John Fricks

Assessment of the 2010 global measles mortality reduction goal: results from a model of surveillance data

BACKGROUND In 2008 all WHO member states endorsed a target of 90% reduction in measles mortality by 2010 over 2000 levels. We developed a model to estimate progress made towards this goal. METHODS We constructed a state-space model with population and immunisation coverage estimates and reported surveillance data to estimate annual national measles cases, distributed across age classes. We estimated deaths by applying age-specific and country-specific case-fatality ratios to estimated cases in each age-country class. FINDINGS Estimated global measles mortality decreased 74% from 535,300 deaths (95% CI 347,200-976,400) in 2000 to 139,300 (71,200-447,800) in 2010. Measles mortality was reduced by more than three-quarters in all WHO regions except the WHO southeast Asia region. India accounted for 47% of estimated measles mortality in 2010, and the WHO African region accounted for 36%. INTERPRETATION Despite rapid progress in measles control from 2000 to 2007, delayed implementation of accelerated disease control in India and continued outbreaks in Africa stalled momentum towards the 2010 global measles mortality reduction goal. Intensified control measures and renewed political and financial commitment are needed to achieve mortality reduction targets and lay the foundation for future global eradication of measles. FUNDING US Centers for Disease Control and Prevention (PMS 5U66/IP000161).

Monte Carlo Analysis of Neck Linker Extension in Kinesin Molecular Motors

Kinesin stepping is thought to involve both concerted conformational changes and diffusive movement, but the relative roles played by these two processes are not clear. The neck linker docking model is widely accepted in the field, but the remainder of the step – diffusion of the tethered head to the next binding site – is often assumed to occur rapidly with little mechanical resistance. Here, we investigate the effect of tethering by the neck linker on the diffusive movement of the kinesin head, and focus on the predicted behavior of motors with naturally or artificially extended neck linker domains. The kinesin chemomechanical cycle was modeled using a discrete-state Markov chain to describe chemical transitions. Brownian dynamics were used to model the tethered diffusion of the free head, incorporating resistive forces from the neck linker and a position-dependent microtubule binding rate. The Brownian dynamics and chemomechanical cycle were coupled to model processive runs consisting of many 8 nm steps. Three mechanical models of the neck linker were investigated: Constant Stiffness (a simple spring), Increasing Stiffness (analogous to a Worm-Like Chain), and Reflecting (negligible stiffness up to a limiting contour length). Motor velocities and run lengths from simulated paths were compared to experimental results from Kinesin-1 and a mutant containing an extended neck linker domain. When tethered by an increasingly stiff spring, the head is predicted to spend an unrealistically short amount of time within the binding zone, and extending the neck is predicted to increase both the velocity and processivity, contrary to experiments. These results suggest that the Worm-Like Chain is not an adequate model for the flexible neck linker domain. The model can be reconciled with experimental data if the neck linker is either much more compliant or much stiffer than generally assumed, or if weak kinesin-microtubule interactions stabilize the diffusing head near its binding site.

Time-domain methods for diffusive transport in soft matter

Passive microrheology [12] utilizes measurements of noisy, entropic fluctuations (i.e., diffusive properties) of micron-scale spheres in soft matter to infer bulk frequency-dependent loss and storage moduli. Here, we are concerned exclusively with diffusion of Brownian particles in viscoelastic media, for which the Mason-Weitz theoretical-experimental protocol is ideal, and the more challenging inference of bulk viscoelastic moduli is decoupled. The diffusive theory begins with a generalized Langevin equation (GLE) with a memory drag law specified by a kernel [7, 16, 22, 23]. We start with a discrete formulation of the GLE as an autoregressive stochastic process governing microbead paths measured by particle tracking. For the inverse problem (recovery of the memory kernel from experimental data) we apply time series analysis (maximum likelihood estimators via the Kalman filter) directly to bead position data, an alternative to formulas based on mean-squared displacement statistics in frequency space. For direct modeling, we present statistically exact GLE algorithms for individual particle paths as well as statistical correlations for displacement and velocity. Our time-domain methods rest upon a generalization of well-known results for a single-mode exponential kernel [1, 7, 22, 23] to an arbitrary M-mode exponential series, for which the GLE is transformed to a vector Ornstein-Uhlenbeck process.

