• MeSH
• Electrophysiology MeSH
• Neurons physiology   MeSH
• Stochastic Processes MeSH

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

• MeSH
• Stochastic Processes MeSH
• Models, Theoretical * MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH

• MeSH
• Time Factors MeSH
• Stochastic Processes MeSH
• Models, Theoretical MeSH
• Science MeSH
• Publication type
• Monograph MeSH

• Conspectus
• Statistika
• NML Fields
• statistika, zdravotnická statistika

• MeSH
• Mathematics MeSH
• Molecular Dynamics Simulation MeSH
• Publication type
• Monograph MeSH

• Conspectus
• Matematika
• NML Fields
• přírodní vědy

We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.

• MeSH
• Models, Biological MeSH
• Cell Cycle genetics   MeSH
• Humans MeSH
• Gene Expression Regulation MeSH
• Mammals MeSH
• Signal Transduction MeSH
• Stochastic Processes MeSH
• Systems Biology * MeSH
• Animals MeSH
• Check Tag
• Humans MeSH
• Animals MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH

This study has the purpose of assessing the changes in the efficiency scores caused by any additional variable introduced in a Stochastic Frontier Analysis, one of the most spread parametric methods which is able to differentiate the technical inefficiency of the unit assessed from the statistical noise and other exogenous factors that affect efficiency. The study will begin with the model Health Adjusted Life expectancy as input and Life Expectancy as output. After analyzing the results, maternal mortality will be added as input in the set and the model will be re-run. Data will be interpreted. A third input, Gini index, will be introduced in the last part of the analysis, in order to assess the new results of the model. As secondary objective, the study will evaluate the efficiency of the 27 European Union Health Systems and the changes from one model to another. The results show that by adding variables, the stochastic frontier and the efficiency scores change. Nonetheless, the direction of change is not random and the results are consistent with the theory.

• MeSH
• Humans MeSH
• Mathematics MeSH
• Maternal Mortality * MeSH
• Life Expectancy MeSH
• Statistics as Topic * MeSH
• Pregnancy MeSH
• Check Tag
• Humans MeSH
• Pregnancy MeSH
• Female MeSH
• Publication type
• Research Support, Non-U.S. Gov't MeSH

• MeSH
• Action Potentials MeSH
• Time Factors MeSH
• Models, Neurological MeSH
• Neurons physiology   MeSH
• Numerical Analysis, Computer-Assisted MeSH
• Computer Simulation MeSH
• Stochastic Processes MeSH

Five parameters of one of the most common neuronal models, the diffusion leaky integrate-and-fire model, also known as the Ornstein-Uhlenbeck neuronal model, were estimated on the basis of intracellular recording. These parameters can be classified into two categories. Three of them (the membrane time constant, the resting potential and the firing threshold) characterize the neuron itself. The remaining two characterize the neuronal input. The intracellular data were collected during spontaneous firing, which in this case is characterized by a Poisson process of interspike intervals. Two methods for the estimation were applied, the regression method and the maximum-likelihood method. Both methods permit to estimate the input parameters and the membrane time constant in a short time window (a single interspike interval). We found that, at least in our example, the regression method gave more consistent results than the maximum-likelihood method. The estimates of the input parameters show the asymptotical normality, which can be further used for statistical testing, under the condition that the data are collected in different experimental situations. The model neuron, as deduced from the determined parameters, works in a subthreshold regimen. This result was confirmed by both applied methods. The subthreshold regimen for this model is characterized by the Poissonian firing. This is in a complete agreement with the observed interspike interval data.

• MeSH
• Action Potentials physiology   MeSH
• Cell Membrane physiology   MeSH
• Financing, Organized MeSH
• Humans MeSH
• Brain physiology   MeSH
• Neural Pathways physiology   MeSH
• Synaptic Transmission physiology   MeSH
• Neural Networks, Computer MeSH
• Neurons physiology   MeSH
• Signal Processing, Computer-Assisted MeSH
• Poisson Distribution MeSH
• Stochastic Processes MeSH
• Synapses physiology   MeSH
• Animals MeSH
• Check Tag
• Humans MeSH
• Animals MeSH

Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.

• MeSH
• Algorithms MeSH
• Diagnosis, Computer-Assisted methods   MeSH
• Carcinoma, Ductal, Breast MeSH
• Fractals MeSH
• Risk Assessment methods   MeSH
• Humans MeSH
• Breast Neoplasms diagnosis   pathology   MeSH
• Pathology methods   MeSH
• Computer Simulation MeSH
• Stochastic Processes MeSH
• Check Tag
• Humans MeSH
• Female MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Comparative Study MeSH

Parameters in diffusion neuronal models are divided into two groups; intrinsic and input parameters. Intrinsic parameters are related to the properties of the neuronal membrane and are assumed to be known throughout the paper. Input parameters characterize processes generated outside the neuron and methods for their estimation are reviewed here. Two examples of the diffusion neuronal model, which are based on the integrate-and-fire concept, are investigated--the Ornstein--Uhlenbeck model as the most common one and the Feller model as an illustration of state-dependent behavior in modeling the neuronal input. Two types of experimental data are assumed-intracellular describing the membrane trajectories and extracellular resulting in knowledge of the interspike intervals. The literature on estimation from the trajectories of the diffusion process is extensive and thus the stress in this review is set on the inference made from the interspike intervals.

• MeSH
• Models, Neurological MeSH
• Neurons MeSH
• Publication type
• Research Support, Non-U.S. Gov't MeSH
• Review MeSH