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Results for “deterministic processes”

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PubMed1996

Deterministic pressure dissociation and unfolding of triose phosphate isomerase: persistent heterogeneity of a protein dimer.

Subunit dissociation and unfolding of dimeric rabbit muscle triose phosphate isomerase (TIM) induced by hydrostatic pressure were investigated. Changes in fluorescence emission of TIM (both intrinsic and of covalently attached probes) indicated that pressure ranging from 1 bar to 3.5 kbar promoted subunit dissociation and unfolding. Instrinsic fluorescence changes upon unfolding by pressure included a 27 nm red-shift of the emission, a decrease in fluorescence anisotropy from 0.14 to about 0.01, and a 1.5-fold increase in fluorescence quantum yield, similar to that observed in the presence of guanidine hydrochloride. Kinetics of pressure-induced fluorescence changes were slow (t 1/2 approximately 15 min) and little dependent on pressure. In order to selectively monitor subunit dissociation, fluorescence resonance energy transfer (FRET) measurements were carried out with TIM that was separately labeled with 5-((((2-iodoacetyl)-amino)ethyl)amino)naphthalene-1-sulfonic acid (1,5-IAEDANS) or fluorescein-5-isothiocyanate (FITC). FRET measurements indicated that subunit dissociation and unfolding took place concomitantly, both under equilibrium conditions and in kinetic experiments in which dissociation/unfolding was triggered by a sudden increase in pressure. Release of pressure caused monomer refolding and dimerization. Contrary to what would be expected for a process involving subunit dissociation, pressure effects on TIM were not dependent on protein concentration. Experiments involving a series of pressure jumps demonstrated persistent heterogeneity in sensitivity toward pressure in the ensemble of TIM dimers. This kind of deterministic behavior is similar to that exhibited by higher order protein aggregates and indicates that not all individual dimers are energetically identical in solution. The heterogeneity of native TIM revealed by sensitivity to pressure could not be detected by traditional means of protein separation, such as polyacrylamide gel electrophoresis (under both native and denaturing conditions) and size exclusion gel chromatography. This suggests that energetic heterogeneity originates from conformational heterogeneity of the protein. The possible biological relevance of the deterministic character of stability of TIM is discussed.

Animals↗
PubMed2005

Modelling predation as a capped rate stochastic process, with applications to fish recruitment.

Many mathematical models use functions the value of which cannot exceed some physically or biologically imposed maximum value. A model can be described as 'capped-rate' when the rate of change of a variable cannot exceed a maximum value. This presents no problem when the models are deterministic but, in many applications, results from deterministic models are at best misleading. The need to account for stochasticity, both demographic and environmental, in models is therefore important but, as this paper shows, incorporating stochasticity into capped-rate models is not trivial. A method using queueing theory is presented, which allows randomness and spatial heterogeneity to be incorporated rigorously into capped rate models. The method is applied to the feeding and growth of fish larvae.

Animals↗
PubMedDate not supplied

A modeling study on the sustainability of a certification-and-monitoring program for paratuberculosis in cattle.

Certification-and-monitoring programs for paratuberculosis are based on repetitive herd testing to establish a herd's health status. The available tests have poor sensitivity. Infected but undetected herds may remain among certified "paratuberculosis-free" herds. The objective was to determine if truly free herds acquire a certified status and keep it over time when infected but undetected herds remain. The Dutch program was used as a basis to construct a mechanistic deterministic model of the evolution over 25 years of the number of herds per health status. Three health states for herds were defined: not detected as infected in the certification process to obtain a free status; not detected as infected by any of the repetitive tests for monitoring the certified free status; detected as infected. Among undetected herds, two types were defined: truly free versus undetected but infected. Transitions between states were due to the purchase of an infected animal, infection via the environment, clearance via culling or sales, detection of an infected animal, and certification. A sensitivity analysis was carried out. We showed that--for a 100% specific test only--most of the truly free herds at the beginning of the program got a certified free status and kept it over time. Most infected herds were either detected as infected or cleared. The number of certified truly free herds increased with a decrease in the animal-level prevalence or in the risk of purchasing an infected cattle, for example by restricting purchases to cattle from herds at the highest level of certification.

Animal Husbandry↗
PubMed1997

Time-frequency plane Wiener filtering of the high-resolution ECG: background and time-frequency representations.

