3 research outputs found
Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity
We describe a novel geometric methodology for analyzing free-energy and
kinetics of assembly driven by short-range pair-potentials in an implicit
solvent, and provides illustrations of its unique capabilities.
An atlas is a labeled partition of the assembly landscape into a topological
roadmap of maximal, contiguous, nearly-equipotential-energy conformational
regions or macrostates, together with their neighborhood relationships. The new
methodology decouples the roadmap generation from sampling and produces: (1) a
query-able atlas of local potential energy minima, their basin structure,
energy barriers, and neighboring basins; (2) paths between a specified pair of
basins; and (3) approximations of relative path lengths, basin volumes
(configurational entropy), and path probabilities.
Results demonstrating the core algorithm's capabilities have been generated
by a resource-light, opensource software implementation EASAL. EASAL atlases
several hundred thousand macrostates in minutes on a standard laptop.
Subsequent path and basin computations each take seconds. The core algorithm's
correctness, time complexity, and efficiency-accuracy tradeoffs are formally
guaranteed using modern geometric constraint systems.
The methodology further links geometric variables of the input assembling
units to a type of intuitive topological bar-code of the output atlas, which in
turn determine stable assembled structures and kinetics. This succinct
input-output relationship facilitates reverse analysis, and control towards
design.
We use the novel convex Cayley (distance-based) parametrization that is
unique to assembly, as opposed to folding. Sampling microstates with
macrostate-specific Cayley parameters avoids gradient-descent search used by
all prevailing methods. This increases sampling efficiency, significantly
reduces the number of repeated and discarded samples
Corner-Sharing Tetrahedra for Modeling Micro-Structure
State-of-the-art representations of volumetric multi-scale shape and
structure can be classified into three broad categories: continuous,
continuous-from-discrete, and discrete representations. We propose modeling
micro-structure with a class of discrete Corner-Sharing Tetrahedra (CoSTs).
CoSTs can represent bar-joint, tensegrity, line-incidence, and similar
constraint systems that capture local physical constraints and global
multi-scale properties for design and analysis. The paper develops a palette of
simple geometry processing operations on CoSTs including graph manipulation,
hierarchical refinement, randomization, and generating associated continuous
representations
Efficient Atlasing and Search of Configuration Spaces of Point-Sets Constrained by Distance Intervals
For configurations of point-sets that are pairwise constrained by distance
intervals, the EASAL software implements a suite of algorithms that
characterize the structure and geometric properties of the configuration space.
The algorithms generate, describe and explore these configuration spaces using
generic rigidity properties, classical results for stratification of
semi-algebraic sets, and new results for efficient sampling by convex
parametrization. The paper reviews the key theoretical underpinnings, major
algorithms and their implementation. The paper outlines the main applications
such as the computation of free energy and kinetics of assembly of
supramolecular structures or of clusters in colloidal and soft materials. In
addition, the paper surveys select experimental results and comparisons.Comment: The first version of this article has serious unintended display and
typesetting issues that were overlooked before the upload; it should be
considered withdraw