Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.

/pdf/stochastic-thermodynamics-fluctuation-theorems-and-molecular-2epwyvmpf0.pdf

Stochastic thermodynamics, fluctuation theorems and molecular machines

The specific bonding of DNA base pairs provides the chemical foundation for genetics. This powerful molecular recognition system can be used in nanotechnology to direct the assembly of highly structured materials with specific nanoscale features, as well as in DNA computation to process complex information. The exploitation of DNA for material purposes presents a new chapter in the history of the molecule.

/pdf/dna-in-a-material-world-28gymklany.pdf

DNA in a material world

The shapes of eukaryotic cells and ultimately the organisms that they form are defined by cycles of mechanosensing, mechanotransduction and mechanoresponse Local sensing of force or geometry is transduced into biochemical signals that result in cell responses even for complex mechanical parameters such as substrate rigidity and cell-level form These responses regulate cell growth, differentiation, shape changes and cell death Recent tissue scaffolds that have been engineered at the micro- and nanoscale level now enable better dissection of the mechanosensing, transduction and response mechanisms

https://faculty.washington.edu/nsniadec/ME599/S09/private/25Vogel.pdf

Local force and geometry sensing regulate cell functions.

The widespread use of molecular machines in biology has long suggested that great rewards could come from bridging the gap between synthetic molecular systems and the machines of the macroscopic world. In the last two decades, it has proved possible to design synthetic molecular systems with architectures where triggered large amplitude positional changes of submolecular components occur. Perhaps the best way to appreciate the technological potential of controlled molecular-level motion is to recognize that nanomotors and molecular-level machines lie at the heart of every significant biological process. Over billions of years of evolution, nature has not repeatedly chosen this solution for performing complex tasks without good reason. When mankind learns how to build artificial structures that can control and exploit molecular level motion and interface their effects directly with other molecular-level substructures and the outside world, it will potentially impact on every aspect of functional molecule and materials design. An improved understanding of physics and biology will surely follow.

The first steps on the long path to the invention of artificial molecular machines were arguably taken in 1827 when the Scottish botanist Robert Brown observed the haphazard motion of tiny particles under his microscope.1,2 The explanation for Brownian motion, that it is caused by bombardment of the particles by molecules as a consequence of the kinetic theory of matter, was later provided by Einstein, followed by experimental verification by Perrin.3,4 The random thermal motion of molecules and its implications for the laws of thermodynamics in turn inspired Gedankenexperiments (“thought experiments”) that explored the interplay (and apparent paradoxes) of Brownian motion and the Second Law of Thermodynamics. Richard Feynman’s famous 1959 lecture “There’s plenty of room at the bottom” outlined some of the promise that manmade molecular machines might hold.5,6 However, Feynman’s talk came at a time before chemists had the necessary synthetic and analytical tools to make molecular machines. While interest among synthetic chemists began to grow in the 1970s and 1980s, progress accelerated in the 1990s, particularly with the invention of methods to make mechanically interlocked molecular systems (catenanes and rotaxanes) and control and switch the relative positions of their components.7−24

Here, we review triggered large-amplitude motions in molecular structures and the changes in properties these can produce. We concentrate on conformational and configurational changes in wholly covalently bonded molecules and on catenanes and rotaxanes in which switching is brought about by various stimuli (light, electrochemistry, pH, heat, solvent polarity, cation or anion binding, allosteric effects, temperature, reversible covalent bond formation, etc.). Finally, we discuss the latest generations of sophisticated synthetic molecular machine systems in which the controlled motion of subcomponents is used to perform complex tasks, paving the way to applications and the realization of a new era of “molecular nanotechnology”.

