•A general model of DNA unwinding by monomeric helicase is presented.•Dynamics of DNA unwinding by helicase XPD is analytically studied.•Dynamics of DNA unwinding by helicase XPD is compared with that of helicase RecQ.•DNA unwinding dynamics of different monomeric helicases is studied.XPD (Xeroderma pigmentosum complementation group D) is a prototypical 5′ – 3′ translocating DNA helicase that exhibits frequent backward steps during DNA unwinding. Here, we propose a model of DNA unwinding by XPD. With the model we explain why XPD exhibits frequent backsteps while other helicases show rare backsteps. We explain quantitatively the single-molecule data on probability of –1-bp step and mean dwell time of one step versus ATP concentration for XPD at fixed large external force applied to the ends of the DNA hairpin to unzip the hairpin. We study DNA unwinding velocity, probability of –1-bp step and mean dwell time of one step for XPD versus external force at various ATP concentrations. We compare DNA unwinding dynamics of the 5′ – 3′ helicase XPD with that of 3′ – 5′ helicase RecQ. Our results show that the DNA unwinding velocity of XPD is sensitively dependent on the external force, which is contrast to RecQ that shows insensitive dependence of DNA unwinding velocity on the external force, explaining the experimental data showing that RecQ is an “optimally active” helicase while XPD is a “partially active” helicase. The DNA unwinding dynamics of different helicases under the external force is also studied.

•A model of processive movement of dimeric kinesin on microtubule is proposed.•Effects of solution viscosity on movement are studied.•Effects of neck linker docking and external force on movement are studied.•Movement dynamics of kinesins with extended neck linkers is studied.•Movement dynamics of kinesins with one head attached by a large-size particle is studied.Dimeric kinesin can move processively on microtubule filaments by hydrolyzing ATP. Diverse aspects of its movement dynamics have been studied extensively by using various experimental methods. However, the detailed molecular mechanism of the processive movement is still undetermined and a model that can provide a consistent and quantitative explanation of the diverse experimental data is still lacking. Here, we present such a model, with which we study the movement dynamics of the dimer under variations of solution viscosity, external load, ATP concentration, neck linker length, effect of neck linker docking, effect of a large-size particle attached to one kinesin head, etc., providing consistent and quantitative explanations of the available diverse experimental data. Moreover, predicted results are also provided.

•Models of NA unwinding by monomeric and hexameric helicases are presented.•Both monomeric and hexameric helicases use active mechanism to unwind NA duplex.•Experimental data on NA unwinding dynamics are quantitatively explained.•Experimental data on ssNA translocation dynamics are quantitatively explained.Helicases are a ubiquitous class of enzymes that use the energy of ATP hydrolysis to unwind nucleic acid (NA) duplex. According to the structures, helicases can be classified as the non-ring-shaped (or monomeric) and ring-shaped (or hexameric). To understand the NA unwinding mechanism, here we study theoretically the unwinding dynamics of both the monomeric and hexameric helicases based on our proposed model. Various available single-molecule experimental data on unwinding speed of both the monomeric and hexameric helicases versus the external force applied to the ends of the NA duplex to unzip the duplex or versus the stability of the NA duplex are consistently and quantitatively explained. We provide quantitative explanations of the experimental data showing that while the unwinding speeds of some monomeric helicases are insensitively dependent on the external force they are sensitively dependent on the stability of the NA duplex. The experimental data showing that wild-type Rep translocates along ssDNA with a lower speed than RepΔ2B (removal of the 2B subdomain of Rep) and that RepΔ2B monomer can unwind DNA whereas the wild-type monomer is unable to unwind DNA are also quantitatively explained. Our studies indicate that although the monomeric and hexameric helicases show very different features on the dependence of NA unwinding speed upon the external force, they use much similar active mechanisms to unwind NA duplex.

The peptidyl transferase antibiotic sparsomycin can induce efficient ribosomal translocation in the absence of EF-G and GTP. However, how the antibiotic facilitates the translocation is unclear. Here, two models of antibiotic-induced translocation are considered, in which the interaction of the antibiotic with the peptidyl-tRNA in the A/P state, besides behaving as a pawl in the “Brownian ratchet”, also has an effect of compromising the interaction of the 30S subunit with the mRNA-tRNA complex (Model I) or facilitating the forward 30S head rotation which results in the ribosomal unlocking (Model II). It is shown that although the results obtained with Model I can explain the available experimental data on the translocation through the single-stranded mRNA, they are inconsistent with the experimental data on the translocation through the mRNA duplex; by contrast, the results obtained with Model II can explain quantitatively all of the available experimental data. With model II it is further shown that the efficient translocation induced by the binding of sparsomycin results mainly from the facilitation of the forward 30S head rotation, whereas the effect as the pawl plays only a little role. In addition, it is noted that the mRNA movement is brought about by the reverse intersubunit rotation rather than driven directly by the forward 30S head rotation, and the mechanism of antibiotic-induced translocation is similar to that of EF-G-catalyzed translocation.

