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.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS299 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Molecular motors, brownian ratchets, and reflected diffusions

Molecular motors are protein structures that play a central role in accomplishing mechanical work inside a cell. While chemical reactions fuel this work, it is not exactly known how this chemical-mechanical conversion occurs. Recent advances in microbiological techniques have enabled at least indirect observations of molecular motors which in turn have led to significant effort in the mathematical modeling of these motors in the hope of shedding light on the underlying mechanisms involved in intracellular transport. Kinesin which moves along microtubules that are spread throughout the cell is a prime example of the type of motors that are studied in this work. The motion is linked to the presence of a chemical, ATP, but how the ATP is involved in motion is not clearly understood. One commonly used model for the dynamics of Kinesin in the biophysics literature is the Brownian ratchet mechanism. In this work, we give a precise mathematical formulation of a Brownian ratchet (or more generally a diffusion ratchet) via an infinite system of stochastic differential equations with reflection. This formulation is seen to arise in the weak limit of a natural discrete space model that is often used to describe motor dynamics in the literature. Expressions for asymptotic velocity and effective diffusivity of a biological motor modeled via a Brownian ratchet are obtained. Linearly progressive biomolecular motors often carry cargos via an elastic linkage. A two-dimensional coupled stochastic dynamical system is introduced to model the dynamics of the motor-cargo pair. By proving that an associated two dimensional Markov process has a unique stationary distribution, it is shown that the asymptotic velocity of a motor pulling a cargo is well defined as a certain Law of Large Number limit, and finally an expression for the asymptotic velocity in terms of the invariant measure of the Markov process is obtained

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

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

Renewal reward perspective on linear switching diffusion systems

In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport, micro-organisms like bacteria, or animals moving within and responding to their environment. For example, in cells the movement of vesicles, organelles and other cargo are affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate the effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal-reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection-reaction-diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed framework are illustrated for case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of motor proteins.Comment: 35 pages, 6 figure

Exploratory Spatial Analysis of in vitro Respiratory Syncytial Virus Co-infections

The cell response to virus infection and virus perturbation of that response is dynamic and is reflected by changes in cell susceptibility to infection. In this study, we evaluated the response of human epithelial cells to sequential infections with human respiratory syncytial virus strains A2 and B to determine if a primary infection with one strain will impact the ability of cells to be infected with the second as a function of virus strain and time elapsed between the two exposures. Infected cells were visualized with fluorescent markers, and location of all cells in the tissue culture well were identified using imaging software. We employed tools from spatial statistics to investigate the likelihood of a cell being infected given its proximity to a cell infected with either the homologous or heterologous virus. We used point processes, K-functions, and simulation procedures designed to account for specific features of our data when assessing spatial associations. Our results suggest that intrinsic cell properties increase susceptibility of cells to infection, more so for RSV-B than for RSV-A. Further, we provide evidence that the primary infection can decrease susceptibility of cells to the heterologous challenge virus but only at the 16 h time point evaluated in this study. Our research effort highlights the merits of integrating empirical and statistical approaches to gain greater insight on in vitro dynamics of virus-host interactions

Involvement of Noradrenergic Neurotransmission in the Stress- but not Cocaine-Induced Reinstatement of Extinguished Cocaine-Induced Conditioned Place Preference in Mice: Role for β-2 Adrenergic Receptors

The responsiveness of central noradrenergic systems to stressors and cocaine poses norepinephrine as a potential common mechanism through which drug re-exposure and stressful stimuli promote relapse. This study investigated the role of noradrenergic systems in the reinstatement of extinguished cocaine-induced conditioned place preference by cocaine and stress in male C57BL/6 mice. Cocaine- (15 mg/kg, i.p.) induced conditioned place preference was extinguished by repeated exposure to the apparatus in the absence of drug and reestablished by a cocaine challenge (15 mg/kg), exposure to a stressor (6-min forced swim (FS); 20–25°C water), or administration of the α-2 adrenergic receptor (AR) antagonists yohimbine (2 mg/kg, i.p.) or BRL44408 (5, 10 mg/kg, i.p.). To investigate the role of ARs, mice were administered the nonselective β-AR antagonist, propranolol (5, 10 mg/kg, i.p.), the α-1 AR antagonist, prazosin (1, 2 mg/kg, i.p.), or the α-2 AR agonist, clonidine (0.03, 0.3 mg/kg, i.p.) before reinstatement testing. Clonidine, prazosin, and propranolol failed to block cocaine-induced reinstatement. The low (0.03 mg/kg) but not high (0.3 mg/kg) clonidine dose fully blocked FS-induced reinstatement but not reinstatement by yohimbine. Propranolol, but not prazosin, blocked reinstatement by both yohimbine and FS, suggesting the involvement of β-ARs. The β-2 AR antagonist ICI-118551 (1 mg/kg, i.p.), but not the β-1 AR antagonist betaxolol (10 mg/kg, i.p.), also blocked FS-induced reinstatement. These findings suggest that stress-induced reinstatement requires noradrenergic signaling through β-2 ARs and that cocaine-induced reinstatement does not require AR activation, even though stimulation of central noradrenergic neurotransmission is sufficient to reinstate