Live-cell imaging reveals the trade-off between target search flexibility and efficiency for Cas9 and Cas12a

CRISPR-Cas systems have widely been adopted as genome editing tools, with two frequently employed Cas nucleases being SpyCas9 and LbCas12a. Although both nucleases use RNA guides to find and cleave target DNA sites, the two enzymes differ in terms of protospacer-adjacent motif (PAM) requirements, guide architecture and cleavage mechanism. In the last years, rational engineering led to the creation of PAM-relaxed variants SpRYCas9 and impLbCas12a to broaden the targetable DNA space. By employing their catalytically inactive variants (dCas9/dCas12a), we quantified how the protein-specific characteristics impact the target search process. To allow quantification, we fused these nucleases to the photoactivatable fluorescent protein PAmCherry2.1 and performed single-particle tracking in cells of Escherichia coli. From our tracking analysis, we derived kinetic parameters for each nuclease with a non-targeting RNA guide, strongly suggesting that interrogation of DNA by LbdCas12a variants proceeds faster than that of SpydCas9. In the presence of a targeting RNA guide, both simulations and imaging of cells confirmed that LbdCas12a variants are faster and more efficient in finding a specific target site. Our work demonstrates the trade-off of relaxing PAM requirements in SpydCas9 and LbdCas12a using a powerful framework, which can be applied to other nucleases to quantify their DNA target search.

Quantitative parameters of bacterial RNA polymerase open-complex formation, stabilization and disruption on a consensus promoter

Transcription initiation is the first step in gene expression, and is therefore strongly regulated in all domains of life. The RNA polymerase (RNAP) first associates with the initiation factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\sigma$\end{document} to form a holoenzyme, which binds, bends and opens the promoter in a succession of reversible states. These states are critical for transcription regulation, but remain poorly understood. Here, we addressed the mechanism of open complex formation by monitoring its assembly/disassembly kinetics on individual consensus lacUV5 promoters using high-throughput single-molecule magnetic tweezers. We probed the key protein–DNA interactions governing the open-complex formation and dissociation pathway by modulating the dynamics at different concentrations of monovalent salts and varying temperatures. Consistent with ensemble studies, we observed that RNAP-promoter open (RP_O) complex is a stable, slowly reversible state that is preceded by a kinetically significant open intermediate (RP_I), from which the holoenzyme dissociates. A strong anion concentration and type dependence indicates that the RP_O stabilization may involve sequence-independent interactions between the DNA and the holoenzyme, driven by a non-Coulombic effect consistent with the non-template DNA strand interacting with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\sigma$\end{document} and the RNAP \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\beta$\end{document} subunit. The temperature dependence provides the energy scale of open-complex formation and further supports the existence of additional intermediates.

High-throughput single-molecule experiments reveal heterogeneity, state switching, and three interconnected pause states in transcription

Pausing by bacterial RNA polymerase (RNAp) is vital in the recruitment of regulatory factors, RNA folding, and coupled translation. While backtracking and intra-structural isomerization have been proposed to trigger pausing, our mechanistic understanding of backtrack-associated pauses and catalytic recovery remains incomplete. Using high-throughput magnetic tweezers, we examine the Escherichia coli RNAp transcription dynamics over a wide range of forces and NTP concentrations. Dwell-time analysis and stochastic modeling identify, in addition to a short-lived elemental pause, two distinct long-lived backtrack pause states differing in recovery rates. We identify two stochastic sources of transcription heterogeneity: alterations in short-pause frequency that underlies elongation-rate switching, and variations in RNA cleavage rates in long-lived backtrack states. Together with effects of force and Gre factors, we demonstrate that recovery from deep backtracks is governed by intrinsic RNA cleavage rather than diffusional Brownian dynamics. We introduce a consensus mechanistic model that unifies our findings with prior models.

