Thursday, November 15 |
07:00 - 09:00 |
Breakfast (Vistas Dining Room) |
09:00 - 09:30 |
Mike Dowd: Sequential Monte Carlo approaches for inference in dynamical systems: application to spatio-temporal models of ocean biogeochemistry ↓ State space models are widely used for integrating ecological data with dynamical models in order to estimate the system state and parameters. Many such dynamical models are stochastic with strong nonlinearities, and the observations used are frequently non-Gaussian. The consequence is that sampling based inference must be used for many realistic state space models. The fundamental building block for doing this are sequential Monte Carlo methods, such as the particle filter, which provides the basis for likelihood based methods (like multiple iterated filtering) as well as Bayesian approaches (like particle MCMC). Unfortunately, basic particle filters do not scale well as the dimensionality of the state space increases, requiring exponentially larger sample sizes. In practice, this means that purely time-dependent ecological models have been emphasized, and the spatial aspects either ignored or approximated. In this talk, I present work on the extension of state space models so that spatio-temporal dynamic ecological systems can be effectively treated. The approaches involve approximations, along with the design of novel sequential Monte Carlo approaches. The problems that motivate, and are used to illustrate this work, are the marine plankton models used in biological oceanography (the so-called PZND - phytoplankton, zooplankton, nutrient, detritus - class of models). These time-dependent models are generally embedded within ocean circulation model that provide the spatial context. Here, we will consider both one- and three-dimensional ocean models. (TCPL 201) |
09:30 - 10:00 |
Oliver Maclaren: Lessons for biological parameter estimation from large-scale engineering inverse problems ↓ This talk is about transferring methods and lessons from the field of large-scale engineering inverse problems to the types of models used in computational and mathematical biology. This is motivated by my recent work with geothermal reservoir engineers and inverse problems experts on estimating parameter fields in large-scale simulation models of geothermal systems. Initial attempts to transfer techniques from my work on biological parameter estimation to these problems were somewhat successful, but new challenges quickly appeared.
In particular, the simulation models used in these areas are particularly expensive to compute, parameters are frequently in the form of complex spatial fields, and a diverse range of regularisation types and prior models are required to capture known or suspected structures. To address these issues we have worked to a) replace expensive models with cheaper models while accounting for the associated bias and overconfidence that this can introduce, b) compute model derivatives efficiently using the adjoint method and related techniques and c) implement nonlinear parameter identifiability analysis and regularisation parameter selection methods.
I will discuss how the methods and lessons I've learned in tackling these new problems might be transferred back to parameter estimation and uncertainty quantification problems in computational and mathematical biology. (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 11:00 |
Barbara Holland: Assessing model adequacy in molecular phylogenetics ↓ Molecular phylogenetics is concerned with estimating the evolutionary relationships amongst species on the basis of molecular sequence data (typically aligned DNA or amino acid sequences). Statistical approaches to this problem have been developed where evolution is modelled as a Markov process acting on a tree. Given a specific tree along with parameter choices in our Markov model, these models allow us to calculate the probability of seeing any particular pattern of nucleotides at the tips of the tree (i.e. in the modern-day species). We can then calculate a likelihood score for a sequence alignment given our model; from here we can use maximum likelihood or Bayesian approaches to find choices of tree and model parameters that give the best explanation of the sequence data. This provides a nice framework for inference, but there are some interesting challenges that arise. For instance
• Our model is a mix of combinatorial structure (the branching pattern in the tree) and continuous parameters (e.g. rates of change from one particular nucleotide to another, lengths of edges in the tree), this makes it difficult to assess the uncertainty in our estimates, i.e. what is 95% CI for a tree.
• It is a common maxim that just because a model fits “best” doesn’t mean it fits “well”. However, it is surprisingly difficult to do anything analogous to residual diagnostics in a phylogenetic context. Our models basically give us a multinomial distribution on site patterns. Even for just 10 species there are 410 ~ 1 million possible site patterns, and in any particular sequence alignment most will not be observed. We need more tools to help us visualise how well our models fit and where they break down.
• How sure are we that evolution is tree-like? There are many biological processes (hybridisation, recombination, lateral gene transfer) that cannot be well modelled by a tree. As soon as we move away from the tree assumption we need to think harder about model selection issues as statistical identifiability can become a problem.
