Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.     

Simple Method for Introducing Elemental Mercury into Biological Growth Systems

Elemental mercury can be introduced into closed aqueous growth environments and sampled therefrom without loss of elemental mercury to the atmosphere.     

生物系统中脂质过氧化检测方法的评述

生物体系中脂质过氧化的检测方法是脂质过氧化反应机理研究能否取得成功的关键因素之一.检测生物体系中脂质过氧化的方法有多种,但各种检测方法在不同的实验中都显示出一定的优缺点,近年来应用较多并且很有前途的实验方法是高压液相色谱法以及化学发光法等.     

生物源性基因疫苗的运送系统

基因疫苗具有很多独特的优点,已经成为疫苗研究领域的热点。但由于其免疫原性相对较弱,限制了基因疫苗的广泛应用。人们一直在寻求一种理想的基因疫苗运送系统,它不仅能将基因疫苗导入体内,还能提高基因疫苗的免疫原性,诱导机体产生持续高水平的免疫应答反应。     

Use of Fourier Series for the Analysis of Biological Systems

In an attempt to quantitate the physical behavior of biological systems, Fourier analysis has been applied to the respiratory and circulatory systems by a number of investigators. The validity of this application has been questioned on the basis that these systems are nonlinear and not strictly periodic. If these objections were valid much of the more recent work in this field would have to be re-evaluated. The applicability of Fourier analysis to these two systems was therefore investigated, both theoretically and experimentally, using on-line analysis on a LINC (laboratory instrument computer) digital computer. In normal anesthetized dogs errors introduced by deviations from periodicity and linearity were found to be within the range of measurement errors. In sinusoidally perfused aortas the amount of second harmonic produced by the vessel was less than 5%. In addition, the magnitude of errors due to faulty determination of cycle length, sampling techniques, aliasing, and A-D (analogue to digital) conversion were evaluated and found to be within the noise level of the measuring equipment when appropriate techniques were employed. Utmost care has to be used in the coupling between a transducer and the system to be measured, and dynamic calibration before each experiment is a prerequisite for successful analysis. With presently available equipment the static measurement errors can be reduced to ±0.2 cm H₂O for pressure transducers, 0.1 cm³/sec for electromagnetic flowmeters, and 5 × 10^-4 cm for measurement of radius changes. The frequency response of this equipment once properly coupled to the system is flat to at least 20 cycle/sec.     

Robustness Analysis of Stochastic Biochemical Systems

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.     

随机Lotka-Volterra系统的稳定性

利用Lyapunov方法与K．lto公式及鞅的理论,研究了随机Lotka-Volterra系统正平衡点的全局渐近稳定性．得到了随机全局渐近稳定的主要定理,并以确定性系统的全局稳定性作为定理的推论．     

3D Modelling of Biological Systems for Biomimetics

1　IntroductionBasedonthereviewofthepreviousworkof 3Dgeometricalmodellingtechniquesandsystemsdevelopedforindustrial,medicalandanimationapplications,thispaperdiscussestheproblemsassociatedwiththeexist ingtechniquesandsystems ,especiallywhenappliedto3Dmodellingof plants ,insectsandanimalsforbiomimeticsresearchanddevelopment .Then ,paperproposessomeareasofresearchinterestsin 3Dmod ellingofplants ,insectsandanimalsforBiomimetics .Toavoidtherepeating ,inthispaper ,biologicalobjectswillbeusedtorep…     

Stochastic Finite Element Analysis of Biological Systems: Comparison of a Simple Intervertebral Disc Model with Experimental Results

Statistical methods allow the effects of uncertainty to be incorporated into finite element models. This has potential benefits for the analysis of biological systems where natural variability can give rise to substantial uncertainty in both material and geometrical properties. In this study, a simple model of the intervertebral disc under compression was created and analysed as both a deterministic and a stochastic system. Factorial analysis was used to determine the important parameters to be included in the stochastic analysis. The predictions from the model were compared to experimental results from 21 sheep discs. The size and shape of the distribution of the axial deformations predicted by the model was consistent with the experimental results given that the number of model solutions far exceeded the number of experimental results. Stochastic models could be valuable in determining the range and most likely value of stress in a tissue or implant.     

Fluorescent Nanoparticles for the Measurement of Ion Concentration in Biological Systems

Tightly regulated ion homeostasis throughout the body is necessary for the prevention of such debilitating states as dehydration.¹ In contrast, rapid ion fluxes at the cellular level are required for initiating action potentials in excitable cells.² Sodium regulation plays an important role in both of these cases; however, no method currently exists for continuously monitoring sodium levels in vivo ³ and intracellular sodium probes ⁴ do not provide similar detailed results as calcium probes. In an effort to fill both of these voids, fluorescent nanosensors have been developed that can monitor sodium concentrations in vitro and in vivo.^5,6 These sensors are based on ion-selective optode technology and consist of plasticized polymeric particles in which sodium specific recognition elements, pH-sensitive fluorophores, and additives are embedded.^7-9 Mechanistically, the sodium recognition element extracts sodium into the sensor. ¹⁰ This extraction causes the pH-sensitive fluorophore to release a hydrogen ion to maintain charge neutrality within the sensor which causes a change in fluorescence. The sodium sensors are reversible and selective for sodium over potassium even at high intracellular concentrations.⁶ They are approximately 120 nm in diameter and are coated with polyethylene glycol to impart biocompatibility. Using microinjection techniques, the sensors can be delivered into the cytoplasm of cells where they have been shown to monitor the temporal and spatial sodium dynamics of beating cardiac myocytes.¹¹ Additionally, they have also tracked real-time changes in sodium concentrations in vivo when injected subcutaneously into mice.³ Herein, we explain in detail and demonstrate the methodology for fabricating fluorescent sodium nanosensors and briefly demonstrate the biological applications our lab uses the nanosensors for: the microinjection of the sensors into cells; and the subcutaneous injection of the sensors into mice.     