This paper introduces the concept of a posteriori Wiener filtering (APWF), performed in the time-frequency plane. The objective is to improve the signal-to-noise ratio (SNR) of the ensemble-averaged high-resolution electrocardiogram (HRECG). APWF was developed to address the problem of a limited ensemble size for estimating ensemble-averaged evoked potentials. For the HRECG, we identify the major challenge as adapting the time-frequency structure of the filter to that of low-level cardiac signals. Technical limitations and the characteristics of HRECG signals make time-frequency analysis of the ensemble average problematic. Normal and abnormal signal components are difficult to distinguish due to low time-frequency energy concentration and limited spectrotemporal resolution. However, considering the entire ensemble of repetitive ECG records, signal and noise components are separable in the time-frequency plane. This forms the basis of the new time-frequency plane Wiener (TFPW) filter, applicable to any ensemble averaging problem involving repetitive deterministic signals mixed with uncorrelated noise.

Electrocardiography↗
PubMedDate not supplied

Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages.

When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find thresholds in this paper was to embed a system of ordinary non-linear differential equations in a stochastic process, accommodating the formation and dissolution of marital partnerships in a heterosexual population, extra-marital sexual contacts, and diseases such as HIV/AIDS with stages. A symbolic representation of the Jacobian matrix of this system was derived. To determine whether this matrix was stable or non-stable at a particular parameter point, the Jacobian was evaluated at a disease-free equilibrium and its eigenvalues were computed. The stability or non-stability of the matrix was then determined by checking if all real parts of the eigenvalues were negative. By writing software to repeat this process for a selected set of points in the parameter space, it was possible to develop search engines for finding points in the parameter space where thresholds were crossed. The results of a set of Monte Carlo simulation experiments were reported which suggest that, by combining the stochastic and deterministic paradigms within a single formulation, it was possible to obtain more informative interpretations of simulation experiments than if attention were confined solely to either paradigm.

Acquired Immunodeficiency Syndrome↗
PubMed2003

Endogenous context for visual processing of human faces and other objects.

The human ability to quickly recognise faces and objects is an important skill. This skill may be facilitated by the prior existence of context-setting functional brain states. MEG was used to test the hypothesis that such states may be defined neurophysiologically. One type of state was identified by evaluating deterministic features in the dynamics of pre-stimulus brain activity in 10 individuals engaging in an object categorisation task. These states followed a statistical gamma-distribution similar to that seen in models of percept duration of competing stimuli. Both an early (42 ms) and a late (440 ms) response were only seen for face stimuli that were presented during states in which the MEG data displayed low determinism. A second type of state was identified by evaluating amplitudes of pre-stimulus brain activity. Between 140 and 150 ms, activity was highest for face as well as non-face stimuli presented during a low amplitude state. These findings suggest that detectable states may provide an endogenous context for object processing, independently of experimental parameters.

Adult↗
PubMed2001

An introduction to microevolution: rate, pattern, process.

This special issue of Genetica brings together a diverse collection of contributions that examine evolution within and among populations (i.e., microevolution), and the role that microevolution plays in the formation of new species and morphological forms (i.e., macroevolution). Many of the papers present evidence of microevolution occurring over contemporary time frames, further validating the near ubiquity of ongoing evolution in the world around us. Several synthetic reviews of empirical work help to define the conditions under which microevolution is or is not likely to occur. Some of the studies speak directly to current controversies in evolutionary biology, such as the relative roles of determinism and contingency, and the nature of the relationship between microevolution and macroevolution. In general, microevolution seems driven largely by deterministic mechanisms, particularly natural selection, but contingency plays a role in (1) determining whether or not suitable conditions are present for evolution to proceed, and (2) guiding the precise manner by which evolution proceeds. Several theoretical treatments and empirical reviews confirm previous research in showing that microevolutionary processes are at least capable of generating macroevolutionary trends. Macroevolution may indeed reflect microevolution writ large but the pattern by which it arises is perhaps best characterized as microevolution writ in fits and starts.

Adaptation, Biological↗
PubMed2002

A quantitative risk analysis tool for design/simulation of wastewater treatment plants.

Uncertainty is a central concept in the decision-making process, especially when dealing with biological systems subject to large natural variations. In the design of activated sludge systems, a conventional approach in dealing with uncertainty is implicitly translating it into above-normal safety factors, which in some cases may even increase the capital investments by an order of magnitude. To obviate this problem, an alternative design approach explicitly incorporating uncertainty is herein proposed. A probabilistic Monte Carlo engine is coupled to deterministic wastewater treatment plant (WWTP) models. The paper provides a description of the approach and a demonstration of the general adequacy of the method. The procedure is examined in an upgrade of a conventional WWTP towards stricter effluent standards on nutrients. The results suggest that the procedure can support the decision-making process under uncertainty conditions and that it can enhance the likelihood of meeting effluent standards without entailing above-normal capital investments. The analysis led to reducing the capital investment by 43%, producing savings of more than 1.2 million euro.