The ribosome can translate through the duplex region or secondary structure of mRNA. Recent single-molecule experimental data showed that downstream mRNA secondary structures have more sensitive effects on deacylated tRNA dissociation from the E site than on tRNA translocation in the 50S subunit. However, it is unclear how the downstream mRNA secondary structure can affect the tRNA dissociation from the E site, which is distant from the secondary structure. Here, based on our proposed ribosomal translocation model, we theoretically study the dynamics of tRNA translocation in the 50S subunit, mRNA translocation and tRNA dissociation, giving quantitative explanations of the single-molecule experimental data. It is shown that the effect of the downstream mRNA secondary structure on tRNA dissociation is via the effect on mRNA translocation, while the mRNA secondary structure has no effect on the rate of deacylated tRNA dissociation from the posttranslocation state. The slow mRNA translocation, which results in slow tRNA dissociation, derives from the occurrence of the futile transition, which is induced by the energy barrier from base pair unwinding to resist the forward translocation. The reduced translation rate through the mRNA secondary structure is induced by the slow mRNA translocation rather than the slow tRNA dissociation.

A ribosome is an enzyme that catalyzes translation of the genetic information encoded in messenger RNA (mRNA) into proteins. Besides translation through the single-stranded mRNA, the ribosome is also able to translate through the duplex region of mRNA via unwinding the duplex. Here, based on our proposed ribosome translation model, we study analytically the dynamics of Escherichia coli ribosome translation through the duplex region of mRNA, and compare with the available single molecule experimental data. It is shown that the ribosome uses only one active mechanism (mechanical unwinding), rather than two active mechanisms (open-state stabilization and mechanical unwinding), as proposed before, to unwind the duplex. The reduced rate of translation through the duplex region is due to the occurrence of futile transitions, which are induced by the energy barrier from the duplex unwinding to the forward translocation along the single-stranded mRNA. Moreover, we also present predicted results of the average translation rate versus the external force acting on the ribosome translating through the duplex region and through the single-stranded region of mRNA, which can be easily tested by future experiments.

A mathematical model is proposed for processive primer extension by eukaryotic DNA primase. The model uses available experimental data to predict rate constants for the dynamic behavior of primase activity as a function of NTP concentration. The model also predicts some data such as the binding affinities of the primase for the DNA template and for the RNA primer.

It is puzzling that in spite of its single-headed structure, myosin-IX can move processively along actin. Here, based on the experimental evidence that the strong binding of myosin to actin in rigor state induces structural changes to several local actin monomers, a Brownian ratchet model is proposed to describe this processive movement. In the model, the actin plays an active role in the motility of single-headed myosin, in contrast to the common belief that the actin acts only as a passive track for the motility of the myosin. The unidirectional movement is due to both the asymmetric periodic potential of the myosin interacting with actin and the forward Stokes force induced by the relative rotation of the neck domain to the motor domain, while the processivity is determined by the binding affinity of the myosin for actin in ATP state. This gives a good explanation to the high processivity of myosin-IX, which results from its high binding affinity for actin in ATP state due to the presence of unique loop 2 insertion or N-terminal extension. The experimental results on the motility of myosin-IX such as the step size, large forward/backward stepping ratio, run length, stall force, etc, are explained well.

Telomerase is a unique reverse transcriptase that extends the single-stranded 3′ overhangs of telomeres by copying a short template sequence within the integral RNA component of the enzyme. It shows processive nucleotide and repeat addition activities, which are realized via two types of movements: translocation of the DNA:RNA hybrid away from the active site following each nucleotide addition and translocation of the 3′ end of the DNA primer relative to the RNA template after each round of repeat synthesis. Here, a model is presented to describe these two types of translocation events by the recombinant Tetrahymena telomerase, via the modification of the model that has been proposed recently. Using the present model, the dynamics of the dissociation of the DNA primer from the telomerase and the dynamics of the disruption of the DNA:RNA hybrid and then repositioning of the product 3′ end to the beginning of the template are studied quantitatively. Their effects on the repeat addition processivity are theoretically studied. The theoretical results are in agreement with the available experimental data.Research Highlights►A model is proposed for the processive nucleotide and repeat additions by the recombinant telomerase. ►Dissociation dynamics of the DNA primer from the telomerase is studied. ►Dynamics of repeat addition processivity is studied.

