with constant coefficients and their corresponding stochastic analogs (stochastic compartmental systems with linear rate laws) have the same pdfs of residence times for the same initial distributions of inputs. Furthermore, these are independent of inflows. Then I show that does not hold for non-linear deterministic systems and their stochastic analogs (stochastic compartmental systems with non-linear rate laws). In fact, for given initial distributions of inputs, the pdfs of non-linear determistic systems without inflows and of their stochastic analogs, are functions of the initial amounts injected. For systems with inflows, the pdfs change as the inflows influence the occupancies of the compartments of the system; they are state-dependent pdfs.

Kinetics↗
PubMed2004

Cytosolic processing of proteasomal cleavage products can enhance the presentation efficiency of MHC-1 epitopes.

The vertebrate immune system is able to detect abnormal body cells by the specific repertoire of 8 - 12 residues long peptides (= epitopes or peptide antigens) presented at the cell surface by the MHC-1 molecule complex. The generation of an epitope starts with the degradation of endogenous proteins into primary oligomeric fragments by cytosolic proteases, predominantly the proteasome. These primary fragments may be further attacked by various amino peptidases resident in the cytosol or, alternatively, may escape from this attack by entering the endoplasmic reticulum (ER) by the transporter associated with antigen presentation (TAP). To study the possible consequences of this scenario for the efficiency of antigen presentation we have applied kinetic modelling. The mathematical model comprises the generation of primary oligomeric fragments containing the definitive epitope, the successive N-terminal shortening of these primary fragments by cytosolic amino peptidases and the TAP-mediated transport of cytosolic peptides into the ER. Because the number of peptide molecules may become very small we have performed deterministic and stochastic simulations of the kinetic model. Our simulations show that cytosolic N-terminal trimming of primary fragments may drastically increase loading epitope precursors into the ER. In particular, a primary fragment generated with a low rate of TAP transport into the ER may nevertheless become a potent epitope precursor if at least one of its N-terminal trimming products will be efficiently transported.

Animals↗
PubMed2005

Modelling event-related responses in the brain.

The aim of this work was to investigate the mechanisms that shape evoked electroencephalographic (EEG) and magneto-encephalographic (MEG) responses. We used a neuronally plausible model to characterise the dependency of response components on the models parameters. This generative model was a neural mass model of hierarchically arranged areas using three kinds of inter-area connections (forward, backward and lateral). We investigated how responses, at each level of a cortical hierarchy, depended on the strength of connections or coupling. Our strategy was to systematically add connections and examine the responses of each successive architecture. We did this in the context of deterministic responses and then with stochastic spontaneous activity. Our aim was to show, in a simple way, how event-related dynamics depend on extrinsic connectivity. To emphasise the importance of nonlinear interactions, we tried to disambiguate the components of event-related potentials (ERPs) or event-related fields (ERFs) that can be explained by a linear superposition of trial-specific responses and those engendered nonlinearly (e.g., by phase-resetting). Our key conclusions were; (i) when forward connections, mediating bottom-up or extrinsic inputs, are sufficiently strong, nonlinear mechanisms cause a saturation of excitatory interneuron responses. This endows the system with an inherent stability that precludes nondissipative population dynamics. (ii) The duration of evoked transients increases with the hierarchical depth or level of processing. (iii) When backward connections are added, evoked transients become more protracted, exhibiting damped oscillations. These are formally identical to late or endogenous components seen empirically. This suggests that late components are mediated by reentrant dynamics within cortical hierarchies. (iv) Bilateral connections produce similar effects to backward connections but can also mediate zero-lag phase-locking among areas. (v) Finally, with spontaneous activity, ERPs/ERFs can arise from two distinct mechanisms: For low levels of (stimulus related and ongoing) activity, the systems response conforms to a quasi-linear superposition of separable responses to the fixed and stochastic inputs. This is consistent with classical assumptions that motivate trial averaging to suppress spontaneous activity and disclose the ERP/ERF. However, when activity is sufficiently high, there are nonlinear interactions between the fixed and stochastic inputs. This interaction is expressed as a phase-resetting and represents a qualitatively different explanation for the ERP/ERF.

Animals↗