David Spieler

In Vivo Control of CpG and Non-CpG DNA Methylation by DNA Methyltransferases

The enzymatic control of the setting and maintenance of symmetric and non-symmetric DNA methylation patterns in a particular genome context is not well understood. Here, we describe a comprehensive analysis of DNA methylation patterns generated by high resolution sequencing of hairpin-bisulfite amplicons of selected single copy genes and repetitive elements (LINE1, B1, IAP-LTR-retrotransposons, and major satellites). The analysis unambiguously identifies a substantial amount of regional incomplete methylation maintenance, i.e. hemimethylated CpG positions, with variant degrees among cell types. Moreover, non-CpG cytosine methylation is confined to ESCs and exclusively catalysed by Dnmt3a and Dnmt3b. This sequence position–, cell type–, and region-dependent non-CpG methylation is strongly linked to neighboring CpG methylation and requires the presence of Dnmt3L. The generation of a comprehensive data set of 146,000 CpG dyads was used to apply and develop parameter estimated hidden Markov models (HMM) to calculate the relative contribution of DNA methyltransferases (Dnmts) for de novo and maintenance DNA methylation. The comparative modelling included wild-type ESCs and mutant ESCs deficient for Dnmt1, Dnmt3a, Dnmt3b, or Dnmt3a/3b, respectively. The HMM analysis identifies a considerable de novo methylation activity for Dnmt1 at certain repetitive elements and single copy sequences. Dnmt3a and Dnmt3b contribute de novo function. However, both enzymes are also essential to maintain symmetrical CpG methylation at distinct repetitive and single copy sequences in ESCs.

Bounding the equilibrium distribution of Markov population models

SUMMARY We propose a bounding technique for the equilibrium probability distribution of continuous-time Markov chains with population structure and infinite state space. We use Lyapunov functions to determine a finite set of states that contains most of the equilibrium probability mass. Then we apply a refinement scheme based on stochastic complementation to derive lower and upper bounds on the equilibrium probability for each state within that set. To show the usefulness of our approach, we present experimental results for several examples from biology. Copyright

Parameter identification for Markov models of biochemical reactions

We propose a numerical technique for parameter inference in Markov models of biological processes. Based on time-series data of a process we estimate the kinetic rate constants by maximizing the likelihood of the data. The computation of the likelihood relies on a dynamic abstraction of the discrete state space of the Markov model which successfully mitigates the problem of state space largeness. We compare two variants of our method to state-of-the-art, recently published methods and demonstrate their usefulness and efficiency on several case studies from systems biology.

Approximate maximum likelihood estimation for stochastic chemical kinetics

Recent experimental imaging techniques are able to tag and count molecular populations in a living cell. From these data mathematical models are inferred and calibrated. If small populations are present, discrete-state stochastic models are widely-used to describe the discreteness and randomness of molecular interactions. Based on time-series data of the molecular populations, the corresponding stochastic reaction rate constants can be estimated. This procedure is computationally very challenging, since the underlying stochastic process has to be solved for different parameters in order to obtain optimal estimates. Here, we focus on the maximum likelihood method and estimate rate constants, initial populations and parameters representing measurement errors.

Fault, Compensation and Termination in WS-BPEL 2.0 -- A Comparative Analysis

One of the most challenging aspects in Web Service composition is guaranteeing transactional integrity. This is usually achieved by providing mechanisms for fault, compensation and termination (FCT) handling. WS-BPEL 2.0, the de-facto standard language for Business Process Orchestration provides powerful scope-based FCT-handling mechanisms. However, the lack of a formal semantics makes it difficult to understand and implement these constructs, and renders rigid analysis impossible. The general concept of compensating long-running business transactions has been studied in different formal theories, such as cCSP and Sagas, but none of them is specific to WS-BPEL 2.0. Other approaches aim at providing formal semantics for FCT-handling in WS-BPEL 2.0, but only concentrate on specific aspects. Therefore, they cannot be used for a comparative analysis of FCT-handling in WS-BPEL 2.0. In this paper we discuss the BPEL approach to FCT-handling in the light of recent research. We provide formal semantics for the WS-BPEL 2.0 FCT-handling mechanisms which aims at capturing the FCT-part of the WS-BPEL 2.0 specification in full detail. We then compare the WS-BPEL 2.0 approach to FCT-handling to existing formal theories.

Infinite level-dependent QBD processes and matrix-analytic solutions for stochastic chemical kinetics

Systems of stochastic chemical kinetics are modeled as infinite level-dependent quasi-birth-and-death (LDQBD) processes. For these systems, in contrast to many other applications, levels have an increasing number of states as the level number increases and the probability mass may reside arbitrarily far away from lower levels. Ideas from Lyapunov theory are combined with existing matrix-analytic formulations to obtain accurate approximations to the stationary probability distribution when the infinite LDQBD process is ergodic. Results of numerical experiments on a set of problems are provided.

On-the-fly verification and optimization of DTA-properties for large Markov chains

We consider continuous-time Markov chains (CTMC) with very large or infinite state spaces which are, for instance, used to model biological processes or to evaluate the performance of computer and communication networks. We propose a numerical integration algorithm to approximate the probability that a process conforms to a specification that belongs to a subclass of deterministic timed automata (DTAs). We combat the state space explosion problem by using a dynamic state space that contains only the most relevant states. In this way we avoid an explicit construction of the state-transition graph of the composition of the DTA and the CTMC. We also show how to maximize the probability of acceptance of the DTA for parametric CTMCs and substantiate the usefulness of our approach with experimental results from biological case studies.

Characterizing oscillatory and noisy periodic behavior in markov population models

In systems biology, an interesting problem is to analyze and characterize the oscillatory and periodic behavior of a chemical reaction system. Traditionally, those systems have been treated deterministically and continuously via ordinary differential equations. In case of high molecule counts with respect to the volume this treatment is justified. But otherwise, stochastic fluctuations can have a high influence on the characteristics of a system as has been shown in recent publications. In this paper we develop an efficient numerical approach for analyzing the oscillatory and periodic character of user-defined observations on Markov population models (MPMs). MPMs are a special kind of continuous-time Markov chains that allow for a discrete representation of unbounded population counts for several population types and transformations between populations. Examples are chemical species and the reactions between them.

Model Checking CSL for Markov Population Models

Markov population models (MPMs) are a widely used modelling formalism in the area of computational biology and related areas. The semantics of a MPM is an infinite-state continuous-time Markov chain. In this paper, we use the established continuous stochastic logic (CSL) to express properties of Markov population models. This allows us to express important measures of biological systems, such as probabilistic reachability, survivability, oscillations, switching times between attractor regions, and various others. Because of the infinite state space, available analysis techniques only apply to a very restricted subset of CSL properties. We present a full algorithm for model checking CSL for MPMs, and provide experimental evidence showing that our method is effective.

Numerical analysis of long-run properties for Markov population models

One of the most versatile modeling formalism is the one given by Markov chains as used for the performance analysis of queuing systems or for cost benefit ratio optimizations in the financial sector In systems biology, chemical reaction networks have originally been studied using deterministic models. However, when it recently became apparent that only stochastic effects can explain certain phenomenons, Markov chains again turned out to be a suitable modeling formalism in the form of Markov population models. Those Markov chains possess a structured but potentially infinite state space where each state encodes the current counts of a fixed number of population types. Due to the infinite state space, classical steady state analysis methods can not be used directly. Hence, this doctoral thesis presents a highly efficient method to compute a finite state space truncation entailing most of the steady state probability mass. Further, stochastic complementation is lifted to the infinite state space setting and is combined with truncation based reachability analysis and aggregation to derive state wise steady state bounds. This method achieves high performance even for stiff systems. Particular attention is paid on a system’s ability to maintain stable oscillations and thus optimized analysis methods are developed alongside. In order to prove their applicability, all techniques are evaluated on a large variety of biological models.