DNA topoisomerase II is a homodimeric molecular machine that uses ATP hydrolysis to untangle DNA by passing one double-stranded DNA duplex (T-segment) through another double-stranded duplex (G-segment). However, despite extensive studies, the dynamics of ATP-dependent T-transport is still not very clear. Here, based on the proposal that transport of the T-segment through the transiently cleaved G-segment and the opened C-gate of the enzyme is via a free diffusion mechanism, the dynamics of T-transport are studied theoretically. Our results show that, to complete passage of the strand with nearly 100% efficiency, the C-gate is required to open by a width that is only slightly larger than the width of DNA duplex and for a time shorter than 100 μs in the presence of several kBT binding affinities of the T-segment for the B′ domains. The results are implied by our understanding of the opening and closing dynamics of the C-gate. Moreover, the dependence of chemomechanical coupling efficiency on degrees of DNA supercoiling by gyrases can also be explained by using our results. On the basis of these theoretical results and previous experimental data, a modified two-gate model for chemomechanical coupling of the topoisomerase II enzyme is proposed.

During reverse transcription, besides the obligatory strand transfers associated with replication at the ends of the viral genome, multiple strand transfers often occur associated with replication within internal regions. Here, based on previous structural and biochemical studies, a model is proposed for processive DNA synthesis along a single template mediated by reverse transcriptase and, based on this model, the mechanism of inter- or intramolecular strand transfers during minus DNA synthesis is presented. A strand-transfer event involves two steps, with the first one being the annealing of the nascent DNA with acceptor RNA at the upstream position of the reverse transcriptase while the second one being the jumping of the polymerase active site to the acceptor. Using the model, the promotion of strand transfer by pausing and high frequent deletions induced by strand transfers can be well explained. We present analytical studies of the efficiency of single strand-transfer event and of the efficiency of multiple-strand-transfer events, with which the high negative interference can be well explained. The dependence of strand-transfer efficiency on the ratio between polymerase and RNase H rates, the role of the polymerase-dependent and polymerase-independent cleavages in strand transfers and the efficiency of nonhomologous strand transfer are analytically studied. The theoretical results are in agreement with the available experimental data. Moreover, some predicted results of the dependence of negative interference on the ratio of polymerase over RNase H rates are presented.

•A model of −1 FS is proposed.•Long pausing associated with −1 FS is explained and studied.•tRNA transit and sampling dynamics in the long-paused rotated state is studied.•EF-G sampling dynamics in the long-paused rotated state is studied.•Mean rotated-state lifetimes are studied.It has been characterized that the programmed ribosomal −1 frameshifting often occurs at the slippery sequence on the presence of a downstream mRNA pseudoknot. In some prokaryotic cases such as the dnaX gene of Escherichia coli, an additional stimulatory signal—an upstream, internal Shine–Dalgarno (SD) sequence—is also necessary to stimulate the efficient −1 frameshifting. However, the molecular and physical mechanism of the −1 frameshifting is poorly understood. Here, we propose a model of the pathway of the −1 translational frameshifting during ribosome translation of the dnaX −1 frameshift mRNA. With the model, the single-molecule fluorescence data (Chen et al. (2014) [29]) on the dynamics of the shunt either to long pausing or to normal translation, the tRNA transit and sampling dynamics in the long-paused rotated state, the EF-G sampling dynamics, the mean rotated-state lifetimes, etc., are explained quantitatively. Moreover, the model is also consistent with the experimental data (Yan et al. (2015) [30]) on translocation excursions and broad branching of frameshifting pathways. In addition, we present some predicted results, which can be easily tested by future optical trapping experiments.

•Kinetics of EF-G binding and dissociation associated with –1 FS is studied.•Kinetics of tRNA movement associated with –1 FS is studied.•Available biochemical and single-molecule experimental data on –1 FS are explained consistently.Programmed –1 translational frameshifting is a process where the translating ribosome shifts the reading frame, which is directed by at least two stimulatory elements in the mRNA—a slippery sequence and a downstream secondary structure. Despite a lot of theoretical and experimental studies, the detailed pathway and mechanism of the –1 frameshifting remain unclear. Here, in order to understand the pathway and mechanism we consider two models to study the kinetics of the –1 frameshifting, providing quantitative explanations of the recent biochemical data of Caliskan et al. (Cell 2014, 157, 1619–1631). One model is modified from that proposed by Caliskan et al. and the other is modified from that proposed in the previous work to explain the single-molecule experimental data. It is shown that by adjusting values of some fundamental parameters both models can give quantitative explanations of the biochemical data of Caliskan et al. on the kinetics of EF-G binding and dissociation and on the kinetics of movement of tRNAs inside the ribosome. However, for the former model some adjusted parameter values deviate significantly from those determined from the available single-molecule experiments, while for the latter model all parameter values are consistent with the available biochemical and single-molecule experimental data. Thus, the latter model most likely reflects the pathway and mechanism of the –1 frameshifting.