1.1. The Language Used To Describe Molecular Machines
Terminology needs to be properly and appropriately defined and these meanings used consistently to effectively convey scientific concepts. Nowhere is the need for accurate scientific language more apparent than in the field of molecular machines. Much of the terminology used to describe molecular-level machines has its origins in observations made by biologists and physicists, and their findings and descriptions have often been misinterpreted and misunderstood by chemists. In 2007 we formalized definitions of some common terms used in the field (e.g., “machine”, “switch”, “motor”, “ratchet”, etc.) so that chemists could use them in a manner consistent with the meanings understood by biologists and physicists who study molecular-level machines.14

The word “machine” implies a mechanical movement that accomplishes a useful task. This Review concentrates on systems where a stimulus triggers the controlled, relatively large amplitude (or directional) motion of one molecular or submolecular component relative to another that can potentially result in a net task being performed. Molecular machines can be further categorized into various classes such as “motors” and “switches” whose behavior differs significantly.14 For example, in a rotaxane-based “switch”, the change in position of a macrocycle on the thread of the rotaxane influences the system only as a function of state. Returning the components of a molecular switch to their original position undoes any work done, and so a switch cannot be used repetitively and progressively to do work. A “motor”, on the other hand, influences a system as a function of trajectory, meaning that when the components of a molecular motor return to their original positions, for example, after a 360° directional rotation, any work that has been done is not undone unless the motor is subsequently rotated by 360° in the reverse direction. This difference in behavior is significant; no “switch-based” molecular machine can be used to progressively perform work in the way that biological motors can, such as those from the kinesin, myosin, and dynein superfamilies, unless the switch is part of a larger ratchet mechanism.14

Artificial Molecular Machines

The basic features of DNA were elucidated during the half-century following the discovery of the double helix. But it is only during the past decade that researchers have been able to manipulate single molecules of DNA to make direct measurements of its mechanical properties. These studies have illuminated the nature of interactions between DNA and proteins, the constraints within which the cellular machinery operates, and the forces created by DNA-dependent motors.

/pdf/ten-years-of-tension-single-molecule-dna-mechanics-3j5v7uo3it.pdf

Ten years of tension: single-molecule DNA mechanics

f Abstract Mechanical processes are involved in nearly every facet of the cell cycle. Mechanical forces are generated in the cell during processes as diverse as chromosomal segregation, replication, transcription, translation, translocation of proteins across membranes, cell locomotion, and catalyzed protein and nucleic acid folding and unfolding, among others. Because force is a product of all these reactions, biochemists are beginning to directly apply external forces to these processes to alter the extent or even the fate of these reactions hoping to reveal their underlying molecular mechanisms. This review provides the conceptual framework to understand the role of mechanical force in biochemistry.

/pdf/mechanical-processes-in-biochemistry-1n3ff6l3gt.pdf

Mechanical processes in biochemistry.

Escherichia coli RNA polymerase translocates along the DNA discontinuously during the elongation phase of transcription, spending proportionally more time at some template positions, known as pause and arrest sites, than at others. Current models of elongation suggest that the enzyme backtracks at these locations, but the dynamics are unresolved. Here, we study the role of lateral displacement in pausing and arrest by applying force to individually transcribing molecules. We find that an assisting mechanical force does not alter the translocation rate of the enzyme, but does reduce the efficiency of both pausing and arrest. Moreover, arrested molecules cannot be rescued by force, suggesting that arrest occurs by a bipartite mechanism: the enzyme backtracks along the DNA followed by a conformational change of the ternary complex (RNA polymerase, DNA and transcript), which cannot be reversed mechanically.

https://www.pnas.org/content/pnas/99/18/11682.full.pdf

Using mechanical force to probe the mechanism of pausing and arrest during continuous elongation by Escherichia coli RNA polymerase