A kinetic model predicts SpCas9 activity, improves off-target classification, and reveals the physical basis of targeting fidelity

The S. pyogenes (Sp) Cas9 endonuclease is an important gene-editing tool. SpCas9 is directed to target sites based on complementarity to a complexed single-guide RNA (sgRNA). However, SpCas9-sgRNA also binds and cleaves genomic off-targets with only partial complementarity. To date, we lack the ability to predict cleavage and binding activity quantitatively, and rely on binary classification schemes to identify strong off-targets. We report a quantitative kinetic model that captures the SpCas9-mediated strand-replacement reaction in free-energy terms. The model predicts binding and cleavage activity as a function of time, target, and experimental conditions. Trained and validated on high-throughput bulk-biochemical data, our model predicts the intermediate R-loop state recently observed in single-molecule experiments, as well as the associated conversion rates. Finally, we show that our quantitative activity predictor can be reduced to a binary off-target classifier that outperforms the established state-of-the-art. Our approach is extensible, and can characterize any CRISPR-Cas nuclease - benchmarking natural and future high-fidelity variants against SpCas9; elucidating determinants of CRISPR fidelity; and revealing pathways to increased specificity and efficiency in engineered systems.

Systematic decomposition of sequence determinants governing CRISPR/Cas9 specificity

The specificity of CRISPR/Cas9 genome editing is largely determined by the sequences of guide RNA (gRNA) and the targeted DNA, yet the sequence-dependent rules underlying off-target effects are not fully understood. To systematically explore the sequence determinants governing CRISPR/Cas9 specificity, here we describe a dual-target system to measure the relative cleavage rate between off- and on-target sequences (off-on ratios) of 1902 gRNAs on 13,314 synthetic target sequences, and reveal a set of sequence rules involving 2 factors in off-targeting: 1) a guide-intrinsic mismatch tolerance (GMT) independent of the mismatch context; 2) an "epistasis-like" combinatorial effect of multiple mismatches, which are associated with the free-energy landscape in R-loop formation and are explainable by a multi-state kinetic model. These sequence rules lead to the development of MOFF, a model-based predictor of Cas9-mediated off-target effects. Moreover, the "epistasis-like" combinatorial effect suggests a strategy of allele-specific genome editing using mismatched guides. With the aid of MOFF prediction, this strategy significantly improves the selectivity and expands the application domain of Cas9-based allele-specific editing, as tested in a high-throughput allele-editing screen on 18 cancer hotspot mutations.

Inhibition of SARS-CoV-2 polymerase by nucleotide analogs from a single-molecule perspective

The absence of 'shovel-ready' anti-coronavirus drugs during vaccine development has exceedingly worsened the SARS-CoV-2 pandemic. Furthermore, new vaccine-resistant variants and coronavirus outbreaks may occur in the near future, and we must be ready to face this possibility. However, efficient antiviral drugs are still lacking to this day, due to our poor understanding of the mode of incorporation and mechanism of action of nucleotides analogs that target the coronavirus polymerase to impair its essential activity. Here, we characterize the impact of remdesivir (RDV, the only FDA-approved anti-coronavirus drug) and other nucleotide analogs (NAs) on RNA synthesis by the coronavirus polymerase using a high-throughput, single-molecule, magnetic-tweezers platform. We reveal that the location of the modification in the ribose or in the base dictates the catalytic pathway(s) used for its incorporation. We show that RDV incorporation does not terminate viral RNA synthesis, but leads the polymerase into backtrack as far as 30 nt, which may appear as termination in traditional ensemble assays. SARS-CoV-2 is able to evade the endogenously synthesized product of the viperin antiviral protein, ddhCTP, though the polymerase incorporates this NA well. This experimental paradigm is essential to the discovery and development of therapeutics targeting viral polymerases.

Inhibition of SARS-CoV-2 polymerase by nucleotide analogs: a single molecule perspective

The nucleotide analog Remdesivir (RDV) is the only FDA-approved antiviral therapy to treat infection by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The physical basis for efficient utilization of RDV by SARS-CoV-2 polymerase is unknown. Here, we characterize the impact of RDV and other nucleotide analogs on RNA synthesis by the polymerase using a high-throughput, single-molecule, magnetic-tweezers platform. The location of the modification in the ribose or in the base dictates the catalytic pathway(s) used for its incorporation. We reveal that RDV incorporation does not terminate viral RNA synthesis, but leads the polymerase into deep backtrack, which may appear as termination in traditional ensemble assays. SARS-CoV-2 is able to evade the endogenously synthesized product of the viperin antiviral protein, ddhCTP, though the polymerase incorporates this nucleotide analog well. This experimental paradigm is essential to the discovery and development of therapeutics targeting viral polymerases.

