Gabriel Rosser

Signal-dependent turnover of the bacterial flagellar switch protein FliM

Most biological processes are performed by multiprotein complexes. Traditionally described as static entities, evidence is now emerging that their components can be highly dynamic, exchanging constantly with cellular pools. The bacterial flagellar motor contains ∼13 different proteins and provides an ideal system to study functional molecular complexes. It is powered by transmembrane ion flux through a ring of stator complexes that push on a central rotor. The Escherichia coli motor switches direction stochastically in response to binding of the response regulator CheY to the rotor switch component FliM. Much is known of the static motor structure, but we are just beginning to understand the dynamics of its individual components. Here we measure the stoichiometry and turnover of FliM in functioning flagellar motors, by using high-resolution fluorescence microscopy of E. coli expressing genomically encoded YPet derivatives of FliM at physiological levels. We show that the ∼30 FliM molecules per motor exist in two discrete populations, one tightly associated with the motor and the other undergoing stochastic turnover. This turnover of FliM molecules depends on the presence of active CheY, suggesting a potential role in the process of motor switching. In many ways the bacterial flagellar motor is as an archetype macromolecular assembly, and our results may have further implications for the functional relevance of protein turnover in other large molecular complexes.

Simplified Multitarget Tracking Using the PHD Filter for Microscopic Video Data

The probability hypothesis density (PHD) filter from the theory of random finite sets is a well-known method for multitarget tracking. We present the Gaussian mixture (GM) and improved sequential Monte Carlo implementations of the PHD filter for visual tracking. These implementations are shown to provide advantages over previous PHD filter implementations on visual data by removing complications such as clustering and data association and also having beneficial computational characteristics. The GM-PHD filter is deployed on microscopic visual data to extract trajectories of free-swimming bacteria in order to analyze their motion. Using this method, a significantly larger number of tracks are obtained than was previously possible. This permits calculation of reliable distributions for parameters of bacterial motion. The PHD filter output was tested by checking agreement with a careful manual analysis. A comparison between the PHD filter and alternative tracking methods was carried out using simulated data, demonstrating superior performance by the PHD filter in a range of realistic scenarios.

Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions-a crime case study

ABSTRACT Many physical and sociological processes are represented as discrete events in time and space. These spatio-temporal point processes are often sparse, meaning that they cannot be aggregated and treated with conventional regression models. Models based on the point process framework may be employed instead for prediction purposes. Evaluating the predictive performance of these models poses a unique challenge, as the same sparseness prevents the use of popular measures such as the root mean squared error. Statistical likelihood is a valid alternative, but this does not measure absolute performance and is therefore difficult for practitioners and researchers to interpret. Motivated by this limitation, we develop a practical toolkit of evaluation metrics for spatio-temporal point process predictions. The metrics are based around the concept of hotspots, which represent areas of high point density. In addition to measuring predictive accuracy, our evaluation toolkit considers broader aspects of predictive performance, including a characterisation of the spatial and temporal distributions of predicted hotspots and a comparison of the complementarity of different prediction methods. We demonstrate the application of our evaluation metrics using a case study of crime prediction, comparing four varied prediction methods using crime data from two different locations and multiple crime types. The results highlight a previously unseen interplay between predictive accuracy and spatio-temporal dispersion of predicted hotspots. The new evaluation framework may be applied to compare multiple prediction methods in a variety of scenarios, yielding valuable new insight into the predictive performance of point process-based prediction.

The effect of sampling rate on observed statistics in a correlated random walk

Tracking the movement of individual cells or animals can provide important information about their motile behaviour, with key examples including migrating birds, foraging mammals and bacterial chemotaxis. In many experimental protocols, observations are recorded with a fixed sampling interval and the continuous underlying motion is approximated as a series of discrete steps. The size of the sampling interval significantly affects the tracking measurements, the statistics computed from observed trajectories, and the inferences drawn. Despite the widespread use of tracking data to investigate motile behaviour, many open questions remain about these effects. We use a correlated random walk model to study the variation with sampling interval of two key quantities of interest: apparent speed and angle change. Two variants of the model are considered, in which reorientations occur instantaneously and with a stationary pause, respectively. We employ stochastic simulations to study the effect of sampling on the distributions of apparent speeds and angle changes, and present novel mathematical analysis in the case of rapid sampling. Our investigation elucidates the complex nature of sampling effects for sampling intervals ranging over many orders of magnitude. Results show that inclusion of a stationary phase significantly alters the observed distributions of both quantities.

