The combinatorial nature of many important mathematical problems, including nondeterministic-polynomial-time (NP)-complete problems, places a severe limitation on the problem size that can be solved with conventional, sequentially operating electronic computers. There have been significant efforts in conceiving parallel-computation approaches in the past, for example: DNA computation, quantum computation, and microfluidics-based computation. However, these approaches have not proven, so far, to be scalable and practical from a fabrication and operational perspective. Here, we report the foundations of an alternative parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. Exploring the network in a parallel fashion using a large number of independent, molecularmotor-propelled agents then solves the mathematical problem. This approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power consumption and heat dissipation. We provide a proof-of-concept demonstration of such a device by solving, in a parallel fashion, the small instance {2, 5, 9} of the subset sum problem, which is a benchmark NPcomplete problem. Finally, we discuss the technical advances necessary to make our system scalable with presently available technology.parallel computing | molecular motors | NP complete | biocomputation | nanotechnology M any combinatorial problems of practical importance, such as the design and verification of circuits (1), the folding (2) and design (3) of proteins, and optimal network routing (4), require that a large number of possible candidate solutions are explored in a brute-force manner to discover the actual solution. Because the time required for solving these problems grows exponentially with their size, they are intractable for conventional electronic computers, which operate sequentially, leading to impractical computing times even for medium-sized problems. Solving such problems therefore requires efficient parallel-computation approaches (5). However, the approaches proposed so far suffer from drawbacks that have prevented their implementation. For example, DNA computation, which generates mathematical solutions by recombining DNA strands (6, 7), or DNA static (8) or dynamic (9) nanostructures, is limited by the need for impractically large amounts of DNA (10-13). Quantum computation is limited in scale by decoherence and by the small number of qubits that can be integrated (14). Microfluidics-based parallel computation (15) is difficult to scale up in practice due to rapidly diverging physical size and complexity of the computation devices with the size of the problem, as well as the need for impractically large external pressure.Here, we propose a parallel-computation approach, which is based on encoding combinatorial problems into the geometry of a physical network of lithographically defined channels, followed by exploration of the network in a par...

Generation of force and movement by actomyosin cross-bridges is the molecular basis of muscle contraction, but generally accepted ideas about cross-bridge properties have recently been questioned. Of the utmost significance, evidence for nonlinear cross-bridge elasticity has been presented. We here investigate how this and other newly discovered or postulated phenomena would modify cross-bridge operation, with focus on post-power-stroke events. First, as an experimental basis, we present evidence for a hyperbolic [MgATP]-velocity relationship of heavy-meromyosin-propelled actin filaments in the in vitro motility assay using fast rabbit skeletal muscle myosin (28-29°C). As the hyperbolic [MgATP]-velocity relationship was not consistent with interhead cooperativity, we developed a cross-bridge model with independent myosin heads and strain-dependent interstate transition rates. The model, implemented with inclusion of MgATP-independent detachment from the rigor state, as suggested by previous single-molecule mechanics experiments, accounts well for the [MgATP]-velocity relationship if nonlinear cross-bridge elasticity is assumed, but not if linear cross-bridge elasticity is assumed. In addition, a better fit is obtained with load-independent than with load-dependent MgATP-induced detachment rate. We discuss our results in relation to previous data showing a nonhyperbolic [MgATP]-velocity relationship when actin filaments are propelled by myosin subfragment 1 or full-length myosin. We also consider the implications of our results for characterization of the cross-bridge elasticity in the filament lattice of muscle.

The findings give general insight into mechanics of cytoskeletal polymers that interact with molecular motors, aid rational development of nanotechnological applications and have implications for structure and in vivo functions of fascin-actin bundles.

Salt-bridge interactions between acidic and basic amino acids contribute to the structural stability of proteins and to protein-protein interactions. A conserved salt-bridge is a canonical feature of the α-defensin antimicrobial peptide family, but the role of this common structural element has not been fully elucidated. We have investigated mouse Paneth cell α-defensin cryptdin-4 (Crp4) and peptide variants with mutations at Arg7 or Glu15 residue positions to disrupt the salt-bridge and assess the consequences on Crp4 structure, function, and stability. NMR analyses showed that both (R7G)-Crp4 and (E15G)-Crp4 adopt native-like structures, evidence of fold plasticity that allows peptides to reshuffle side chains and stabilize the structure in the absence of the salt-bridge. In contrast, introduction of a large hydrophobic side chain at position 15, as in (E15L)-Crp4 cannot be accommodated in the context of the Crp4 primary structure. Regardless of which side of the salt-bridge was mutated, salt-bridge variants retained bactericidal peptide activity with differential microbicidal effects against certain bacterial cell targets, confirmation that the salt-bridge does not determine bactericidal activity per se. The increased structural flexibility induced by salt-bridge disruption enhanced peptide sensitivity to proteolysis. Although sensitivity to proteolysis by MMP7 was unaffected by most Arg7 and Glu15 substitutions, every salt-bridge variant was degraded extensively by trypsin. Moreover, the salt-bridge facilitates adoption of the characteristic α-defensin fold as shown by the impaired in vitro refolding of (E15D)-proCrp4, the most conservative salt-bridge disrupting replacement. In Crp4, therefore, the canonical α-defensin salt-bridge facilitates adoption of the characteristic α-defensin fold, which decreases structural flexibility and confers resistance to degradation by proteinases.

Actin filaments have key roles in cell motility but are generally claimed to be passive interaction partners in actin-myosin-based motion generation. Here, we present evidence against this static view based on an altered myosin-induced actin filament gliding pattern in an in vitro motility assay at varied [MgATP]. The statistics that characterize the degree of meandering of the actin filament paths suggest that for [MgATP] ≥ 0.25 mM, the flexural rigidity of heavy meromyosin (HMM)-propelled actin filaments is similar (without phalloidin) or slightly lower (with phalloidin) than that of HMM-free filaments observed in solution without surface tethering. When [MgATP] was reduced to ≤0.1 mM, the actin filament paths in the in vitro motility assay became appreciably more winding in both the presence and absence of phalloidin. This effect of lowered [MgATP] was qualitatively different from that seen when HMM was mixed with ATP-insensitive, N-ethylmaleimide-treated HMM (NEM-HMM; 25-30%). In particular, the addition of NEM-HMM increased a non-Gaussian tail in the path curvature distribution as well as the number of events in which different parts of an actin filament followed different paths. These effects were the opposite of those observed with reduced [MgATP]. Theoretical modeling suggests a 30-40% lowered flexural rigidity of the actin filaments at [MgATP] ≤ 0.1 mM and local bending of the filament front upon each myosin head attachment. Overall, the results fit with appreciable structural changes in the actin filament during actomyosin-based motion generation, and modulation of the actin filament mechanical properties by the dominating chemomechanical actomyosin state.