Abstract Non-equilibrium fluctuations can drive vecto- rial transport along an anisotropic structure in an isother- mal medium by biasing the effect of thermal noise (k B T). Mechanisms based on this principle are often called Brown- ian ratchets and have been invoked as a possible explana- tion for the operation of biomolecular motors and pumps. We discuss the thermodynamics and kinetics for the oper- ation of microscopic ratchet motors under conditions rele- vant to biology, showing how energy provided by external fluctuations or a non-equilibrium chemical reaction can cause unidirectional motion or uphill pumping of a sub- stance. Our analysis suggests that molecular pumps such as Na,K-ATPase and molecular motors such as kinesin and myosin may share a common underlying mechanism. Key words Free energy transduction · Molecular motors · Ion pumps · Ratchets · Maxwells demon Introduction We normally think of vectorial motion as arising from mac- roscopic forces that provide directionality, such as an object falling in a gravitational field, or migration of charged pro- teins in an applied electric field. Recent work has shown theoretically (Astumian and Bier 1994; Astumian 1997; Hanggi and Bartusek 1996; Magnasco 1993; Prost et al. 1994) and experimentally (Rousselet et al. 1994) that exter- nal random fluctuations acting on a particle in an anisotropic medium can cause unidirectional motion in an isothermal medium without a macroscopic force or spatial chemical gradient. Earlier analogous work from a chemical kinetic perspective established that fluctuations of rate constants in a catalyzed chemical reaction can drive the reaction to pro- ceed unidirectionally even if the affinity of the reaction (the chemical force) is zero at every instant (Tsong and Astu- mian 1986; Astumian et al. 1987, 1989; Astumian and Rob- ertson 1993). These results are counterintuitive since ran- dom fluctuations in most cases destroy rather than create or- dered behavior. In fact it might seem at first glance that fluc- tuation induced directed motion is contrary to the second law of thermodynamics and could be used to create a per- petual motion machine. Showing in detail why this is not the case strongly motivates the development of rigorous models that can be understood at the level of basic physics. Aside from theoretical interest, ratchet models share many features with the motion of biomolecular motors such as kinesin (Svoboda et al. 1993) and myosin (Finer et al. 1994), and ion pumps such as Na,K ATPase and Ca ATPase (Lauger 1991) (see Fig. 1). These molecules also bring about net motion without a macroscopic force. The energy for driving flow comes typically from hydrolysis of ATP, but how this chemical reaction defines a preferred direction of motion is far from clear. Recent experiments have demonstrated that, consistent with a ratchet mecha- nism (Tsong and Astumian 1986; Westerhoff et al. 1986; Astumian et al. 1987), external oscillating (Serpersu and Tsong 1984; Liu et al. 1990) or fluctuating (Xie et al. 1994, 1997) electric fields can drive transport by a molecular ion pump, the Na,K ATPase. Energy from the field substitutes for the energy normally provided by ATP hydrolysis even though the average value of the field is zero. Recent mod- els for fluctuation driven transport provide an explicit mechanism for coupling energy from a non-equilibrium chemical reaction to cause local fluctuations similar to those imposed externally to drive unidirectional transport (Tsong and Astumian 1986; Fulinski 1994). Despite sharing the similar function of using chemical energy to drive vectorial transport, mechanisms of molec- ular motors and pumps are typically pictured entirely dif- ferently. Molecular pumps are most often modeled in terms of chemical kinetics, where ATP energy is used to change the relative affinities of and barrier heights between dif- ferent binding sites by sequentially favoring different con- formational states of the protein as ATP is bound, hydro- lyzed, and the products released. The conformational re- Eur Biophys J (1998) 27: 474– 489 © Springer-Verlag 1998 Received: 18 February 1998 / Revised version: 5 May 1998 / Accepted: 14 May 1998 R. Dean Astumian · Imre Derényi Fluctuation driven transport and models of molecular motors and pumps ARTICLE R. D. Astumian () · I. Derényi Departments of Surgery and of Biochemistry and Molecular Biology, University of Chicago, MC 6035, Chicago, IL 60637, USA e-mail: dastumia@surgery.bsd.uchicago.edu