How the Escherichia coli GroEL͞ES chaperonin assists folding of a substrate protein remains to be uncovered. Recently, it was suggested that confinement into the chaperonin cage itself can significantly accelerate folding of a substrate. Performing comprehensive molecular simulations of eight proteins confined into various sizes L of chaperonin-like cage, we explore how and to what extent protein thermodynamics and folding mechanisms are altered by the cage. We show that a substrate protein is remarkably stabilized by confinement; the estimated increase in denaturation temperature ⌬Tf is as large as Ϸ60°C. For a protein of size R0, the stabilization ⌬Tf scales as (R0͞L) , where Ϸ 3, which is consistent with a mean field theory of polymer. We also found significant free energy cost of confining a protein, which increases with R0͞L, indicating that the confinement requires external work provided by the chaperonin system. In kinetic study, we show the folding is accelerated in a modestly well confined case, which is consistent with a recent experimental result on ribulose-1,5-bisphosphate carboxylase-oxygenase folding and simulation results of a ␤ hairpin. Interestingly, the acceleration of folding is likely to be larger for a protein with more complex topology, as quantified by the contact order. We also show how ensemble of folding pathways are altered by the chaperonin-like cage calculating a variant of value used in the study of spontaneous folding. The Escherichia coli GroEL͞ES chaperonin is the bestcharacterized molecular chaperone that assists in vivo protein folding (1, 2). The cylindrical structure of GroEL complex and its conformational change upon binding to ATP and GroES have been experimentally determined (1, 3, 4). The ATPdependent chaperonin cycle has been studied, and how these structural changes are coupled with substrate binding and release has been elucidated (5-7). Many protein-engineered GroEL molecules were used to identify residues and͞or segments that are important for substrate binding, ATP hydrolysis, and so on (8, 9). With all of these, machinery of the chaperonin was reasonably well uncovered.On the other hand, how substrate folding is assisted by the chaperonin is less understood. There are at least two different, but not mutually exclusive, scenarios regarding this issue (10, 11). The first ''Anfinsen cage'' model indicates that the chaperonin provides a passive cage that separates a substrate protein from other macromolecules, removing the danger of aggregation (10). In the other ''iterative annealing'' scenario, a substrate protein is mechanically forced to unfold upon binding to GroEL and it folds upon transfer into the chaperonin cavity or release from GroEL. This cycle is repeated until a substrate reaches the native state (12)(13)(14)38). Both Anfinsen cage and mechanical unfolding effects may be present in reality. Here, we address yet another factor that can assist substrate folding. Using an engineered chaperonin system that inhibits the chaperonin cycle, Brinker et al. (15) ...

In the thermodynamic limit, the existence of a maximal efficiency of energy conversion attainable by a Carnot cycle consisting of quasi-static isothermal and adiabatic processes precludes the existence of a perpetual machine of the second kind, whose cycles yield positive work in an isothermal environment. We employ the recently developed framework of the energetics of stochastic processes (called 'stochastic energetics'), to re-analyze the Carnot cycle in detail, taking account of fluctuations, without taking the thermodynamic limit. We find that both in this non-macroscopic situation, both processes of connection to and disconnection from heat baths and adiabatic processes that cause distortion of the energy distribution are sources of inevitable irreversibility within the cycle. Also, the so-called null-recurrence property of the cumulative efficiency of energy conversion over many cycles and the irreversible property of isolated, purely mechanical processes under external 'macroscopic' operations are discussed in relation to the impossibility of a perpetual machine, or Maxwell's demon. This analysis may serve as the basis for the design and analysis of mesoscopic energy converters in the near future. 05.90+m, 05.40-a, 05.70-a, 02.50-r

We formulate energetics of the forced thermal ratchet [M. O. Magnasco, Phys. Rev. Lett. 71, 1477(1993] and evaluate its efficiency of energy transformation. We show that the presence of thermal fluctuation cannot increase the efficiency of the energy transformation in the original system of Magnasco, which is contrary to his claim that "There is a region of the operating regime where the efficiency is optimized at finite temperatures." We also discuss the maximum efficiency of the forced thermal ratchet. [S0031-9007(98)06408-4] PACS numbers: 05.40.+j, 87.10.+e Molecular motors are known to have the high efficiency of energy transformation even in the presence of thermal fluctuation [1]. Motivated by the interesting fact, recent studies of thermal ratchet models [2] are showing how work should be extracted from nonequilibrium fluctuations [3][4][5][6][7][8][9][10][11]. Fluctuation-induced work has been a subject not only for biological interest but also for the foundation of statistical physics: Thermal fluctuation-induced motion in ratchet systems were also investigated earlier [2][3][4].One of the important findings among ratchet models was by Magnasco [7] where he showed that the Brownian particle in periodic potential with broken symmetry, the so-called ratchet, can exhibit a nonzero net drift if the particle is subject to an external fluctuation having sufficient time correlation. He also studied the temperature dependence on the fluctuation-induced current in the system and showed that the current can be maximized at a finite temperature. This interesting finding has been interpreted that the existence of thermal fluctuation does not disturb the fluctuation-induced motion and even facilitates the efficiency of energy transformation.The latter claim is quite surprising, because thermal fluctuation is naively considered to disturb effective operation of a machine. In mesoscopic systems as in molecular motors, one cannot escape from the effect of thermal fluctuation. Therefore, Magnasco's finding has been followed and analyzed further by much literature (see references in Ref. [11]). We show, however, this interpretation is incorrect, by energetic analysis [12,13] of Magnasco's original system [7]. The efficiency of energy transformation is not maximized at finite temperature: The maximum efficiency is realized in the absence of thermal fluctuation. It turns out that the following problem has not yet been solved: Can thermal fluctuation facilitate the efficiency of energetic transformation from force fluctuation into work in general ratchet systems?Let us consider a forced ratchet system subject to an external load against global motion:where x represents the state of the ratchet, j͑t͒ is a thermal noise satisfying ͗j͑t͒j͑t 0 ͒͘ 2kTd͑t 2 t 0 ͒, "͗· · ·͘" is an operator of ensemble average, F͑t͒ is an external fluctuation with temporal period t, F͑t 1 t͒ F͑t͒, R t 0 dt F͑t͒ 0, and V L is a potential due to the load, ≠V L ≠x l . 0. The geometry of the potential, V ͑x͒ V 0 ͑x͒ 1 V L ͑x͒, is displayed in Fig.

Molecular motors in biological systems are expected to use ambient fluctuation. In a recent paper [Phys. Rev. Lett. 80, 5251 (1998)], it was shown that the following question was unanswered: Can thermal noise facilitate energy conversion by ratchet system? We consider it using stochastic energetics, and show that there exist systems where thermal noise helps the energy conversion.

When a small dynamical system that is initially in contact with a heat bath is detached from this heat bath and then caused to undergo a quasi-static adiabatic process, the resulting statistical distribution of the system's energy differs from that of an equilibrium ensemble. Subsequent contact of the system with another heat bath is inevitably irreversible, hence the entire process cannot be reversed without a net energy transfer to the heat baths.