Multiplexed vortex beam-based optical tweezers generated with spiral phase mask.

The design and implementation of a multiplexed spiral phase mask in an experimental optical tweezers setup are presented. This diffractive optical element allows the generation of multiple concentric vortex beams with independent topological charges and without amplitude modulation. The generalization of the phase mask for multiple concentric vortices is also shown. The design for a phase mask of two multiplexed vortices with different topological charges is developed. We experimentally show the transfer of angular momentum to the optically trapped microparticles by enabling nearly independent orbiting dynamics around the optical axis within each vortex. The angular velocity of the confined particles versus the optical power in the focal region is also discussed for different combinations of topological charges.

Fluctuation relations for irreversible emergence of information.

Information theory and Thermodynamics have developed closer in the last years, with a growing application palette in which the formal equivalence between the Shannon and Gibbs entropies is exploited. The main barrier to connect both disciplines is the fact that information does not imply a dynamics, whereas thermodynamic systems unfold with time, often away from equilibrium. Here, we analyze chain-like systems comprising linear sequences of physical objects carrying symbolic meaning. We show that, after defining a reading direction, both reversible and irreversible informations emerge naturally from the principle of microscopic reversibility in the evolution of the chains driven by a protocol. We find fluctuation equalities that relate entropy, the relevant concept in communication, and energy, the thermodynamically significant quantity, examined along sequences whose content evolves under writing and revision protocols. Our results are applicable to nanoscale chains, where information transfer is subject to thermal noise, and extendable to virtually any communication system.

Heat Generation in Single Magnetic Nanoparticles under Near-Infrared Irradiation.

Heat generation by pointlike structures is an appealing concept for its implications in nanotechnology and biomedicine. The way to pump energy that excites heat locally and the synthesis of nanostructures that absorb such energy are key issues in this endeavor. High-frequency alternating magnetic or near-infrared optical fields are used to induce heat in iron oxide nanoparticles, a combined solution that is being exploited in hyperthermia treatments. However, the temperature determination around a single iron oxide nanoparticle remains a challenge. We study the heat released from iron oxide nanostructures under near-infrared illumination on a one-by-one basis by optical tweezers. To measure the temperature, we follow the medium viscosity changes around the trapped particle as a function of the illuminating power, thus avoiding the use of thermal probes. Our results help interpret temperature, a statistical parameter, in the nanoscale and the concept of heat production by nanoparticles under thermal agitation.

Photoluminescence Activation of Organic Dyes via Optically Trapped Quantum Dots.

Laser tweezers afford quantum dot (QD) manipulation for use as localized emitters. Here, we demonstrate fluorescence by radiative energy transfer from optically trapped colloidal QDs (donors) to fluorescent dyes (acceptors). To this end, we synthesized silica-coated QDs of different compositions and triggered their luminescence by simultaneous trapping and two-photon excitation in a microfluidic chamber filled with dyes. This strategy produces a near-field light source with great spatial maneuverability, which can be exploited to scan nanostructures. In this regard, we demonstrate induced photoluminescence of dye-labeled cells via optically trapped silica-coated colloidal QDs placed at their vicinity. Allocating nanoscale donors at controlled distances from a cell is an attractive concept in fluorescence microscopy because it dramatically reduces the number of excited dyes, which improves resolution by preventing interferences from the whole sample, while prolonging dye luminescence lifetime due to the lower power absorbed from the QDs.

Single-Stranded Condensation Stochastically Blocks G-Quadruplex Assembly in Human Telomeric RNA.

TERRA is an RNA molecule transcribed from human subtelomeric regions toward chromosome ends potentially involved in regulation of heterochromatin stability, semiconservative replication, and telomerase inhibition, among others. TERRA contains tandem repeats of the sequence GGGUUA, with a strong tendency to fold into a four-stranded arrangement known as a parallel G-quadruplex. Here, we demonstrate by using single-molecule force spectroscopy that this potential is limited by the inherent capacity of RNA to self-associate randomly and further condense into entropically more favorable structures. We stretched RNA constructions with more than four and less than eight hexanucleotide repeats, thus unable to form several G-quadruplexes in tandem, flanked by non-G-rich overhangs of random sequence by optical tweezers on a one by one basis. We found that condensed RNA stochastically blocks G-quadruplex folding pathways with a near 20% probability, a behavior that is not found in DNA analogous molecules.

Writing, Proofreading and Editing in Information Theory.

Information is a physical entity amenable to be described by an abstract theory. The concepts associated with the creation and post-processing of the information have not, however, been mathematically established, despite being broadly used in many fields of knowledge. Here, inspired by how information is managed in biomolecular systems, we introduce writing, entailing any bit string generation, and revision, as comprising proofreading and editing, in information chains. Our formalism expands the thermodynamic analysis of stochastic chains made up of material subunits to abstract strings of symbols. We introduce a non-Markovian treatment of operational rules over the symbols of the chain that parallels the physical interactions responsible for memory effects in material chains. Our theory underlies any communication system, ranging from human languages and computer science to gene evolution.

Thermodynamic framework for information in nanoscale systems with memory.

