Adam M. Johansen

Single-molecule level analysis of the subunit composition of the T cell receptor on live T cells

The T cell receptor (TCR) expressed on most T cells is a protein complex consisting of TCRαβ heterodimers that bind antigen and cluster of differentiation (CD) 3εδ, εγ, and ζζ dimers that initiate signaling. A long-standing controversy concerns whether there is one, or more than one, αβ heterodimer per complex. We used a form of single-molecule spectroscopy to investigate this question on live T cell hybridomas. The method relies on detecting coincident fluorescence from single molecules labeled with two different fluorophores, as the molecules diffuse through a confocal volume. The fraction of events that are coincident above the statistical background is defined as the “association quotient,” Q. In control experiments, Q was significantly higher for cells incubated with wheat germ agglutinin dual-labeled with Alexa488 and Alexa647 than for cells incubated with singly labeled wheat germ agglutinin. Similarly, cells expressing the homodimer, CD28, gave larger values of Q than cells expressing the monomer, CD86, when incubated with mixtures of Alexa488- and Alexa647-labeled antibody Fab fragments. T cell hybridomas incubated with mixtures of anti-TCRβ Fab fragments labeled with each fluorophore gave a Q value indistinguishable from the Q value for CD86, indicating that the dominant form of the TCR comprises single αβ heterodimers. The values of Q obtained for CD86 and the TCR were low but nonzero, suggesting that there is transient or nonrandom confinement, or diffuse clustering of molecules at the T cell surface. This general method for analyzing the subunit composition of protein complexes could be extended to other cell surface or intracellular complexes, and other living cells.

Particle methods for maximum likelihood estimation in latent variable models

Abstract Standard methods for maximum likelihood parameter estimation in latent variable models rely on the Expectation-Maximization algorithm and its Monte Carlo variants. Our approach is different and motivated by similar considerations to simulated annealing; that is we build a sequence of artificial distributions whose support concentrates itself on the set of maximum likelihood estimates. We sample from these distributions using a sequential Monte Carlo approach. We demonstrate state-of-the-art performance for several applications of the proposed approach.

Toward Automatic Model Comparison: An Adaptive Sequential Monte Carlo Approach

Model comparison for the purposes of selection, averaging, and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a particular class. Substantial progress has been made in recent years, but difficulties remain in the implementation of existing schemes. This article presents adaptive sequential Monte Carlo (SMC) sampling strategies to characterize the posterior distribution of a collection of models, as well as the parameters of those models. Both a simple product estimator and a combination of SMC and a path sampling estimator are considered and existing theoretical results are extended to include the path sampling variant. A novel approach to the automatic specification of distributions within SMC algorithms is presented and shown to outperform the state of the art in this area. The performance of the proposed strategies is demonstrated via an extensive empirical study. Comparisons with state-of-the-art algorithms show that the proposed algorithms are always competitive, and often substantially superior to alternative techniques, at equal computational cost and considerably less application-specific implementation effort. Supplementary materials for this article are available online.

A simple approach to maximum intractable likelihood estimation

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then maximised is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios.

Simulation of the annual loss distribution in operational risk via Panjer recursions and Volterra integral equations for value-at-risk and expected shortfall estimation

Following the Loss Distributional Approach (LDA), this article develops two procedures for simulation of an annual loss distribution for modeling of Operational Risk. First, we provide an overview of the typical compound-process LDA used widely in Operational Risk modeling, before expanding upon the current literature on evaluation and simulation of annual loss distributions. We present two novel Monte Carlo simulation procedures. In doing so, we make use of Panjer recursions and the Volterra integral equation of the second kind to reformulate the problem of evaluation of the density of a random sum as the calculation of an expectation. We demonstrate the use of importance sampling and trans-dimensional Markov Chain Monte Carlo algorithms to efficiently evaluate this expectation. We further demonstrate their use in the calculation of Value at Risk and Expected Shortfall.

On solving integral equations using Markov chain Monte Carlo methods

In this paper, we propose an original approach to the solution of Fredholm equations of the second kind. We interpret the standard Von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on a union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov chain Monte Carlo (MCMC) methods such as Reversible Jump MCMC to approximate the solution numerically. This can be an attractive alternative to standard Sequential Importance Sampling (SIS) methods routinely used in this context. To motivate our approach, we sketch an application to value function estimation for a Markov decision process. Two computational examples are also provided.

Quantifying the Uncertainty in Change Points

Quantifying the uncertainty in the location and nature of change points in time series is important in a variety of applications. Many existing methods for estimation of the number and location of change points fail to capture fully or explicitly the uncertainty regarding these estimates, whilst others require explicit simulation of large vectors of dependent latent variables. This article proposes methodology for approximating the full posterior distribution of various change point characteristics in the presence of parameter uncertainty. The methodology combines recent work on evaluation of exact change point distributions conditional on model parameters via finite Markov chain imbedding in a hidden Markov model setting, and accounting for parameter uncertainty and estimation via Bayesian modelling and sequential Monte Carlo. The combination of the two leads to a flexible and computationally efficient procedure, which does not require estimates of the underlying state sequence. We illustrate that good estimation of the posterior distributions of change point characteristics is provided for simulated data and functional magnetic resonance imaging data. We use the methodology to show that the modelling of relevant physical properties of the scanner can influence detection of change points and their uncertainty.

Dynamic filtering of static dipoles in magnetoencephalography

We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model. In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation.

Current–voltage characteristics of nonplanar cold field emitters

Conventional Fowler–Nordheim theory assumes that the emitter is planar, while most tips used in practice have curved emitting surfaces. Using a revised potential distribution, standard image theory and a dimensionless parameter x, we express the experimental current as a multiple σ of the current calculated using standard free-electron supply. A plot of σ(x) for one carbon emitter shows a maximum at a value of x corresponding to the known emitter radius. The calculated field strength at the emitter surface varies little with x. The values found for σ are sensitive to the accuracy of calculation and, to test the theory further, it is desirable both to improve the modelling of image effects and to obtain measurements of current–voltage characteristics and emitting radii together for more types of emitter.

Microtubule organization within mitotic spindles revealed by serial block face scanning electron microscopy and image analysis

ABSTRACT Serial block face scanning electron microscopy (SBF-SEM) is a powerful method to analyze cells in 3D. Here, working at the resolution limit of the method, we describe a correlative light–SBF-SEM workflow to resolve microtubules of the mitotic spindle in human cells. We present four examples of uses for this workflow that are not practical by light microscopy and/or transmission electron microscopy. First, distinguishing closely associated microtubules within K-fibers; second, resolving bridging fibers in the mitotic spindle; third, visualizing membranes in mitotic cells, relative to the spindle apparatus; and fourth, volumetric analysis of kinetochores. Our workflow also includes new computational tools for exploring the spatial arrangement of microtubules within the mitotic spindle. We use these tools to show that microtubule order in mitotic spindles is sensitive to the level of TACC3 on the spindle. Summary: Spatial analysis of microtubule organisation in mitotic cells by using 3D imaging and mathematical modelling.