Multiscale Analysis of Biological Systems

It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essentially characterized by an entanglement of bottom-up and top-down influences following from their evolutionary history. A self-consistent multiscale scheme is proposed to capture the ensuing circular causality. Its differences with standard mean-field self-consistent equations and slow-fast decompositions are discussed. As such, this scheme offers a way to unravel the multilevel architecture of living systems and their regulation. Two examples, genome functions and biofilms, are detailed.     

High-Resolution Two-Dimensional J-Resolved NMR Spectroscopy for Biological Systems

NMR spectroscopy is a principal tool in metabolomic studies and can, in theory, yield atom-level information critical for understanding biological systems. Nevertheless, NMR investigations on biological tissues generally have to contend with field inhomogeneities originating from variations in macroscopic magnetic susceptibility; these field inhomogeneities broaden spectral lines and thereby obscure metabolite signals. The congestion in one-dimensional NMR spectra of biological tissues often leads to ambiguities in metabolite identification and quantification. We propose an NMR approach based on intermolecular double-quantum coherences to recover high-resolution two-dimensional (2D) J-resolved spectra from inhomogeneous magnetic fields, such as those created by susceptibility variations in intact biological tissues. The proposed method makes it possible to acquire high-resolution 2D J-resolved spectra on intact biological samples without recourse to time-consuming shimming procedures or the use of specialized hardware, such as magic-angle-spinning probes. Separation of chemical shifts and J couplings along two distinct dimensions is achieved, which reduces spectral crowding and increases metabolite specificity. Moreover, the apparent J coupling constants observed are magnified by a factor of 3, facilitating the accurate measurement of small J couplings, which is useful in metabolic analyses. Dramatically improved spectral resolution is demonstrated in our applications of the technique on pig brain tissues. The resulting spectra contain a wealth of chemical shift and J-coupling information that is invaluable for metabolite analyses. A spatially localized experiment applied on an intact fish (Crossocheilus siamensis) reveals the promise of the proposed method in in vivo metabolite studies. Moreover, the proposed method makes few demands on spectrometer hardware and therefore constitutes a convenient and effective manner for metabonomics study of biological systems.     

Size-Independent Differences between the Mean of Discrete Stochastic Systems and the Corresponding Continuous Deterministic Systems

In this paper, it is shown that for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is a stable stationary state for the discrete stochastic system, and other finite states have zero probability of existence at large times. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.     

Stochastic Modelling for Systems Biology. * Darren J. Wilkinson

‘Stochastic Modelling for Systems Biology’ was designedto fill an important gap in the educational materials availablefor students learning about modelling methods for biologicalsystems. Specifically, while stochastic models are emergingas perhaps the preferred method for modelling cellular and subcellularbiochemistry in research practice, they remain unfamiliar tomost of those who are not specialists in the field. The underlyingmathematical and computational methods are well described inthe literature of other fields, but the translation to biologicalpractice is largely documented only in the current scientificliterature. There are few teaching materials available for thesemodels, particularly     

StochPy: A Comprehensive,User-Friendly Tool for Simulating Stochastic Biological Processes

Single-cell and single-molecule measurements indicate the importance of stochastic phenomena in cell biology. Stochasticity creates spontaneous differences in the copy numbers of key macromolecules and the timing of reaction events between genetically-identical cells. Mathematical models are indispensable for the study of phenotypic stochasticity in cellular decision-making and cell survival. There is a demand for versatile, stochastic modeling environments with extensive, preprogrammed statistics functions and plotting capabilities that hide the mathematics from the novice users and offers low-level programming access to the experienced user. Here we present StochPy (Stochastic modeling in Python), which is a flexible software tool for stochastic simulation in cell biology. It provides various stochastic simulation algorithms, SBML support, analyses of the probability distributions of molecule copy numbers and event waiting times, analyses of stochastic time series, and a range of additional statistical functions and plotting facilities for stochastic simulations. We illustrate the functionality of StochPy with stochastic models of gene expression, cell division, and single-molecule enzyme kinetics. StochPy has been successfully tested against the SBML stochastic test suite, passing all tests. StochPy is a comprehensive software package for stochastic simulation of the molecular control networks of living cells. It allows novice and experienced users to study stochastic phenomena in cell biology. The integration with other Python software makes StochPy both a user-friendly and easily extendible simulation tool.     

Dimensionality Reduction of Bistable Biological Systems

Time hierarchies, arising as a result of interactions between system’s components, represent a ubiquitous property of dynamical biological systems. In addition, biological systems have been attributed switch-like properties modulating the response to various stimuli across different organisms and environmental conditions. Therefore, establishing the interplay between these features of system dynamics renders itself a challenging question of practical interest in biology. Existing methods are suitable for systems with one stable steady state employed as a well-defined reference. In such systems, the characterization of the time hierarchies has already been used for determining the components that contribute to the dynamics of biological systems. However, the application of these methods to bistable nonlinear systems is impeded due to their inherent dependence on the reference state, which in this case is no longer unique. Here, we extend the applicability of the reference-state analysis by proposing, analyzing, and applying a novel method, which allows investigation of the time hierarchies in systems exhibiting bistability. The proposed method is in turn used in identifying the components, other than reactions, which determine the systemic dynamical properties. We demonstrate that in biological systems of varying levels of complexity and spanning different biological levels, the method can be effectively employed for model simplification while ensuring preservation of qualitative dynamical properties (i.e., bistability). Finally, by establishing a connection between techniques from nonlinear dynamics and multivariate statistics, the proposed approach provides the basis for extending reference-based analysis to bistable systems.