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At least 1,315 records · Page 73Linked to original sources
PubMed2005

Population modeling for a captive squirrel monkey colony.

Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached with the use of two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model that is capable of accommodating random variations in biological phenomena, as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model are replaced by probability distributions fitted into historical data from colony records. With the use of Crystal Ball (Decisioneering, Inc., Denver, CO) software, user-selected distributions are embedded in appropriate cells in the spreadsheet model. A Monte Carlo simulation scheme running within the spreadsheet draws (on each cycle) random values for input parameters from the distribution embedded in each relevant cell, and thus generates output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision-maker with a mathematical habitat for statistical analysis in a stochastic setting. In addition to providing standard statistical measures (e.g., mean, variance, and range) that describe the location and shape of the distribution, this approach offers the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.

Animals↗
PubMed1995

EEG dipole localization bounds and MAP algorithms for head models with parameter uncertainties.

The Cramer-Rao bound for unbiased dipole location estimation is derived under the assumption of a general head model parameterized by deterministic and stochastic parameters. The expression thus characterizes fundamental limits on EEG dipole localization performance due to the effects of both model uncertainty and statistical measurements noise. Expressions are derived for the cases of multivariate Gaussian and gamma distribution priors, and examples are given to illustrate the derived bounds when the radii and conductivities of a four-concentric sphere head model are allowed to be random. The joint MAP estimate of location/model parameters is then examined as a means of achieving robustness to deviations from an ideal head model. Random variations in both the multiple sphere radii and the layer conductivities are shown, via the stochastic Cramer-Rao bounds and Monte Carlo simulation of the MAP estimator, to have the most impact on localization performance in high SNR regions, where finite sample effects are not the limiting factors. This corresponds most often to spatial regions that are close to the scalp electrodes.

Algorithms↗
PubMed2002

Pattern of variation in avian population growth rates.

A central question in population ecology is to understand why population growth rates differ over time. Here, we describe how the long-term growth of populations is not only influenced by parameters affecting the expected dynamics, for example form of density dependence and specific population growth rate, but is also affected by environmental and demographic stochasticity. Using long-term studies of fluctuations of bird populations, we show an interaction between the stochastic and the deterministic components of the population dynamics: high specific growth rates at small densities r(1) are typically positively correlated with the environmental variance sigma(e)(2). Furthermore, theta, a single parameter describing the form of the density regulation in the theta-logistic density-regulation model, is negatively correlated with r(1). These patterns are in turn correlated with interspecific differences in life-history characteristics. Higher specific growth rates, larger stochastic effects on the population dynamics and stronger density regulation at small densities are found in species with large clutch sizes or high adult mortality rates than in long-lived species. Unfortunately, large uncertainties in parameter estimates, as well as strong stochastic effects on the population dynamics, will often make even short-term population projections unreliable. We illustrate that the concept of population prediction interval can be useful in evaluating the consequences of these uncertainties in the population projections for the choice of management actions.

Analysis of Variance↗
PubMed2002

A stochastic nonlinear autoregressive algorithm reflects nonlinear dynamics of heart-rate fluctuations.

Current methods for detecting nonlinear determinism in a time series require long and stationary data records, as most of them assume that the observed dynamics arise only from the internal, deterministic workings of the system, and the stochastic portion of the signal (the noise component) is assumed to be negligible. To explicitly account for the stochastic portion of the data we recently developed a method based on a stochastic nonlinear autoregressive (SNAR) algorithm. The method iteratively estimates nonlinear autoregressive models for both the deterministic and stochastic portions of the signal. Subsequently, the Lyapunov exponents (LE) are calculated for the estimated models in order to examine if nonlinear determinism is present in the deterministic portion of the fitted model. To determine if nonlinear dynamic analysis of heart-rate fluctuations can be used to assess arrhythmia susceptibility by predicting the outcome of invasive cardiac electrophysiologic study (EPS), we applied the SNAR algorithm to noninvasively measured resting sinus-rhythm heart-rate signals obtained from 16 patients. Our analysis revealed that a positive LE was highly correlated to a patient with a positive outcome of EPS. We found that the statistical accuracy of the SNAR algorithm in predicting the outcome of EPS was 88% (sensitivity=100%, specificity=75%, positive predictive value=80%, negative predictive value=100%, p=0.0019). Our results suggest that the SNAR algorithm may serve as a noninvasive probe for screening high-risk populations for malignant cardiac arrhythmias.

