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1 Programmed ribosomal frameshifting is a translational recoding event in which ribosomes slip backward along messenger RNA presumably due to increased tension disrupting the codon-anticodon interaction at the ribosome's coding site. Single-molecule physical methods and recent experiments characterizing the physical properties of mRNA's slippery sequence as well as the mechanical stability of downstream mRNA structure motifs that give rise to frameshifting are discussed. Progress in technology, experimental assays, and data analysis methods hold promise for accurate physical modeling and quantitative understanding of -1 programmed ribosomal frameshifting.

Many viruses produce multiple proteins from a single mRNA sequence by encoding overlapping genes. One mechanism to decode both genes, which reside in alternate reading frames, is ?1 programmed ribosomal frameshifting. Although recognized for over 25?years, the molecular and physical mechanism of ?1 frameshifting remains poorly understood. We have developed a mathematical model that treats mRNA translation and associated ?1 frameshifting as a stochastic process in which the transition probabilities are based on the energetics of local molecular interactions. The model predicts both the location and efficiency of ?1 frameshift events in HIV-1. Moreover, we compute ?1 frameshift efficiencies upon mutations in the viral mRNA sequence and variations in relative tRNA abundances, predictions that are directly testable in experiment.

Ribosomal frameshifting on viral RNAs relies on the mechanical properties of structural elements, often pseudoknots and more rarely stem-loops, that are unfolded by the ribosome during translation. In human immunodeficiency virus (HIV)-1 type B a long hairpin containing a three-nucleotide bulge is responsible for efficient frameshifting. This three-nucleotide bulge separates the hairpin in two domains: an unstable lower stem followed by a GC-rich upper stem. Toeprinting and chemical probing assays suggest that a hairpin-like structure is retained when ribosomes, initially bound at the slippery sequence, were allowed multiple EF-G catalyzed translocation cycles. However, while the upper stem remains intact the lower stem readily melts. After the first, and single step of translocation of deacylated tRNA to the 30 S P site, movement of the mRNA stem-loop in the 5′ direction is halted, which is consistent with the notion that the downstream secondary structure resists unfolding. Mechanical stretching of the hairpin using optical tweezers only allows clear identification of unfolding of the upper stem at a force of 12.8 ± 1.0 pN. This suggests that the lower stem is unstable and may indeed readily unfold in the presence of a translocating ribosome.

Many viruses regulate translation of polycistronic mRNA using a −1 ribosomal frameshift induced by an RNA pseudoknot. When the ribosome encounters the pseudoknot barrier that resists unraveling, transient mRNA–tRNA dissociation at the decoding site, results in a shift of the reading frame. The eukaryotic frameshifting pseudoknot from the beet western yellow virus (BWYV) has been well characterized, both structurally and functionally. Here, we show that in order to obtain eukaryotic levels of frameshifting efficiencies using prokaryotic Escherichia coli ribosomes, which depend upon the structural integrity of the BWYV pseudoknot, it is necessary to shorten the mRNA spacer between the slippery sequence and the pseudoknot by 1 or 2 nucleotides (nt). Shortening of the spacer is likely to re-establish tension and/or ribosomal contacts that were otherwise lost with the smaller E. coli ribosomes. Chemical probing experiments for frameshifting and nonframeshifting BWYV constructs were performed to investigate the structural integrity of the pseudoknot confined locally at the mRNA entry site. These data, obtained in the pretranslocation state, show a compact overall pseudoknot structure, with changes in the conformation of nucleotides (i.e., increase in reactivity to chemical probes) that are first “hit” by the ribosomal helicase center. Interestingly, with the 1-nt shortened spacer, this increase of reactivity extends to a downstream nucleotide in the first base pair (bp) of stem 1, consistent with melting of this base pair. Thus, the 3 bp that will unfold upon translocation are different in both constructs with likely consequences on unfolding kinetics.

To access the genetic code to be transcribed to RNA, RNA polymerases must first open a “transcription bubble” in the DNA. Structural studies suggest that the minimal model of initiation by T7 bacterophage RNA polymerase (T7 RNAP) consists of two distinct steps: initial binding, in which the T7 RNAP binds to and bends the DNA, and opening, achieved by “scrunching” of the DNA. Since both steps involve mechanical deformation of the DNA, both may be affected by downstream DNA tension. Using an oscillating two-bead optical tweezers assay, we have measured the lifetime of single T7 RNAP-DNA initation complexes under tension. Global maximumlikelihood fitting of force-dependent and non-force-dependent versions of this minimal model shows that there is no conclusively discernible force-dependence of initiation in the measured 0-2 pN DNA tension range.

