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1.
This paper presents a stochastic model, a theoretical multi-variate probability function describing concentrations of reactants in a closed biochemical system at equilibrium. The theory applies to the complete range of biochemical systems from single enzyme reactions to combinations of reactions to complete pathways. Prior to examining the general system, probability functions are derived for the following systems as examples: a reaction with a competitive inhibitor, a bisubstrate reaction using the ping-pong mechanism and a series of two mono-substrate reactions. The theory of Markov processes is used to derive the probability functions for each of the example systems and then for the general system which includes the example systems as special cases. The probability function for any appropriate biochemical system proves to be the product of independent Poisson probabilities conditioned on the conservation equations. Finally, the implications of the theory are briefly discussed and possible extensions proposed.  相似文献   

2.
3.
Schinazi RB 《Genetics》2006,174(1):545-547
We propose a simple stochastic model based on the two successive mutations hypothesis to compute cancer risks. Assume that only stem cells are susceptible to the first mutation and that there are a total of D stem cell divisions over the lifetime of the tissue with a first mutation probability mu(1) per division. Our model predicts that cancer risk will be low if m = mu(1)D is low even in the case of very advantageous mutations. Moreover, if mu(1)D is low the mutation probability of the second mutation is practically irrelevant to the cancer risk. These results are in contrast with existing models but in agreement with a conjecture of Cairns. In the case where m is large our model predicts that the cancer risk depends crucially on whether the first mutation is advantageous or not. A disadvantageous or neutral mutation makes the risk of cancer drop dramatically.  相似文献   

4.
This paper presents analytical expressions for estimating average process batch flow times through a stochastic manufacturing system with overlapping operations. It is shown that the traditional queueing methodology cannot be directly applied to this setting, as the use of the overlapping operations principle causes the arrival process of sublots at the second stage to be a non-renewal process. An embedded queueing model is then proposed, which provides a tool to estimate the flow time reductions caused by the use of overlapping operations. Moreover, we provide expressions to estimate the production disruptions occurring at the second stage. The results of our research confirm the general intuition that the overlapping operations principle leads to less congestion, and hence a smoother flow of work through the system. On the other hand however, lot splitting inevitably requires more material handling on the shop floor. The expressions provided in this paper allow the quantification of the trade-off between these two effects, e.g., by gauging them within the scope of a cost model.  相似文献   

5.
A stochastic model for prostate-specific antigen levels   总被引:1,自引:0,他引:1  
We introduce a continuous stochastic model for the prostate-specific antigen (PSA) levels following radiotherapy and derive solutions for the associated partial differential (Kolmogorov-Chapman) equation. The solutions describe the evolution of the time-dependent density for PSA levels which take into account an absorbing condition along the boundary and various initial conditions. We include implications for single-dose and multi-dose radiation treatment regimens and discuss parameter estimation and sensitivity issues.  相似文献   

6.
A stochastic bioburden model for spacecraft sterilization   总被引:1,自引:0,他引:1  
An important factor in the calculation of sterilization cycles for spacecraft is the bioburden on the surface of the spacecraft at the start of the cycle. This bioburden must be predicted by the use of models. This paper presents a stochastic model for the prediction of the bioburden on the surfaces of spacecraft. This model has many desirable properties as well as being consistent with observations.This work was conducted under Contract No. W-12,853, Planetary Programs, Office, of Space Science and Applications, NASA Headquarters, Washington, D.C.  相似文献   

7.
Disentangling the processes leading populations to extinction is a major topic in ecology and conservation biology. The difficulty to find a mate in many species is one of these processes. Here, we investigate the impact of self-incompatibility in flowering plants, where several inter-compatible classes of individuals exist but individuals of the same class cannot mate. We model pollen limitation through different relationships between mate availability and fertilization success. After deriving a general stochastic model, we focus on the simple case of distylous plant species where only two classes of individuals exist. We first study the dynamics of such a species in a large population limit and then, we look for an approximation of the extinction probability in small populations. This leads us to consider inhomogeneous random walks on the positive quadrant. We compare the dynamics of distylous species to self-fertile species with and without inbreeding depression, to obtain the conditions under which self-incompatible species can be less sensitive to extinction while they can suffer more pollen limitation.  相似文献   

8.
We investigate the dynamics of head lice infections in schools, by consideringa model for endemic infection based on a stochastic SIS (susceptible-infected-susceptible) epidemic model, with the addition of an external source of infection. We deduce a range of properties of our model, including the length of a single outbreak of infection. We use the stationary distribution of the number of infected individuals, in conjunction with data from a recent study carried out in Welsh schools on the prevalence of head lice infections, and employ maximum likelihood methods to obtain estimates of the model parameters. A complication is that, for each school, only a sample of the pupils was checked for infection. Our likelihood function takes account of the missing data by incorporating a hypergeometric sampling element. We arrive at estimates of the ratios of the “within school” and “external source” transmission rates to the recovery rate and use these to obtain estimates for various quantities of interest.   相似文献   

9.
A stochastic model for gene induction.   总被引:4,自引:0,他引:4  
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10.
Fewster RM 《Biometrics》2003,59(3):640-649
We use a spatiotemporal Markov process to model the spread of an ecological population through its environment over time. Available habitat is divided into sites, and a parametric function of spatial variables is used to model the probability that one site is colonized from another. This allows us both to make predictions about the future spread of a population, and to determine which are the important factors governing colonizations. The model evolves in discrete time, allowing the population distribution to change seasonally in accordance with breeding patterns. Discrete time formulations are natural for ecological populations, but are problematic due to difficulties of fitting and predicting over irregular time intervals. The model described here can accommodate years of missing data and can therefore fit and predict at irregular intervals. Two methods of approximating the likelihood are described and applied to ornithological survey data for the woodlark, Lullula arborea, from Thetford Forest in the U.K.  相似文献   

11.
A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model's behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka's Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values or rm and K. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetle Tribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.  相似文献   

12.
A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.  相似文献   

13.
For many progressive chronic diseases, there exist useful prognostic indicators for the course of the disease and the survival of the patient. The evolution of such an indicator is modelled as a monotone transformation of a pure birth process with killing. Explicit formulas are derived for the probability distribution of this process at an arbitrary time, the distribution of the first-passage times, the joint distribution of the survival time and the maximum of the process, and the marginals of this joint distribution. In two examples, the general formulas are evaluated in closed form.  相似文献   

14.

