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.

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.

For a common class of two-dimensional (2D) mechanisms called 1-dof tree-decomposable linkages , we present a software package, CayMos, which uses new theoretical results from Sitharam and Wang [2014] and Sitharam et al. [2011a, 2011b] to implement efficient algorithmic solutions for (a) meaningfully representing and visualizing the connected components in the Euclidean realization space; (b) finding a path of continuous motion between two realizations in the same connected component, with or without restricting the realization type (sometimes called orientation type); and (c) finding two “closest” realizations in different connected components.

We study the well documented problem of systematically navigating the potentially exponentially many roots or realizations of well-constrained, variational geometric constraint systems. We give a scalable method called the Equation and Solution Manager (ESM) that can be used both for automatic searches and visual, user-driven searches for desired realizations. The method incrementally assembles the desired solution of the entire system and avoids combinatorial explosion by offering the user a visual walk-through of the solutions to recursively constructed subsystems and by permitting the user to make gradual, adaptive solution choices.We isolate requirements on companion methods that are essential and desirable for efficient, meaningful solution space navigation. Specifically, they permit (a) incorporation of many existing approaches to solution space steering or navigation into the ESM; and (b) integration of the ESM into a standard geometric constraint solver architecture. We address the latter challenge and explain how the integration is achieved. Additionally, we sketch the ESM implementation as part of an opensource, 2D and 3D geometric constraint solver, FRONTIER.

Most computer science departments provide their students with a mathematical foundation which enables them to master theoretic concepts. However, students often express the concern that they are applying their theoretic background to "toy" problems only. They wonder what "real" problems look like and whether or not their background will be sufficient for them when they are faced with an industrial situation. At the same time companies who are hoping to hire well prepared computer programmers, systems analysts, and other technical staff express their concern that recent graduates entering the workforce are not adequately prepared for dealing with large problems in a real world setting. The approach presented here addresses the problem of bridging the gap between theory and practice by actively seeking out industrial partners who provide academics with real problems that can be addressed by teams of students in the academic setting.

ACO function f ofn bits, there is a polynomial p such that any p(log n)-wzse decomposable distribution '~oois" f.In other words, f cannot distinguish