TEASER

We revise Remdesivir's mechanism of action and reveal SARS-CoV-2 ability to evade interferon-induced antiviral ddhCTP.

The nucleotide addition cycle of the SARS-CoV-2 polymerase

Coronaviruses have evolved elaborate multisubunit machines to replicate and transcribe their genomes. Central to these machines are the RNA-dependent RNA polymerase subunit (nsp12) and its intimately associated cofactors (nsp7 and nsp8). We have used a high-throughput magnetic-tweezers approach to develop a mechanochemical description of this core polymerase. The core polymerase exists in at least three catalytically distinct conformations, one being kinetically consistent with incorporation of incorrect nucleotides. We provide the first evidence that an RdRp uses a thermal ratchet instead of a power stroke to transition from the pre- to post-translocated state. Ultra-stable magnetic tweezers enables the direct observation of coronavirus polymerase deep and long-lived backtrack that are strongly stimulated by secondary structure in the template. The framework presented here elucidates one of the most important structure-dynamics-function relationships in human health today, and will form the grounds for understanding the regulation of this complex.

Temperature controlled high-throughput magnetic tweezers show striking difference in activation energies of replicating viral RNA-dependent RNA polymerases

RNA virus survival depends on efficient viral genome replication, which is performed by the viral RNA dependent RNA polymerase (RdRp). The recent development of high throughput magnetic tweezers has enabled the simultaneous observation of dozens of viral RdRp elongation traces on kilobases long templates, and this has shown that RdRp nucleotide addition kinetics is stochastically interrupted by rare pauses of 1-1000 s duration, of which the short-lived ones (1-10 s) are the temporal signature of a low fidelity catalytic pathway. We present a simple and precise temperature controlled system for magnetic tweezers to characterize the replication kinetics temperature dependence between 25°C and 45°C of RdRps from three RNA viruses, i.e. the double-stranded RNA bacteriophage Φ6, and the positive-sense single-stranded RNA poliovirus (PV) and human rhinovirus C (HRV-C). We found that Φ6 RdRp is largely temperature insensitive, while PV and HRV-C RdRps replication kinetics are activated by temperature. Furthermore, the activation energies we measured for PV RdRp catalytic state corroborate previous estimations from ensemble pre-steady state kinetic studies, further confirming the catalytic origin of the short pauses and their link to temperature independent RdRp fidelity. This work will enable future temperature controlled study of biomolecular complex at the single molecule level.

Argonaute bypasses cellular obstacles without hindrance during target search

Argonaute (Ago) proteins are key players in both gene regulation (eukaryotes) and host defense (prokaryotes). Acting on single-stranded nucleic-acid substrates, Ago relies on base pairing between a small nucleic-acid guide and its complementary target sequences for specificity. To efficiently scan nucleic-acid chains for targets, Ago diffuses laterally along the substrate and must bypass secondary structures as well as protein barriers. Using single-molecule FRET in conjunction with kinetic modelling, we reveal that target scanning is mediated through loose protein-nucleic acid interactions, allowing Ago to slide short distances over secondary structures, as well as to bypass protein barriers via intersegmental transfer. Our combined single-molecule experiment and kinetic modelling approach may serve as a platform to dissect search processes and study the effect of sequence on search kinetics for other nucleic acid-guided proteins.

Hybridization Kinetics Explains CRISPR-Cas Off-Targeting Rules

Due to their specificity, efficiency, and ease of programming, CRISPR-associated nucleases are popular tools for genome editing. On the genomic scale, these nucleases still show considerable off-target activity though, posing a serious obstacle to the development of therapies. Off targeting is often minimized by choosing especially high-specificity guide sequences, based on algorithms that codify empirically determined off-targeting rules. A lack of mechanistic understanding of these rules has so far necessitated their ad hoc implementation, likely contributing to the limited precision of present algorithms. To understand the targeting rules, we kinetically model the physics of guide-target hybrid formation. Using only four parameters, our model elucidates the kinetic origin of the experimentally observed off-targeting rules, thereby rationalizing the results from both binding and cleavage assays. We favorably compare our model to published data from CRISPR-Cas9, CRISPR-Cpf1, CRISPR-Cascade, as well as the human Argonaute 2 system.

