Our group now works in three focus areas: 1) we experimentally investigate bacterial hunting dynamics and hydrodynamics; 2) we develop and adapt tools from statistics (most recently Bayesian nonparametrics) to infer models of dynamics from spectroscopy and imaging data (from the level of single molecules to cells); 3) we build mesoscopic statistical mechanical models to understand macromolecular and solvent dynamics in crowded environments as well as to tackle questions regarding molecular motor and vesicle transport efficiency.
1. Hydrodynamic hunters
Bacterial predation presents an interesting conceptual challenge. Bacterial predators must at once detect moving prey on the basis of limited information and, if their (bacterial) prey move, they must forecast their prey's future position. Thus, the search for prey appears as a difficult problem. Indeed our experimental work has revealed few statistical signatures of a targeted search for prey by our predator (Bdellovibrio bacteriovorus -- Bb). Instead, hydrodynamics may play a role in Bb's hunting strategy. We have a number of microscopy experiments underway to understand bacterial hunting dynamics both in vivo and in vitro.
2. Data worth a thousand words
Current biophysical imaging and spectroscopy methods can probe time (< 10-6 s), length (10-9 m) and force (10-12 N) scales relevant to the life cycle of a cell. These methods have revealed that all steps involved in molecular biology's central dogma (transcription, translation and DNA replication) are intrinsically stochastic. Despite the wealth of experimental data, the ability to gain meaningful insight from experiments on such small scales is severely limited by fundamental challenges common to all biological systems: current methods cannot capture complex processes in their full multi-dimensional detail. At best, current experiments provide a small slit through the curtains of the intricate cellular theatre on display by probing complex processes along just one or a few observable coordinates. Building models from such limited data is a central challenge in biophysics. Current modeling methods -- which we call forward methods -- are ill-equipped to tackle this challenge. Forward methods begin by positing models (such as reaction networks, coupled reaction-diffusion or multi-state models) and subsequently cross-check the model conclusions with experimental data. There are several disadvantages to this forward approach. First, forward models are rarely expressed using measurable quantities. Thus, model features and parameters must be fit to data. Second, the data's rich structure does not inform the model because the model's form is presupposed from the onset. Thus, in principle, other models could have worked equally well. To address these questions, we develop inverse modeling methods to directly infer stochastic models of complex biological systems from imaging and spectroscopy data with as few adjustable parameters as possible. Most recently our work has focused on developing the tools of Bayesian nonparametrics, an exciting rapidly evolving area of statistics, to tackle problems in biophysics. More in this soon! Through our analysis, we hope to learn about the following key issues that lie beyond the predictive ability of current models: How variable is protein structure and function inside living cells? What is the mechanism behind intracellular anomalous diffusion of proteins? How variable are protein assembly sizes? How do cells integrate noisy signal? Here is a concrete example of such a project:
2.1 Tackling the 'single molecule counting problem'
Protein-protein interactions are the basis for most biological information processing and cellular control. A quantitative characterization of these interactions is an essential prerequisite for developing a mechanistic understanding of cell biology and the disease states associated with defective protein complexes. Nonetheless, characterizing protein complexes as they occur in their native cellular environment is a major challenge since complexes can involve up to many tens of proteins within approximately a 10nm range. Thus, there is currently no routine way to determine how many proteins of type X, say, are in a given complex in living cells. We have thus been focused on developing methods that can determine the stoichiometry of protein complexes in living cells using available data from PALM (a superresolution microscopy method) as well as photobleaching data. The methodology we propose here is closely inspired by our group's work in inverse methods that we are simultaneously applying to other forms of spectroscopy (including fluorescence correlation and single particle tracking). For more details, see publications tab.
3. Molecular motor efficiency and vesicle transport
Most recently we have been theoretically and computationally investigating the role of correlated fluctuations (colored noise) and hydrodynamic memory effects on the motion of small particles (i.e., the micron scale and below). In particular, we are developing and deploying efficient numerical simulation methods—including the use of fluctuating hydrodynamics to model fluid flow and generalized Langevin dynamics to model particle motion—that allow us to gain physical insight into how biological systems can transport nanoscale objects and materials in noisy liquid environments. At the 2019 APS March Meeting, in the talk entitled Hydrodynamic Brownian motion and nanoscale transport efficiency in liquids (the slides and animations have been made available for viewing and download via figshare and via the Open Science Framework), we provided a glimpse into how the effort required to transport (neutrally buoyant) nanoparticles is altered by the presence of hydrodynamic memory effects.
We are detailing our investigation in a sequence of articles that we hope will be useful to researchers and engineers working in and across such interdisciplinary subject areas as biological/chemical physics, nanofluidics, and nanoengineering. Our first two articles investigate the cases of one- and two-particle transport in the absence of thermal noise (zero-temperature dynamics): Long-time persistence of hydrodynamic memory boosts microparticle transport, published as a Rapid Communication article in Physics Review Research and Hydrodynamic interaction facilitates the unsteady transport of two neighboring vesicles, published in the Journal of Chemical Physics. In our most recent paper, which has been recently accepted for publication as a Journal of Chemical Physics Communications article and a preprint of which is available on the arXiv, we examine the effect of hydrodynamic memory on single-particle transport at finite temperatures, we uncovered a counterintuitive effect whereby transport in a bumpy potential, such as a tilted washboard, is not disrupted at low and high temperatures but suppressed intermediate temperatures. We find that hydrodynamic memory tends to mitigate the effect of thermal fluctuations on the suppression of transport by reducing the range of temperatures over which itinerancy is possible, as well as delaying the onset of particle trapping in potential energy minima. These results have important implications for the relevance of memory effects on particle transport phenomena, such as motor-vesicle transport in living cells.