Ribosome structure and mechanism are largely conserved among all known forms of life. Therefore, the motions associated with translation may be among the most ancient and fundamental in biology. However, the molecular mechanism of translocation, the coordinated movement of tRNAs and associated mRNA on the ribosome, has eluded scientists and remains obscure. Single–molecule experiments using optical tweezers and fluorescence microscope are starting to shed new light on these questions. For example, we have observed that moderate forces reverse direction of motion and ribosomes seem to slip backward into the 5' direction along a poly(U) message. Although the detailed molecular mechanism for ribosome slippage is not fully understood, these observations raise interesting biological questions about e.g. −1 frameshifting. Is the −1 frameshift essential for HIV−1 replication a result of tension in the message? Single–molecule experiments open the way towards quantitative modeling of ribosome motion and related phenomena such as −1 frameshifting.

It recently has been shown that the observed noise amplitude of an intrinsically noisy system may be reduced by causing the underlying state to fluctuate [Phys. Rev. Lett. 86, 950 (2001)]]. This paper extends the previous theory by considering the full power spectrum of the output signal, interpreting noise reduction in terms of the low-frequency end of the spectrum as well as the integrated spectrum. Our treatment accounts for arbitrarily sized fluctuations and deals with both continuous and discretely sampled observations. We show that noise suppression is possible if and only if the stationary average of the intensity of state-dependent noise decreases. We apply our analysis to an example involving saturable electrical conduction discussed in the original paper by Vilar and Rubí.

Motor proteins such as kinesin, myosin and polymerase convert chemical energy into work through a cycle that involves nucleotide hydrolysis. Kinetic rates in the cycle that depend upon load identify transitions at which structural changes, such as power strokes or diffusive motions, are likely to occur. Here we show, by modelling data obtained with a molecular force clamp, that kinesin mechanochemistry can be characterized by a mechanism in which a load-dependent isomerization follows ATP binding. This model quantitatively accounts for velocity data over a wide range of loads and ATP levels, and indicates that movement may be accomplished through two sequential 4-nm substeps. Similar considerations account for kinesin processivity, which is found to obey a load-dependent Michaelis-Menten relationship.

Kinesin is a two-headed, ATP-driven motor protein that moves processively along microtubules in discrete steps of 8 nm, probably by advancing each of its heads alternately in sequence. Molecular details of how the chemical energy stored in ATP is coupled to mechanical displacement remain obscure. To shed light on this question, a force clamp was constructed, based on a feedback-driven optical trap capable of maintaining constant loads on single kinesin motors. The instrument provides unprecedented resolution of molecular motion and permits mechanochemical studies under controlled external loads. Analysis of records of kinesin motion under variable ATP concentrations and loads revealed several new features. First, kinesin stepping appears to be tightly coupled to ATP hydrolysis over a wide range of forces, with a single hydrolysis per 8-nm mechanical advance. Second, the kinesin stall force depends on the ATP concentration. Third, increased loads reduce the maximum velocity as expected, but also raise the apparent Michaelis-Menten constant. The kinesin cycle therefore contains at least one load-dependent transition affecting the rate at which ATP molecules bind and subsequently commit to hydrolysis. It is likely that at least one other load-dependent rate exists, affecting turnover number. Together, these findings will necessitate revisions to our understanding of how kinesin motors function.

The RNA homopolymer poly(A) forms single-stranded helices due to base-stacking, the mechanical properties of which may affect the biological function of naturally-occurring A-repeat sequences. Since RNA is a polyanion, screening and binding by cations enhances this helix formation by shielding charges along its backbone from each other.The poly(A) single helix may be disrupted by application of tension, as by optical tweezers, allowing the energetics of helix formation to be estimated in addition to the mechanical properties of the helical and randomly-coiled states.Using optical tweezers, we measured the force-extension behavior of poly(A) under a variety of buffer conditions, finding that the effect of sodium is consistent with Debye screening but that magnesium and other Group II cations are likely to be binding and forming inner-sphere (direct) contacts with poly(A), stabilizing the helix more than would be expected for screening alone. The mode of binding appears to be dependent on cation species, with distinct differences between binding by strontium and by magnesium and calcium.To obtain quantitative information from these force-extension measurements, we have developed a new model for the force-extension behavior of poly(A) and similar helicogenic polymers, which unlike previous models takes into account Debye screening effects and the semiflexible nature of the helical state. Fitting this model to our data, we obtain estimates of helix formation energies and find evidence that magnesium binding distorts the poly(A) single helix into a mechanically distinct state.

