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...

Complex Cooperativity Cooperativity in multisubunit protein complexes is classically understood in terms of either a concerted model, in which all subunits switch conformation simultaneously, or a sequential model, in which a subunit switches conformation whenever a ligand binds. More recently, a “conformational spread” model has suggested that a conformational coupling between subunits and between subunit and ligand is probabilistic. Using high-resolution optical microscopy, Bai et al. (p. 685 ; see the Perspective by Hilser ) observed multistate switching of the bacterial flagellar switch complex that was previously understood in terms of a concerted allosteric model. The conformational spread model gives quantitative agreement with the data.

The dynamic lateral segregation of signaling proteins into microdomains is proposed to facilitate signal transduction, but the constraints on microdomain size, mobility, and diffusion that might realize this function are undefined. Here we interrogate a stochastic spatial model of the plasma membrane to determine how microdomains affect protein dynamics. Taking lipid rafts as representative microdomains, we show that reduced protein mobility in rafts segregates dynamically partitioning proteins, but the equilibrium concentration is largely independent of raft size and mobility. Rafts weakly impede small-scale protein diffusion but more strongly impede long-range protein mobility. The long-range mobility of raft-partitioning and raftexcluded proteins, however, is reduced to a similar extent. Dynamic partitioning into rafts increases specific interprotein collision rates, but to maximize this critical, biologically relevant function, rafts must be small (diameter, 6 to 14 nm) and mobile. Intermolecular collisions can also be favored by the selective capture and exclusion of proteins by rafts, although this mechanism is generally less efficient than simple dynamic partitioning. Generalizing these results, we conclude that microdomains can readily operate as protein concentrators or isolators but there appear to be significant constraints on size and mobility if microdomains are also required to function as reaction chambers that facilitate nanoscale protein-protein interactions. These results may have significant implications for the many signaling cascades that are scaffolded or assembled in plasma membrane microdomains.