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作者： MOHAMED NASURUDEEN MOHAMED BAHRUDEEN Tampere University of Technology

学位级别：硕士

Recent studies of gene expression in Escherichia coli using novel in vivo measurement techniques revealed that protein and RNA numbers from a gene differ between genet- ically identical cells. To unravel the causes for this, measurements were conducted and models were developed. These studies revealed that this diversity arises from extrinsic and intrinsic noise. The former is due to cell-to-cell variability in numbers of molecules involved, such as RNA polymerase (RNAp), transcription factors, etc. The latter is due to the stochastic nature of the chemical reactions combined with the fact that the mole- cules and genes involved exist in small numbers. One aspect that has not been given much attention so far, is the unique nature of the dynamics of transcription of each promoter of the gene regulatory network (GRN). This process has multiple rate-limiting steps whose duration differs between promoters. How this may diversify the variability in RNA and protein numbers between genes is unknown. To address this, we use single-cell empirical data and stochastic models with empirically validated parameter values and study how the kinetics of transcription of a gene affects the influence of extrinsic noise on the kinetics. Interestingly, we find that promoters whose open complex formation is longer lasting tend to suppress the propagation of ex- trinsic noise that affects only the steps prior to initiation of the open complex formation. In particular, our studies indicate that the cell-to-cell variability in RNA numbers depends on the transcription kinetics. As such, it is sequence-dependent. Further, in a 2-gene tog- gle switch, we find that its mean switching frequency depends on the transcription kinet- ics of the promoters but not on the cell-to-cell RNAp variability. On the other hand, the cell-to-cell variability in switching frequency is affected by these two variables. Mean- while, in a Repressilator network (3 genes where each gene represses the next), we meas- u

关键词： transcription initiation kinetics gene regulatory networks stochastic simulation algorithm extrinsic noise cell-to-cell variability

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Tvorba spolehlivostních modelů pro pokročilé číslicové systémy

Tvorba spolehlivostních modelů pro pokročilé číslicov...

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作者： Wanka, Mario Brno University of Technology

Cílem této práce je simulovat vliv spolehlivosti obvodů detekujících chybu u komponent pokročilých digitálních systémů. Prvně je definována spolehlivost a skutečnosti... 详细信息

Cílem této práce je simulovat vliv spolehlivosti obvodů detekujících chybu u komponent pokročilých digitálních systémů. Prvně je definována spolehlivost a skutečnosti s ní související a jsou představeny Markovské modely. Tyto jsou využity pro samotný simulátor, který je představený v následující kapitole. Jedná se o ad-hoc řešení a použití tohoto simulátoru je detailně popsáno. Stejně tak je popsáno jeho chování v průzných situacích a s různou konfigurací. Na závěr jsou ukázány a diskutovány výsledky experimentů se spolehlivostí obvodů detekujících chybu pro různé modely. Dle výsledků práce je zřejmé, že zásadním faktorem pro zajištění spolehlivosti systému je krátkodobé maskování chyby a dlouhodobé udržení opravovatelnosti.

关键词： Spolehlivost Markovský model Systémy zatížené chybou stochastický simulační algoritmus Pravděpodobnost bezporuchového provozu Reliability Markov model systems with faults stochastic simulation algorithm Probability of failure-free service Text

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Tvorba spolehlivostních modelů pro pokročilé číslicové systémy

Tvorba spolehlivostních modelů pro pokročilé číslicov...

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作者： Trávníček, Jan Brno University of Technology

Tato práce se zabývá problematikou spolehlivosti systémů. Nejprve je zde diskutován samotný pojem spolehlivosti a její ukazatele, kterými spolehlivost můžeme konkrétně vy... 详细信息

Tato práce se zabývá problematikou spolehlivosti systémů. Nejprve je zde diskutován samotný pojem spolehlivosti a její ukazatele, kterými spolehlivost můžeme konkrétně vyjadřovat. V~další kapitole jsou popsány možné spolehlivostní modely pro jednoduché a složitější systémy. Dále jsou zde popsány základní postupy pro tvorbu spolehlivostních modelů. Čtvrtá kapitola je věnována velmi důležitým markovským modelům. Markovské modely jsou velmi silným a komplexním nástrojem pro výpočet spolehlivosti složitých systému. Je zde vysvětlena vhodnost jejich použití pro obnovované systémy, které mohou obsahovat absorpční stavy. Další kapitola popisuje zálohu systému. Diskutuje výhody a nevýhody statické, dynamické a hybridní zálohy. Také je zde popsán vliv různé úrovně zatížení na životnost součástek. Šestá kapitola je věnována implementaci, popisu aplikace a vstupního souboru ve formátu XML. Jsou zde také diskutovány naměřené výsledky získané při experimentálních výpočtech.