Computer Simulation↗
PubMed2005

Accelerated stochastic simulation of the stiff enzyme-substrate reaction.

The enzyme-catalyzed conversion of a substrate into a product is a common reaction motif in cellular chemical systems. In the three reactions that comprise this process, the intermediate enzyme-substrate complex is usually much more likely to decay into its original constituents than to produce a product molecule. This condition makes the reaction set mathematically "stiff." We show here how the simulation of this stiff reaction set can be dramatically speeded up relative to the standard stochastic simulation algorithm (SSA) by using a recently introduced procedure called the slow-scale SSA. The speedup occurs because the slow-scale SSA explicitly simulates only the relatively rare conversion reactions, skipping over occurrences of the other two less interesting but much more frequent reactions. We describe, explain, and illustrate this simulation procedure for the isolated enzyme-substrate reaction set, and then we show how the procedure extends to the more typical case in which the enzyme-substrate reactions occur together with other reactions and species. Finally, we explain the connection between this slow-scale SSA approach and the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] formula, which has long been used in deterministic chemical kinetics to describe the enzyme-substrate reaction.

Algorithms↗
PubMed2006

An optimal number of molecules for signal amplification and discrimination in a chemical cascade.

Understanding the information processing ability of signal transduction pathways is of great importance because of their crucial roles in triggering various cellular responses. Despite continuing theoretical investigation, some important aspects of signal transduction such as a transient response and its connection to stochasticity originating from a small number of molecules have not yet been well understood. It is, however, through these aspects that unexpected and nontrivial properties of the information processing emerge. In this article, we analyze the transient behavior of a simple signaling cascade by taking into account the stochasticity originating from the small number of molecules. We identify several properties of the signaling cascade that emerge as a result of the interplay between the stochasticity and transient dynamics of the cascade. We specifically demonstrate that each step of the cascade has an optimal number of signaling molecules at which the average signal amplitude becomes maximal. We further investigate the connection between a finite number of molecules and the ability of the cascade to discriminate between true and error signals, which cannot be inferred from deterministic descriptions. The implications of our results are discussed from both biological and mathematical viewpoints.

Computer Simulation↗
PubMed2000

Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model.

We consider open systems where cars move according to the deterministic Nagel-Schreckenberg rules [K. Nagel and M. Schreckenberg, J. Phys. I 2, 2221 (1992)] and with maximum velocity v(max)>1, which is an extension of the asymmetric exclusion process (ASEP). It turns out that the behavior of the system is dominated by two features: (a) the competition between the left and the right boundary, (b) the development of so-called "buffers" due to the hindrance that an injected car feels from the front car at the beginning of the system. As a consequence, there is a first-order phase transition between the free flow and the congested phase accompanied by the collapse of the buffers, and the phase diagram essentially differs from that for v(max)=1 (ASEP).

Journal Article↗
PubMed2001

Diffusion of particles bouncing on a one-dimensional periodically corrugated floor.

We report on a class of spatially extended mechanical systems sustaining a transport process of diffusive type. These systems consist of a point particle subject to a constant vertical acceleration and bouncing on a one-dimensional periodically corrugated floor. We show that the deterministic dynamics of these systems is chaotic with small elliptic islands for many parameter values. The motion of particles perturbed by a small noise has a horizontal diffusion that is normal. In such a case, we show that the diffusion coefficient oscillates periodically as the energy of particles increases. In the absence of noise, there still exists an effective numerical value for the diffusion coefficient and this value has an irregular dependence on energy.

Journal Article↗
PubMed1990

[The EEG and thinking].

The on-going EEG contains information on thinking strategies during cognitive and creative tasks and during listening to music. This was demonstrated by a method taking use of the fact that both the amount of local current production and the degree of electric coupling of brain regions is characteristically changed by mental tasks. In groups of volunteers the significant changes of absolute power and coherence caused by different mental tasks are computed and entered into schematic brain maps (EEG probability maps). The results indicate the existence of general brain strategies even in mental activities as specific as those referred to above. Moreover, several relationships between EEG, psychological test scores, degree of special education and intelligence were found. Studies with extreme value validation according to intelligence and creativity test scores yielded significant differences between the groups of the best and the poorest performers during a creative task in the EEG. The EEG thus can be conceived of as deterministic chaos with different degrees of organization according to its information content. In this context, the question arises as to a possible function of the EEG for the optimization of thinking processes.

Cognition↗
PubMed2006

Incorporating known sources of uncertainty to determine precautionary harvests of saltwater crocodiles.

