Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Advanced computing for systems biology

Systems biology is based on computational modelling and simulation of large networks of interacting components. Models may be intended to capture processes, mechanisms, components and interactions at different levels of fidelity. Input data are often large and geographically disperse, and may require the computation to be moved to the data, not vice versa. In addition, complex system-level problems require collaboration across institutions and disciplines. Grid computing can offer robust, scaleable solutions for distributed data, compute and expertise. We illustrate some of the range of computational and data requirements in systems biology with three case studies: one requiring large computation but small data (orthologue mapping in comparative genomics), a second involving complex terabyte data (the Visible Cell project) and a third that is both computationally and data-intensive (simulations at multiple temporal and spatial scales). Authentication, authorisation and audit systems are currently not well scalable and may present bottlenecks for distributed collaboration particularly where outcomes may be commercialised. Challenges remain in providing lightweight standards to facilitate the penetration of robust, scalable grid-type computing into diverse user communities to meet the evolving demands of systems biology.

Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Environmental scanning electron microscope imaging of vesicle systems

The structural characteristics of liposomes have been widely investigated and there is certainly a strong understanding of their morphological characteristics. Imaging of these systems, using techniques such as freeze-fracturing methods, transmission electron microscopy, and cryo-electron imaging, has allowed us to appreciate their bilayer structures and factors that influence this. However, there are a few methods that study these systems in their natural hydrated state; commonly, the liposomes are visualized after drying, staining and/or fixation of the vesicles. Environmental scanning electron microscopy (ESEM) offers the ability to image a liposome in its hydrated state without the need for prior sample preparation. We were the first to use ESEM to study the liposomes and niosomes, and have been able to dynamically follow the hydration of lipid films and changes in liposome suspensions as water condenses onto, or evaporates from, the sample in real-time. This provides an insight into the resistance of liposomes to coalescence during dehydration, thereby providing an alternative assay for liposome formulation and stability.

A structural method for the design of fault tolerant distributed control systems

Distributed digital control systems provide alternatives to conventional, centralised digital control systems. Typically, a modern distributed control system will comprise a multi-processor or network of processors, a communications network, an associated set of sensors and actuators, and the systems and applications software. This thesis addresses the problem of how to design robust decentralised control systems, such as those used to control event-driven, real-time processes in time-critical environments. Emphasis is placed on studying the dynamical behaviour of a system and identifying ways of partitioning the system so that it may be controlled in a distributed manner. A structural partitioning technique is adopted which makes use of natural physical sub-processes in the system, which are then mapped into the software processes to control the system. However, communications are required between the processes because of the disjoint nature of the distributed (i.e. partitioned) state of the physical system. The structural partitioning technique, and recent developments in the theory of potential controllability and observability of a system, are the basis for the design of controllers. In particular, the method is used to derive a decentralised estimate of the state vector for a continuous-time system. The work is also extended to derive a distributed estimate for a discrete-time system. Emphasis is also given to the role of communications in the distributed control of processes and to the partitioning technique necessary to design distributed and decentralised systems with resilient structures. A method is presented for the systematic identification of necessary communications for distributed control. It is also shwon that the structural partitions can be used directly in the design of software fault tolerant concurrent controllers. In particular, the structural partition can be used to identify the boundary of the conversation which can be used to protect a specific part of the system. In addition, for certain classes of system, the partitions can be used to identify processes which may be dynamically reconfigured in the event of a fault. These methods should be of use in the design of robust distributed systems.

Using quantitative analysis to implement autonomic IT systems

The software underpinning today’s IT systems needs to adapt dynamically and predictably to rapid changes in system workload, environment and objectives. We describe a software framework that achieves such adaptiveness for IT systems whose components can be modelled as Markov chains. The framework comprises (i) an autonomic architecture that uses Markov-chain quantitative analysis to dynamically adjust the parameters of an IT system in line with its state, environment and objectives; and (ii) a method for developing instances of this architecture for real-world systems. Two case studies are presented that use the framework successfully for the dynamic power management of disk drives, and for the adaptive management of cluster availability within data centres, respectively.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

The design of a support department simulator for use in the design of manufacturing systems