Adult↗
PubMed2003

Development of a structured model for batch cultures of lactic acid bacteria.

A combined stochastic-deterministic model able to predict the growth curve of microorganisms, from inoculation to death, is presented. The proposed model is based on the assumption that microorganisms can experience two different physiological states: non-proliferating and proliferating. The former being the physiological state of the cells right after their inoculation into the new extracellular environment; the latter the state of microorganisms after adaptation to the new medium. To validate the model, a Lactobacillus bulgaricus strain was tested in a medium at pH 4.6 at two different temperatures (42 degrees C and 35 degrees C). Curves representing the bacterial growth cycle were satisfactorily fitted by means of the proposed model. Moreover, due to the mechanistic structure of the proposed model, valuable quantitative information on the following was obtained: rate of conversion of non-proliferating cells into proliferating cells, growth and death rate of proliferating cells, and rate of nutrient consumption.

Cell Division↗
PubMed2004

Pesticide residues in food--acute dietary exposure.

Consumer risk assessment is a crucial step in the regulatory approval of pesticide use on food crops. Recently, an additional hurdle has been added to the formal consumer risk assessment process with the introduction of short-term intake or exposure assessment and a comparable short-term toxicity reference, the acute reference dose. Exposure to residues during one meal or over one day is important for short-term or acute intake. Exposure in the short term can be substantially higher than average because the consumption of a food on a single occasion can be very large compared with typical long-term or mean consumption and the food may have a much larger residue than average. Furthermore, the residue level in a single unit of a fruit or vegetable may be higher by a factor (defined as the variability factor, which we have shown to be typically x3 for the 97.5th percentile unit) than the average residue in the lot. Available marketplace data and supervised residue trial data are examined in an investigation of the variability of residues in units of fruit and vegetables. A method is described for estimating the 97.5th percentile value from sets of unit residue data. Variability appears to be generally independent of the pesticide, the crop, crop unit size and the residue level. The deposition of pesticide on the individual unit during application is probably the most significant factor. The diets used in the calculations ideally come from individual and household surveys with enough consumers of each specific food to determine large portion sizes. The diets should distinguish the different forms of a food consumed, eg canned, frozen or fresh, because the residue levels associated with the different forms may be quite different. Dietary intakes may be calculated by a deterministic method or a probabilistic method. In the deterministic method the intake is estimated with the assumptions of large portion consumption of a 'high residue' food (high residue in the sense that the pesticide was used at the highest recommended label rate, the crop was harvested at the smallest interval after treatment and the residue in the edible portion was the highest found in any of the supervised trials in line with these use conditions). The deterministic calculation also includes a variability factor for those foods consumed as units (eg apples, carrots) to allow for the elevated residue in some single units which may not be seen in composited samples. In the probabilistic method the distribution of dietary consumption and the distribution of possible residues are combined in repeated probabilistic calculations to yield a distribution of possible residue intakes. Additional information such as percentage commodity treated and combination of residues from multiple commodities may be incorporated into probabilistic calculations. The IUPAC Advisory Committee on Crop Protection Chemistry has made 11 recommendations relating to acute dietary exposure.

Animals↗
PubMed2004

Self-organization vs Watchmaker: stochastic gene expression and cell differentiation.

Cell differentiation and organism development are traditionally described in deterministic terms of program and design, echoing a conventional clockwork perception of the cell on another scale. However, the current experimental reality of stochastic gene expression and cell plasticity is poorly consistent with the ideas of design, purpose and determinism, suggesting that the habit of classico-mechanistic interpretation of life phenomena may handicap our ability to adequately comprehend and model biological systems. An alternative conceptualization of cell differentiation and development is proposed where the developing organism is viewed as a dynamic self-organizing system of adaptive interacting agents. This alternative interpretation appears to be more consistent with the probabilistic nature of gene expression and the phenomena of cell plasticity, and is coterminous with the novel emerging image of the cell as a self-organizing molecular system. I suggest that stochasticity, as a principle of differentiation and adaptation, and self-organization, as a concept of emergence, have the potential to provide an interpretational framework that unites phenomena across different scales of biological organization, from molecules to societies.

