Sequential Importance Sampling for Online Bayesian Changepoint Detection

Online detection of abrupt changes in the parameters of a generative model for a time series is useful when modelling data in areas of application such as finance, robotics, and biometrics. We present an algorithm based on Sequential Importance Sampling which allows this problem to be solved in an online setting without relying on conjugate priors. Our results are exact and unbiased as we avoid using posterior approximations, and only rely on Monte Carlo integration when computing predictive probabilities. We apply the proposed algorithm to three example data sets. In two of the examples we compare our results to previously published analyses which used conjugate priors. In the third example we demonstrate an application where conjugate priors are not available. Avoiding conjugate priors allows a wider range of models to be considered with Bayesian changepoint detection, and additionally allows the use of arbitrary informative priors to quantify the uncertainty more flexibly

Analysis of signalling pathways using the prism model checker

We describe a new modelling and analysis approach for signal transduction networks in the presence of incomplete data. We illustrate the approach with an example, the RKIP inhibited ERK pathway [1]. Our models are based on high level descriptions of continuous time Markov chains: reactions are modelled as synchronous processes and concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis of queries such as if a concentration reaches a certain level, will it remain at that level thereafter? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

Probabilistic reasoning and inference for systems biology

One of the important challenges in Systems Biology is reasoning and performing hypotheses testing in uncertain conditions, when available knowledge may be incomplete and the experimental data may contain substantial noise. In this thesis we develop methods of probabilistic reasoning and inference that operate consistently within an environment of uncertain knowledge and data. Mechanistic mathematical models are used to describe hypotheses about biological systems. We consider both deductive model based reasoning and model inference from data. The main contributions are a novel modelling approach using continuous time Markov chains that enables deductive derivation of model behaviours and their properties, and the application of Bayesian inferential methods to solve the inverse problem of model inference and comparison, given uncertain knowledge and noisy data. In the first part of the thesis, we consider both individual and population based techniques for modelling biochemical pathways using continuous time Markov chains, and demonstrate why the latter is the most appropriate. We illustrate a new approach, based on symbolic intervals of concentrations, with an example portion of the ERK signalling pathway. We demonstrate that the resulting model approximates the same dynamic system as traditionally defined using ordinary differential equations. The advantage of the new approach is quantitative logical analysis; we formulate a number of biologically significant queries in the temporal logic CSL and use probabilistic symbolic model checking to investigate their veracity. In the second part of the thesis, we consider the inverse problem of model inference and testing of alternative hypotheses, when models are defined by non-linear ordinary differential equations and the experimental data is noisy and sparse. We compare and evaluate a number of statistical techniques, and implement an effective Bayesian inferential framework for systems biology based on Markov chain Monte Carlo methods and estimation of marginal likelihoods by annealing-melting integration. We illustrate the framework with two case studies, one of which involves an open problem concerning the mediation of ERK phosphorylation in the ERK pathway

Analysis of the fluctuations of the tumour/host interface

In a recent analysis of metabolic scaling in solid tumours we found a scaling law that interpolates between the power laws μ∝V and μ∝V2∕3, where μ is the metabolic rate expressed as the glucose absorption rate and V is the tumour volume. The scaling law fits quite well both in vitro and in vivo data, however we also observed marked fluctuations that are associated with the specific biological properties of individual tumours. Here we analyse these fluctuations, in an attempt to find the population-wide distribution of an important parameter (A) which expresses the total extent of the interface between the solid tumour and the non-cancerous environment. Heuristic considerations suggest that the values of the A parameter follow a lognormal distribution, and, allowing for the large uncertainties of the experimental data, our statistical analysis confirms this