Information is represented by linear strings of symbols with memory that carry errors as a result of their stochastic nature. Proofreading and edition are assumed to improve certainty although such processes may not be effective. Here, we develop a thermodynamic theory for material chains made up of nanoscopic subunits with symbolic meaning in the presence of memory. This framework is based on the characterization of single sequences of symbols constructed under a protocol and is used to derive the behavior of ensembles of sequences similarly constructed. We then analyze the role of proofreading and edition in the presence of memory finding conditions to make revision an effective process, namely, to decrease the entropy of the chain. Finally, we apply our formalism to DNA replication and RNA transcription finding that Watson and Crick hybridization energies with which nucleotides are branched to the template strand during the copying process are optimal to regulate the fidelity in proofreading. These results are important in applications of information theory to a variety of solid-state physical systems and other biomolecular processes.

A DNA-centered explanation of the DNA polymerase translocation mechanism.

DNA polymerase couples chemical energy to translocation along a DNA template with a specific directionality while it replicates genetic information. According to single-molecule manipulation experiments, the polymerase-DNA complex can work against loads greater than 50 pN. It is not known, on the one hand, how chemical energy is transduced into mechanical motion, accounting for such large forces on sub-nanometer steps, and, on the other hand, how energy consumption in fidelity maintenance integrates in this non-equilibrium cycle. Here, we propose a translocation mechanism that points to the flexibility of the DNA, including its overstretching transition, as the principal responsible for the DNA polymerase ratcheting motion. By using thermodynamic analyses, we then find that an external load hardly affects the fidelity of the copying process and, consequently, that translocation and fidelity maintenance are loosely coupled processes. The proposed translocation mechanism is compatible with single-molecule experiments, structural data and stereochemical details of the DNA-protein complex that is formed during replication, and may be extended to RNA transcription.

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

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.

Information management in DNA replication modeled by directional, stochastic chains with memory.

Stochastic chains represent a key variety of phenomena in many branches of science within the context of information theory and thermodynamics. They are typically approached by a sequence of independent events or by a memoryless Markov process. Stochastic chains are of special significance to molecular biology, where genes are conveyed by linear polymers made up of molecular subunits and transferred from DNA to proteins by specialized molecular motors in the presence of errors. Here, we demonstrate that when memory is introduced, the statistics of the chain depends on the mechanism by which objects or symbols are assembled, even in the slow dynamics limit wherein friction can be neglected. To analyze these systems, we introduce a sequence-dependent partition function, investigate its properties, and compare it to the standard normalization defined by the statistical physics of ensembles. We then apply this theory to characterize the enzyme-mediated information transfer involved in DNA replication under the real, non-equilibrium conditions, reproducing measured error rates and explaining the typical 100-fold increase in fidelity that is experimentally found when proofreading and edition take place. Our model further predicts that approximately 1 kT has to be consumed to elevate fidelity in one order of magnitude. We anticipate that our results are necessary to interpret configurational order and information management in many molecular systems within biophysics, materials science, communication, and engineering.

Role of the central cations in the mechanical unfolding of DNA and RNA G-quadruplexes.

Cations are known to mediate diverse interactions in nucleic acids duplexes but they are critical in the arrangement of four-stranded structures. Here, we use all-atom molecular dynamics simulations with explicit solvent to analyse the mechanical unfolding of representative intramolecular G-quadruplex structures: a parallel, a hybrid and an antiparallel DNA and a parallel RNA, in the presence of stabilising cations. We confirm the stability of these conformations in the presence of [Formula: see text] central ions and observe distortions from the tetrad topology in their absence. Force-induced unfolding dynamics is then investigated. We show that the unfolding events in the force-extension curves are concomitant to the loss of coordination between the central ions and the guanines of the G-quadruplex. We found lower ruptures forces for the parallel configuration with respect to the antiparallel one, while the behaviour of the force pattern of the parallel RNA appears similar to the parallel DNA. We anticipate that our results will be essential to interpret the fine structure rupture profiles in stretching assays at high resolution and will shed light on the mechanochemical activity of G-quadruplex-binding machinery.

A Temperature-Jump Optical Trap for Single-Molecule Manipulation.

To our knowledge, we have developed a novel temperature-jump optical tweezers setup that changes the temperature locally and rapidly. It uses a heating laser with a wavelength that is highly absorbed by water so it can cover a broad range of temperatures. This instrument can record several force-distance curves for one individual molecule at various temperatures with good thermal and mechanical stability. Our design has features to reduce convection and baseline shifts, which have troubled previous heating-laser instruments. As proof of accuracy, we used the instrument to carry out DNA unzipping experiments in which we derived the average basepair free energy, entropy, and enthalpy of formation of the DNA duplex in a range of temperatures between 5°C and 50°C. We also used the instrument to characterize the temperature-dependent elasticity of single-stranded DNA (ssDNA), where we find a significant condensation plateau at low force and low temperature. Oddly, the persistence length of ssDNA measured at high force seems to increase with temperature, contrary to simple entropic models.

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).

Single-molecule portrait of DNA and RNA double helices.