Animals↗
PubMed1996

Visual evoked potential enhancement by an artificial neural network filter.

The application of an artificial neural network filter (ANNF) to estimate the visual evoked potential (VEP) is presented. VEP is the gross electrical response of the brain to visual stimuli. Due to the low SNR, it is difficult to extract response from individual stimulus trials. The ANNF we used estimates the deterministic component of the signal and removes the noise uncorrelated with the stimulus, even when the noise is colored. The ANNF is trained through back-error propagation with a data set consisting of a training signal and a target signal. The training signal is the raw VEP from a single trial having a SNR of about -5 dB, while the target signal has a higher SNR which is achieved by ensemble averaging 100 stimulus trials. Simulated signals were generated to test the performance of the ANNF. Results show that the ANNF could greatly enhance the SNR of the VEP to single visual stimulus. Thus the total number of ensembles is reduced. In clinical applications, the traditional ensemble averaging method requires a hundred ensembles to determine the VEP. When ANNF is used, about 20 ensembles are sufficient for the same purpose.

Adolescent↗
PubMed2003

Hybrid global optimization algorithms for protein structure prediction: alternating hybrids.

Hybrid global optimization methods attempt to combine the beneficial features of two or more algorithms, and can be powerful methods for solving challenging nonconvex optimization problems. In this paper, novel classes of hybrid global optimization methods, termed alternating hybrids, are introduced for application as a tool in treating the peptide and protein structure prediction problems. In particular, these new optimization methods take the form of hybrids between a deterministic global optimization algorithm, the alphaBB, and a stochastically based method, conformational space annealing (CSA). The alphaBB method, as a theoretically proven global optimization approach, exhibits consistency, as it guarantees convergence to the global minimum for twice-continuously differentiable constrained nonlinear programming problems, but can benefit from computationally related enhancements. On the other hand, the independent CSA algorithm is highly efficient, though the method lacks theoretical guarantees of convergence. Furthermore, both the alphaBB method and the CSA method are found to identify ensembles of low-energy conformers, an important feature for determining the true free energy minimum of the system. The proposed hybrid methods combine the desirable features of efficiency and consistency, thus enabling the accurate prediction of the structures of larger peptides. Computational studies for met-enkephalin and melittin, employing sequential and parallel computing frameworks, demonstrate the promise for these proposed hybrid methods.

Algorithms↗
PubMed2001

The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord.

Spontaneous episodic activity occurs throughout the developing nervous system because immature circuits are hyperexcitable. It is not fully understood how the temporal pattern of this activity is regulated. Here, we study the role of activity-dependent depression of network excitability in the generation and regulation of spontaneous activity in the embryonic chick spinal cord. We demonstrate that the duration of an episode of activity depends on the network excitability at the beginning of the episode. We found a positive correlation between episode duration and the preceding inter-episode interval, but not with the following interval, suggesting that episode onset is stochastic whereas episode termination occurs deterministically, when network excitability falls to a fixed level. This is true over a wide range of developmental stages and under blockade of glutamatergic or GABAergic/glycinergic synapses. We also demonstrate that during glutamatergic blockade the remaining part of the network becomes more excitable, compensating for the loss of glutamatergic synapses and allowing spontaneous activity to recover. This compensatory increase in the excitability of the remaining network reflects the progressive increase in synaptic efficacy that occurs in the absence of activity. Therefore, the mechanism responsible for the episodic nature of the activity automatically renders this activity robust to network disruptions. The results are presented using the framework of our computational model of spontaneous activity in the developing cord. Specifically, we show how they follow logically from a bistable network with a slow activity-dependent depression switching periodically between the active and inactive states.

