Methods in Statistical Kinetics

Mechanical regulation of the helicase activity of Zika virus NS3

Zika virus (ZIKV) is a positive-sense single-stranded RNA virus that infects humans and can cause birth defects and neurological disorders. Its non-structural protein 3 (NS3) contains a protease domain and a helicase domain, both of which play essential roles during the viral life cycle. However, it has been shown that ZIKV NS3 has an inherently weak helicase activity, making it unable to unwind long RNA duplexes alone. How this activity is stimulated to process the viral genome and whether the two domains of NS3 are functionally coupled remain unclear. Here, we used optical tweezers to characterize the RNA-unwinding properties of ZIKV NS3-including its processivity, velocity, and step size-at the single-molecule level. We found that external forces that weaken the stability of the duplex RNA substrate significantly enhance the helicase activity of ZIKV NS3. On the other hand, we showed that the protease domain increases the binding affinity of NS3 to RNA but has only a minor effect on unwinding per se. Our findings suggest that the ZIKV NS3 helicase is activated on demand in the context of viral replication, a paradigm that may be generalizable to other flaviviruses.

Bounds on skewness and kurtosis of steady-state currents

Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to dynamics and thermodynamics of a transport setup. Specifically, several distinct bounds on these quantities are either analytically derived or numerically conjectured, which are applicable to (1) noninteracting fermionic systems, (2) noninteracting bosonic systems, (3) thermally driven classical Markovian systems, and (4) unicyclic Markovian networks. Finally, it is demonstrated that violation of the obtained inequalities can provide a broad spectrum of information about the physics of the analyzed system; e.g., it can enable one to infer the presence of interactions or unitary dynamics, unravel the topology of the Markovian network, or characterize the nature of thermodynamic forces driving the system. In particular, relevant information about the microscopic dynamics can be gained even at equilibrium when the current variance-a standard measure of current fluctuations-is determined mostly by the thermal noise.

Relating cellular signaling timescales to single-molecule kinetics: A first-passage time analysis of Ras activation by SOS

Son of Sevenless (SOS) is a Ras guanine nucleotide exchange factor (GEF) that plays a central role in numerous cellular signaling pathways. Like many other signaling molecules, SOS is autoinhibited in the cytosol and activates only after recruitment to the membrane. The mean activation time of individual SOS molecules has recently been measured to be ∼60 s, which is unexpectedly long and seemingly contradictory with cellular signaling timescales, which have been measured to be as fast as several seconds. Here, we rectify this discrepancy using a first-passage time analysis to reconstruct the effective signaling timescale of multiple SOS molecules from their single-molecule activation kinetics. Along with corresponding experimental measurements, this analysis reveals how the functional response time, comprised of many slowly activating molecules, can become substantially faster than the average molecular kinetics. This consequence stems from the enzymatic processivity of SOS in a highly out-of-equilibrium reaction cycle during receptor triggering. Ultimately, rare, early activation events dominate the macroscopic reaction dynamics.

Optical tweezers in single-molecule biophysics

Optical tweezers have become the method of choice in single-molecule manipulation studies. In this Primer, we first review the physical principles of optical tweezers and the characteristics that make them a powerful tool to investigate single molecules. We then introduce the modifications of the method to extend the measurement of forces and displacements to torques and angles, and to develop optical tweezers with single-molecule fluorescence detection capabilities. We discuss force and torque calibration of these instruments, their various modes of operation and most common experimental geometries. We describe the type of data obtained in each experimental design and their analyses. This description is followed by a survey of applications of these methods to the studies of protein-nucleic acid interactions, protein/RNA folding and molecular motors. We also discuss data reproducibility, the factors that lead to the data variability among different laboratories and the need to develop field standards. We cover the current limitations of the methods and possible ways to optimize instrument operation, data extraction and analysis, before suggesting likely areas of future growth.