Using mechanical unfolding by optical tweezers (OT) and steered molecular dynamics (SMD) simulations, we have demonstrated the critical role of Mg(2+) ions for the resistance of the Beet Western Yellow Virus (BWYV) pseudoknot (PK) to unfolding. The two techniques were found to be complementary, providing information at different levels of molecular scale. Findings from the OT experiments indicated a critical role of stem 1 for unfolding of the PK, which was confirmed in the SMD simulations. The unfolding pathways of wild type and mutant appeared to depend upon pH and nucleotide sequence. SMD simulations support the notion that the stability of stem 1 is critical for -1 frameshifting. The all-atom scale nature of the SMD enabled clarification of the precise role of two Mg(2+) ions, Mg45 and Mg52, as identified in the BWYV X-ray crystallography structure, in -1 frameshifting. On the basis of simulations with "partially" and "fully" hydrated Mg(2+) ions, two possible mechanisms of stabilizing stem 1 are proposed. In both these cases Mg(2+) ions play a critical role in stabilizing stem 1, either by directly forming a salt bridge between the strands of stem 1 or by stabilizing parallel orientation of the strands in stem 1, respectively. These findings explain the unexpected drop in frameshifting efficiency to null levels of the C8U mutant in a manner consistent with experimental observations.

We have developed a novel micromanipulator consisting of multiple optical traps created by scanning one single beam trap along a variable number of positions. Among other things, this enables the orientation of irregularly shaped and relatively large structures which could not be oriented by just one trap as is demonstrated on long Escherichia coli bacteria filaments. We expect that the multiple trap manipulator will broaden the field of applications of optical trapping as a micromanipulation technique. For example, it facilitates the study of mechanical properties of extended structures as illustrated by a "bending"-experiment using E. coli bacterium filaments. A special application of the multiple trap manipulator is the "indirect trapping" of objects which we did by keeping them held between other optically trapped particles. Indirect trapping makes it possible to trap particles which either cannot be trapped directly due to their optical properties (refractive index) or for which exposure to the laser radiation is undesirable. The multiple optical trap manipulator is controlled interactively by a UNIX workstation coupled to a VME instrumentation bus. This provides great flexibility in the control of the position and the orientation of the optical traps. Micromanipulation makes it desirable to have real time 3D microscopy for imaging and guidance of the optical traps. Therefore we integrated optical micromanipulation and a specially developed real-time confocal microscope. This so called bilateral confocal scanning laser microscope (bilateral CSLM) [Brakenhoff and Visscher, J Microsc 165:139-146, 1992] produces images at video rate.

Confocal microscopy is very useful in biology because of its three dimensional imaging capacities and has proven to be an excellent tool to study the 3D organization of, for instance, cell structures. This property of confocal microscopy makes it also very suitable for observation during guidance of the three dimensional manipulation of single cells or cell elements. Therefore we decided to integrate a confocal microscope and a single beam optical manipulator into a single instrument. The advantage of optical manipulation over mechanical techniques is that it is non-invasive and therefore may be applied on living (micro-) organisms and cells. The creation of an effective single beam optical trap requires the use of a high numerical aperture (N.A.) objective to focus the laser beam. In this paper we briefly discuss the vertical or axial force exerted on a sphere in a single beam trap. The axial force on a sphere placed on the optical axis, caused by reflection and refraction, is calculated applying a electromagnetic vector diffraction theory to determine the field distribution in the focal region. One of the results is that the particle also experiences a vertical trapping force towards the focusing lens when it is in the strongly convergent part of the field in addition to the known negative signed trapping force in the divergent part of the field. Further we describe an instrumental approach to realize optical trapping in which the optical trap position is controlled by moving the focusing objective only. At present we have demonstrated the practical use of the presented optical trap control on the spatial x, y, z manipulation of micro-sized polystyrene spheres (1–7 μm) and of yeast cells.