The composition and geometry of the genetic information carriers were described as double-stranded right helices sixty years ago. The flexibility of their sugar-phosphate backbones and the chemistry of their nucleotide subunits, which give rise to the RNA and DNA polymers, were soon reported to generate two main structural duplex states with biological relevance: the so-called A and B forms. Double-stranded (ds) RNA adopts the former whereas dsDNA is stable in the latter. The presence of flexural and torsional stresses in combination with environmental conditions in the cell or in the event of specific sequences in the genome can, however, stabilize other conformations. Single-molecule manipulation, besides affording the investigation of the elastic response of these polymers, can test the stability of their structural states and transition models. This approach is uniquely suited to understanding the basic features of protein binding molecules, the dynamics of molecular motors and to shedding more light on the biological relevance of the information blocks of life. Here, we provide a comprehensive single-molecule analysis of DNA and RNA double helices in the context of their structural polymorphism to set a rigorous interpretation of their material response both inside and outside the cell. From early knowledge of static structures to current dynamic investigations, we review their phase transitions and mechanochemical behaviour and harness this fundamental knowledge not only through biological sciences, but also for Nanotechnology and Nanomedicine.

Laser heating tunability by off-resonant irradiation of gold nanoparticles.

Temperature changes in the vicinity of a single absorptive nanostructure caused by local heating have strong implications in technologies such as integrated electronics or biomedicine. Herein, the temperature changes in the vicinity of a single optically trapped spherical Au nanoparticle encapsulated in a thermo-responsive poly(N-isopropylacrylamide) shell (Au@pNIPAM) are studied in detail. Individual beads are trapped in a counter-propagating optical tweezers setup at various laser powers, which allows the overall particle size to be tuned through the phase transition of the thermo-responsive shell. The experimentally obtained sizes measured at different irradiation powers are compared with average size values obtained by dynamic light scattering (DLS) from an ensemble of beads at different temperatures. The size range and the tendency to shrink upon increasing the laser power in the optical trap or by increasing the temperature for DLS agree with reasonable accuracy for both approaches. Discrepancies are evaluated by means of simple models accounting for variations in the thermal conductivity of the polymer, the viscosity of the aqueous solution and the absorption cross section of the coated Au nanoparticle. These results show that these parameters must be taken into account when considering local laser heating experiments in aqueous solution at the nanoscale. Analysis of the stability of the Au@pNIPAM particles in the trap is also theoretically carried out for different particle sizes.

Optical tweezers to study viruses.

A virus is a complex molecular machine that propagates by channeling its genetic information from cell to cell. Unlike macroscopic engines, it operates in a nanoscopic world under continuous thermal agitation. Viruses have developed efficient passive and active strategies to pack and release nucleic acids. Some aspects of the dynamic behavior of viruses and their substrates can be studied using structural and biochemical techniques. Recently, physical techniques have been applied to dynamic studies of viruses in which their intrinsic mechanical activity can be measured directly. Optical tweezers are a technology that can be used to measure the force, torque and strain produced by molecular motors, as a function of time and at the single-molecule level. Thanks to this technique, some bacteriophages are now known to be powerful nanomachines; they exert force in the piconewton range and their motors work in a highly coordinated fashion for packaging the viral nucleic acid genome. Nucleic acids, whose elasticity and condensation behavior are inherently coupled to the viral packaging mechanisms, are also amenable to examination with optical tweezers. In this chapter, we provide a comprehensive analysis of this laser-based tool, its combination with imaging methods and its application to the study of viruses and viral molecules.

Mechanical unfolding of long human telomeric RNA (TERRA).

We report the first single molecule investigation of TERRA molecules. By using optical-tweezers and other biophysical techniques, we have found that long RNA constructions of up to 25 GGGUUA repeats form higher order structures comprised of single parallel G-quadruplex blocks, which unfold at lower forces than their DNA counterparts.

Mechanical identities of RNA and DNA double helices unveiled at the single-molecule level.

Double-stranded (ds) RNA is the genetic material of a variety of viruses and has been recently recognized as a relevant molecule in cells for its regulatory role. Despite that the elastic response of dsDNA has been thoroughly characterized in recent years in single-molecule stretching experiments, an equivalent study with dsRNA is still lacking. Here, we have engineered long dsRNA molecules for their individual characterization contrasting information with dsDNA molecules of the same sequence. It is known that dsRNA is an A-form molecule unlike dsDNA, which exhibits B-form in physiological conditions. These structural types are distinguished at the single-molecule level with atomic force microscopy (AFM) and are the basis to understand their different elastic response. Force-extension curves of dsRNA with optical and magnetic tweezers manifest two main regimes of elasticity, an entropic regime whose end is marked by the A-form contour-length and an intrinsic regime that ends in a low-cooperative overstretching transition in which the molecule extends to 1.7 times its A-form contour-length. DsRNA does not switch between the A and B conformations in the presence of force. Finally, dsRNA presents both a lower stretch modulus and overstretching transition force than dsDNA, whereas the electrostatic and intrinsic contributions to the persistence length are larger.

Entropy involved in fidelity of DNA replication.

Information has an entropic character which can be analyzed within the framework of the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. Here, we introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication.