Stochastic Simulation Algorithm Research Articles

Integrated reservoir and basin modeling in understanding the petroleum system and evaluating prospects: The Cenomanian reservoir, Bahariya Formation, at Falak Field, Shushan Basin, Western Desert, Egypt

Robust inferences on understanding the reservoir heterogeneity and processes of the respective petroleum system are essential to reduce risks throughout the petroleum exploration and development phases. In this paper we present integrated static reservoir modeling and basin modeling to better characterise the reservoir rock; hydrocarbon-bearing sandstones of the Cenomanian Bahariya Formation. This reservoir is an element of the petroleum system; whose times of hydrocarbon generation-migration-accumulation, and entrapment, are also to be addressed; in Falak Field, Meleiha Area, Shushan Basin, Western Desert, Egypt. We utilized dataset including seismic profiles and well logs of four wells. Stratigraphic and structural modeling was performed to delineate the reservoir framework, then facies and petrophysical modeling, using stochastic simulation algorithms, was performed to delineate the reservoir architecture. 1D basin modeling was performed to retrieve the geohistory and maturation models of the area. Combining both reservoir and basin models was aimed, in this study, at identifying new petroleum prospects and estimating the volume of hydrocarbons within the reservoir intervals of the study area. According to the constructed reservoir and basin models, we identified three new petroleum prospect areas; to the NE, NW, and southern parts of Falak Field; that lead to reliable consistent inferences reasonably have sound impact on the oilfield development phases of the area.

A kinetic Fokker–Planck approach to model hard-sphere gas mixtures

Since its first introduction, it has always been a subject of research to find models for a meaningful approximation of the highly accurate but complex Boltzmann equation. In the kinetic Fokker–Planck (FP) approach, a FP operator in velocity space is employed to approximate the collision integral of the Boltzmann equation. Instead of directly solving the resulting FP equation, a Monte Carlo technique is used to model an associated random process. This approach leads to an efficient stochastic solution algorithm. In recent years, the FP ansatz has become increasingly popular. Nevertheless, the modeling of gas mixtures in the context of kinetic FP has so far only been addressed in a very few papers. This article introduces a kinetic FP model that is capable of describing gas mixtures with particles interacting according to the hard-sphere collision model. The model is constructed to reproduce Grad’s 13 moment equations on a Navier–Stokes level of accuracy for gas mixtures with an arbitrary number of constituents. A stochastic simulation algorithm is derived that ensures a correct evolution of the species diffusion velocities and the species temperatures for a homogeneous gas, regardless of the applied time step size. It is shown that the proposed model is capable of correctly predicting shear stresses, heat fluxes, and diffusion velocities for different test cases, employing a He–Ar mixture.

A Diffusion Based Embedding of the Stochastic Simulation Algorithm in Continuous Space

A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function Reaction Dynamics (GFRD), and variations thereon -- each offering trade-offs with respect to the ranges of phenomena they can model, their computational tractability, and the difficulty of fitting them to experimental measurements. Here, we develop a multiscale approach combining efficient SSA-like sampling suitable for well-mixed systems with aspects of the slower but space-aware GFRD model, assuming as with GFRD that reactions occur in a spatially heterogeneous environment that must be explicitly modeled. Our method extends the SSA approach in two major ways. First, we sample bimolecular association reactions following diffusive motion with a time-dependent reaction propensity. Second, reaction locations are sampled from within overlapping diffusion spheres describing the spatial probability densities of individual reactants. We show the approach to provide efficient simulation of spatially heterogeneous biochemistry in comparison to alternative methods via application to a Michaelis-Menten model.

Sismonr: simulation of in silico multi-omic networks with adjustable ploidy and post-transcriptional regulation in R

We present sismonr, an R package for an integral generation and simulation of in silico biological systems. The package generates gene regulatory networks, which include protein-coding and non-coding genes along with different transcriptional and post-transcriptional regulations. The effect of genetic mutations on the system behaviour is accounted for via the simulation of genetically different in silico individuals. The ploidy of the system is not restricted to the usual haploid or diploid situations but can be defined by the user to higher ploidies. A choice of stochastic simulation algorithms allows us to simulate the expression profiles of the genes in the in silico system. We illustrate the use of sismonr by simulating the anthocyanin biosynthesis regulation pathway for three genetically distinct in silico plants. The sismonr package is implemented in R and Julia and is publicly available on the CRAN repository (https://CRAN.R-project.org/package=sismonr). A detailed tutorial is available from GitHub at https://oliviaab.github.io/sismonr/. Supplementary data are available at Bioinformatics online.

HybridModels: An R Package for the Stochastic Simulation of Disease Spreading in Dynamic Networks

Disease spreading simulations are traditionally performed using coupled differential equations. However, in the setting of metapopulations, most of the solutions provided by this method do not account for the dynamic topography of subpopulations. Conversely, the alternative approach of individual-based modeling (IBM) may add computational cost and complexity. Hybrid models allow for the study of disease spreading because they combine both aforementioned approaches by separating them across different scales: a local scale that addresses subpopulation dynamics using coupled differential equations and a global scale that addresses the contact between these subpopulations using IBM. We present a simple way of simulating the spread of disease in dynamic networks using the high-level statistical computational language R and the hybridModels package. We built four examples using disease spread models at the local scale in several different networks: an animal movement network; a three-node network, whose model solution using a stochastic simulation algorithm is compared with the ordinary differential equations approach; the commuting of individuals between patches, which we compare with the permanent migration of individuals; and the commuting of individuals within the metropolitan area of São Paulo.

Stochastic Simulation to Visualize Gene Expression and Error Correction in Living Cells

ABSTRACT Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential equation approach by generating typical system histories, instead of just statistical measures such as the mean and variance of a population. Simple simulations are now easy for students to construct from scratch—that is, without recourse to black-box packages. In some cases, their results can also be compared directly with single-molecule experimental data. After introducing the stochastic simulation algorithm, this article gives two case studies involving gene expression and error correction, respectively. For gene expression, stochastic simulation results are compared with experimental data, an important research exercise for biophysics students. For error correction, several proofreading models are compared to find the minimal components necessary for sufficient accuracy in translation. Animations of the stochastic error correction models provide insight into the proofreading mechanisms. Code samples and resulting animations showing results are given in the online Supplemental Material.

RETRACTED: Stochastic simulation for time and space fractional differential equations

In this paper, we aim to study the stochastic simulation for time and space fractional differential equations. First, we prove that the stochastic solution of the time and space fractional differential equation is a stable subordinated process driven by the stable Lévy motion. Then, the absorbent term is employed for this equation; we find the corresponding parent process yields to be driven by a tempered stable process. At last, we design an algorithm to simulate the trajectory of the proposed process. The Monte Carlo methods are also employed to get the approximated solution of the fractional differential equations. The contribution of this paper is to establish the relation between the time and space fractional differential equations and stochastic process, and provide the stochastic simulation algorithm for this fractional differential equations.

Heterogeneous responses to low level death receptor activation are explained by random molecular assembly of the Caspase-8 activation platform.

Ligand binding to death receptors activates apoptosis in cancer cells. Stimulation of death receptors results in the formation of intracellular multiprotein platforms that either activate the apoptotic initiator Caspase-8 to trigger cell death, or signal through kinases to initiate inflammatory and cell survival signalling. Two of these platforms, the Death-Inducing Signalling Complex (DISC) and the RIPoptosome, also initiate necroptosis by building filamentous scaffolds that lead to the activation of mixed lineage kinase domain-like pseudokinase. To explain cell decision making downstream of death receptor activation, we developed a semi-stochastic model of DISC/RIPoptosome formation. The model is a hybrid of a direct Gillespie stochastic simulation algorithm for slow assembly of the RIPoptosome and a deterministic model of downstream caspase activation. The model explains how alterations in the level of death receptor-ligand complexes, their clustering properties and intrinsic molecular fluctuations in RIPoptosome assembly drive heterogeneous dynamics of Caspase-8 activation. The model highlights how kinetic proofreading leads to heterogeneous cell responses and results in fractional cell killing at low levels of receptor stimulation. It reveals that the noise in Caspase-8 activation—exclusively caused by the stochastic molecular assembly of the DISC/RIPoptosome platform—has a key function in extrinsic apoptotic stimuli recognition.

Volumetric estimation and OOIP calculation of the Ronier4 block of Ronier oilfield in the Bongor basin, Chad

Ronier oilfield is located in the Bongor basin, lies to the southeast of Chad Lake in Africa is about 300 km from the southeast of capital N’djamena. The Bongor Basin is located at the crossing part of the Central Africa rift zone and the West Africa rift zone. Is a Mesozoic-Cenozoic rift basin developing the effects of Central Africa Shear zone? The successive discovery of well Ronier 1 in 2007 and well Ronier 4 in 2008 has indicated that they have a potential for commercial exploitation. The reservoir is a braided river delta front facies sediment with a proportion of 78% of sand and 22% of shale. In the actual work, Stochastic Gaussian Simulation algorithm under the phase control based on the collocated co-Kriging is adopted and the models of porosity, permeability and saturation are established. The porosity distributed mainly between 17 to 27%, and 19% on average. Due to the higher logging interpreting oil saturation, 60–72%, which conflicts with the irreducible water saturation of core obtained in the laboratory, a conservative value of 60% was used as the oil saturation of the OOIP calculation this time. The geological models were created this time mainly for Block Ronier 4, which include: KublaI-1, KublaI-2, Mimosa I and Mimosa II. The Original Oil in Place is 321 MMSTB, while the Gas Initial in Place is 514 MSTCF will be developed.

Stochastic simulation algorithms for computational systems biology: Exact, approximate, and hybrid methods

Nowadays, mathematical modeling is playing a key role in many different research fields. In the context of system biology, mathematical models and their associated computer simulations constitute essential tools of investigation. Among the others, they provide a way to systematically analyze systems perturbations, develop hypotheses to guide the design of new experimental tests, and ultimately assess the suitability of specific molecules as novel therapeutic targets. To these purposes, stochastic simulation algorithms (SSAs) have been introduced for numerically simulating the time evolution of a well-stirred chemically reacting system by taking proper account of the randomness inherent in such a system. In this work, we review the main SSAs that have been introduced in the context of exact, approximate, and hybrid stochastic simulation. Specifically, we will introduce the direct method (DM), the first reaction method (FRM), the next reaction method (NRM) and the rejection-based SSA (RSSA) in the area of exact stochastic simulation. We will then present the τ-leaping method and the chemical Langevin method in the area of approximate stochastic simulation and an implementation of the hybrid RSSA (HRSSA) in the context of hybrid stochastic-deterministic simulation. Finally, we will consider the model of the sphingolipid metabolism to provide an example of application of SSA to computational system biology by exemplifying how different simulation strategies may unveil different insights into the investigated biological phenomenon. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Analytical and Computational Methods > Computational Methods.

Multiscale Stochastic Reaction\u2013Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations

Two multiscale algorithms for stochastic simulations of reaction–diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction–diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches.

Analysis and remedy of negativity problem in hybrid stochastic simulation algorithm and its application

BackgroundThe hybrid stochastic simulation algorithm, proposed by Haseltine and Rawlings (HR), is a combination of differential equations for traditional deterministic models and Gillespie’s algorithm (SSA) for stochastic models. The HR hybrid method can significantly improve the efficiency of stochastic simulations for multiscale biochemical networks. Previous studies on the accuracy analysis for a linear chain reaction system showed that the HR hybrid method is accurate if the scale difference between fast and slow reactions is above a certain threshold, regardless of population scales. However, the population of some reactant species might be driven negative if they are involved in both deterministic and stochastic systems.ResultsThis work investigates the negativity problem of the HR hybrid method, analyzes and tests it with several models including a linear chain system, a nonlinear reaction system, and a realistic biological cell cycle system. As a benchmark, the second slow reaction firing time is used to measure the effect of negative populations on the accuracy of the HR hybrid method. Our analysis demonstrates that usually the error caused by negative populations is negligible compared with approximation errors of the HR hybrid method itself, and sometimes negativity phenomena may even improve the accuracy. But for systems where negative species are involved in nonlinear reactions or some species are highly sensitive to negative species, the system stability will be influenced and may lead to system failure when using the HR hybrid method. In those circumstances, three remedies are studied for the negativity problem.ConclusionThe results of different models and examples suggest that the Zero-Reaction rule is a good remedy for nonlinear and sensitive systems considering its efficiency and simplicity.

Universality in stochastic enzymatic futile cycle

• Enzymatic futile cycle model is solved within the stochastic framework. • At thermodynamic limit, species probabilities follow universal Poisson distribution . • Normal distribution at large N limit is independent of thermodynamical parameters. • Noise, which can induce switching mechanism, could be a key regulating element. • The patterns of states driven by noise may correspond to distinct cellular states. The enzymatic futile cycle model, which is believe to regulate functional mechanism of bimolecular networks and associated signal processing, is solved analytically within the stochastic framework. The obtained probability distributions of substrate and product at stochastic to deterministic transition exhibit Poisson distribution, and with large ⟨ x ⟩ limit Normal distribution which are independent of thermodynamic variables indicating universal behavior of molecular distribution. The dynamics of the substrate and product, by simulating the reaction network using stochastic simulation algorithm , exhibit switching mechanism driven by noise in the system. We also observe various distinct noise driven patterns which may correspond to various cellular states. We propose that this noise induce switching mechanism and patterns could be a key element to regulate and control signal processing in molecular networks of cellular system, and may exhibit in the phenotype.

A new stochastic simulation algorithm for image-based classification: Feature-space indicator simulation

Traditional parametric methods for classification of land use and land cover (LULC) types using remote sensing imagery assume a global distribution model and fail to consider local variation of categorical variables. Differently, non-parametric methods do not make any statistical assumptions but are typically sensitive to the sample sizes of training sample data that usually require a high cost to collect in the field. Geostatistical classifiers, such as indicator kriging and simulation, are local variability-based methods that exhibit great potential for image-based classification of LULC types. However, variogram models required are highly sensitive to the spatial configuration of training samples as well as sample size given a study area. Moreover, when a large number of spectral variables are considered into kriging systems, modeling the variograms and cross-variograms would be problematic. To circumvent these issues, this study extended the geostatistical methods from a 2-dimensional geographic space to a m-dimensional image feature space to derive feature-space indicator variograms (FSIVs). Moreover, a novel stochastic simulation classification algorithm, Feature-Space Indicator Simulation (FSIS), was proposed and examined for classification of LULC types in Duolun County located in Inner Mongolia and in Huang-Feng-Qiao (HFQ) forest farm, Hunan of China. In Duolun, six LULC types were involved and in HFQ a complicated forest landscape consisting of nine forest types plus water, built-up area, and agricultural/bare soil, was classified. The classification results of FSIS were compared with another feature-space geostatistical classifier – feature-space indicator kriging (FSIK), a traditional parametric method – maximum likelihood (ML), a widely used nonparametric method – support vector machine (SVM), and a recently popular method – random forest (RF). The results showed that compared with ML, SVM and RF, in both study areas FSIS statistically significantly increased the accuracy of the classifications by 10.0–29.9% for percentage correct and 19.0–47.6% for Kappa statistic. Compared with FSIK, FSIS also improved the classification accuracy but the accuracy increases were relatively smaller with the percentages correct of 3.5% and 7.6% and the Kappa values of 4.6% and 8.6% for Duolun and HFQ, respectively. Moreover, FSIS led to the spatial uncertainties of the classification estimates as the quality measure of the estimates. In addition, the results also demonstrated that FSIVs were sensitive to the within-class heterogeneity but not very much to the size of training samples. Overall, FSIS exhibited the greater potential to improve the classification accuracy of LULC and forest types using remote sensing image.

Uniformization techniques for stochastic simulation of chemical reaction networks.

This work considers the method of uniformization for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformization can be beneficial in the context of time-inhomogeneous models, such as chemical reaction networks incorporating extrinsic noise. This paper lays focus on the understanding of uniformization from the viewpoint of sample paths of chemical reaction networks. In particular, an efficient pathwise stochastic simulation algorithm for time-homogeneous models is presented which is complexity-wise equal to Gillespie's direct method. This new approach therefore enlarges the class of problems for which the uniformization approach forms a computationally attractive choice. Furthermore, as a new application of the uniformization method, we provide a novel variance reduction method for (raw) moment estimators of chemical reaction networks based upon the combination of stratification and uniformization.

