Francisco J. Cao

Efficiency of Brownian motors

The efficiency of different types of Brownian motors is calculated analytically and numerically. We find that motors based on flashing ratchets present a low efficiency and an unavoidable entropy production. On the other hand, a certain class of motors based on adiabatically changing potentials, named reversible ratchets, exhibit a higher efficiency and the entropy production can be arbitrarily reduced.

Feedback Control in a Collective Flashing Ratchet

An ensemble of Brownian particles in a feedback controlled flashing ratchet is studied. The ratchet potential is switched on and off depending on the position of the particles, with the aim of maximizing the current. We study in detail a protocol which maximizes the instant velocity of the center of mass of the ensemble at any time. This protocol is optimal for one particle and performs better than any periodic flashing for ensembles of moderate size, but is defeated by a random or periodic switching for large ensembles.

Active DNA unwinding dynamics during processive DNA replication.

Duplication of double-stranded DNA (dsDNA) requires a fine-tuned coordination between the DNA replication and unwinding reactions. Using optical tweezers, we probed the coupling dynamics between these two activities when they are simultaneously carried out by individual Phi29 DNA polymerase molecules replicating a dsDNA hairpin. We used the wild-type and an unwinding deficient polymerase variant and found that mechanical tension applied on the DNA and the DNA sequence modulate in different ways the replication, unwinding rates, and pause kinetics of each polymerase. However, incorporation of pause kinetics in a model to quantify the unwinding reaction reveals that both polymerases destabilize the fork with the same active mechanism and offers insights into the topological strategies that could be used by the Phi29 DNA polymerase and other DNA replication systems to couple unwinding and replication reactions.

Thermodynamics of feedback controlled systems

We compute the entropy reduction in feedback controlled systems due to the repeated operation of the controller. This was the lacking ingredient to establish the thermodynamics of these systems, and in particular of Maxwells demons. We illustrate some of the consequences of our general results by deriving the maximum work that can be extracted from isothermal feedback controlled systems. As a case example, we finally study a simple system that performs an isothermal information-fueled particle pumping.

Closed-loop control strategy with improved current for a flashing ratchet

We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this letter, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.

Mechano-chemical kinetics of DNA replication: identification of the translocation step of a replicative DNA polymerase

During DNA replication replicative polymerases move in discrete mechanical steps along the DNA template. To address how the chemical cycle is coupled to mechanical motion of the enzyme, here we use optical tweezers to study the translocation mechanism of individual bacteriophage Phi29 DNA polymerases during processive DNA replication. We determine the main kinetic parameters of the nucleotide incorporation cycle and their dependence on external load and nucleotide (dNTP) concentration. The data is inconsistent with power stroke models for translocation, instead supports a loose-coupling mechanism between chemical catalysis and mechanical translocation during DNA replication. According to this mechanism the DNA polymerase works by alternating between a dNTP/PPi-free state, which diffuses thermally between pre- and post-translocated states, and a dNTP/PPi-bound state where dNTP binding stabilizes the post-translocated state. We show how this thermal ratchet mechanism is used by the polymerase to generate work against large opposing loads (∼50 pN).

Fluctuation dynamics of bilayer vesicles with intermonolayer sliding: Experiment and theory

The presence of coupled modes of membrane motion in closed shells is extensively predicted by theory. The bilayer structure inherent to lipid vesicles is suitable to support hybrid modes of curvature motion coupling membrane bending with the local reorganization of the bilayer material through relaxation of the dilatational stresses. Previous experiments evidenced the existence of such hybrid modes facilitating membrane bending at high curvatures in lipid vesicles [Rodríguez-García, R., Arriaga, L.R., Mell, M., Moleiro, L.H., López-Montero, I., Monroy, F., 2009. Phys. Rev. Lett. 102, 128201.]. For lipid bilayers that are able to undergo intermonolayer sliding, the experimental fluctuation spectra are found compatible with a bimodal schema. The usual tension/bending fluctuations couple with the hybrid modes in a mechanical interplay, which becomes progressively efficient with increasing vesicle radius, to saturate at infinity radius into the behavior expected for a flat membrane. Grounded on the theory of closed shells, we propose an approximated expression of the bimodal spectrum, which predicts the observed dependencies on the vesicle radius. The dynamical features obtained from the autocorrelation functions of the vesicle fluctuations are found in quantitative agreement with the proposed theory.

Optimal operation of feedback flashing ratchets

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. We discuss different strategies for this operation with the aim of maximizing the net flux of particles in the collective version of a flashing ratchet consisting of N overdamped Brownian particles. We show the optimal protocols for the one-particle ratchet and for the collective ratchet with an infinite number of particles. Finally we comment on the unsolved problem of the optimal strategy for any other number of particles.

Threshold feedback control for a collective flashing ratchet: Threshold dependence

We study the threshold control protocol for a collective flashing ratchet. In particular, we analyze the dependence of the current on the values of the thresholds. We have found analytical expressions for the small threshold dependence both for the few and for the many particle cases. For few particles the current is a decreasing function of the thresholds, thus, the maximum current is reached for zero thresholds. In contrast, for many particles the optimal thresholds have a nonzero finite value. We have numerically checked the relation that allows to obtain the optimal thresholds for an infinite number of particles from the optimal period of the periodic protocol. These optimal thresholds for an infinite number of particles give good results for many particles. In addition, they also give good results for few particles due to the smooth dependence of the current up to these threshold values.

DNA synthesis determines the binding mode of the human mitochondrial single-stranded DNA-binding protein.

Abstract Single-stranded DNA-binding proteins (SSBs) play a key role in genome maintenance, binding and organizing single-stranded DNA (ssDNA) intermediates. Multimeric SSBs, such as the human mitochondrial SSB (HmtSSB), present multiple sites to interact with ssDNA, which has been shown in vitro to enable them to bind a variable number of single-stranded nucleotides depending on the salt and protein concentration. It has long been suggested that different binding modes might be used selectively for different functions. To study this possibility, we used optical tweezers to determine and compare the structure and energetics of long, individual HmtSSB–DNA complexes assembled on preformed ssDNA and on ssDNA generated gradually during ‘in situ’ DNA synthesis. We show that HmtSSB binds to preformed ssDNA in two major modes, depending on salt and protein concentration. However, when protein binding was coupled to strand-displacement DNA synthesis, only one of the two binding modes was observed under all experimental conditions. Our results reveal a key role for the gradual generation of ssDNA in modulating the binding mode of a multimeric SSB protein and consequently, in generating the appropriate nucleoprotein structure for DNA synthetic reactions required for genome maintenance.