A mass action model of a fibroblast growth factor signaling pathway and its simplification

We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951–66, 2005, Biosystems 83, 152–66, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925–9938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter

Value Iteration for Long-run Average Reward in Markov Decision Processes

Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks

Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games

Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus on zero-sum goals and cannot reason about scenarios where entities are endowed with different objectives. In this paper, we propose probabilistic model checking techniques for concurrent stochastic games based on Nash equilibria. We extend the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to allow reasoning about players with distinct quantitative goals, which capture either the probability of an event occurring or a reward measure. We present algorithms to synthesise strategies that are subgame perfect social welfare optimal Nash equilibria, i.e., where there is no incentive for any players to unilaterally change their strategy in any state of the game, whilst the combined probabilities or rewards are maximised. We implement our techniques in the PRISM-games tool and apply them to several case studies, including network protocols and robot navigation, showing the benefits compared to existing approaches

Physiotherapeutic management in the separation of the white borderline

Dissolution of the white border of the rectus abdominal muscle is a disruption of the functioning of the rectus muscle, which results in loosening of the white border. As a result, a characteristic muscle stretch is visible. This defect affects a significant number of pregnant women and is not just an aesthetic problem. There are many factors that contribute to the above-mentioned ailments. To get the best treatment results, it is important to diagnose the problem early. For this purpose, special tests are used. The ease with which they are made enables the patient to control the separation of the frontier by the patient. The implementation of therapy should take place already in the first days after delivery. It is important to start therapy with posture corrective exercises, breathing exercises and learning how to properly perform everyday activities. Then we implement exercises that involve the abdominal muscles. The exercise program can be supplemented with dynamic slicing. A holistic approach to the problem and combining different forms of therapy allows you to obtain optimal results

Quantitative multi-objective verification for probabilistic systems

We present a verification framework for analysing multiple quantitative objectives of systems that exhibit both nondeterministic and stochastic behaviour. These systems are modelled as probabilistic automata, enriched with cost or reward structures that capture, for example, energy usage or performance metrics. Quantitative properties of these models are expressed in a specification language that incorporates probabilistic safety and liveness properties, expected total cost or reward, and supports multiple objectives of these types. We propose and implement an efficient verification framework for such properties and then present two distinct applications of it: firstly, controller synthesis subject to multiple quantitative objectives; and, secondly, quantitative compositional verification. The practical applicability of both approaches is illustrated with experimental results from several large case studies

Oral administration of Lactococcus lactis expressing synthetic genes of myelin antigens in decreasing experimental autoimmune encephalomyelitis in rats

ABSTRACT Background: Multiple sclerosis is a human autoimmunological disease that causes neurodegeneration. One of the potential ways to stop its development is induction of oral tolerance, whose effect lies in decreasing immune response to the fed antigen. It was shown on animal models that administration of specific epitopes of the three main myelin proteins, myelin oligodendrocyte glycoprotein (MOG), myelin basic protein (MBP) and proteolipid protein (PLP) results in induction of oral tolerance and suppression of disease symptoms. Application of bacterial cells to produce and deliver antigens to gut mucosa seems to be an attractive method for oral tolerance induction in treatment of diseases with autoimmune background. Material/Methods: Synthetic genes of MOG35-55, MBP85-97 and PLP139-151 myelin epitopes were generated and cloned in Lactococcus lactis under a CcpA-regulated promoter. The tolerogenic effect of bacterial preparations was tested on experimental autoimmune encephalomyelitis, the animal model of MS. EAE was induced in rats by intradermal injection of guinea pig homogenate into hind paws. Results: Rats were administered preparations containing whole-cell lysates of L. lactis producing myelin antigens using different feeding schemes. Our study demonstrates that 20-fold, but not 4-fold, intragastric administration of autoantigen-expressing L. lactis cells under specific conditions reduces the clinical symptoms of EAE in rats. Conclusions: The present study evaluates the use of myelin antigens produced in L. lactis in inhibiting the on-set of experimental autoimmune encephalomyelitis in rats. Obtained results indicate that application of such recombinant cells can be an attractive method of oral tolerance induction

A Study of the PDGF Signaling Pathway with PRISM

In this paper, we apply the probabilistic model checker PRISM to the analysis of a biological system -- the Platelet-Derived Growth Factor (PDGF) signaling pathway, demonstrating in detail how this pathway can be analyzed in PRISM. We show that quantitative verification can yield a better understanding of the PDGF signaling pathway.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Digital Financial Inclusion in a Cashless Society

Quarriers commissioned the Rix Inclusive Research team to carry out an evaluation study to explore how people with learning disabilities manage and use their money, what works and what is difficult. This report details the activities undertaken by the research team as part of this phase. It provides an account of the aims and objectives, methodology, points of discussion, conclusion, and recommendations for Phase 2 of the project, which will consider possible practical solutions to support people with learning disabilities to move from cash to cashless (digital) payments, and towards digital finance overall, in order to fully participate in the cashless society

Model Checking Probabilistic Real-Time Properties for Service-Oriented Systems with Service Level Agreements

The assurance of quality of service properties is an important aspect of service-oriented software engineering. Notations for so-called service level agreements (SLAs), such as the Web Service Level Agreement (WSLA) language, provide a formal syntax to specify such assurances in terms of (legally binding) contracts between a service provider and a customer. On the other hand, formal methods for verification of probabilistic real-time behavior have reached a level of expressiveness and efficiency which allows to apply them in real-world scenarios. In this paper, we suggest to employ the recently introduced model of Interval Probabilistic Timed Automata (IPTA) for formal verification of QoS properties of service-oriented systems. Specifically, we show that IPTA in contrast to Probabilistic Timed Automata (PTA) are able to capture the guarantees specified in SLAs directly. A particular challenge in the analysis of IPTA is the fact that their naive semantics usually yields an infinite set of states and infinitely-branching transitions. However, using symbolic representations, IPTA can be analyzed rather efficiently. We have developed the first implementation of an IPTA model checker by extending the PRISM tool and show that model checking IPTA is only slightly more expensive than model checking comparable PTA.Comment: In Proceedings INFINITY 2011, arXiv:1111.267