Molecular combustion motors.

We construct a molecular model of an internal combustion engine, by coupling a Brownian ratchet with an exothermic chemical cycle. We derive explicitly the thermodynamically allowed couplings, and show that almost every such coupling will result in motion. We compute from this formalism the maximal transmission efficiency of Brownian gears. Cells have a service infrastructure, just like cities have steam tunnels and subways and trucks delivering food to supermarkets. There are several related aspects to this infrastructure. Various substances have to be shipped from the place where they are produced to the place where they are needed. This involves transporting them both within regions of the cells and across regions [1,2]. Within a region, transport is achieved, for instance, through protein motors which walk on a complex and dynamic set of highways (the cytoskeleton), and can pull along vesicles containing those substances. The motors consume energy-carrying molecules (adenosine triphos-phate or ATP) to walk. These motors are extraordinarily tiny: the motor domain of kinesin is about 12 nm across, about 50 times smaller than the smallest transistor we can manufacture on microchips. Their length scale and energy scale reveal they are essentially Brownian machines, In this Letter, I will try to outline a mathematical framework with which one can describe how a Brownian machine can convert chemical energy into mechanical motion. A little over 30 years ago, Feynman described a Brow-nian motor which has been the basis of many models [3]. A paddle sits in a box with gas at a certain temper* ture and is subject to Brownian fluctuations. The paddle is coupled to a ratchet device which, supposedly, should "rectify" these fluctuations to provide motile power. The ratchet sits in a box at some other temperature and can itself random walk. Feynman shows that this contraption obeys precisely the formulas for a Carnot cycle, so it is a Brownian analog of a steam engine. Since then, several models formally related to the Feynrnan ratchet have been applied to microscopic systems. Fox described rotary molecular assemblers [4], Vale and Oosawa tried to use a Feynman ratchet to describe protein motors [5], Oster and co-workers studied polymerization ratchets [6,7], Simon et al. understood protein translocation across membranes [8], and Ajdari and Prost proposed a setup for high performance chromatography by showing that periodically turning a ratchetlike potential on and off will generate transport [9]. Recently I observed that a ratchet can …