Force-dependent stimulation of RNA unwinding by SARS-CoV-2 nsp13 helicase

The superfamily 1 helicase nonstructural protein 13 (nsp13) is required for SARS-CoV-2 replication. The mechanism and regulation of nsp13 has not been explored at the single-molecule level. Specifically, force-dependent unwinding experiments have yet to be performed for any coronavirus helicase. Here, using optical tweezers, we find that nsp13 unwinding frequency, processivity, and velocity increase substantially when a destabilizing force is applied to the RNA substrate. These results, along with bulk assays, depict nsp13 as an intrinsically weak helicase that can be activated >50-fold by piconewton forces. Such force-dependent behavior contrasts the known behavior of other viral monomeric helicases, such as hepatitis C virus NS3, and instead draws stronger parallels to ring-shaped helicases. Our findings suggest that mechanoregulation, which may be provided by a directly bound RNA-dependent RNA polymerase, enables on-demand helicase activity on the relevant polynucleotide substrate during viral replication.

Sensitivity analysis of the reaction occurrence and recurrence times in steady-state biochemical networks

Continuous-time stationary Markov jump processes among discrete sites are encountered in disparate biochemical ambits. Sites and connecting dynamical events form a 'network' in which the sites are the available system's states, and the events are site-to-site transitions, or even neutral processes in which the system does not change site but the event is however detectable. Examples include conformational transitions in single biomolecules, stochastic chemical kinetics in the space of the molecules copy numbers, and even macroscopic steady-state reactive mixtures if one adopts the viewpoint of a tagged molecule (or even of a molecular moiety) whose state may change when it is involved in a chemical reaction. Among the variety of dynamical descriptors, here we focus on the first occurrence times (starting from a given site) and on the recurrence times of an event of interest. We develop the sensitivity analysis for the lowest moments of the statistical distribution of such times with respect to the rate constants of the network. In particular, simple expressions and inequalities allow us to establish a direct relationship between selective variation of rate constants and effect on average times and variances. As illustrative cases we treat the substrate inhibition in enzymatic catalysis in which a tagged enzyme molecule jumps between three states, and the basic two-site model of stochastic gene expression in which the single gene switches between active and inactive forms.

Phragmoplast Orienting Kinesin 2 Is a Weak Motor Switching between Processive and Diffusive Modes

Plant development and morphology relies on the accurate insertion of new cell walls during cytokinesis. However, how a plant cell correctly orients a new wall is poorly understood. Two kinesin class-12 members, phragmoplast orienting kinesin 1 (POK1) and POK2, are involved in the process, but how these molecular machines work is not known. Here, we used in vivo and single-molecule in vitro measurements to determine how Arabidopsis thaliana POK2 motors function mechanically. We found that POK2 is a very weak, on average plus-end-directed, moderately fast kinesin. Interestingly, POK2 switches between processive and diffusive modes characterized by an exclusive-state mean-squared-displacement analysis. Our results support a model that POK motors push against peripheral microtubules of the phragmoplast for its guidance. This pushing model may mechanically explain the conspicuous narrowing of the division site. Together, our findings provide mechanical insight into how active motors accurately position new cell walls in plants.

Individual-Molecule Perspective Analysis of Chemical Reaction Networks: The Case of a Light-Driven Supramolecular Pump

The first study in which stochastic simulations of a two‐component molecular machine are performed in the mass‐action regime is presented. This system is an autonomous molecular pump consisting of a photoactive axle that creates a directed flow of rings through it by exploiting light energy away from equilibrium. The investigation demonstrates that the pump can operate in two regimes, both experimentally accessible, in which light‐driven steps can be rate‐determining or not. The number of photons exploited by an individual molecular pump, as well as the precision of cycling and the overall efficiency, critically rely on the operating regime of the machine. This approach provides useful information not only to guide the chemical design of a self‐assembling molecular device with desired features, but also to elucidate the effect of the environment on its performance, thus facilitating its experimental investigation.

Biological Pathway Specificity in the Cell-Does Molecular Diversity Matter?

Biology arises from the crowded molecular environment of the cell, rendering it a challenge to understand biological pathways based on the reductionist, low-concentration in vitro conditions generally employed for mechanistic studies. Recent evidence suggests that low-affinity interactions between cellular biopolymers abound, with still poorly defined effects on the complex interaction networks that lead to the emergent properties and plasticity of life. Mass-action considerations are used here to underscore that the sheer number of weak interactions expected from the complex mixture of cellular components significantly shapes biological pathway specificity. In particular, on-pathway-i.e., "functional"-become those interactions thermodynamically and kinetically stable enough to survive the incessant onslaught of the many off-pathway ("nonfunctional") interactions. Consequently, to better understand the molecular biology of the cell a further paradigm shift is needed toward mechanistic experimental and computational approaches that probe intracellular diversity and complexity more directly. Also see the video abstract here https://youtu.be/T19X_zYaBzg.