Gene transcription by the enzyme RNA polymerase is tightly regulated. In many cases, such as in the lac operon in Escherichia coli, this regulation is achieved through the action of protein factors on DNA. Because DNA is an elastic polymer, its response to enzymatic processing can lead to mechanical perturbations (e.g., linear stretching and supercoiling) that can affect the operation of other DNA processing complexes acting elsewhere on the same substrate molecule. Using an optical-tweezers assay, we measured the binding kinetics between single molecules of bacteriophage T7 RNA polymerase and DNA, as a function of tension. We found that increasing DNA tension under conditions that favor formation of the open complex results in destabilization of the preinitiation complex. Furthermore, with zero ribonucleotides present, when the closed complex is favored, we find reduced tension sensitivity, implying that it is predominantly the open complex that is sensitive. This result strongly supports the “scrunching” model for T7 transcription initiation, as the applied tension acts against the movement of the DNA into the scrunched state, and introduces linear DNA tension as a potential regulatory quantity for transcription initiation.

Mechanical unfolding of −1 frameshift signals such as RNA pseudoknots have aimed to test the hypothesis that the stability of the pseudoknot (PK) is directly correlated to the frameshifting efficiency. Here we report unfolding of the Beet Western Yellow Virus (BWYV) PK by optical tweezers complemented by computer simulations using steered molecular dynamics (SMD). Three BWYV PK scenarios were studied: the wild-type PK in the presence and absence of Mg2+, and mutations of nucleic base C8 known to completely abolish −1 frameshifting by disrupting pseudoknot stability at the core of its structure. Despite significant differences in loading rates, we found the experimental and computational results to be remarkably consistent.The SMD simulations provide a detailed sequence of molecular unfolding events that can be assigned to the force-extension profiles obtained with the optical tweezers. In the absence of Mg2+, stretching of the PK using the optical tweezers does not result in the observation of any unfolding transitions, which is consistent with the SMD simulation that demonstrates the essential role of Mg2+ for the formation of a very strong salt bridge between G4, C5, G16, and C17 nucleotides. The C8 mutants, like wild-type unfolding in the absence of Mg2+, unfold readily and at low force, consistent with the absence of any −1 frameshifting activity for these mutants.

To access the genetic code to be transcribed to RNA, RNA polymerases must first melt the DNA, opening a “transcription bubble”. In single molecule optical tweezers studies of initiation by T7 bacteriophage RNA polymerase (T7 RNAP), we have found that the lifetime of the initiation complex is strongly dependent on tension applied to the upstream DNA, indicating, in accord with structural studies, that initiation by T7 RNAP likely involves mechanical deformation of the DNA. The tension dependence diminishes considerably in the absence of free ribonucleotides, suggesting that this mechanical deformation of the DNA template does not coincide with binding, but instead with the opening of the transcription bubble. A new maximum-likelihood method will be presented, in which data do not have to be grouped into force bins, to identify the force-dependent step or steps in initiation by T7 RNAP and to estimate the associated rates and distances to the transition state from these experiments. This method is generalizable to systems with more complicated kinetic pathways, as long as there are two observable states (e.g. bound and unbound) and an irreversible final transition.

In addition to serving as the genetic template for protein synthesis in the ribosome, RNA folds in sequence-dependent ways to form structures that have regulatory or catalytic functions. Homopolymeric polyadenylic acid (poly(A))is known to form, due to base-stacking, single-stranded helices in solutions with ionic strength high enough to screen the self-repulsion of RNA's negatively charged backbone (e.g. 500 mM Na+), giving it elastic properties different than those of a random RNA sequence. Understanding the behavior of these helical sequences is necessary, for example, to in turn understand the folding of A-rich regions of riboswitches or the binding of poly(A) binding protein to mRNA's poly(A) tail.When stretched using optical tweezers, well-screened poly(A) shows a clear helix-coil transition, manifested as a shoulder or plateau on the force-extension curve. By stretching poly(A) to sufficiently high force in low ionic strength solutions, we can probe the relative strengths of backbone repulsion and base stacking and moreover investigate the role of possible tight or diffuse binding of di- and polyvalent cations, thus furthering our understanding of helix formation in poly(A) sequences.We have found that the helix-coil transition is less distinct at 100 mM Na+ than at 500 mM Na+ and totally absent at 10 mM Na+. These results and their implications, and additionally the effect of the divalent cation Mg++ on elasticity of poly(A), will be presented.