Computational inference in systems biology

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs

Detecting beta-amyloid aggregation from the time-resolved emission spectra

Aggregation of beta-amyloids is one of key processes responsible for the development of Alzheimer's desease. Early molecular-level detection of beta-amyloid oligomers may help in early diagnosis and in the development of new intervention therapies. Our previous studies on changes in beta-amyloid's single tyrosine intrinsic fluorescence response during aggregation demonstrated a four-exponential fluorescence intensity decay, and that the ratio of the pre-exponential factors indicated the extent of aggregation in the early stages of the process before the beta-sheets are formed. Here we present a complementary approach based on time-resolved emission spectra (TRES) of amyloid's tyrosine excited at 279 nm and fluorescent in the window 240-450 nm. TRES has been used to demonstrate sturctural changes occuring on the nanosecond time scale after excitation which has significant advantages over using steady-state spectra. We demonstrate this by resolving the fluorescent species and revealing that beta-amyloid's monomers show very fast dielectric relaxation and its oligomers display a substantial spectral shift due to dielectric relaxation, which gradually decreases when oligomers become larger

Resolving environmental microheterogeneity and dielectric relaxation in fluorescence kinetics of protein

The fluorescence intensity decay of protein is easily measurable and reports on the intrinsic fluorophore-local environment interactions on the sub-nm spatial and sub-ns temporal scales, which are consistent with protein activity in numerous biomedical and industrial processes. This makes time-resolved fluorescence a perfect tool for understanding, monitoring and controlling these processes at the molecular level, but the complexity of the decay, which has been traditionally fitted to multi-exponential functions, has hampered the development of this technique over the last few decades. Using the example of tryptophan in HSA we present the alternative to the conventional approach to modelling intrinsic florescence intensity decay in protein where the key factors determining fluorescence decay, i.e. the excited-state depopulation and the dielectric relaxation (Toptygin and Brand 2000 Chem. Phys. Lett. 322 496–502), are represented by the individual relaxation functions. This allows quantification of both effects separately by determining their parameters from the global analysis of a series of fluorescence intensity decays measured at different detection wavelengths. Moreover, certain pairs of the recovered parameters of tryptophan were found to be correlated, indicating the influence of the dielectric relaxation on the transient rate of the electronic transitions. In this context the potential for the dual excited state depopulation /dielectric relaxation fluorescence lifetime sensing is discussed

A subsystems approach for parameter estimation of ODE models of hybrid systems

We present a new method for parameter identification of ODE system descriptions based on data measurements. Our method works by splitting the system into a number of subsystems and working on each of them separately, thereby being easily parallelisable, and can also deal with noise in the observations.Comment: In Proceedings HSB 2012, arXiv:1208.315

A model checking approach to the parameter estimation of biochemical pathways

Model checking has historically been an important tool to verify models of a wide variety of systems. Typically a model has to exhibit certain properties to be classed ‘acceptable’. In this work we use model checking in a new setting; parameter estimation. We characterise the desired behaviour of a model in a temporal logic property and alter the model to make it conform to the property (determined through model checking). We have implemented a computational system called MC2(GA) which pairs a model checker with a genetic algorithm. To drive parameter estimation, the fitness of set of parameters in a model is the inverse of the distance between its actual behaviour and the desired behaviour. The model checker used is the simulation-based Monte Carlo Model Checker for Probabilistic Linear-time Temporal Logic with numerical constraints, MC2(PLTLc). Numerical constraints as well as the overall probability of the behaviour expressed in temporal logic are used to minimise the behavioural distance. We define the theory underlying our parameter estimation approach in both the stochastic and continuous worlds. We apply our approach to biochemical systems and present an illustrative example where we estimate the kinetic rate constants in a continuous model of a signalling pathway

Insulin aggregation tracked by its intrinsic TRES

Time-resolved emission spectra (TRES) have been used to detect conformational changes of intrinsic tyrosines within bovine insulin at a physiological pH. The approach offers the ability to detect the initial stages of insulin aggregation at the molecular level. The data analysis has revealed the existence of at least three fluorescent species undergoing dielectric relaxation and significant spectral changes due to insulin aggregation. The results indicate the suitability of the intrinsic TRES approach for insulin studies and for monitoring its stability during storage and aggregation in insulin delivery devices