Coming Together: RNAs and Proteins Assemble under the Single-Molecule Fluorescence Microscope

RNAs, across their numerous classes, often work in concert with proteins in RNA-protein complexes (RNPs) to execute critical cellular functions. Ensemble-averaging methods have been instrumental in revealing many important aspects of these RNA-protein interactions, yet are insufficiently sensitive to much of the dynamics at the heart of RNP function. Single-molecule fluorescence microscopy (SMFM) offers complementary, versatile tools to probe RNP conformational and compositional changes in detail. In this review, we first outline the basic principles of SMFM as applied to RNPs, describing key considerations for labeling, imaging, and quantitative analysis. We then sample applications of in vitro and in vivo single-molecule visualization using the case studies of pre-messenger RNA (mRNA) splicing and RNA silencing, respectively. After discussing specific insights single-molecule fluorescence methods have yielded, we briefly review recent developments in the field and highlight areas of anticipated growth.

A molecular assembly phase transition and kinetic proofreading modulate Ras activation by SOS

The guanine nucleotide exchange factor (GEF) Son of Sevenless (SOS) is a key Ras activator that is autoinhibited in the cytosol and activates upon membrane recruitment. Autoinhibition release involves structural rearrangements of the protein at the membrane and thus introduces a delay between initial recruitment and activation. In this study, we designed a single-molecule assay to resolve the time between initial receptor-mediated membrane recruitment and the initiation of GEF activity of individual SOS molecules on microarrays of Ras-functionalized supported membranes. The rise-and-fall shape of the measured SOS activation time distribution and the long mean time scale to activation (~50 seconds) establish a basis for kinetic proofreading in the receptor-mediated activation of Ras. We further demonstrate that this kinetic proofreading is modulated by the LAT (linker for activation of T cells)-Grb2-SOS phosphotyrosine-driven phase transition at the membrane.

Direct observation of individual tubulin dimers binding to growing microtubules

The biochemical basis of microtubule growth has remained elusive for over 30 years despite being fundamental for both cell division and associated chemotherapy strategies. Here, we combine interferometric scattering microscopy with recombinant tubulin to monitor individual tubulins binding to and dissociating from growing microtubule tips. We make direct, single-molecule measurements of tubulin association and dissociation rates. We detect two populations of transient dwell times and determine via binding-interface mutants that they are distinguished by the formation of one interprotofilament bond. Applying a computational model, we find that slow association kinetics with strong interactions along protofilaments best recapitulate our data and, furthermore, predicts plus-end tapering. Overall, we provide the most direct and complete experimental quantification of how microtubules grow to date.

Structural conditions on complex networks for the Michaelis-Menten input-output response

The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.

Putting Humpty-Dumpty Together: Clustering the Functional Dynamics of Single Biomolecular Machines Such as the Spliceosome

The spliceosome is a biomolecular machine that, in all eukaryotes, accomplishes site-specific splicing of introns from precursor messenger RNAs (pre-mRNAs) with high fidelity. Operating at the nanometer scale, where inertia and friction have lost the dominant role they play in the macroscopic realm, the spliceosome is highly dynamic and assembles its active site around each pre-mRNA anew. To understand the structural dynamics underlying the molecular motors, clocks, and ratchets that achieve functional accuracy in the yeast spliceosome (a long-standing model system), we have developed single-molecule fluorescence resonance energy transfer (smFRET) approaches that report changes in intra- and intermolecular interactions in real time. Building on our work using hidden Markov models (HMMs) to extract kinetic and conformational state information from smFRET time trajectories, we recognized that HMM analysis of individual state transitions as independent stochastic events is insufficient for a biomolecular machine as complex as the spliceosome. In this chapter, we elaborate on the recently developed smFRET-based Single-Molecule Cluster Analysis (SiMCAn) that dissects the intricate conformational dynamics of a pre-mRNA through the splicing cycle in a model-free fashion. By leveraging hierarchical clustering techniques developed for Bioinformatics, SiMCAn efficiently analyzes large datasets to first identify common molecular behaviors. Through a second level of clustering based on the abundance of dynamic behaviors exhibited by defined functional intermediates that have been stalled by biochemical or genetic tools, SiMCAn then efficiently assigns pre-mRNA FRET states and transitions to specific splicing complexes, with the potential to find heretofore undescribed conformations. SiMCAn thus arises as a general tool to analyze dynamic cellular machines more broadly.

Phosphotyrosine-mediated LAT assembly on membranes drives kinetic bifurcation in recruitment dynamics of the Ras activator SOS

The assembly of cell surface receptors with downstream signaling molecules is a commonly occurring theme in multiple signaling systems. However, little is known about how these assemblies modulate reaction kinetics and the ultimate propagation of signals. Here, we reconstitute phosphotyrosine-mediated assembly of extended linker for the activation of T cells (LAT):growth factor receptor-bound protein 2 (Grb2):Son of Sevenless (SOS) networks, derived from the T-cell receptor signaling system, on supported membranes. Single-molecule dwell time distributions reveal two, well-differentiated kinetic species for both Grb2 and SOS on the LAT assemblies. The majority fraction of membrane-recruited Grb2 and SOS both exhibit fast kinetics and single exponential dwell time distributions, with average dwell times of hundreds of milliseconds. The minor fraction exhibits much slower kinetics, extending the dwell times to tens of seconds. Considering this result in the context of the multistep process by which the Ras GEF (guanine nucleotide exchange factor) activity of SOS is activated indicates that kinetic stabilization from the LAT assembly may be important. This kinetic proofreading effect would additionally serve as a stochastic noise filter by reducing the relative probability of spontaneous SOS activation in the absence of receptor triggering. The generality of receptor-mediated assembly suggests that such effects may play a role in multiple receptor proximal signaling processes.

Monitoring the Waiting Time Sequence of Single Ras GTPase Activation Events Using Liposome Functionalized Zero-Mode Waveguides

Activation of small GTPases of the Ras superfamily by guanine nucleotide exchange factors (GEFs) is a key step in numerous cell signaling processes. Unveiling the detailed molecular mechanisms of GEF-GTPase signaling interactions is of great importance due to their central roles in cell biology, including critical disease states, and their potential as therapeutic targets. Here we present an assay to monitor individual Ras activation events catalyzed by single molecules of the GEF Son of Sevenless (SOS) in the natural membrane environment. The assay employs zero-mode waveguide (ZMW) nanostructures containing a single Ras-functionalized liposome. The ZMWs facilitate highly localized excitation of fluorophores in the vicinity of the liposome membrane, allowing direct observation of individual Ras activation events as single SOS enzymes catalyze exchange of unlabeled nucleotides bound to Ras with fluorescently labeled nucleotides from solution. The system is compatible with continuous recording of long sequences of individual enzymatic turnover events over hour-long time scales. The single turnover waiting time sequence is a molecular footprint that details the temporal characteristics of the system. Data reported here reveal long-lived activity states that correspond to well-defined conformers of SOS at the membrane. Liposome functionalized ZMWs allow for studies of nucleotide exchange reactions at single GTPase resolution, providing a platform to gauge the mechanisms of these processes.

Quantifying the Assembly of Multicomponent Molecular Machines by Single-Molecule Total Internal Reflection Fluorescence Microscopy

Large, dynamic macromolecular complexes play essential roles in many cellular processes. Knowing how the components of these complexes associate with one another and undergo structural rearrangements is critical to understanding how they function. Single-molecule total internal reflection fluorescence (TIRF) microscopy is a powerful approach for addressing these fundamental issues. In this article, we first discuss single-molecule TIRF microscopes and strategies to immobilize and fluorescently label macromolecules. We then review the use of single-molecule TIRF microscopy to study the formation of binary macromolecular complexes using one-color imaging and inhibitors. We conclude with a discussion of the use of TIRF microscopy to examine the formation of higher-order (i.e., ternary) complexes using multicolor setups. The focus throughout this article is on experimental design, controls, data acquisition, and data analysis. We hope that single-molecule TIRF microscopy, which has largely been the province of specialists, will soon become as common in the tool box of biophysicists and biochemists as structural approaches have become today.

Skewness and Kurtosis in Statistical Kinetics

We obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to a well-known lower bound on the randomness parameter, the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network. Our results demonstrate that evaluating these higher order moments with single molecule data can lead to information about the enzymatic scheme that is not contained in the randomness parameter.

Untangling reaction pathways through modern approaches to high-throughput single-molecule force-spectroscopy experiments

Single-molecule experiments provide a unique means for real-time observation of the activity of individual biomolecular machines. Through such techniques, insights into the mechanics of for example, polymerases, helicases, and packaging motors have been gleaned. Here we describe the recent advances in single-molecule force spectroscopy instrumentation that have facilitated high-throughput acquisition at high spatiotemporal resolution. The large datasets attained by such methods can capture rare but important events, and contain information regarding stochastic behaviors covering many orders of magnitude in time. We further discuss analysis of such data sets, and with a special focus on the pause states described in the general literature on RNA polymerase pausing we compare and contrast the signatures of different reaction pathways.

Stepping and crowding of molecular motors: statistical kinetics from an exclusion process perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.

Mechanochemical tuning of myosin-I by the N-terminal region

Myosins are molecular motors that generate force to power a wide array of motile cellular functions. Myosins have the inherent ability to change their ATPase kinetics and force-generating properties when they encounter mechanical loads; however, little is known about the structural elements in myosin responsible for force sensing. Recent structural and biophysical studies have shown that myosin-I isoforms, Myosin-Ib (Myo1b) and Myosin-Ic (Myo1c), have similar unloaded kinetics and sequences but substantially different responses to forces that resist their working strokes. Myo1b has the properties of a tension-sensing anchor, slowing its actin-detachment kinetics by two orders of magnitude with just 1 pN of resisting force, whereas Myo1c has the properties of a slow transporter, generating power without slowing under 1-pN loads that would stall Myo1b. To examine the structural elements that lead to differences in force sensing, we used single-molecule and ensemble kinetic techniques to show that the myosin-I N-terminal region (NTR) plays a critical role in tuning myosin-I mechanochemistry. We found that replacing the Myo1c NTR with the Myo1b NTR changes the identity of the primary force-sensitive transition of Myo1c, resulting in sensitivity to forces of <2 pN. Additionally, we found that the NTR plays an important role in stabilizing the post-power-stroke conformation. These results identify the NTR as an important structural element in myosin force sensing and suggest a mechanism for generating diversity of function among myosin isoforms.

Processivity of the kinesin-2 KIF3A results from rear head gating and not front head gating

The kinesin-2 family motor KIF3A/B works together with dynein to bidirectionally transport intraflagellar particles, melanosomes, and neuronal vesicles. Compared with kinesin-1, kinesin-2 is less processive, and its processivity is more sensitive to load, suggesting that processivity may be controlled by different gating mechanisms. We used stopped-flow and steady-state kinetics experiments, along with single-molecule and multimotor assays to characterize the entire kinetic cycle of a KIF3A homodimer that exhibits motility similar to that of full-length KIF3A/B. Upon first encounter with a microtubule, the motor rapidly exchanges both mADP and mATP. When adenosine 5'-[(β,γ)-imido]triphosphate was used to entrap the motor in a two-head-bound state, exchange kinetics were unchanged, indicating that rearward strain in the two-head-bound state does not alter nucleotide binding to the front head. A similar lack of front head gating was found when intramolecular strain was enhanced by shortening the neck linker domain from 17 to 14 residues. In single-molecule assays in ADP, the motor dissociates at 2.1 s(-1), 20-fold slower than the stepping rate, demonstrating the presence of rear head gating. In microtubule pelleting assays, the KD(Mt) is similar in ADP and ATP. The data and accompanying simulations suggest that, rather than KIF3A processivity resulting from strain-dependent regulation of nucleotide binding (front head gating), the motor spends a significant fraction of its hydrolysis cycle in a low affinity state but dissociates only slowly from this state. This work provides a mechanism to explain differences in the load-dependent properties of kinesin-1 and kinesin-2.

smFRET studies of the 'encounter' complexes and subsequent intermediate states that regulate the selectivity of ligand binding

The selectivity with which a biomolecule can bind its cognate ligand when confronted by the vast array of structurally similar, competing ligands that are present in the cell underlies the fidelity of some of the most fundamental processes in biology. Because they collectively comprise one of only a few methods that can sensitively detect the 'encounter' complexes and subsequent intermediate states that regulate the selectivity of ligand binding, single-molecule fluorescence, and particularly single-molecule fluorescence resonance energy transfer (smFRET), approaches have revolutionized studies of ligand-binding reactions. Here, we describe a widely used smFRET strategy that enables investigations of a large variety of ligand-binding reactions, and discuss two such reactions, aminoacyl-tRNA selection during translation elongation and splice site selection during spliceosome assembly, that highlight both the successes and challenges of smFRET studies of ligand-binding reactions. We conclude by reviewing a number of emerging experimental and computational approaches that are expanding the capabilities of smFRET approaches for studies of ligand-binding reactions and that promise to reveal the mechanisms that control the selectivity of ligand binding with unprecedented resolution.

Analytic approaches to stochastic gene expression in multicellular systems

Deterministic thermodynamic models of the complex systems, which control gene expression in metazoa, are helping researchers identify fundamental themes in the regulation of transcription. However, quantitative single cell studies are increasingly identifying regulatory mechanisms that control variability in expression. Such behaviors cannot be captured by deterministic models and are poorly suited to contemporary stochastic approaches that rely on continuum approximations, such as Langevin methods. Fortunately, theoretical advances in the modeling of transcription have assembled some general results that can be readily applied to systems being explored only through a deterministic approach. Here, I review some of the recent experimental evidence for the importance of genetically regulating stochastic effects during embryonic development and discuss key results from Markov theory that can be used to model this regulation. I then discuss several pairs of regulatory mechanisms recently investigated through a Markov approach. In each case, a deterministic treatment predicts no difference between the mechanisms, but the statistical treatment reveals the potential for substantially different distributions of transcriptional activity. In this light, features of gene regulation that seemed needlessly complex evolutionary baggage may be appreciated for their key contributions to reliability and precision of gene expression.

The Ca2+-activated Cl- channel ANO1/TMEM16A regulates primary ciliogenesis

The Ca²⁺-activated Cl⁻ channel ANO1/TMEM16A is located in the primary cilium, and blocking it pharmacologically or knocking it down with shRNA interferes with ciliogenesis. Before ciliogenesis, the channel is organized into a torus-shaped structure (the “nimbus”) enriched in proteins required for ciliogenesis.

Many cells possess a single, nonmotile, primary cilium highly enriched in receptors and sensory transduction machinery that plays crucial roles in cellular morphogenesis. Although sensory transduction requires ion channels, relatively little is known about ion channels in the primary cilium (with the exception of TRPP2). Here we show that the Ca²⁺-activated Cl⁻ channel anoctamin-1 (ANO1/TMEM16A) is located in the primary cilium and that blocking its channel function pharmacologically or knocking it down with short hairpin RNA interferes with ciliogenesis. Before ciliogenesis, the channel becomes organized into a torus-shaped structure (“the nimbus”) enriched in proteins required for ciliogenesis, including the small GTPases Cdc42 and Arl13b and the exocyst complex component Sec6. The nimbus excludes F-actin and coincides with a ring of acetylated microtubules. The nimbus appears to form before, or independent of, apical docking of the mother centriole. Our data support a model in which the nimbus provides a scaffold for staging of ciliary components for assembly very early in ciliogenesis and chloride transport by ANO1/TMEM16A is required for the genesis or maintenance of primary cilia.

Kinesin-8 is a low-force motor protein with a weakly bound slip state

During the cell cycle, kinesin-8s control the length of microtubules by interacting with their plus ends. To reach these ends, the motors have to be able to take many steps without dissociating. However, the underlying mechanism for this high processivity and how stepping is affected by force are unclear. Here, we tracked the motion of yeast (Kip3) and human (Kif18A) kinesin-8s with high precision under varying loads using optical tweezers. Surprisingly, both kinesin-8 motors were much weaker compared with other kinesins. Furthermore, we discovered a force-induced stick-slip motion: the motor frequently slipped, recovered from this state, and then resumed normal stepping motility without detaching from the microtubule. The low forces are consistent with kinesin-8s being regulators of microtubule dynamics rather than cargo transporters. The weakly bound slip state, reminiscent of a molecular safety leash, may be an adaptation for high processivity.

Extracting signal from noise: kinetic mechanisms from a Michaelis-Menten-like expression for enzymatic fluctuations

Enzyme-catalyzed reactions are naturally stochastic, and precision measurements of these fluctuations, made possible by single-molecule methods, promise to provide fundamentally new constraints on the possible mechanisms underlying these reactions. We review some aspects of statistical kinetics: a new field with the goal of extracting mechanistic information from statistical measures of fluctuations in chemical reactions. We focus on a widespread and important statistical measure known as the randomness parameter. This parameter is remarkably simple in that it is the squared coefficient of variation of the cycle completion times, although it places significant limits on the minimal complexity of possible enzymatic mechanisms. Recently, a general expression has been introduced for the substrate dependence of the randomness parameter that is for rate fluctuations what the Michaelis-Menten expression is for the mean rate of product generation. We discuss the information provided by the new kinetic parameters introduced by this expression and demonstrate that this expression can simplify the vast majority of published models.

First-passage problems in DNA replication: effects of template tension on stepping and exonuclease activities of a DNA polymerase motor

A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits the template as the track for its own motor-like mechanical movement. In the polymerase mode it elongates the nascent DNA by one nucleotide in each step. However, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode. In the latter mode it excises the wrong nucleotide before switching back to its polymerase mode. We develop a stochastic kinetic model of DNA replication that mimics an in vitro experiment where single-stranded DNA, subjected to a mechanical tension F, is converted to double-stranded DNA by a single DNAP. The F-dependence of the average rate of replication, which depends on the rates of both polymerase and exonuclease activities of the DNAP, is in good qualitative agreement with the corresponding experimental results. We introduce nine novel distinct conditional dwell times of a DNAP. Using the method of first-passage times, we also derive the exact analytical expressions for the probability distributions of these conditional dwell times. The predicted F-dependences of these distributions are, in principle, accessible to single-molecule experiments.

Statistical analysis of molecular signal recording

A molecular device that records time-varying signals would enable new approaches in neuroscience. We have recently proposed such a device, termed a “molecular ticker tape”, in which an engineered DNA polymerase (DNAP) writes time-varying signals into DNA in the form of nucleotide misincorporation patterns. Here, we define a theoretical framework quantifying the expected capabilities of molecular ticker tapes as a function of experimental parameters. We present a decoding algorithm for estimating time-dependent input signals, and DNAP kinetic parameters, directly from misincorporation rates as determined by sequencing. We explore the requirements for accurate signal decoding, particularly the constraints on (1) the polymerase biochemical parameters, and (2) the amplitude, temporal resolution, and duration of the time-varying input signals. Our results suggest that molecular recording devices with kinetic properties similar to natural polymerases could be used to perform experiments in which neural activity is compared across several experimental conditions, and that devices engineered by combining favorable biochemical properties from multiple known polymerases could potentially measure faster phenomena such as slow synchronization of neuronal oscillations. Sophisticated engineering of DNAPs is likely required to achieve molecular recording of neuronal activity with single-spike temporal resolution over experimentally relevant timescales.

Recording of physiological signals from inaccessible microenvironments is often hampered by the macroscopic sizes of current recording devices. A signal-recording device constructed on a molecular scale could advance biology by enabling the simultaneous recording from millions or billions of cells. We recently proposed a molecular device for recording time-varying ion concentration signals: DNA polymerases (DNAPs) copy known template DNA strands with an error rate dependent on the local ion concentration. The resulting DNA polymers could then be sequenced, and with the help of statistical techniques, used to estimate the time-varying ion concentration signal experienced by the polymerase. We develop a statistical framework to treat this inverse problem and describe a technique to decode the ion concentration signals from DNA sequencing data. We also provide a novel method for estimating properties of DNAP dynamics, such as polymerization rate and pause frequency, directly from sequencing data. We use this framework to explore potential application scenarios for molecular recording devices, achievable via molecular engineering within the biochemical parameter ranges of known polymerases. We find that accurate recording of neural firing rate responses across several experimental conditions would likely be feasible using molecular recording devices with kinetic properties similar to those of known polymerases.