Correction: Kinetic analysis methods applied to single motor protein trajectories

Correction for ‘Kinetic analysis methods applied to single motor protein trajectories’ by A. L. Nord et al., Phys. Chem. Chem. Phys., 2018, 20, 18775–18781.

Kinetic analysis methods applied to single motor protein trajectories

Molecular motors convert chemical or electrical energy into mechanical displacement, either linear or rotary. Under ideal circumstances, single-molecule measurements can spatially and temporally resolve individual steps of the motor, revealing important properties of the underlying mechanochemical process. Unfortunately, steps are often hard to resolve, as they are masked by thermal noise. In such cases, details of the mechanochemistry can nonetheless be recovered by analyzing the fluctuations in the recorded traces. Here, we expand upon existing statistical analysis methods, providing two new avenues to extract the motor step size, the effective number of rate-limiting chemical states per translocation step, and the compliance of the link between the motor and the probe particle. We first demonstrate the power and limitations of these methods using simulated molecular motor trajectories, and we then apply these methods to experimental data of kinesin, the bacterial flagellar motor, and F1-ATPase.

Signatures of Nucleotide Analog Incorporation by an RNA-Dependent RNA Polymerase Revealed Using High-Throughput Magnetic Tweezers

RNA viruses pose a threat to public health that is exacerbated by the dearth of antiviral therapeutics. The RNA-dependent RNA polymerase (RdRp) holds promise as a broad-spectrum, therapeutic target because of the conserved nature of the nucleotide-substrate-binding and catalytic sites. Conventional, quantitative, kinetic analysis of antiviral ribonucleotides monitors one or a few incorporation events. Here, we use a high-throughput magnetic tweezers platform to monitor the elongation dynamics of a prototypical RdRp over thousands of nucleotide-addition cycles in the absence and presence of a suite of nucleotide analog inhibitors. We observe multiple RdRp-RNA elongation complexes; only a subset of which are competent for analog utilization. Incorporation of a pyrazine-carboxamide nucleotide analog, T-1106, leads to RdRp backtracking. This analysis reveals a mechanism of action for this antiviral ribonucleotide that is corroborated by cellular studies. We propose that induced backtracking represents a distinct mechanistic class of antiviral ribonucleotides.

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Several unique conformational states of an elongating RdRp exist

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Only one conformation incorporates nucleotide analogs with therapeutic potential

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An analog thought to be a chain terminator actually promotes RdRp backtracking

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Distinctive behavior of backtrack-inducing analog on virus variants in cell culture

Pausing controls branching between productive and non-productive pathways during initial transcription in bacteria

Transcription in bacteria is controlled by multiple molecular mechanisms that precisely regulate gene expression. It has been recently shown that initial RNA synthesis by the bacterial RNA polymerase (RNAP) is interrupted by pauses; however, the pausing determinants and the relationship of pausing with productive and abortive RNA synthesis remain poorly understood. Using single-molecule FRET and biochemical analysis, here we show that the pause encountered by RNAP after the synthesis of a 6-nt RNA (ITC6) renders the promoter escape strongly dependent on the NTP concentration. Mechanistically, the paused ITC6 acts as a checkpoint that directs RNAP to one of three competing pathways: productive transcription, abortive RNA release, or a new unscrunching/scrunching pathway. The cyclic unscrunching/scrunching of the promoter generates a long-lived, RNA-bound paused state; the abortive RNA release and DNA unscrunching are thus not as tightly linked as previously thought. Finally, our new model couples the pausing with the abortive and productive outcomes of initial transcription.