Collagen is the most abundant protein in the extracellular matrix (ECM), where its structural organization conveys mechanical information to cells Using optical-tweezers-based microrheology, we investigated mechanical properties both of collagen molecules at a range of concentrations in acidic solution where fibrils cannot form and of gels of collagen fibrils formed at neutral pH, as well as the development of microscale mechanical heterogeneity during the self-assembly process The frequency scaling of the complex shear modulus even at frequencies of ∼10 kHz was not able to resolve the flexibility of collagen molecules in acidic solution In these solutions, molecular interactions cause significant transient elasticity, as we observed for 5 mg/ml solutions at frequencies above ∼200 Hz We found the viscoelasticity of solutions of collagen molecules to be spatially homogeneous, in sharp contrast to the heterogeneity of self-assembled fibrillar collagen systems, whose elasticity varied by more than an order of magnitude and in power-law behavior at different locations within the sample By probing changes in the complex shear modulus over 100-minute timescales as collagen self-assembled into fibrils, we conclude that microscale heterogeneity appears during early phases of fibrillar growth and continues to develop further during this growth phase Experiments in which growing fibrils dislodge microspheres from an optical trap suggest that fibril growth is a force-generating process These data contribute to understanding how heterogeneities develop during self-assembly, which in turn can help synthesis of new materials for cellular engineering

/pdf/microrheological-characterization-of-collagen-systems-from-1thbh11nxs.pdf

Microrheological Characterization of Collagen Systems: From Molecular Solutions to Fibrillar Gels

The design of bioinspired nanostructures and materials of defined size and shape is challenging as it pushes our understanding of biomolecular assembly to its limits. In such endeavors, DNA is the current building block of choice because of its predictable and programmable self-assembly. The use of peptide- and protein-based systems, however, has potential advantages due to their more-varied chemistries, structures and functions, and the prospects for recombinant production through gene synthesis and expression. Here, we present the design and characterization of two complementary peptides programmed to form a parallel heterodimeric coiled coil, which we use as the building blocks for larger, supramolecular assemblies. To achieve the latter, the two peptides are joined via peptidic linkers of variable lengths to produce a range of assemblies, from flexible fibers of indefinite length, through large colloidal-scale assemblies, down to closed and discrete nanoscale objects of defined stoichiometry. We posit that the different modes of assembly reflect the interplay between steric constraints imposed by short linkers and the bulk of the helices, and entropic factors that favor the formation of many smaller objects as the linker length is increased. This approach, and the resulting linear and proteinogenic polypeptides, represents a new route for constructing complex peptide-based assemblies and biomaterials.

/pdf/squaring-the-circle-in-peptide-assembly-from-fibers-to-2mgsgjdjbm.pdf

Squaring the Circle in Peptide Assembly: From Fibers to Discrete Nanostructures by de Novo Design

Holographic optical tweezers (HOTs) enable the manipulation of multiple traps independently in three dimensions in real time. Application of this technique to force measurements requires calibration of trap stiffness and its position dependence. Here, we determine the trap stiffness of HOTs as they are steered in two dimensions. To do this, we trap a single particle in a multiple-trap configuration and analyze the power spectrum of the laser deflection on a position-sensitive photodiode. With this method, the relative trap strengths can be determined independent of exact particle size, and high stiffnesses can be probed because of the high bandwidth of the photodiode. We find a trap stiffness for each of three HOT traps of kappa approximately 26 pN/microm per 100 mW of laser power. Importantly, we find that this stiffness remains constant within +/- 4% over 20 microm displacements of a trap. We also investigate the minimum step size achievable when steering a trap with HOTs, and find that traps can be stepped and detected within approximately 2 nm in our instrument, although there is an underlying position modulation of the traps of comparable scale that arises from SLM addressing. The independence of trap stiffness on steering angle over wide ranges and the nanometer positioning accuracy of HOTs demonstrate the applicability of this technique to quantitative study of force response of extended biomaterials such as cells or elastomeric protein networks.

Nancy R. Forde

Papers

Mechanical processes in biochemistry.

Using mechanical force to probe the mechanism of pausing and arrest during continuous elongation by Escherichia coli RNA polymerase

Microrheological Characterization of Collagen Systems: From Molecular Solutions to Fibrillar Gels

Squaring the Circle in Peptide Assembly: From Fibers to Discrete Nanostructures by de Novo Design

Calibration of dynamic holographic optical tweezers for force measurements on biomaterials.