Single molecule experiments in biophysics: exploring the thermal behavior of nonequilibrium small systems

Biomolecules carry out very specialized tasks inside the cell where energies involved are few tens of k_BT, small enough for thermal fluctuations to be relevant in many biomolecular processes. In this paper I discuss a few concepts and present some experimental results that show how the study of fluctuation theorems applied to biomolecules contributes to our understanding of the nonequilibrium thermal behavior of small systems.Comment: Proceedings of the 22nd Statphys Conference 2004 (Bangalore,India). Invited contributio

Extracting Structural Information of a Heteropolymer from Force-Extension Curves

We present a theory for the reverse analysis on the sequence information of a single H/P two-letter random hetero-polymer (RHP) from its force-extension(f-z) curves during quasi static stretching. Upon stretching of a self-assembled RHP, it undergoes several structural transitions. The typical elastic response of a hetero-polymeric globule is a set of overlapping saw-tooth patterns. With consideration of the height and the position of the overlapping saw-tooth shape, we analyze the possibility of extracting the binding energies of the internal domains and the corresponding block sizes of the contributing conformations.Comment: 5 figures 7 page

Statistical mechanics of RNA folding: a lattice approach

We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA consists of just one hairpin. Using exact arguments and Monte Carlo simulations we determine the phase diagram for this case. We show that the denaturation transition is first order and can either occur directly or through an intermediate molten phase.Comment: 8 pages, 9 figure

End-joining long nucleic acid polymers

Many experiments involving nucleic acids require the hybridization and ligation of multiple DNA or RNA molecules to form a compound molecule. When one of the constituents is single stranded, however, the efficiency of ligation can be very low and requires significant individually tailored optimization. Also, when the molecules involved are very long (>10 kb), the reaction efficiency typically reduces dramatically. Here, we present a simple procedure to efficiently and specifically end-join two different nucleic acids using the well-known biotin–streptavidin linkage. We introduce a two-step approach, in which we initially bind only one molecule to streptavidin (STV). The second molecule is added only after complete removal of the unbound STV. This primarily forms heterodimers and nearly completely suppresses formation of unwanted homodimers. We demonstrate that the joining efficiency is 50 ± 25% and is insensitive to molecule length (up to at least 20 kb). Furthermore, our method eliminates the requirement for specific complementary overhangs and can therefore be applied to both DNA and RNA. Demonstrated examples of the method include the efficient end-joining of DNA to single-stranded and double-stranded RNA, and the joining of two double-stranded RNA molecules. End-joining of long nucleic acids using this procedure may find applications in bionanotechnology and in single-molecule experiments

Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies

The description of nonequilibrium processes in nano-sized objects, where the typical energies involved are a few times, is increasingly becoming central to disciplines as diverse as condensed-matter physics, materials science, and biophysics. Major recent developments towards a unified treatment of arbitrarily large fluctuations in small systems are described by fluctuation theorems that relate the probabilities of a system absorbing from or releasing to the bath a given amount of energy in a nonequilibrium process. Here we experimentally verify the Crooks Fluctuation Theorem (CFT) under weak and strong nonequilibrium conditions by using optical tweezers to measure the irreversible mechanical work during the unfolding and refolding of a small RNA hairpin and an RNA three-helix junction. We also show that the CFT provides a powerful way to obtain folding free energies in biomolecules by determining the crossing between the unfolding and refolding irreversible work distributions. The method makes it possible to obtain folding free energies in nonequilibrium processes that dissipate up to of the average total work exerted, thereby paving the way for reconstructing free energy landscapes along reaction coordinates in nonequilibrium single-molecule experiments.Comment: PDF file, 19 pages. Supplementary information available online at www.nature.co

Single Molecule Statistics and the Polynucleotide Unzipping Transition

We present an extensive theoretical investigation of the mechanical unzipping of double-stranded DNA under the influence of an applied force. In the limit of long polymers, there is a thermodynamic unzipping transition at a critical force value of order 10 pN, with different critical behavior for homopolymers and for random heteropolymers. We extend results on the disorder-averaged behavior of DNA's with random sequences to the more experimentally accessible problem of unzipping a single DNA molecule. As the applied force approaches the critical value, the double-stranded DNA unravels in a series of discrete, sequence-dependent steps that allow it to reach successively deeper energy minima. Plots of extension versus force thus take the striking form of a series of plateaus separated by sharp jumps. Similar qualitative features should reappear in micromanipulation experiments on proteins and on folded RNA molecules. Despite their unusual form, the extension versus force curves for single molecules still reveal remnants of the disorder-averaged critical behavior. Above the transition, the dynamics of the unzipping fork is related to that of a particle diffusing in a random force field; anomalous, disorder-dominated behavior is expected until the applied force exceeds the critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure

mRNA pseudoknot structures can act as ribosomal roadblocks

Several viruses utilize programmed ribosomal frameshifting mediated by mRNA pseudoknots in combination with a slippery sequence to produce a well defined stochiometric ratio of the upstream encoded to the downstream-encoded protein. A correlation between the mechanical strength of mRNA pseudoknots and frameshifting efficiency has previously been found; however, the physical mechanism behind frameshifting still remains to be fully understood. In this study, we utilized synthetic sequences predicted to form mRNA pseudoknot-like structures. Surprisingly, the structures predicted to be strongest lead only to limited frameshifting. Two-dimensional gel electrophoresis of pulse labelled proteins revealed that a significant fraction of the ribosomes were frameshifted but unable to pass the pseudoknot-like structures. Hence, pseudoknots can act as ribosomal roadblocks, prohibiting a significant fraction of the frameshifted ribosomes from reaching the downstream stop codon. The stronger the pseudoknot the larger the frameshifting efficiency and the larger its roadblocking effect. The maximal amount of full-length frameshifted product is produced from a structure where those two effects are balanced. Taking ribosomal roadblocking into account is a prerequisite for formulating correct frameshifting hypotheses

Quantum Fluctuation Theorems

Recent advances in experimental techniques allow one to measure and control systems at the level of single molecules and atoms. Here gaining information about fluctuating thermodynamic quantities is crucial for understanding nonequilibrium thermodynamic behavior of small systems. To achieve this aim, stochastic thermodynamics offers a theoretical framework, and nonequilibrium equalities such as Jarzynski equality and fluctuation theorems provide key information about the fluctuating thermodynamic quantities. We review the recent progress in quantum fluctuation theorems, including the studies of Maxwell's demon which plays a crucial role in connecting thermodynamics with information.Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Fundamental Aspects and New Directions", (Springer International Publishing, 2018

Formation of a Silicate L 3 Phase with Continuously Adjustable Pore Sizes

the magnitude of the gain. Thus, the delay time of ϳ0.5 s observed in REFERENCES AND NOTES ___________________________ Since the demonstration that surfactants could be used in the fabrication of silica mesophases (1), amphiphiles have been used to produce inorganic materials with a variety of mesomorphic structures, including lamellar, hexagonally packed tubular, and cubic forms (2-12). Surfactant-induced assembly of inorganic structures is now recognized as a way to make novel nanoporous materials with larger pore sizes than was previously possible. However, techniques developed thus far have limited capability to produce very large pores of a predetermined size. Here we describe the synthesis and characterization of a new, random, bicontinuous silicate mesomorph for which predetermined pore sizes, over a very large size range, may be obtained. Most procedures for forming mesoporous silicates rely on the micelle-forming properties of a surfactant, typically at a low surfactant concentration. The addition of an inorganic precursor, such as an alkoxysilane, leads to association and coassembly into a mesophase precipitant whose structural dimensions are controlled by the surfactant length. Polymerization of the inorganic precursor and removal of the surfactant results in a rigid silica shell conforming to the structural shape of the mesophase. However, the use of dilute surfactant solutions limits the ability to predict the topology of the mesophase. Also, the typical product of the process is a powder of micrometer-sized particles, thereby limiting uses in filtration, optical, or electronic applications, where large-area thin films or large uniform monoliths of material are required. Finally, the pore volume is filled with surfactant; that is, the surfactant must be removed before the pores can be accessed. These difficulties may be partially avoided by the use of high-concentration surfactant systems in which either the inorganic precursors minimally perturb a preexisting surfactant-water liquid crystalline (LC) structure or the LC nature of the system may be recovered under appropriate experimental conditions, as shown by Attard et al. (6). Also, because the inorganic precursor does not precipitate out of solution, the resultant material conforms to the shape of the container in which it forms, thereby allowing fabrication of large monoliths of a desired size and shape. However, even in these cases, the pore size is limited by the surfactant and the limited range of compositions on the phase diagram for a given mesomorphic structure. Applications of silicate mesophases as filtration media, optical materials, and nanocomposites would be facilitated if th