The dynamics of backtracking long pauses by RNA polymerase is quantitatively studied based on our proposed model. Analytical formulas are obtained for the dependence of mean backtracking time and mean lifetime of backtracking long pauses on the binding affinity V0 of RNAP to the DNA and RNA lattices, an important parameter for the transcription elongation complex. By comparison of the theoretically with experimentally obtained mean backtracking times, the value of binding affinity V0 is predicted. Using the predicted V0, the effects of external load on the mean backtracking time, on the lifetime of the backtracking long pauses and on the exit from the backtracking long pauses are studied. The results are in agreement with the available experimental data and, moreover, some predicted results are presented. In addition, using this V0 we study the processivity of RNA polymerase under no and sideways forces.

•A model of mRNA translocation with inclusion of 30S head rotations is presented.•Experimental data on biphasic kinetics of translocation are quantitatively explained.•Experimental data on kinetics of 30S head rotation are quantitatively explained.The ribosomal translocation involves both intersubunit rotations between the small 30S and large 50S subunits and the intrasubunit rotations of the 30S head relative to the 30S body. However, the detailed molecular mechanism on how the intersubunit and intrasubunit rotations are related to the translocation remains unclear. Here, based on available structural data a model is proposed for the ribosomal translocation, into which both the intersubunit and intrasubunit rotations are incorporated. With the model, we provide quantitative explanations of in vitro experimental data showing the biphasic character in the fluorescence change associated with the mRNA translocation and the character of a rapid increase that is followed by a slow single-exponential decrease in the fluorescence change associated with the 30S head rotation. The calculated translation rate is also consistent with the in vitro single-molecule experimental data.

Translocation is an essential step in the elongation cycle of protein synthesis in which mRNA that is coupled with tRNAs by codon–anticodon interaction is moved through the ribosome. It has been well documented that the kinetics of mRNA translocation generally shows biphasic character. However, the physical basis of the phenomenon is unclear. Here, to explain the phenomenon we consider two models. In one model (Model I), besides the classical non-rotated and rotated conformations of the ribosome there also exists an intermediate conformation between the two classical conformations. The mRNA translocation occurs via proceeding from the rotated (hybrid) pretranslocation to intermediate to non-rotated posttranslocation state. In another model (Model II), only the classical non-rotated and rotated conformations are considered. Before EF-G binding, the ribosomal complex is in either the classical non-rotated or rotated (hybrid) pretranslocation state, with the equilibrium with each other. EF-G can bind to both states and then the mRNA translocation occurs via proceeding either directly from the hybrid to non-rotated posttranslocation state or from the non-rotated pretranslocation to hybrid to non-rotated posttranslocation state. Analytical studies showed that Model I is unable to explain the biphasic character of mRNA translocation. By contrast, Model II can not only provide a good explanation of the biphasic character of mRNA translocation but also explain the kinetics of the reverse ribosomal rotation from the rotated to non-rotated conformation, which can be fit to a single exponential. Thus, Model II could be the appropriate one for the kinetic pathway of mRNA translocation.

Conventional kinesin, a homodimeric motor protein that transports cargo in various cells, walks limpingly along microtubule. Here, based on our previously proposed partially coordinated hand-over-hand model, we present a new mechanism for the limping behaviors of both wild-type and mutant kinesin homodimers. The limping is caused by different vertical forces acting on the heads in two successive steps during the processive movement of the dimer. From the model, various theoretical results, such as the dependences of the mean dwell time and dwell time ratio on the coiled-coil length and on the external load as well as the effect of vertical force on velocity, are in good agreement with previous experimental results. We predict that a high degree of limping will correlate strongly with a high sensitivity of ATP turnover rate to upwards force.

Ribosomal translocation catalyzed by EF-G hydrolyzing GTP entails multiple conformational changes of ribosome and positional changes of tRNAs and mRNA in the ribosome. However, the detailed dynamic relations among these changes and EF-G sampling are not clear. Here, based on our proposed pathway of ribosomal translocation, we study theoretically the dynamic relations among these changes exhibited in the single molecule data and those exhibited in the ensemble kinetic data. It is shown that the timing of these changes in the single molecule data and that in the ensemble kinetic data show very different. The theoretical results are in agreement with both the available ensemble kinetic experimental data and the single molecule experimental data.