Manufacturing firms are driven by competitive pressures to continually improve the effectiveness and efficiency of their organisations. For this reason, manufacturing engineers often implement changes to existing processes, or design new production facilities, with the expectation of making further gains in manufacturing system performance. This thesis relates to how the likely outcome of this type of decision should be predicted prior to its implementation. The thesis argues that since manufacturing systems must also interact with many other parts of an organisation, the expected performance improvements can often be significantly hampered by constraints that arise elsewhere in the business. As a result, decision-makers should attempt to predict just how well a proposed design will perform when these other factors, or 'support departments', are taken into consideration. However, the thesis also demonstrates that, in practice, where quantitative analysis is used to evaluate design decisions, the analysis model invariably ignores the potential impact of support functions on a system's overall performance. A more comprehensive modelling approach is therefore required. A study of how various business functions interact establishes that to properly represent the kind of delays that give rise to support department constraints, a model should actually portray the dynamic and stochastic behaviour of entities in both the manufacturing and non-manufacturing aspects of a business. This implies that computer simulation be used to model design decisions but current simulation software does not provide a sufficient range of functionality to enable the behaviour of all of these entities to be represented in this way. The main objective of the research has therefore been the development of a new simulator that will overcome limitations of existing software and so enable decision-makers to conduct a more holistic evaluation of design decisions. It is argued that the application of object-oriented techniques offers a potentially better way of fulfilling both the functional and ease-of-use issues relating to development of the new simulator. An object-oriented analysis and design of the system, called WBS/Office, are therefore presented that extends to modelling a firm's administrative and other support activities in the context of the manufacturing system design process. A particularly novel feature of the design is the ability for decision-makers to model how a firm's specific information and document processing requirements might hamper shop-floor performance. The simulator is primarily intended for modelling make-to-order batch manufacturing systems and the thesis presents example models created using a working version of WBS/Office that demonstrate the feasibility of using the system to analyse manufacturing system designs in this way.

Dynamic QoS management and optimisation in service-based systems

Service-based systems that are dynamically composed at run time to provide complex, adaptive functionality are currently one of the main development paradigms in software engineering. However, the Quality of Service (QoS) delivered by these systems remains an important concern, and needs to be managed in an equally adaptive and predictable way. To address this need, we introduce a novel, tool-supported framework for the development of adaptive service-based systems called QoSMOS (QoS Management and Optimisation of Service-based systems). QoSMOS can be used to develop service-based systems that achieve their QoS requirements through dynamically adapting to changes in the system state, environment and workload. QoSMOS service-based systems translate high-level QoS requirements specified by their administrators into probabilistic temporal logic formulae, which are then formally and automatically analysed to identify and enforce optimal system configurations. The QoSMOS self-adaptation mechanism can handle reliability- and performance-related QoS requirements, and can be integrated into newly developed solutions or legacy systems. The effectiveness and scalability of the approach are validated using simulations and a set of experiments based on an implementation of an adaptive service-based system for remote medical assistance.

Models and performances of wireless MIMO and cooperative communication systems

Multiple-antenna systems offer significant performance enhancement and will be applied to the next generation broadband wireless communications. This thesis presents the investigations of multiple-antenna systems – multiple-input multiple-output (MIMO) and cooperative communication (CC) – and their performances in more realistic propagation environments than those reported previously. For MIMO systems, the investigations are conducted via theoretical modelling and simulations in a double-scattering environment. The results show that the variations of system performances depend on how scatterer density varies in flat fading channels, and that in frequency-selective fading channels system performances are affected by the length of the coding block as well as scatterer density. In realistic propagation environments, the fading correlation also has an impact on CC systems where the antennas can be further apart than those in MIMO systems. A general stochastic model is applied to studying the effects of fading correlation on the performances of CC systems. This model reflects the asymmetry fact of the wireless channels in a CC system. The results demonstrate the varied effects of fading correlation under different protocols and channel conditions. Performances of CC systems are further studied at the packet level, using both simulations and an experimental testbed. The results obtained have verified various performance trade-offs of the cooperative relaying network (CRN) investigated in different propagation environments. The results suggest that a proper selection of the relaying algorithms and other techniques can meet the requirements of quality of service for different applications.