This Article describes a novel geometric methodology for analyzing free energy and kinetics of assembly driven by short-range pair-potentials in an implicit solvent and provides a proof-of-concept illustration of its unique capabilities. An atlas is a labeled partition of the assembly landscape into a 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 queryable atlas of local potential energy minima, their basin structure, energy barriers, and neighboring basins; (2) paths between a specified pair of basins, each path being a sequence of conformational regions or macrostates below a desired energy threshold; and (3) approximations of relative path lengths, basin volumes (configurational entropy), and path probabilities. Results demonstrating the core algorithm’s capabilities and high computational efficiency have been generated by a resource-light, curated open source software implementation EASAL (Efficient Atlasing and Search of Assembly Landscapes, 10.1145/3204472ACM Trans. Math. Softw.201844148; see software, Efficient Atlasing and Search of Assembly Landscapes2016; video, Video Illustrating the opensource software EASAL2016; and user guide, EASAL software user guide2016). Running on a laptop with Intel­(R) Core­(TM) i7-7700@3.60 GHz CPU with 16GB of RAM, EASAL atlases several hundred thousand conformational regions or macrostates in minutes using a single compute core. Subsequent path and basin computations each take seconds. A parallelized EASAL version running on the same laptop with 4 cores gives a 3× speedup for atlas generation. The core algorithm’s correctness, time complexity, and efficiency–accuracy trade-offs are formally guaranteed using modern distance geometry, geometric constraint systems and combinatorial rigidity. The methodology further links the shape of the input assembling units to a type of intuitive and queryable 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 toward design. A novel feature that is crucial to both the high sampling efficiency and decoupling of roadmap generation from sampling is a recently developed theory of convex Cayley (distance-based) custom parametrizations specific to assembly, as opposed to folding. Representing microstates with macrostate-specific Cayley parameters, to generate microstate samples, avoids gradient-descent search used by all prevailing methods. Further, these parametrizations convexify conformational regions or macrostates. This ratchets up sampling efficiency, significantly reducing number of repeated and discarded samples. These features of the new stand-alone methodology can also be used to complement the strengths of prevailing methodologies including Molecular Dynamics, Monte Carlo, and Fast Fourier Transform based methods.

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 article reviews the key theoretical underpinnings, major algorithms, and their implementation. The article 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 article surveys select experimental results and comparisons.

Icosahedral viruses are under a micrometer in diameter, their infectious genome encapsulated by a shell assembled by a multiscale process, starting from an integer multiple of 60 viral capsid or coat protein (VP) monomers. We predict and validate inter-atomic hotspot interactions between VP monomers that are important for the assembly of 3 types of icosahedral viral capsids: Adeno Associated Virus serotype 2 (AAV2) and Minute Virus of Mice (MVM), both T = 1 single stranded DNA viruses, and Bromo Mosaic Virus (BMV), a T = 3 single stranded RNA virus. Experimental validation is by in-vitro, site-directed mutagenesis data found in literature. We combine ab-initio predictions at two scales: at the interface-scale , we predict the importance ( cruciality ) of an interaction for successful subassembly across each interface between symmetry-related VP monomers; and at the capsid-scale , we predict the cruciality of an interface for successful capsid assembly. At the interface-scale, we measure cruciality by changes in the capsid free-energy landscape partition function when an interaction is removed. The partition function computation uses atlases of interface subassembly landscapes, rapidly generated by a novel geometric method and curated opensource software EASAL (efficient atlasing and search of assembly landscapes). At the capsid-scale, cruciality of an interface for successful assembly of the capsid is based on combinatorial entropy. Our study goes all the way from resource-light, multiscale computational predictions of crucial hotspot inter-atomic interactions to validation using data on site-directed mutagenesis’ effect on capsid assembly. By reliably and rapidly narrowing down target interactions, (no more than 1.5 hours per interface on a laptop with Intel Core i5-2500K @ 3.2 Ghz CPU and 8GB of RAM) our predictions can inform and reduce time-consuming in-vitro and in-vivo experiments, or more computationally intensive in-silico analyses.

The growing performance and decreasing price of embedded processors are opening many doors, for both developers in the industry and in academia. However, the complexities of these systems can create serious developmental bottlenecks. Sophisticated software packages such as OpenCV can assist in both the functional development and educational aspects of these otherwise complex applications; such tools lend themselves very well to use by the academic community, in particular in providing examples of algorithm implementation. However the task of migrating this software to embedded platforms poses its own challenges. This paper will review how to mitigate some of these issues, including C++ implementation, memory constraints, floating-point support, and opportunities to maximise performance using vendor-optimised libraries and integrated accelerators or co-processors. Finally, we will introduce a new effort by Texas Instruments to optimise vision systems by running OpenCV on the C6000 TM digital signal processor architecture. Benchmarks will show the advantage of using the DSP by comparing the performance of a DSP+ARM® system-on-chip (SoC) processor against an ARM-only device.

This work measures baseline sampling characteristics that highlight fundamental differences between sampling methods for assembly driven by short-ranged pair potentials. Such granular comparison is essential for fast, flexible, and accurate hybridization of complementary methods. Besides sampling speed, efficiency, and accuracy of uniform grid coverage, other sampling characteristics measured are (i) accuracy of covering narrow low energy regions that have low effective dimension (ii) ability to localize sampling to specific basins, and (iii) flexibility in sampling distributions. As a proof of concept, we compare a recently developed geometric methodology EASAL (Efficient Atlasing and Search of Assembly Landscapes) and the traditional Monte Carlo (MC) method for sampling the energy landscape of two assembling trans-membrane helices, driven by short-range pair potentials. By measuring the above-mentioned sampling characteristics, we demonstrate that EASAL provides localized and accurate coverage of crucial regions of the energy landscape of low effective dimension, under flexible sampling distributions, with much fewer samples and computational resources than MC sampling. EASAL’s empirically validated theoretical guarantees permit credible extrapolation of these measurements and comparisons to arbitrary number and size of assembling units. Promising avenues for hybridizing the complementary advantages of the two methods are discussed.