This talk will give an introduction to statistical phylogenetics and survey some of the above issues. (TCPL 201) |
11:00 - 11:30 |
Paul Francois: Untangling the hairball: fitness based reduction of biological networks ↓ Complex mathematical models of interaction networks are routinely used for prediction in systems biology. However, it is difficult to reconcile network complexities with a formal understanding of their behavior. I will describe a simple procedure to reduce biological models to functional submodules, using statistical mechanics of complex systems combined with a fitness-based approach inspired by in silico evolution. I will illustrate our approach on different models of immune recognition by T cells. An intractable model of immune recognition with close to a hundred individual transition rates is reduced to a simple two-parameter model. We identify three different mechanisms for early immune recognition, and automatically discovers similar functional modules in different models of the same process, allowing for model classification and comparison. Our procedure can be applied to biological networks based on rate equations using a fitness function that quantifies phenotypic performance. (TCPL 201) |
11:30 - 12:00 |
Discussion (TCPL 201) |
12:00 - 13:30 |
Lunch (Vistas Dining Room) |
13:30 - 14:00 |
Jill Gallaher: Systemic dynamics and effects from multiple metastases during adaptive therapy in prostate cancer ↓ Despite the growing acknowledgement that heterogeneity is driving treatment failure in advanced cancers, it is not often recognized that a successful treatment must be designed with the evolutionary response of the disease in mind. Adaptive therapy is an evolutionary-based treatment strategy that aims to balance cell kill with toxicity, by exploiting the competition between the resistant and sensitive populations. The aim is to keep a constant tumor volume by adjusting the dose such that a shrinking tumor will receive a lower dose while a growing tumor will receive a higher dose. It has been shown to be effective in pre-clinical mouse studies of triple negative breast cancer and clinical trials of metastatic castrate-resistant prostate cancer. Decision-making in the clinic is based on a systemic marker of tumor burden (prostate specific antigen, PSA, in prostate cancer). However, a systemic measure of disease ignores effects from multiple distinct metastatic lesions. We use an off-lattice agent-based model calibrated to the timescales of the prostate cancer trial to investigate how number, size and composition of multiple metastatic lesions treated with adaptive therapy affects the systemic dynamics of disease burden. (TCPL 201) |
14:00 - 14:30 |
Susanna Röblitz: Empirical Bayes methods for prior estimation in systems biology modelling ↓ One of the main goals of mathematical modelling in systems biology related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Therefore, before applying Bayes’ rule separately to the data of each patient (which is typically performed using a non-informative prior), it is meaningful to use empirical Bayes methods in order to construct an informative prior from all available data.
In the non-parametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad-hoc choices which lack invariance under reparametrization of the model and hence result in inconsistent estimates for equivalent models.
We introduce the empirical reference prior, a non-parametric, transformation-invariant estimator for the prior distribution, which represents a symbiosis between the objective and empirical Bayes methodologies.
We demonstrate the performance of this approach by applying it to an ordinary differential equation model for the human menstrual cycle, a typical example from systems biology modelling. (TCPL 201) |
14:30 - 15:00 |
Coffee Break (TCPL Foyer) |
15:00 - 15:30 |
Jonathan Harrison: Experimental verification of a coarse-grained model predicts that production is rate-limiting for mRNA localization ↓ Identifying bottlenecks in a cellular process indicates key targets for regulation by the cell. However, in many cases, these rate-limiting steps are not identified or well understood. mRNA localization by molecular-motor-driven transport is crucial for cell polarization, but the rate-limiting processes underlying the localization processes are not fully understood. To make progress on this important problem, we use a combined experiment-theory approach to examine the rate-limiting steps in the localization of gurken/TGF-alpha mRNA in Drosophila egg chambers. We construct a coarse-grained model of the localisation that encodes simplified descriptions of the range of steps involved in localization, including production and transport between and within cells. Using Bayesian inference, we relate this model to quantitative single molecule fluorescence in situ hybridization data, and draw three main conclusions. First, we characterize the formation of higher order assemblies of RNA-protein complexes in the oocyte. Second, by analysing steady state behaviour in the model, we estimate the extent of the bias in transport directionality through ring canals between cells. Finally, by parameterizing the full dynamic model, we provide estimates for the rates of the different steps of localization, and predict that the rate of mRNA production, rather than transport, is rate-limiting. Together, our results strongly suggest that production is rate-limiting for gurken mRNA localization in Drosophila development, but that mRNA localization is a tightly regulated process. (TCPL 201) |
15:30 - 16:00 |
John Fricks: Estimating velocity from time traces of molecular motors ↓ How does one measure the velocity of an object? Seems like a simple question. However, in cell biology – with lots of measurement error, Brownian dynamics, and attachment-detachment dynamics – this can be anything but simple. As a case-study, we will look at molecular motors, such as kinesin and dynein, which in a laboratory setting carry a cargo along a microtubule until detachment after a random time. Should we take the total displacement over the total time until detachment and average these velocities over different paths? Should the shorter paths be discounted in the analysis? Should we concatenate paths instead? Should we use a mean squared displacement analysis, and how would observational error effect this approach? These and other possible approaches will be explored. (TCPL 201) |
16:00 - 16:30 |
David Umulis: Three-dimensional finite element modeling of dynamic BMP gradient formation in zebrafish embryonic development ↓ Bone Morphogenetic Proteins (BMPs) play a significant role in dorsal-ventral (DV) patterning of the early zebrafish embryo. BMP signaling is regulated by extracellular, intracellular, and cell membrane components. BMPs pattern the embryo during development at the same time that cells grow and divide to enclose the yolk during a process called epiboly. We developed a new three-dimensional growing finite element model to simulate the BMP patterning and epiboly process during the blastula stage. Quantitative whole mount RNA scope data of BMP2b and phosphorylated-SMAD data are collected and analyzed to precisely test the hypotheses of gradient formation in our model. We found that the growth model results in consistent spatially and temporally evolving BMP signaling dynamics within a range of biophysical parameters including a minimal rate of ligand diffusion. (TCPL 201) |
18:00 - 19:30 |
Dinner (Vistas Dining Room) |