Interaction potentials from arbitrary multi-particle trajectory data

Abstract

Understanding the complex physics of particle-based systems at the nanoscale and mesoscale increasingly relies on simulation methods, empowered by exponential advances in computing speed. A major impediment to progress lies in reliably obtaining the interaction potential functions that control system behavior - which are key inputs for any simulation approach - and which are often difficult or impossible to obtain directly using traditional experimental methods. Here, we present a straightforward methodology for generating pair potential functions from large multi-particle trajectory datasets, with no operational constraints regarding their state of equilibration, degree of damping or presence of hydrodynamic interactions. Using simulated datasets, we demonstrate that the method is highly robust against trajectory perturbations from Brownian motion and common errors introduced by particle tracking algorithms. Given the recent rapid pace of advancement in high-speed and three-dimensional microscopy and associated particle tracking algorithms, we anticipate a near future experimental regime where easily collected high-dimensional trajectory sets can be rapidly converted to the detailed interaction and hydrodynamic force fields required to replicate the system's physics in simulation.

Errors in Energy Landscapes Measured with Particle Tracking

“…Reconstructing the underlying energy landscape guiding the particles' dynamics is another insightful analysis of Brownian trajectories, which has been used in many of the aforementioned applications [16,17,[22][23][24][25][26][27][28][29]. To calculate this landscape, the statistics of the Brownian particles' positions is measured and assumed to obey Boltzmann distribution [23,27,32,33]. Note that this analysis requires only localizing particles in each frame of the video, while calculating the MSD involves the additional, and often non-trivial, step of linking the particles' successive positions into trajectories [30].…”

“…Several studies have compared the resilience of tracking methods to these errors [2,34], and new Bayesian techniques notably tend to improve the robustness of the extracted trajectories [2,35]. Nevertheless, positioning and trajectory linking are irremediably suffering from errors, which have been recognized to propagate to the measured physical observables [18,27,33,[36][37][38][39][40][41][42][43][44][45][46][47].…”

Microscopic Geometry Characterizes Structure/Potential-Energy Correspondence in a Thermodynamic System

“…liquid) systems. [8][9][10][11][12][13][14][15] However, both direct and inverse methods always involve an essential problem to construct reliable PEL: Generally, the transformation from PEL to structure is a well-posed direct problem, whereas that from structure to PEL is a typical inverse problem: Although different methods have been proposed to characterize PEL for system-specific quantities, it is generally unclear whether the constructed PEL uniquely and/or stably determines a set of known macroscopic property. [16][17][18][19][20][21][22] Up to now, for a modest classical system under pairwise additive interactions, it has been shown that the PE can be determined uniquely from the structural information contained in pair-correlation functions.…”