Animals↗
PubMed1989

Path analysis under generalized marital resemblance: evaluation of the assumptions underlying the mixed homogamy model by the Monte Carlo method.

Path analysis of nuclear family data has been widely applied to resolve genetic and environmental sources of familial resemblance. Here we report the results of a systematic evaluation of the effects of departures from five modeling assumptions often made when analyzing nuclear family data; i) the observed environmental index is unaffected by the genotype, ii) the basis of marital resemblance is correctly specified in the model, iii) there are no intergenerational differences in either the genetic or cultural heritability, iv) there is no genetic dominance, and v) there is no genotype by family environment interaction. "Deterministic simulations" identified various situations where model misspecification could lead to substantial bias in the estimation of the heritabilities. For these situations, "stochastic simulations" were performed to determine whether the "goodness-of-fit" test used in path analysis would correctly reject the misspecified model. In samples of 500 nuclear families, each comprising two parents and two children, the goodness-of-fit test was found to be sensitive to misspecifications of the source of marital resemblance and the existence of intergenerational differences in heritabilities, although reduced power would make the test less sensitive in smaller samples. The test was largely insensitive to misspecifications of possible genetic effects on the environmental index, and to the existence of multiplicative interaction between the genotype and familial environment. When genetic effects on the index are ignored, the genetic heritability (h2) is underestimated, the cultural heritability (c2) is overestimated, but h2+c2 remains unchanged. Neglecting the interaction was found to result in an overestimate of h2.

Consanguinity↗
PubMed1989

Automatic detection of sounds and murmurs in patients with Ionescu-Shiley aortic bioprostheses.

The problems encountered in the automatic detection of cardiac sounds and murmurs are numerous. The phonocardiogram (PCG) is a complex signal produced by deterministic events such as the opening and closing of the heart valves, and by random phenomena such as blood-flow turbulence. In addition, background noise and the dependence of the PCG on the recording sites render automatic detection a difficult task. In the paper we present an iterative automatic detection algorithm based on the a priori knowledge of spectral and temporal characteristics of the first and second heart sounds, the valve opening clicks, and the systolic and diastolic murmurs. The algorithm uses estimates of the PCG envelope and noise level to identify iteratively the position and duration of the significant acoustic events contained in the PCG. The results indicate that it is particularly effective in detecting the second heart sound and the aortic component of the second heart sound in patients with Ionescu-Shiley aortic valve bioprostheses. It has also some potential for the detection of the first heart sound, the systolic murmur and the diastolic murmur.

Algorithms↗
PubMed2005

Parameter estimation in a stochastic model of the tubuloglomerular feedback mechanism in a rat nephron.

A key parameter in the understanding of renal hemodynamics is the gain of the feedback function in the tubuloglomerular feedback mechanism. A dynamic model of autoregulation of renal blood flow and glomerular filtration rate has been extended to include a stochastic differential equations model of one of the main parameters that determines feedback gain. The model reproduces fluctuations and irregularities in the tubular pressure oscillations that the former deterministic models failed to describe. This approach assumes that the gain exhibits spontaneous erratic variations that can be explained by a variety of influences, which change over time (blood pressure, hormone levels, etc.). To estimate the key parameters of the model we have developed a new estimation method based on the oscillatory behavior of the data. The dynamics is characterized by the spectral density, which has been estimated for the observed time series, and numerically approximated for the model. The parameters have then been estimated by the least squares distance between data and model spectral densities. To evaluate the estimation procedure measurements of the proximal tubular pressure from 35 nephrons in 16 rat kidneys have been analyzed, and the parameters characterizing the gain and the delay have been estimated. There was good agreement between the estimated values, and the values obtained for the same parameters in independent, previously published experiments.

Animals↗
PubMed2002

Detection and integration of genotyping errors in statistical genetics.