Crowding-induced transcriptional bursts dictate polymerase and nucleosome density profiles along genes

During eukaryotic transcription, RNA polymerase (RNAP) translocates along DNA molecules covered with nucleosomes and other DNA binding proteins. Though the interactions between a single nucleosome and RNAP are by now fairly well understood, this understanding has not been synthesized into a description of transcription on crowded genes, where multiple RNAP transcribe through nucleosomes while preserving the nucleosome coverage. We here take a deductive modeling approach to establish the consequences of RNAP–nucleosome interactions for transcription in crowded environments. We show that under physiologically crowded conditions, the interactions of RNAP with nucleosomes induce a strong kinetic attraction between RNAP molecules, causing them to self-organize into stable and moving pelotons. The peloton formation quantitatively explains the observed nucleosome and RNAP depletion close to the initiation site on heavily transcribed genes. Pelotons further translate into short-timescale transcriptional bursts at termination, resulting in burst characteristics consistent with instances of bursty transcription observed in vivo. To facilitate experimental testing of our proposed mechanism, we present several analytic relations that make testable quantitative predictions.

Switching between Exonucleolysis and Replication by T7 DNA Polymerase Ensures High Fidelity

DNA polymerase catalyzes the accurate transfer of genetic information from one generation to the next, and thus it is vitally important for replication to be faithful. DNA polymerase fulfills the strict requirements for fidelity by a combination of mechanisms: 1) high selectivity for correct nucleotide incorporation, 2) a slowing down of the replication rate after misincorporation, and 3) proofreading by excision of misincorporated bases. To elucidate the kinetic interplay between replication and proofreading, we used high-resolution optical tweezers to probe how DNA-duplex stability affects replication by bacteriophage T7 DNA polymerase. Our data show highly irregular replication dynamics, with frequent pauses and direction reversals as the polymerase cycles through the states that govern the mechanochemistry behind high-fidelity T7 DNA replication. We constructed a kinetic model that incorporates both existing biochemical data and the, to our knowledge, novel states we observed. We fit the model directly to the acquired pause-time and run-time distributions. Our findings indicate that the main pathway for error correction is DNA polymerase dissociation-mediated DNA transfer, followed by biased binding into the exonuclease active site. The number of bases removed by this proofreading mechanism is much larger than the number of erroneous bases that would be expected to be incorporated, ensuring a high-fidelity replication of the bacteriophage T7 genome.

Cas3-Derived Target DNA Degradation Fragments Fuel Primed CRISPR Adaptation

Prokaryotes use a mechanism called priming to update their CRISPR immunological memory to rapidly counter revisiting, mutated viruses, and plasmids. Here we have determined how new spacers are produced and selected for integration into the CRISPR array during priming. We show that Cas3 couples CRISPR interference to adaptation by producing DNA breakdown products that fuel the spacer integration process in a two-step, PAM-associated manner. The helicase-nuclease Cas3 pre-processes target DNA into fragments of about 30-100 nt enriched for thymine-stretches in their 3' ends. The Cas1-2 complex further processes these fragments and integrates them sequence-specifically into CRISPR repeats by coupling of a 3' cytosine of the fragment. Our results highlight that the selection of PAM-compliant spacers during priming is enhanced by the combined sequence specificities of Cas3 and the Cas1-2 complex, leading to an increased propensity of integrating functional CTT-containing spacers.

Why Argonaute is needed to make microRNA target search fast and reliable

MicroRNA (miRNA) interferes with the translation of cognate messenger RNA (mRNA) by finding, preferentially binding, and marking it for degradation. To facilitate the search process, Argonaute (Ago) proteins come together with miRNA, forming a dynamic search complex. In this review we use the language of free-energy landscapes to discuss recent single-molecule and high-resolution structural data in the light of theoretical work appropriated from the study of transcription-factor search. We suggest that experimentally observed internal states of the Ago-miRNA search complex may have the explicit biological function of speeding up search while maintaining specificity.