Novel methods for analysing bacterial tracks reveal persistence in Rhodobacter sphaeroides

Tracking bacteria using video microscopy is a powerful experimental approach to probe their motile behaviour. The trajectories obtained contain much information relating to the complex patterns of bacterial motility. However, methods for the quantitative analysis of such data are limited. Most swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. It is therefore necessary to segment observed tracks into swimming and reorientation phases to extract useful statistics. We present novel robust analysis tools to discern these two phases in tracks. Our methods comprise a simple and effective protocol for removing spurious tracks from tracking datasets, followed by analysis based on a two-state hidden Markov model, taking advantage of the availability of mutant strains that exhibit swimming-only or reorientating-only motion to generate an empirical prior distribution. Using simulated tracks with varying levels of added noise, we validate our methods and compare them with an existing heuristic method. To our knowledge this is the first example of a systematic assessment of analysis methods in this field. The new methods are substantially more robust to noise and introduce less systematic bias than the heuristic method. We apply our methods to tracks obtained from the bacterial species Rhodobacter sphaeroides and Escherichia coli. Our results demonstrate that R. sphaeroides exhibits persistence over the course of a tumbling event, which is a novel result with important implications in the study of this and similar species.

Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides

Most free-swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. A key open question concerns varying mechanisms by which reorientation occurs. We combine mathematical modelling with analysis of a large tracking dataset to study the poorly understood reorientation mechanism in the monoflagellate species Rhodobacter sphaeroides. The flagellum on this species rotates counterclockwise to propel the bacterium, periodically ceasing rotation to enable reorientation. When rotation restarts the cell body usually points in a new direction. It has been assumed that the new direction is simply the result of Brownian rotation. We consider three variants of a self-propelled particle model of bacterial motility. The first considers rotational diffusion only, corresponding to a non-chemotactic mutant strain. Two further models incorporate stochastic reorientations, describing ‘run-and-tumble’ motility. We derive expressions for key summary statistics and simulate each model using a stochastic computational algorithm. We also discuss the effect of cell geometry on rotational diffusion. Working with a previously published tracking dataset, we compare predictions of the models with data on individual stopping events in R. sphaeroides. This provides strong evidence that this species undergoes some form of active reorientation rather than simple reorientation by Brownian rotation.

Straightforward multi-object video tracking for quantification of mosquito flight activity.

Mosquito flight activity has been studied using a variety of different methodologies, and largely concentrates on female mosquito activity as vectors of disease. Video recording using standard commercially available hardware has limited accuracy for the measurement of flight activity due to the lack of depth-perception in two-dimensional images, but multi-camera observation for three dimensional trajectory reconstructions remain challenging and inaccessible to the majority of researchers. Here, in silico simulations were used to quantify the limitations of two-dimensional flight observation. We observed that, under the simulated conditions, two dimensional observation of flight was more than 90% accurate for the determination of population flight speeds and thus that two dimensional imaging can be used to provide accurate estimates of mosquito population flight speeds, and to measure flight activity over long periods of time. We optimized single camera video imaging to study male Aedes albopictus mosquitoes over a 30 h time period, and tested two different multi-object tracking algorithms for their efficiency in flight tracking. A. Albopictus males were observed to be most active at the start of the day period (06h00-08h00) with the longest period of activity in the evening (15h00-18h00) and that a single mosquito will fly more than 600 m over the course of 24 h. No activity was observed during the night period (18h00-06h00). Simplistic tracking methodologies, executable on standard computational hardware, are sufficient to produce reliable data when video imaging is optimized under laboratory conditions. As this methodology does not require overly-expensive equipment, complex calibration of equipment or extensive knowledge of computer programming, the technology should be accessible to the majority of computer-literate researchers.

FROM BIRDS TO BACTERIA: GENERALISED VELOCITY JUMP PROCESSES WITH RESTING STATES.

There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long-distance movement state and a resting or local movement state. Here, a mathematical description of this process is formulated, adapted from Friedrich et al. (Phys Rev E, 74:041103, 2006b). The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of integro-partial differential equations is tumultuous, and therefore, it is necessary to both simplify and derive summary statistics. An expression for the mean squared displacement is derived, which shows good agreement with experimental data from the bacterium Escherichia coli and the gull Larus fuscus. Finally, a large time diffusive approximation is considered via a Cattaneo approximation (Hillen in Discrete Continuous Dyn Syst Ser B, 5:299–318, 2003). This leads to the novel result that the effective diffusion constant is dependent on the mean and variance of the running time distribution but only on the mean of the waiting time distribution.