Background  

Irreversible electroporation (IRE) is a minimally invasive tissue ablation technique which utilizes electric pulses delivered by electrodes to a targeted area of tissue to produce high amplitude electric fields, thus inducing irreversible damage to the cell membrane lipid bilayer. An important application of this technique is for cancer tissue ablation. Mathematical modelling is considered important in IRE treatment planning. In the past, IRE mathematical modelling used a deterministic single value for the amplitude of the electric field required for causing cell death. However, tissue, particularly cancerous tissue, is comprised of a population of different cells of different sizes and orientations, which in conventional IRE are exposed to complex electric fields; therefore, using a deterministic single value is overly simplistic.  相似文献   

15.
Nernst equation has been directly used to formulate the oxidation reduction potential (ORP) of reversible thermodynamic conditions but applied to irreversible conditions after several assumptions and/or modifications. However, the assumptions are sometimes inappropriate in the quantification of ORP in nonequilibrium system. We propose a linear nonequilibrium thermodynamic model, called microbial related reduction and oxidation reaction (MIRROR Model No. 1) for the interpretation of ORP in biological process. The ORP was related to the affinities of catabolism and anabolism. The energy expenditure of catabolism and anabolism was directly proportional to overpotential (eta), straight coefficient of electrode (L(EE)), and degree of coupling between catabolism and ORP electrode, respectively. Finally, the limitations of MIRROR Model No. 1 were discussed for expanding the applicability of the model.  相似文献   

16.
A stochastic model for the sizes of detectable metastases   总被引:2,自引:0,他引:2  
A stochastic entirely mechanistic model of metastatic progression of cancer is developed. Based on this model the joint conditional distribution of the ordered sizes of detectable metastases given their number, n, is computed. It is shown that this distribution coincides with the joint distribution of order statistics for a random sample of size n derived from some probability distribution, and a formula for the latter is obtained. This formula is specialized for the case of exponentially growing primary and secondary tumors and exponentially distributed metastasis promotion times, and identifiability of model parameters is ascertained. These results allow for estimation of the natural history of cancer. As an example, it is estimated for a breast cancer patient with 31 bone metastases of known sizes. The proposed model for the sizes of detectable metastases provided an excellent fit to these data.  相似文献   

17.
In binocular fusion, pairs of left and right stimuli yielding the same brightness perception constitute an equibrightness curve in a coordinate system whose ordinate and abscissa correspond to the left and right stimulus strengths. A neural network model is presented to elucidate the characteristics of the curve. According to the model, Fechner's paradox is due to the threshold characteristics of the neuron. If the shapes or movements are radically different between the left and right stimuli, the retinal rivalry is caused. That is, only the left stimulus is perceived at one moment and the right stimulus at another moment. The period of left or right eye dominance alternates randomly from time to time. The distribution of the period is approximate to the gamma distribution. In order to account for this fact, a neural network model is proposed, which consists of a pair of neurons receiving inputs with stochastic fluctuations. The computer simulation was carried out with satisfactory results. The model of retinal rivalry is integrated with that of brightness perception.  相似文献   

18.
We study population biology of eusocial insects such as Ropalidia marginata through a stochastic model based on random (matrix) difference equations. This facilitates a study of dynamics of such populations when the survival and other rates vary randomly over time. The worker-brood relatedness, which is a function of the underlying population structure, can be used to explain theories on the evolution of altruism. The effect of demographic parameters and the queen takeover probabilities on the worker-brood relatedness has been studied. Based on the proposed model, we simulate insect colonies where queens are replaced. Simulation results help us to study the effect of various factors on the worker-brood relatedness. Further, we study two estimators of the worker-brood relatedness and suggest procedures for estimating their standard errors. Approximate confidence intervals for the same can be constructed with the help of these results.  相似文献   

19.
Yu M  Tan W  Lin H 《Biochimica et biophysica acta》2012,1818(11):2494-2501
A 1D Fokker-Planck simulation of DNA translocation through an electropore under finite pulses is presented. This study is motivated by applications relevant to DNA electrotransfer into biological cells via electroporation. The results review important insights. The translocation may occur on two disparate time scales, the electrophoretic time (~ms), and the diffusive time (~s), depending on the pulse length. Furthermore, a power-law correlation is observed, F-PST~(V(m)t(p))(a)/N(b), where F-PST is the final probability of successful translocation, V(m) is the transmembrane potential, t(p) is the pulse length, and N is the DNA length in segments. The values for a and b are close to 1 and 1.5, respectively. The simulated results are compared with previous data to interpret the trends. In particular, the diffusive time scale is used to explain the frequency dependence observed in electroporation experiments with uni- and bi-polar pulse trains. The predictions from the current model can be harnessed to help design experiments for the further understanding and quantification of DNA electrotransfer.  相似文献   

20.
A computational model is presented for the detection of coherent motion based on template matching and hidden Markov models. The premise of this approach is that the growth in detection sensitivity is greater for coherent motion of structured forms than for random coherent motion. In this preliminary study, a recent experiment was simulated with the model and the results are shown to be in agreement with the above premise. This model can be extended to be part of a more complex and elaborate computational visual system.  相似文献   

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