It has been demonstrated repeatedly that the degree to which regulation operates and the magnitude of environmental variation in an exploited population will together dictate the type of sustainable harvest achievable. Yet typically, harvest models fail to incorporate uncertainty in the underlying dynamics of the target population by assuming a particular (unknown) form of endogenous control. We use a novel approach to estimate the sustainable yield of saltwater crocodile (Crocodylus porosus) populations from major river systems in the Northern Territory, Australia, as an example of a system with high uncertainty. We used multimodel inference to incorporate three levels of uncertainty in yield estimation: (1) uncertainty in the choice of the underlying model(s) used to describe population dynamics, (2) the error associated with the precision and bias of model parameter estimation, and (3) environmental fluctuation (process error). We demonstrate varying strength of evidence for density regulation (1.3-96.7%) for crocodiles among 19 river systems by applying a continuum of five dynamical models (density-independent with and without drift and three alternative density-dependent models) to time series of density estimates. Evidence for density dependence increased with the number of yearly transitions over which each river system was monitored. Deterministic proportional maximum sustainable yield (PMSY) models varied widely among river systems (0.042-0.611), and there was strong evidence for an increasing PMSY as support for density dependence rose. However, there was also a large discrepancy between PMSY values and those produced by the full stochastic simulation projection incorporating all forms of uncertainty, which can be explained by the contribution of process error to estimates of sustainable harvest. We also determined that a fixed-quota harvest strategy (up to 0.2K, where K is the carrying capacity) reduces population size much more rapidly than proportional harvest (the latter strategy requiring temporal monitoring of population size to adjust harvest quotas) and greatly inflates the risk of resource depletion. Using an iconic species recovering from recent extreme overexploitation to examine the potential for renewed sustainable harvest, we have demonstrated that incorporating major forms of uncertainty into a single quantitative framework provides a robust approach to modeling the dynamics of exploited populations.

Alligators and Crocodiles↗
PubMed2006

Modeling the euglycemic hyperinsulinemic clamp by stochastic differential equations.

The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity. In the present study, 16 subjects with BMI between 18.5 and 63.6 kg/m(2) have been studied with a long-duration (5 hours) EHC. In order to explain the oscillations of glycemia occurring in response to the hyperinsulinization and to the continuous glucose infusion at varying speeds, we first hypothesized a system of ordinary differential equations (ODEs), with limited success. We then extended the model and represented the experiment using a system of stochastic differential equations (SDEs). The latter allow for distinction between (i) random variation imputable to observation error and (ii) system noise (intrinsic variability of the metabolic system), due to a variety of influences which change over time. The stochastic model of the EHC was fitted to data and the system noise was estimated by means of a (simulated) maximum likelihood procedure, for a series of different hypothetical measurement error values. We showed that, for the whole range of reasonable measurement error values: (i) the system noise estimates are non-negligible; and (ii) these estimates are robust to changes in the likely value of the measurement error. Explicit expression of system noise is physiologically relevant in this case, since glucose uptake rate is known to be affected by a host of additive influences, usually neglected when modeling metabolism. While in some of the studied subjects system noise appeared to only marginally affect the dynamics, in others the system appeared to be driven more by the erratic oscillations in tissue glucose transport rather than by the overall glucose-insulin control system. It is possible that the quantitative relevance of the unexpressed effects (system noise) should be considered in other physiological situations, represented so far only with deterministic models.

Blood Glucose↗
PubMed1991

Dynamic population epidemic models.

Most multipopulation epidemic models are of the contact distribution type, in which the locations of successive contacts are chosen independently from appropriate contact distributions. This paper is concerned with an alternative class of models, termed dynamic population epidemic models, in which infectives move among the populations and can infect only within their current population. Both the stochastic and deterministic versions of such models are considered. Their threshold behavior is analyzed in some depth, as are their final outcomes. Velocities of spread of infection are considered when the populations have a spatial structure. A criterion for finding the equivalent contact distribution epidemic for any given dynamic population epidemic is provided, enabling comparisons to be made for the velocities and final outcomes displayed by the two classes of models. The relationship between deterministic and stochastic epidemic models is also discussed briefly.

Disease Outbreaks↗
PubMed2002

On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment.

In this paper we extend the deterministic model for the epidemics induced by virulent phages on bacteria in marine environment introduced by Beretta and Kuang [Math. Biosci. 149 (1998) 57], allowing random fluctuations around the positive equilibrium. The stochastic stability properties of the model are investigated both analytically and numerically suggesting that the deterministic model is robust with respect to stochastic perturbations.

Bacteriophages↗