Backtracking behavior in viral RNA-dependent RNA polymerase provides the basis for a second initiation site

Transcription in RNA viruses is highly dynamic, with a variety of pauses interrupting nucleotide addition by RNA-dependent RNA polymerase (RdRp). For example, rare but lengthy pauses (>20 s) have been linked to backtracking for viral single-subunit RdRps. However, while such backtracking has been well characterized for multi-subunit RNA polymerases (RNAPs) from bacteria and yeast, little is known about the details of viral RdRp backtracking and its biological roles. Using high-throughput magnetic tweezers, we quantify the backtracking by RdRp from the double-stranded (ds) RNA bacteriophage Φ6, a model system for RdRps. We characterize the probability of entering long backtracks as a function of force and propose a model in which the bias toward backtracking is determined by the base paring at the dsRNA fork. We further discover that extensive backtracking provides access to a new 3′-end that allows for the de novo initiation of a second RdRp. This previously unidentified behavior provides a new mechanism for rapid RNA synthesis using coupled RdRps and hints at a possible regulatory pathway for gene expression during viral RNA transcription.

Strand separation establishes a sustained lock at the Tus-Ter replication fork barrier

The bidirectional replication of a circular chromosome by many bacteria necessitates proper termination to avoid the head-on collision of the opposing replisomes. In Escherichia coli, replisome progression beyond the termination site is prevented by Tus proteins bound to asymmetric Ter sites. Structural evidence indicates that strand separation on the blocking (nonpermissive) side of Tus-Ter triggers roadblock formation, but biochemical evidence also suggests roles for protein-protein interactions. Here DNA unzipping experiments demonstrate that nonpermissively oriented Tus-Ter forms a tight lock in the absence of replicative proteins, whereas permissively oriented Tus-Ter allows nearly unhindered strand separation. Quantifying the lock strength reveals the existence of several intermediate lock states that are impacted by mutations in the lock domain but not by mutations in the DNA-binding domain. Lock formation is highly specific and exceeds reported in vivo efficiencies. We postulate that protein-protein interactions may actually hinder, rather than promote, proper lock formation.

Elongation-Competent Pauses Govern the Fidelity of a Viral RNA-Dependent RNA Polymerase

RNA viruses have specific mutation rates that balance the conflicting needs of an evolutionary response to host antiviral defenses and avoidance of the error catastrophe. While most mutations are known to originate in replication errors, difficulties of capturing the underlying dynamics have left the mechanochemical basis of viral mutagenesis unresolved. Here, we use multiplexed magnetic tweezers to investigate error incorporation by the bacteriophage Φ6 RNA-dependent RNA polymerase. We extract large datasets fingerprinting real-time polymerase dynamics over four magnitudes in time, in the presence of nucleotide analogs, and under varying NTP and divalent cation concentrations and fork stability. Quantitative analysis reveals a new pause state that modulates polymerase fidelity and so ties viral polymerase pausing to the biological function of optimizing virulence. Adjusting the frequency of such pauses offers a target for therapeutics and may also reflect an evolutionary strategy for virus populations to track the gradual evolution of their hosts.

Stress-enhanced gelation: a dynamic nonlinearity of elasticity

A hallmark of biopolymer networks is their sensitivity to stress, reflected by pronounced nonlinear elastic stiffening. Here, we demonstrate a distinct dynamical nonlinearity in biopolymer networks consisting of filamentous actin cross-linked by α-actinin-4. Applied stress delays the onset of relaxation and flow, markedly enhancing gelation and extending the regime of solidlike behavior to much lower frequencies. We show that this macroscopic network response can be accounted for at the single molecule level by the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior.

Nonequilibrium fluctuations of a remodeling in vitro cytoskeleton

Motor proteins actively contract the actin cytoskeleton of cells and thereby give rise to nonequilibrium fluctuations as well as changes in the architecture of the cytoskeleton. Here, we show, by video microrheology of a reconstituted cytoskeleton, that motors generate time-dependent nonequilibrium fluctuations, which evolve as the network is remodeled. At earlier times, the fluctuation spectrum is dominated by strong non-Gaussian fluctuations, which arise from large displacements. At later times, directed displacements are infrequent and finally disappear. We show that these effects are due to contractile coarsening of the network into large actin-myosin foci.

Cross-link-governed dynamics of biopolymer networks

Recent experiments show that networks of stiff biopolymers cross-linked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by cross-links in such networks. We show that a single microscopic time scale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times and a shear modulus G ∼ ω(1/2) for low frequencies ω. This model quantitatively describes the measured rheology of actin networks cross-linked with α-actinin-4 over more than four decades in frequency.