Detection of genotyping errors and integration of such errors in statistical analysis are relatively neglected topics, given their importance in gene mapping. A few inopportunely placed errors, if ignored, can tremendously affect evidence for linkage. The present study takes a fresh look at the calculation of pedigree likelihoods in the presence of genotyping error. To accommodate genotyping error, we present extensions to the Lander-Green-Kruglyak deterministic algorithm for small pedigrees and to the Markov-chain Monte Carlo stochastic algorithm for large pedigrees. These extensions can accommodate a variety of error models and refrain from simplifying assumptions, such as allowing, at most, one error per pedigree. In principle, almost any statistical genetic analysis can be performed taking errors into account, without actually correcting or deleting suspect genotypes. Three examples illustrate the possibilities. These examples make use of the full pedigree data, multiple linked markers, and a prior error model. The first example is the estimation of genotyping error rates from pedigree data. The second-and currently most useful-example is the computation of posterior mistyping probabilities. These probabilities cover both Mendelian-consistent and Mendelian-inconsistent errors. The third example is the selection of the true pedigree structure connecting a group of people from among several competing pedigree structures. Paternity testing and twin zygosity testing are typical applications.

Algorithms↗
PubMed2005

Protecting people against radiation exposure in the event of a radiological attack. A report of The International Commission on Radiological Protection.

This report responds to a widely perceived need for professional advice on radiological protection measures to be undertaken in the event of a radiological attack. The report, which is mainly concerned with possible attacks involving 'radioactive dispersion devices', re-affirms the applicability of existing ICRP recommendations to such situations, should they ever occur. Many aspects of the emergency scenarios expected to arise in the event of a radiological attack may be similar to those that experience has shown can arise from radiological accidents, but there may also be important differences. For instance, a radiological attack would probably be targeted at a public area, possibly in an urban environment, where the presence of radiation is not anticipated and the dispersion conditions commonly assumed for a nuclear or radiological emergency, such as at a nuclear installation, may not be applicable. First responders to a radiological attack and other rescuers need to be adequately trained and to have the proper equipment for identifying radiation and radioactive contamination, and specialists in radiological protection must be available to provide advice. It may be prudent to assume that radiological, chemical, and/or biological agents are involved in an attack until it is proven otherwise. This calls for an 'all-hazard' approach to the response. In the aftermath of an attack, the main aim of radiological protection must be to prevent the occurrence of acute health effects attributable to radiation exposure (termed 'deterministic' effects) and to restrict the likelihood of late health effects (termed 'stochastic' effects) such as cancers and some hereditable diseases. A supplementary aim is to minimise environmental contamination from radioactive residues and the subsequent general disruption of daily life. The report notes that action taken to avert exposures is a much more effective protective measure than protective measure the provision of medical treatment after exposure has occurred. Responders involved in recovery, remediation and eventual restoration should be subject to the usual international standards for occupational radiological protection, which are based on ICRP recommendations, including the relevant requirements for occupational dose limitation established in such standards. These restrictions may be relaxed for informed volunteers undertaking urgent rescue operations, and they are not applicable for voluntary life-saving actions. However, specific protection measures are recommended for female workers who may be pregnant or nursing an infant. The immediate countermeasures to protect the public in the rescue phase are primarily caring for people with traumatic injuries and controlling access. Subsequent actions include respiratory protection, personal decontamination, sheltering, iodine prophylaxis (if radio-iodines are involved), and temporary evacuation. In the recovery phase, the relocation and resettlement of people may be needed in extreme cases. This phase may require remedial action, including cleanup, management of the resulting radioactive waste, management of any human remains containing significant amounts of radioactive substances, and dealing with remaining radioactive residues. The guidance given in relation to public protection is based solely on radiological protection considerations and should be seen as a decision-aiding tool to prepare for the aftermath of a radiological attack. It is expected to serve as input to a final decision-making process that may include other societal concerns, consideration of lessons learned in the past (especially these involving the public perception of the risks posed by radioactive contamination) and the participation of interested parties. A radiological attack could also be the cause of radioactive contamination of water, food, and other widely consumed commodities. This possible outcome is considered unlikely to lead to significant internal contamination of a large number of people owing to the large amounts of radioactive material that would be required to cause high levels of contamination of water, food, and other commodities. Nonetheless, the report recommends radiological criteria for restricting the use of commodities under such circumstances. The report concludes by re-iterating that the response to radiological attacks should be planned beforehand following the customary processes for optimisation of radiological protection recommended by ICRP, and that optimised measures should be prepared in advance. Such plans should result in a systematic approach that can be modified if necessary to take into account the prevailing conditions and to invoke actions as warranted by the circumstances. Many potential scenarios clearly cannot induce immediate severe radiation injuries. Therefore, in order to prevent over-reaction, response measures prepared in advance should reflect the real expected gravity of the various possible scenarios.