Single-molecule study of the CUG repeat-MBNL1 interaction and its inhibition by small molecules

Effective drug discovery and optimization can be accelerated by techniques capable of deconvoluting the complexities often present in targeted biological systems. We report a single-molecule approach to study the binding of an alternative splicing regulator, muscleblind-like 1 protein (MBNL1), to (CUG)n = 4,6 and the effect of small molecules on this interaction. Expanded CUG repeats (CUG(exp)) are the causative agent of myotonic dystrophy type 1 by sequestering MBNL1. MBNL1 is able to bind to the (CUG)n-inhibitor complex, indicating that the inhibition is not a straightforward competitive process. A simple ligand, highly selective for CUG(exp), was used to design a new dimeric ligand that binds to (CUG)n almost 50-fold more tightly and is more effective in destabilizing MBNL1-(CUG)4. The single-molecule method and the analysis framework might be extended to the study of other biomolecular interactions.

High degree of coordination and division of labor among subunits in a homomeric ring ATPase

Ring NTPases of the ASCE superfamily perform a variety of cellular functions. An important question about the operation of these molecular machines is how the ring subunits coordinate their chemical and mechanical transitions. Here, we present a comprehensive mechanochemical characterization of a homomeric ring ATPase-the bacteriophage φ29 packaging motor-a homopentamer that translocates double-stranded DNA in cycles composed of alternating dwells and bursts. We use high-resolution optical tweezers to determine the effect of nucleotide analogs on the cycle. We find that ATP hydrolysis occurs sequentially during the burst and that ADP release is interlaced with ATP binding during the dwell, revealing a high degree of coordination among ring subunits. Moreover, we show that the motor displays an unexpected division of labor: although all subunits of the homopentamer bind and hydrolyze ATP during each cycle, only four participate in translocation, whereas the remaining subunit plays an ATP-dependent regulatory role.

A universal pathway for kinesin stepping

Kinesin-1 is an ATP-driven, processive motor that transports cargo along microtubules in a tightly regulated stepping cycle. Efficient gating mechanisms ensure that the sequence of kinetic events proceeds in proper order, generating a large number of successive reaction cycles. To study gating, we created two mutant constructs with extended neck-linkers and measured their properties using single-molecule optical trapping and ensemble fluorescence techniques. Due to a reduction in the inter-head tension, the constructs access an otherwise rarely populated conformational state where both motor heads remain bound to the microtubule. ATP-dependent, processive backstepping and futile hydrolysis were observed under moderate hindering loads. Based on measurements, we formulated a comprehensive model for kinesin motion that incorporates reaction pathways for both forward and backward stepping. In addition to inter-head tension, we find that neck-linker orientation is also responsible for ensuring gating in kinesin.

Mechanistic constraints from the substrate concentration dependence of enzymatic fluctuations

The time it takes an enzyme to complete its reaction is a stochastic quantity governed by thermal fluctuations. With the advent of high-resolution methods of single-molecule manipulation and detection, it is now possible to observe directly this natural variation in the enzymatic cycle completion time and extract kinetic information from the statistics of its fluctuations. To this end, the inverse of the squared coefficient of variation, which we term n(min), is a useful measure of fluctuations because it places a strict lower limit on the number of kinetic states in the enzymatic mechanism. Here we show that there is a single general expression for the substrate dependence of n(min) for a wide range of kinetic models. This expression is governed by three kinetic parameters, which we term N(L), N(S), and alpha. These parameters have simple geometric interpretations and provide clear constraints on possible kinetic mechanisms. As a demonstration of this analysis, we fit the fluctuations in the dwell times of the packaging motor of the bacteriophage varphi29, revealing additional features of the nucleotide loading process in this motor. Because a diverse set of kinetic models display the same substrate dependence for their fluctuations, the expression for this general dependence may prove of use in the characterization and study of the dynamics of a wide range of enzymes.