Statistical Challenges in Microrheology

Microrheology is the study of the properties of a complex fluid through the diffusion dynamics of small particles, typically latex beads, moving through that material. Currently, it is the dominant technique in the study of the physical properties of biological fluids, of the material properties of membranes or the cytoplasm of cells, or of the entire cell. The theoretical underpinning of microrheology was given in Mason and Weitz (Physical Review Letters; 1995), who introduced a framework for the use of path data of diffusing particles to infer viscoelastic properties of its fluid environment. The multi‐particle tracking techniques that were subsequently developed have presented numerous challenges for experimentalists and theoreticians. This study describes some specific challenges that await the attention of statisticians and applied probabilists. We describe relevant aspects of the physical theory, current inferential efforts and simulation aspects of a central model for the dynamics of nano‐scale particles in viscoelastic fluids, the generalized Langevin equation.

Kinesins with extended neck linkers: a chemomechanical model for variable-length stepping.

We develop a stochastic model for variable-length stepping of kinesins engineered with extended neck linkers. This requires that we consider the separation in microtubule binding sites between the heads of the motor at the beginning of a step. We show that this separation is stationary and can be included in the calculation of standard experimental quantities. We also develop a corresponding matrix computational framework for conducting computer experiments. Our matrix approach is more efficient computationally than large-scale Monte Carlo simulation. This efficiency greatly eases sensitivity analysis, an important feature when there is considerable uncertainty in the physical parameters of the system. We demonstrate the application and effectiveness of our approach by showing that the worm-like chain model for the neck linker can explain recently published experimental data. While we have focused on a particular scenario for kinesins, these methods could also be applied to myosin and other processive motors.

A matrix computational approach to kinesin neck linker extension.

Kinesin stepping requires both tethered diffusion of the free head and conformational changes driven by the chemical state of the motor. We present a numerical method using matrix representations of approximating Markov chains and renewal theory to compute important experimental quantities for models that include both tethered diffusion and chemical transitions. Explicitly modeling the tethered diffusion allows for exploration of the model under perturbation of the neck linker; comparisons are made between the computed models and in vitro assays.

An attraction-repulsion point process model for respiratory syncytial virus infections.

How is the progression of a virus influenced by properties intrinsic to individual cells? We address this question by studying the susceptibility of cells infected with two strains of the human respiratory syncytial virus (RSV-A and RSV-B) in an in vitro experiment. Spatial patterns of infected cells give us insight into how local conditions influence susceptibility to the virus. We observe a complicated attraction and repulsion behavior, a tendency for infected cells to lump together or remain apart. We develop a new spatial point process model to describe this behavior. Inference on spatial point processes is difficult because the likelihood functions of these models contain intractable normalizing constants; we adapt an MCMC algorithm called double Metropolis-Hastings to overcome this computational challenge. Our methods are computationally efficient even for large point patterns consisting of over 10,000 points. We illustrate the application of our model and inferential approach to simulated data examples and fit our model to various RSV experiments. Because our model parameters are easy to interpret, we are able to draw meaningful scientific conclusions from the fitted models.

Analysis of single particle diffusion with transient binding using particle filtering

Diffusion with transient binding occurs in a variety of biophysical processes, including movement of transmembrane proteins, T cell adhesion, and caging in colloidal fluids. We model diffusion with transient binding as a Brownian particle undergoing Markovian switching between free diffusion when unbound and diffusion in a quadratic potential centered around a binding site when bound. Assuming the binding site is the last position of the particle in the unbound state and Gaussian observational error obscures the true position of the particle, we use particle filtering to predict when the particle is bound and to locate the binding sites. Maximum likelihood estimators of diffusion coefficients, state transition probabilities, and the spring constant in the bound state are computed with a stochastic Expectation-Maximization (EM) algorithm.

Asymptotic analysis of microtubule-based transport by multiple identical molecular motors.

We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation: (1) highly viscous in vivo transport and (2) dynamics when multiple identical motors are attached to the cargo and microtubule.

Likelihood inference for particle location in fluorescence microscopy

We introduce a procedure to automatically count and locate the fluorescent particles in a microscopy image. Our procedure employs an approximate likelihood estimator derived from a Poisson random field model for photon emission. Estimates of standard errors are generated for each image along with the parameter estimates, and the number of particles in the image is determined using an information criterion and likelihood ratio tests. Realistic simulations show that our procedure is robust and that it leads to accurate estimates, both of parameters and of standard errors. This approach improves on previous ad hoc least squares procedures by giving a more explicit stochastic model for certain fluorescence images and by employing a consistent framework for analysis.