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

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

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

Bayesian Model Selection and Emulation for Protein Fluorescence

Fluorescence decay of amino acids in protein is a complex process for which multiple models have been proposed. Likelihood function evaluation for certain models can be computationally expensive, and as such surrogate models may be introduced to speed up inference. In this paper, Gaussian processes are implemented in likelihood estimation of a range of models defined by convolutions of an initial excitation input and a decay function using both synthetic and real world data. Parameter inference and model selection using the surrogate models are performed and compared against the exact results. Model selection when incorporating surrogate models into the inference process is shown to be consistent

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

Impact of the flavonoid quercetin on beta-amyloid aggregation revealed by intrinsic fluorescence

We report the effects of quercetin, a flavonoid present in human diet, on early stage beta-amyloid (Aβ) aggregation – a seminal event in Alzheimer’s disease. Molecular level changes in Aβ arrangements are monitored by time-resolved emission spectral (TRES) measurements of the fluorescence of Aβ’s single tyrosine intrinsic fluorophore (Tyr). The results suggest that quercetin binds beta-amyloid oligomers at early stages of their aggregation, which leads to the formation of modified oligomers and hinders the creation of beta-sheet structures, potentially preventing the onset of Alzheimer’s disease

Protein fibrillogenesis model tracked by its intrinsic time-resolved emission spectra

The excited-state kinetics of the fluorescence of tyrosine in a de novo protein fibrillogenesis model was investigated as a potential tool for monitoring protein fibre formation and complexation with glucose (glycation). In stark contrast to insulin the time-resolved emission spectra (TRES) recorded over the period of 700 hours in buffered solutions of the model with and without glucose revealed no apparent changes in Tyr fluorescence responses. This indicates the stability of the model and provides a measurement-supported basis for its use as a reference material in fluorescence studies of protein aggregation

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

The aggregation of beta-amyloids is one of the key processes responsible for the development of Alzheimer's disease. 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 the changes in beta-amyloid's single tyrosine intrinsic fluorescence response during aggregation demonstrated a four-exponential fluorescence intensity decay, and the ratio of the pre-exponential factors indicated the extent of the aggregation in the early stages of the process before the beta-sheets were formed. Here we present a complementary approach based on the time-resolved emission spectra (TRES) of amyloid's tyrosine excited at 279 nmand 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.Wedemonstrate 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 the oligomers become larger

Sodium silicate particle size measurements using time-resolved fluorescence anisotropy

Sodium silicates are versatile inorganic chemicals produced by combining silica sand and soda ash (sodium carbonate) under high temperature. When in aqueous solution, they are often used in coating and bonding applications. Additionally, they exhibit a range of attractive characteristics, such as being odorless and non-toxic, high strength and rigidity, resistance to high temperatures and low-cost [1].The important characteristics of silicates are the correlation between the ratio of silica to soda concentrations and the size of the species. Traditionally, the particle sizes of nanoparticles are determined using methods such as Dynamic Light Scattering (DLS) [2], Small-Angle X-Ray Scattering (SAXS) [3], Small Angle Neutron Scattering (SANS) [4] and Transmission Electron Microscopy (TEM) [5]. All these methods are far from ideal and have significant drawbacks: DLS becomes difficult for particles below 10 nm, SAXS and SANS are expensive and complex, and TEM requires complex sample preparations which can lead to alterations of particle sizes [6-8].Here, we present a new way of determining the particle sizes of sodium silicate liquors at high pH using time-resolved fluorescence anisotropy. Different from previous approach of using a single dye label, two fluorescent labels were used in this work [9,10]. Rotational times of the non-binding rhodamine B and electrostatically binding rhodamine 6G were used to determine the medium microviscosity and the silicate particle radius, respectively. This approach of using two dyes ensures that the microviscosity stays accurate in time, unlike in the case when a single dye was used. Applying this method to samples of various pH (prepared by diluting the stock solution of silicate to the concentrations of NaOH ranging from 0.2M to 2M) and different temperatures (10°C to 55°C), therecovered average particle size was found to have an upper limit of 7.0±1.2