The origin of short transcriptional pauses

RNA polymerases are protein molecular machines that transcribe genetic information from DNA into RNA. The elongation of the RNA molecule is frequently interrupted by pauses, the detailed nature of which remains controversial. Here we ask whether backtracking, the central mechanism behind long pauses, could also be responsible for short pauses normally attributed to the ubiquitous pause state. To this end, we model backtracking as a force-biased random walk, giving rise to a broad distribution of pause durations as observed in experiments. Importantly, we find that this single mechanism naturally generates two populations of pauses that are distinct both in duration and trajectory: long-time pauses with the expected behavior of diffusive backtracks, and a new class of short-time backtracks with characteristics similar to those of the ubiquitous pause. These characteristics include an apparent force insensitivity and immobility of the polymerase. Based on these results and a quantitative comparison to published pause trajectories measured with optical tweezers, we suggest that a significant fraction of short pauses are simply due to backtracking.

Continuum approach to wide shear zones in quasistatic granular matter

Slow and dense granular flows often exhibit narrow shear bands, making them ill suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of gravity, slow inclined plane flows and, recently, flows in split-bottom Couette geometries. The wide shear regions in these systems should be amenable to a continuum description, and the theoretical challenge lies in finding constitutive relations between the internal stresses and the flow field. We propose a set of testable constitutive assumptions, including rate independence, and investigate the additional restrictions on the constitutive relations imposed by the flow geometries. The wide shear layers in the highly symmetric linear shear and inclined plane flows are consistent with the simple constitutive assumption that, in analogy with solid friction, the effective-friction coefficient (ratio between shear and normal stresses) is a constant. However, this standard picture of granular flows is shown to be inconsistent with flows in the less symmetric split-bottom geometry--here the effective friction coefficient must vary throughout the shear zone, or else the shear zone localizes. We suggest that a subtle dependence of the effective-friction coefficient on the orientation of the sliding layers with respect to the bulk force is crucial for the understanding of slow granular flows.

Fluctuation-dissipation relation and the Edwards entropy for a glassy granular compaction model

We analytically study a one-dimensional compaction model in the glassy regime. Both correlation and response functions are calculated exactly in the evolving dense and low tapping strength limit, where the density relaxes in a 1/ln t fashion. The response and correlation functions turn out to be connected through a nonequilibrium generalization of the fluctuation-dissipation theorem. The initial response in the average density to an increase in the tapping strength is shown to be negative, while on longer time scales it is shown to be positive. On short time scales the fluctuation-dissipation theorem governs the relation between correlation and response, and we show that such a relationship also exists for the slow degrees of freedom, albeit with a different temperature. The model is further studied within the statistical theory proposed by Edwards and co-workers, and the Edwards entropy is calculated in the large system limit. The fluctuations described by this approach turn out to match the fluctuations as calculated through the dynamical consideration. We thus have an instance where these ideas can be confirmed analytically in a non-mean-field model.

Exact probability function for bulk density and current in the asymmetric exclusion process

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady-state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R. Stinchcombe, Phys. Rev. Lett. 93, 040602 (2004). In particular we derive an exact form for the joint probability function for the bulk density and current, both for finite systems, and also in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques and by introducing a modified version of the original operator algebra. As a by-product of these considerations we also arrive at a very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra. Like the partition function in equilibrium systems, this normalization constant is shown to completely characterize the fluctuations, albeit in a very different manner.

Exact joint density-current probability function for the asymmetric exclusion process

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra.

Marginal scaling scenario and analytic results for a glassy compaction model

A diffusion-deposition model for glassy dynamics in compacting granular systems is treated by time scaling and by a method that provides the exact asymptotic (long-time) behavior. The results include Vogel-Fulcher dependence of rates on density, inverse logarithmic time decay of densities, exponential distribution of decay times, and broadening of noise spectrum. These are all in broad agreement with experiments. The main characteristics result from a marginal rescaling in time of the control parameter (density); this is argued to be generic for glassy systems.