Environmental Exposure↗
PubMed1994

Renal blood flow regulation and arterial pressure fluctuations: a case study in nonlinear dynamics.

The arterial blood pressure, a physiological variable on which all renal excretory processes depend, fluctuates over a wide range of amplitudes and frequencies. Much of this variation originates in nonrenal vascular beds to support nonrenal tasks, and the fluctuations provide a noisy environment in which the kidney is obliged to operate. Were it not for renal blood flow autoregulation, it would be difficult to regulate renal excretory processes so as to maintain whole body variables within narrow bounds. Autoregulation is the noise filter on which other renal processes depend for maintaining a relatively noise-free environment in which to work. Because of the time-varying nature of the blood pressure, we have concentrated in this review on the now substantial body of work on the dynamics of renal blood flow regulation and the underlying mechanisms. Renal vascular control mechanisms are not simply reactive but have their own spontaneous dynamics. Both TGF and the myogenic mechanism oscillate autonomously. The TGF oscillation is the better understood of the two. There is an oscillation of tubular pressure, proximal tubular flow, early distal Cl- concentration, and efferent arteriolar blood flow at approximately 35 mHz; all these variables are synchronized when the measurements are made in a single tubule. The autonomous nature of the oscillation is supported by simulations of the nephron and its vasculature, which show that for a reasonable representation of the dynamics of these structures and of the parameters that govern their behavior, the solutions of the equation set are periodic at the frequency of the observed oscillation, and with the same phase relationships among its variables. The simulations also show that the critical variables for the development of the oscillation are the open-loop gain of the feedback system, and the various delays in the system of which convective transport in the axis of the thick ascending limb and signal transmission between the macula densa and the afferent arteriole are the most important. The oscillation in TGF is an example of nonlinear dynamical behavior and is yet another in a long list of oscillations and related dynamics arising in the inherently nonlinear properties of living systems. Some nonlinear systems can bifurcate to states known collectively as deterministic chaos, and TGF is a clear example of such a system. Rats with two different and unrelated forms of experimental hypertension provide tubular pressure records that pass statistical tests for ordered structure and sensitive dependence on initial conditions in the reconstructed state space, two of the hallmarks of deterministic chaos. These records also pass recent more stringent tests for chaos. The significance of deterministic chaos in the context of renal blood flow regulation is that the system regulating blood flow undergoes a physical change to a different dynamical state, and because the change is deterministic, there is every expectation that the critical change will yield itself to experimental discovery.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1999

Analytical model of susceptibility-induced MR signal dephasing: effect of diffusion in a microvascular network.

A deterministic analytical model that describes the time course of magnetic resonance signal relaxation due to magnetic field inhomogeneity induced by a vascular network is developed. Both static and diffusion dephasing are taken into account. The contribution of the diffusion dephasing is calculated for relatively large vessels (R>10 microm) or short measurement times when the diffusion length is smaller than the vessel radius. The signal is found to possess the following features: a) an initial deviation from the monoexponential relaxation which is more pronounced for the imaginary part of the signal; b) a deviation from monoexponential relaxation at short echo times for the spin-echo (SE) signal measured as a function of the echo time; c) the echo maximum of the SE signal shifted from the nominal echo time to a shorter time; and d) a diffusion effect much stronger for the SE than for the free induction decay experiment. The model presented agrees within its validity domain with a known Monte Carlo simulation.

Brain↗
PubMed2006

Developing Itô stochastic differential equation models for neuronal signal transduction pathways.

Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Itô stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Itô stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Itô stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Itô stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical Langevin equation produces negative concentrations. The Itô stochastic differential equations developed in this work are shown to overcome the problem of obtaining negative values.

Computer Simulation↗