An effective genetic algorithm for the minimum-label spanning tree problem

Given a connected, undirected graph G with labeled edges, the minimum-label spanning tree problem seeks a spanning tree on G to whose edges are attached the smallest possible number of labels. A greedy heuristic for this NP-hard prob-lem greedily chooses labels so as to reduce the number of components in the subgraphs they induce as quickly as possi-ble. A genetic algorithm for the problem encodes candidate solutions as permutations of the labels; an initial segment of such a chromosome lists the labels that appear on the edges in the chromosome's tree. Three versions of the GA apply generic or heuristic crossover and mutation operators and a local search step. In tests on 27 randomly-generated instances of the minimum-label spanning tree problem, ver-sions of the GA that apply generic operators, with and with-out the local search step, perform less well than the greedy heuristic, but a version that applies the local search step and operators tailored to the problem returns solutions that require on average 10 % fewer labels than the heuristic's

Exact Low-Force Kinetics from High-Force Single-Molecule Unfolding Events

Mechanical forces play a key role in crucial cellular processes involving force-bearing biomolecules, as well as in novel single-molecule pulling experiments. We present an exact method that enables one to extrapolate, to low (or zero) forces, entire time-correlation functions and kinetic rate constants from the conformational dynamics either simulated numerically or measured experimentally at a single, relatively higher, external force. The method has twofold relevance: 1), to extrapolate the kinetics at physiological force conditions from molecular dynamics trajectories generated at higher forces that accelerate conformational transitions; and 2), to extrapolate unfolding rates from experimental force-extension single-molecule curves. The theoretical formalism, based on stochastic path integral weights of Langevin trajectories, is presented for the constant-force, constant loading rate, and constant-velocity modes of the pulling experiments. For the first relevance, applications are described for simulating the conformational isomerization of alanine dipeptide; and for the second relevance, the single-molecule pulling of RNA is considered. The ability to assign a weight to each trace in the single-molecule data also suggests a means to quantitatively compare unfolding pathways under different conditions

Energy Landscape for DNA Rotation and Sliding through a Phage Portal

Molecular motors involved in the packaging of DNA in tailed viruses are among the strongest known. The mechanism by which the motors operate has long been speculated to involve a coupling between rotation of the portal pore (the gate through which DNA passes upon its packaging or ejection), and translation of DNA. Recent experimental evidence rules out portal rotation with a substantial degree of certainty. We have created an atomistic model for the interaction between DNA and the portal of the bacteriophage SPP1, on the basis of cryo-electron microscopy images and of a recently solved crystal structure. A free energy surface describing the interaction is calculated using molecular dynamics simulations, and found to be inconsistent with a mechanism in which portal rotation drives DNA import. The low-energy pathways on the surface are used to advance a hypothesis on DNA import compatible with all available experiments. Additionally, temperature-dependent kinetic data are used to validate computed barriers to DNA ejection