关键词： Spolehlivost Spolehlivostní modely Markovský model Markovský řetězec Záloha systému stochastický simulační algoritmus. Reliability Reliability models Markov model Markov chain Standby redundancy stochastic simulation algorithm Text

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stochastic sequence-level model of coupled transcription and translation in prokaryotes

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BMC BIOINFORMATICS 2011年第1期12卷 1-13页

作者： Makela, Jarno Lloyd-Price, Jason Yli-Harja, Olli Ribeiro, Andre S. Tampere Univ Technol Computat Syst Biol Res Grp Dept Signal Proc FI-33101 Tampere Finland Inst Syst Biol Seattle WA 98103 USA

Background: In prokaryotes, transcription and translation are dynamically coupled, as the latter starts before the former is complete. Also, from one transcript, several translation events occur in parallel. To study how events in transcription elongation affect translation elongation and fluctuations in protein levels, we propose a delayed stochastic model of prokaryotic transcription and translation at the nucleotide and codon level that includes the promoter open complex formation and alternative pathways to elongation, namely pausing, arrests, editing, pyrophosphorolysis, RNA polymerase traffic, and premature termination. Stepwise translation can start after the ribosome binding site is formed and accounts for variable codon translation rates, ribosome traffic, back-translocation, drop-off, and trans-translation. Results: First, we show that the model accurately matches measurements of sequence-dependent translation elongation dynamics. Next, we characterize the degree of coupling between fluctuations in RNA and protein levels, and its dependence on the rates of transcription and translation initiation. Finally, modeling sequence-specific transcriptional pauses, we find that these affect protein noise levels. Conclusions: For parameter values within realistic intervals, transcription and translation are found to be tightly coupled in Escherichia coli, as the noise in protein levels is mostly determined by the underlying noise in RNA levels. Sequence-dependent events in transcription elongation, e. g. pauses, are found to cause tangible effects in the degree of fluctuations in protein levels.

关键词： Translation Initiation Synonymous Codon Ribosome Binding Site Transcription Elongation stochastic simulation algorithm

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stochastic SIR model predicts the evolution of COVID-19 epidemics from public health and wastewater data in small and medium-sized municipalities: A one year study

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CHAOS SOLITONS & FRACTALS 2022年第0期164卷 112671页

作者： Pajaro, Manuel Fajar, Noelia M. Alonso, Antonio A. Otero-Muras, Irene IIM CSIC Spanish Natl Res Council BioProc Engn Grp Eduardo Cabello 6 Vigo 36208 Spain Univ A Coruna CITIC Res Ctr Dept Math Campus Elvina S-N La Coruna 15071 Spain CSIC Spanish Natl Res Council Inst Integrat Syst Biol I2SysBio UV Valencia 46980 Spain

The level of unpredictability of the COVID-19 pandemics poses a challenge to effectively model its dynamic evolution. In this study we incorporate the inherent stochasticity of the SARS-CoV-2 virus spread by reinterpreting the classical compartmental models of infectious diseases (SIR type) as chemical reaction systems modeled via the Chemical Master Equation and solved by Monte Carlo Methods. Our model predicts the evolution of the pandemics at the level of municipalities, incorporating for the first time (i) a variable infection rate to capture the effect of mitigation policies on the dynamic evolution of the pandemics (ii) SIR-with-jumps taking into account the possibility of multiple infections from a single infected person and (iii) data of viral load quantified by RT-qPCR from samples taken from Wastewater Treatment Plants. The model has been successfully employed for the prediction of the COVID-19 pandemics evolution in small and medium size municipalities of Galicia (Northwest of Spain).

关键词： SIR model COVID-19 SARS-coV-2 stochastic mechanistic model Chemical master equation stochastic simulation algorithm

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A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

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BMC BIOINFORMATICS 2007年第1期8卷 175-175页

作者： Samant, Asawari Ogunnaike, Babatunde A. Vlachos, Dionisios G. Univ Delaware Dept Chem Engn Newark DE 19716 USA

Background: The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo ( HyMSMC) method that fills in this void. Results: The proposed HyMSMC method blends stochastic singular perturbation concepts, to deal with potential stiffness, with a hybrid of exact and coarse- grained stochastic algorithms, to cope with separation in population sizes. In addition, we introduce the computational singular perturbation ( CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence. We also propose a new criteria of convergence of fast networks to stochastic low- dimensional manifolds, which further accelerates the algorithm. Conclusion: We use several prototype and biological examples, including a gene expression model displaying bistability, to demonstrate the efficiency, accuracy and applicability of the HyMSMC method. Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.