A hybrid method for micro-mesoscopic stochastic simulation of reaction-diffusion systems

The present paper introduces a new micro–meso hybrid algorithm based on the Ghost Cell Method concept in which the microscopic subdomain is governed by the Reactive Multi-Particle Collision (RMPC) dynamics. The mesoscopic subdomain is modeled using the Reaction-Diffusion Master Equation (RDME). The RDME is solved by means of the Inhomogeneous Stochastic Simulation Algorithm. No hybrid algorithm has hitherto used the RMPC dynamics for modeling reactions and the trajectories of each individual particle. The RMPC is faster than other molecular based methods and has the advantage of conserving mass, energy and momentum in the collision and free streaming steps. The new algorithm is tested on three reaction-diffusion systems. In all the systems studied, very good agreement with the deterministic solutions of the corresponding differential equations is obtained. In addition, it has been shown that proper discretization of the computational domain results in significant speed-ups in comparison with the full RMPC algorithm.

Improved Optical Multiplexing with Temporal DNA Barcodes.

Many biochemical events of importance are complex and dynamic. Fluorescence microscopy offers a versatile solution to study the dynamics of biology at the mesoscale. An important challenge in the field is the simultaneous study of several objects of interest, referred to as optical multiplexing. For improved multiplexing, some prior techniques used repeated reporter washing or the geometry of nanostructures; however, these techniques require complex nanostructure assembly, multiple reporters, or advanced multistep drift correction. Here we propose a time-based approach, for improved optical multiplexing, that uses readily available inexpensive reporters and requires minimal preparation efforts. We program short DNA strands, referred hereby as DNA devices, such that they undergo unique conformation changes in the presence of the dye-labeled reporters. The universal fluorescent reporter transiently binds with the devices to report their activity. Since each device is programmed to exhibit different hybridization kinetics, their fluorescent time trace, referred to as the temporal barcode, will be unique. We model our devices using continuous-time Markov chains and use stochastic simulation algorithm to generate their temporal patterns. We first ran simulation experiments with a small number of DNA devices, demonstrating several distinct temporal barcodes, all of which use a single dye color. Later, using nanostructure-based devices, we designed a much larger pool of temporal barcodes and used machine learning for classification of these barcodes. Our simulation experiments and design principles can aid in the experimental demonstration of the DNA devices.

Strategies for integrating uncertainty in iterative geostatistical seismic inversion

Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic properties, overlooking alternative sources of uncertainty such as those associated with poor well-log data, upscaling, and noise within the seismic data. We have expressed uncertain well-log samples, due to bad logging reads and upscaling, in terms of local probability distribution functions (PDFs). Local PDFs are used as conditioning data to a stochastic sequential simulation algorithm, included as the model perturbation within the inversion. The problem of noisy seismic and narrow exploration of the model parameter space, particularly in the early steps of the inversion, is tackled by the introduction of a cap on local correlation coefficients (CCs) responsible for the generation of the new set of models during the next iteration. We evaluate a single geostatistical framework with application to a real case study. When compared against a conventional iterative geostatistical seismic inversion, the integration of additional sources of uncertainty increases the match between real and inverted seismic traces and the variability within the ensemble of models inverted at the last iteration. The selection of the local PDFs plays a central role in the reliability of the inverted elastic models. Avoiding high local CCs at early stages of the inversion increases convergence in terms of global correlation between synthetic and real seismic reflection data at the end of the inversion.

DIFFpop: a stochastic computational approach to simulate differentiation hierarchies with single cell barcoding.

DIFFpop is an R package designed to simulate cellular differentiation hierarchies using either exponentially-expanding or fixed population sizes. The software includes functionalities to simulate clonal evolution due to the emergence of driver mutations under the infinite-allele assumption as well as options for simulation and analysis of single cell barcoding and labeling data. The software uses the Gillespie Stochastic Simulation Algorithm and a modification of expanding or fixed-size stochastic process models expanded to a large number of cell types and scenarios. DIFFpop is available as an R-package along with vignettes on Github (https://github.com/ferlicjl/diffpop). Supplementary data are available at Bioinformatics online.

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require O(logN) or even O(1) operations per update – where N is the number of nodes – display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of O[log(logN)] per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks.