# Robust quantization of a molecular motor motion in a stochastic environment.

@article{Chernyak2009RobustQO, title={Robust quantization of a molecular motor motion in a stochastic environment.}, author={Vladimir Y. Chernyak and Nikolai A. Sinitsyn}, journal={The Journal of chemical physics}, year={2009}, volume={131 18}, pages={ 181101 } }

We explore quantization of the response of a molecular motor to periodic modulation of control parameters. We formulate the pumping-quantization theorem (PQT) that identifies the conditions for robust integer quantized behavior of a periodically driven molecular machine. Implication of PQT on experiments with catenane molecules are discussed.

## 19 Citations

Unification and new extensions of the no-pumping theorems of stochastic pumps

- Physics
- 2014

From molecular machines to quantum dots, a wide range of mesoscopic systems can be modeled by periodically driven Markov processes, or stochastic pumps. Currents in the stochastic pumps are delimited…

Quantization and fractional quantization of currents in periodically driven stochastic systems. II. Full counting statistics.

- Physics, MedicineThe Journal of chemical physics
- 2012

It is shown that the quantized currents that appear at low temperatures are a manifestation of topological invariants in the counting statistics of currents, which provides an approach for classification and extensions of the phenomenon of the robust quantization of currents atLow temperatures to the properties of the countingStatistics which persist to finite temperatures.

Quantization and fractional quantization of currents in periodically driven stochastic systems. I. Average currents.

- Physics, MedicineThe Journal of chemical physics
- 2012

It is shown that under general conditions, the currents in the system on average become quantized or fractionally quantized for adiabatic driving at sufficiently low temperature and the quantitative theory of this quantization is developed in terms of topological invariants.

Directed motion of periodically driven molecular motors: a graph-theoretical approach.

- Computer Science, MedicineThe Journal of chemical physics
- 2013

It is shown that the proposed numerical algorithm allows one to calculate the motion of a system in the space of its microstates even when the considered phase space is combinatorially large.

Hybrid models of molecular machines and the no-pumping theorem.

- Chemistry, PhysicsThe Journal of chemical physics
- 2012

This work introduces a more detailed and realistic class of models in which transitions between metastable states occur by finite-time, diffusive processes rather than sudden jumps, and shows that the no-pumping theorem remains valid within this framework.

A proof by graphical construction of the no-pumping theorem of stochastic pumps

- Computer Science, Mathematics
- 2011

A 'no-pumping theorem' has been obtained, which identifies minimal conditions for generating directed motion or currents in a stochastic pump model of a mesoscopic system evolving under the control of externally varied parameters.

Controlling molecular-scale motion: Exact predictions for driven stochastic systems

- Computer Science
- 2010

A no-pumping theorem is proved which provides conditions for which stochastic pumps with detailed balance exhibit no net directed motion in response to non-adiabatic cyclic driving.

Discrete changes of current statistics in periodically driven stochastic systems

- Mathematics, Physics
- 2010

We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the…

General no-go condition for stochastic pumping.

- Chemistry, MedicineThe Journal of chemical physics
- 2010

This paper gives short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit.

Sensitivity field for nonautonomous molecular rotors.

- Chemistry, MedicineThe Journal of chemical physics
- 2011

A numerical approach to quantify the control of a nonautonomous molecular rotor motion based on the theory of geometric phases to define a sensitivity field in control parameter space that characterizes average motion of a molecule induced by a cyclic perturbation.

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I am writing with a simple plea to balance the voluminous articles about treatment in your journal with a modicum of information about nature and caring effects to rekindle the perception of physicians as healers, not only treaters, who relish the gifts of nature, and foster the humanistic aspect of medicine that has thrived for millennia.