关键词： Probability Distribution Function Fast Mode stochastic simulation algorithm Participation Index Fast Network

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Accelerated maximum likelihood parameter estimation for stochastic biochemical systems

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BMC BIOINFORMATICS 2012年第1期13卷 1-18页

作者： Daigle, Bernie J., Jr. Roh, Min K. Petzold, Linda R. Niemi, Jarad Iowa State Univ Dept Stat Ames IA 50011 USA Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA

Background: A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems;methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. Results: We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods. Conclusions: This work provides

关键词： Simulated Trajectory stochastic Gradient Descent Confidence Ellipse stochastic simulation algorithm Simulated Maximum Likelihood

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Efficient computation of transient solutions of the chemical master equation based on uniformization and quasi-Monte Carlo

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JOURNAL OF CHEMICAL PHYSICS 2008年第15期128卷 54109-1-54109-7页

作者： Hellander, Andreas Uppsala Univ Dept Informat Technol Div Comp Sci SE-75105 Uppsala Sweden Uppsala Univ Dept Informat Technol Div Comp Sci SE-75105 Uppsala Sweden

A quasi-Monte Carlo method for the simulation of discrete time Markov chains is applied to the simulation of biochemical reaction networks. The continuous process is formulated as a discrete chain subordinate to a Poisson process using the method of uniformization. It is shown that a substantial reduction of the number of trajectories that is required for an accurate estimation of the probability density functions (PDFs) can be achieved with this technique. The method is applied to the simulation of two model problems. Although the technique employed here does not address the typical stiffness of biochemical reaction networks, it is useful when computing the PDF by replication. The method can also be used in conjuncture with hybrid methods that reduce the stiffness. (C) 2008 American Institute of Physics.

关键词： stochastic simulation algorithm REACTING SYSTEMS

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Analysis and verification of the HMGB1 signaling pathway

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BMC BIOINFORMATICS 2010年第Sup7期11卷 S10-S10页

作者： Gong, Haijun Zuliani, Paolo Komuravelli, Anvesh Faeder, James R. Clarke, Edmund M. Carnegie Mellon Univ Dept Comp Sci Pittsburgh PA 15213 USA Univ Pittsburgh Dept Computat Biol Pittsburgh PA 15260 USA

Background: Recent studies have found that overexpression of the High-mobility group box-1 (HMGB1) protein, in conjunction with its receptors for advanced glycation end products (RAGEs) and toll-like receptors (TLRs), is associated with proliferation of various cancer types, including that of the breast and pancreatic. Results: We have developed a rule-based model of crosstalk between the HMGB1 signaling pathway and other key cancer signaling pathways. The model has been simulated using both ordinary differential equations (ODEs) and discrete stochastic simulation. We have applied an automated verification technique, Statistical Model Checking, to validate interesting temporal properties of our model. Conclusions: Our simulations show that, if HMGB1 is overexpressed, then the oncoproteins CyclinD/E, which regulate cell proliferation, are overexpressed, while tumor suppressor proteins that regulate cell apoptosis (programmed cell death), such as p53, are repressed. Discrete, stochastic simulations show that p53 and MDM2 oscillations continue even after 10 hours, as observed by experiments. This property is not exhibited by the deterministic ODE simulation, for the chosen parameters. Moreover, the models also predict that mutations of RAS, ARF and P21 in the context of HMGB1 signaling can influence the cancer cell's fate - apoptosis or survival - through the crosstalk of different pathways.

关键词： Model Check stochastic simulation Tumor Suppressor Protein Cell Cycle Regulatory Protein stochastic simulation algorithm

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Bayesian inference of biochemical kinetic parameters using the linear noise approximation

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BMC BIOINFORMATICS 2009年第1期10卷 343-343页

作者： Komorowski, Michal Finkenstadt, Barbel Harper, Claire V. Rand, David A. Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England Univ Warwick Syst Biol Ctr Coventry CV4 7AL W Midlands England Univ Warwick Math Inst Coventry CV4 7AL W Midlands England Univ Liverpool Dept Biol Liverpool L69 3BX Merseyside England

Background: Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results: We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion: The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods.

关键词： Posterior Distribution Transition Density Diffusion Approximation stochastic simulation algorithm Ordinary Differential Equation Model

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