The stochastic model of non-equilibrium mutagen-induced alterations of DNA: implication to genetic instability in cancer

Genetic alterations such as point mutations, chromosomal rearrangements, modification of DNA methylation and chromosome aberrations accumulate during the lifetime of an organism. They can be caused by intrinsic errors in the DNA replication and repair as well as by external factors such as exposure to mutagenic substances or radiation. The main purpose of the present work is to begin an exploration of the stochastic nature of non-equilibrium DNA alteration caused by events such as tautomeric shifts. This is done by modeling the genetic DNA code chain as a sequence of DNA-bit values ('1' for normal bases and '-1' for abnormal bases). We observe the number of DNA-bit changes resulting from the random point mutation process which, in the model, is being induced by a stochastic Brownian mutagen (BM) as it diffuses through the DNA-bit systems. Using both an analytical and Monte Carlo (MC) simulation techniques, we observe the local and global number of DNA-bit changes. It is found that in 1D, the local DNA-bit density behaves like 1/t, the global total number of the switched (abnormal) DNA-bit increases as t. The probability distribution P(b, 0, t) of b(0, t) is log-normal. It is also found that when the number of mutagens is increased, the number of the total abnormal DNA-bits does not grow linearly with the number of mutagens. All analytic results are in good agreement with the simulation results.     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

A stochastic model for the membrane potential of a stimulated neuron

We present a simple model describing the transition between the prefiring, firing and postfiring phases of a single neuron in a large neural net. Using typical values for the physiological parameters that enter the model, we find average interspike times that are close to those reported in experimental measurements.     

Numerical simulation of a stochastic model for cancerous cells submitted to chemotherapy

A stochastic model is proposed to study the problem of inherent resistance by cell populations when chemotherapeutic agents are used to control tumor growth. Stochastic differential equations are introduced and numerically integrated to simulate expected response to the chemotherapeutic strategies as a function of different parameters. Satisfactory demonstration runs of the model indicate that it could represent a useful tool in verifying the results of experimental and clinical chemotherapy courses and planning treatment strategies. Some types of behaviour are illustrated graphically.Work supported by the C.N.R. Grants: 85.02652.01; 86.02116.01     

Calculated ventilation and effort distribution as a measure of respiratory disease and Heliox effectiveness

In spite of numerous clinical studies, there is no consensus on the benefit Heliox mixtures can bring to asthmatic patients in terms of work of breathing and ventilation distribution. In this article we use a 3D finite element mathematical model of the lung to study the impact of asthma on effort and ventilation distribution along with the effect of Heliox compared to air. Lung surface displacement fields extracted from computed tomography medical images are used to prescribe realistic boundary conditions to the model. Asthma is simulated by imposing bronchoconstrictions to some airways of the tracheo-bronchial tree based on statistical laws deduced from the literature. This study illuminates potential mechanisms for patient responsiveness to Heliox when affected by obstructive pulmonary diseases. Responsiveness appears to be function of the pathology severity, as well as its distal position in the tracheo-bronchial tree and geometrical position within the lung.     

Identifiability of a stochastic model for cell debris in flow cytometry

 One of the most important problems in recovering DNA distribution from flow cytometric DNA measurements is the presence of background noise. In this paper, we analyse a probabilistic model recently proposed for background debris distribution and based on a specific probabilistic mechanism for the DNA fragmentation process of the cell nucleus. In particular, we carry out some sufficient conditions to uniquely identify the original DNA distribution from the flow cytometric data. Received: 15 June 1997 / Revised version: 18 November 1997     

Development of a Purification Procedure for the Isolation of Nucleosides from Urine Prior to Mass Spectrometric Analysis

Abstract

A chromatographic separation of nucleosides from urine has been developed in order to facilitate their mass spectrometric analysis for clinical diagnosis. A number of chromatographic resins were studied in order to develop an effective and efficient purification procedure. The optimized sequential protocol comprises a centrifugation, acidification and neutralization step, followed by application of an affinity chromatographic column and finally further separation on an acidic cation exchange column and a basic anion exchanger. This scheme shows effective clean-up of a standard radiolabelled nucleoside with a recovery of 92.5%, and recovery of nucleosides added to urine samples before extraction showed recoveries of 72 – 82%.     

First and second moments and the mean hamming distance in a stochastic replication-mutation model for biological macromolecules

In this work first and second moments for a many species Moran model are calculated. The model describes by means of a time-continuous birth- and death process the evolution of an ensemble of N macromolecules out of n possible species. The molecules may replicate (correct or erroneous, in the latter case producing mutants) and may undergo elimination. Replication and elimination will be coupled in order to keep population size constant. In the case of arbitrary replication rates an expansion of the moments in powers of 1/N is found. For equal replication rates exact calculation of the moments is possible. In the case of a v-cube model (binary macromolecules) the second moments may be used to find a simple expression for the mean Hamming distance in the system. This quantity provides a measure for the localization of the ensemble.Supported by Stiftung Volkswagenwerk     

A numeric study of the noise-induced tremor in a mathematical model of the stretch reflex

A mathematical model of the stretch reflex for the cat soleus muscle is presented. The time-delay differential equations of the model are solved using the fourth-order Runge-Kutta algorithm, introducing a Gaussian-noise term to simulate the environmental noise. The muscle response dynamics are then studied under various levels of average muscle activation. Finally, the feasibility of explaining the so-called physiological tremor from the properties of the stretch reflex mechanisms is discussed by comparing our results with reported experimental evidence.     

Likelihood-based inference for stochastic models of sexual network formation

Sexually-transmitted diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insight focuses attention on the distribution of sexual activity level in a population. In this paper, we develop several stochastic process models for the formation of sexual partnership networks. Using likelihood-based model selection procedures, we assess the fit of the different models to three large distributions of sexual partner counts: (1) Rakai, Uganda, (2) Sweden, and (3) the USA. Five of the six single-sex networks were fit best by the negative binomial model. The American women's network was best fit by a power-law model, the Yule. For most networks, several competing models fit approximately equally well. These results suggest three conclusions: (1) no single unitary process clearly underlies the formation of these sexual networks, (2) behavioral heterogeneity plays an essential role in network structure, (3) substantial model uncertainty exists for sexual network degree distributions. Behavioral research focused on the mechanisms of partnership formation will play an essential role in specifying the best model for empirical degree distributions. We discuss the limitations of inferences from such data, and the utility of degree-based epidemiological models more generally.     

Development and use of a Mathematical model for an antarctic Lake

We describe the development and use of the first mathematical computer model for a polar lake. This dynamic model graphically illustrates seasonal and annual predictions of the changes in the biomass of plankton and attached primary producers, decomposers and consumers, changes in the quantities of potential nutrients and organic matter. The model consists of 100 submodels of which 79 are algebraic equations and 21 are differential equations. It has proven valuable as a means of identifying voids in our limnological program and probable errors in field measurements.Department of StatisticsDepartment of Biology     

Bayesian inference for stochastic kinetic models using a diffusion approximation

This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.     

Parameter estimation in a Gompertzian stochastic model for tumor growth

The problem of estimating parameters in the drift coefficient when a diffusion process is observed continuously requires some specific assumptions. In this paper, we consider a stochastic version of the Gompertzian model that describes in vivo tumor growth and its sensitivity to treatment with antiangiogenic drugs. An explicit likelihood function is obtained, and we discuss some properties of the maximum likelihood estimator for the intrinsic growth rate of the stochastic Gompertzian model. Furthermore, we show some simulation results on the behavior of the corresponding discrete estimator. Finally, an application is given to illustrate the estimate of the model parameters using real data.     

Mean-square stability of a stochastic model for bacteriophage infection with time delays

We consider the stability properties of the positive equilibrium of a stochastic model for bacteriophage infection with discrete time delay. Conditions for mean-square stability of the trivial solution of the linearized system around the equilibrium are given by the construction of suitable Lyapunov functionals. The numerical simulations of the strong solutions of the arising stochastic delay differential system suggest that, even for the original non-linear model, the longer the incubation time the more the phage and bacteria populations can coexist on a stable equilibrium in a noisy environment for very long time.     

A stochastic model of cancer initiation including a bystander effect

A stochastic model of cancer initiation is considered. The model is used to evaluate whether a bystander effect may be important in the pre-malignant and malignant stages of carcinogenesis, and furthermore, on the basis of epidemiological data, to estimate the mutation rates of genes involved in the development of oral leukoplakias. The bystander effect is defined here as the capability of oncogenic mutations to increase the mutation probability of neighbouring (bystander) cells, thus leading potentially to a cascade of neighbouring mutated and neoplastic cells as a pre-stage in the development to leukoplakias and cancer. We find that incidence data for oral cancer are indeed in accordance with a significant bystander effect, operating either alone or in combination with genomic instability in the early stages of carcinogenesis, i.e. the development of neoplasia. Simulations performed gave a picture of how mutations and neoplasia may spread in a tissue, to form characteristic leukoplakias with a core of neoplastic cells. The model also showed that the probability of finding at least one neoplastic cell in the tissue after a given number of years is more sensitive to changes in genomic instability within the cell itself than to changes in a bystander effect. Based on epidemiological data we also calculate the maximum number of oncogenic genes that may be involved in the bystander effect and development of genomic instability. Even if capable of explaining the initial development of oncogenic mutations towards neoplastic cells, the bystander model could not reproduce the observed incidence rates of leukoplakia without assuming a carcinogen mutation probability per cell per year of neoplastic cells practically equal to one. This means that the bystander effect, to be of substantial importance in the final development of neoplastic cells towards leukoplakias, requires a very significant increase in mutation probabilities for bystanders to neoplastic cells. Alternatively, additional mechanisms such as abnormal cell differentiation and uncontrolled proliferation and apoptotis in the neoplastic stage may be of major importance during the development to cancerization.