Maximum likelihood estimation of molecular motor kinetics from staircase dwell-time sequences

Molecular motors, such as kinesin, myosin, or dynein, convert chemical energy into mechanical energy by hydrolyzing ATP. The mechanical energy is used for moving in discrete steps along the cytoskeleton and carrying a molecular load. High resolution single molecule recordings of motor steps appear as a stochastic sequence of dwells, resembling a staircase. Staircase data can also be obtained from other molecular machines such as F1 -ATPase, RNA polymerase, or topoisomerase. We developed a maximum likelihood algorithm that estimates the rate constants between different conformational states of the protein, including motor steps. We model the motor with a periodic Markov model that reflects the repetitive chemistry of the motor step. We estimated the kinetics from the idealized dwell-sequence by numerical maximization of the likelihood function for discrete-time Markov models. This approach eliminates the need for missed event correction. The algorithm can fit kinetic models of arbitrary complexity, such as uniform or alternating step chemistry, reversible or irreversible kinetics, ATP concentration and mechanical force-dependent rates, etc. The method allows global fitting across stationary and nonstationary experimental conditions, and user-defined a priori constraints on rate constants. The algorithm was tested with simulated data, and implemented in the free QuB software.     

Extracting biologically significant patterns from short time series gene expression data

Background  

Time series gene expression data analysis is used widely to study the dynamics of various cell processes. Most of the time series data available today consist of few time points only, thus making the application of standard clustering techniques difficult.     

Myosin IXb is a single-headed minus-end-directed processive motor

Myosin is an actin-based molecular motor that constitutes a diverse superfamily. In contrast to conventional myosin, which binds to actin for only a short time during cross-bridge cycling, recent studies have demonstrated that class V myosin moves along actin filaments for a long distance without dissociating. This would make it suitable for supporting cargo movement in cells. Because myosin V has a two-headed structure with an expanded neck domain, it has been postulated to 'walk' along the 36-nm helical repeat of the actin filament, with one head attached to the actin and leading the other head to the neighbouring helical pitch. Here, we report that myosin IXb, a single-headed myosin, moves processively on actin filaments. Furthermore, we found that myosin IXb is a minus-end-directed motor. In addition to class VI myosin, this is the first myosin superfamily member identified that moves in the reverse direction. The processive movement of the single-headed myosin IXb cannot be explained by a 'hand-over-hand' mechanism. This suggests that an alternative mechanism must be operating for the processive movement of single-headed myosin IXb.     

Myosin-IXb is a single-headed and processive motor.

Class IX myosins are unique among the many classes of known actin-based motors in that the tail region of these myosins contains a GTPase-activating protein domain for the small GTP-binding protein, Rho. Previous studies on human myosin-IXb indicate that this myosin is mechanochemically active and exhibits actin-binding properties similar to the processive motor, myosin-Va. Motility analysis of antibody-tethered myosin-IXb performed using the sliding actin filament assay indicates that this myosin does exhibit properties characteristic of a processive motor. Like myosin-Va, the velocity of myosin-IXb remains constant (38.2 +/- 1.2 nm/s) even at single motor/filament densities. At low motor densities, filaments can be seen passing through and pivoting about single points on the motility surface. Analysis of filament landing rates as a function of motor density also indicates that a single motor is sufficient for filament movement. However, in contrast to myosin-Va, which uses coordinated motion of its two heads to move processively along the filament, hydrodynamic and chemical cross-linking studies indicate that under the conditions tested, myosin-IXb is a single-headed motor consisting of a single heavy chain and associated light chains.     

Extracting abundance information from DNA-based data

The accurate extraction of species-abundance information from DNA-based data (metabarcoding, metagenomics) could contribute usefully to diet analysis and food-web reconstruction, the inference of species interactions, the modelling of population dynamics and species distributions, the biomonitoring of environmental state and change, and the inference of false positives and negatives. However, multiple sources of bias and noise in sampling and processing combine to inject error into DNA-based data sets. To understand how to extract abundance information, it is useful to distinguish two concepts. (i) Within-sample across-species quantification describes relative species abundances in one sample. (ii) Across-sample within-species quantification describes how the abundance of each individual species varies from sample to sample, such as over a time series, an environmental gradient or different experimental treatments. First, we review the literature on methods to recover across-species abundance information (by removing what we call “species pipeline biases”) and within-species abundance information (by removing what we call “pipeline noise”). We argue that many ecological questions can be answered with just within-species quantification, and we therefore demonstrate how to use a “DNA spike-in” to correct for pipeline noise and recover within-species abundance information. We also introduce a model-based estimator that can be used on data sets without a physical spike-in to approximate and correct for pipeline noise.     

Extracting meaning from biological imaging data

Biological imaging continues to improve, capturing continually longer-term, richer, and more complex data, penetrating deeper into live tissue. How do we gain insight into the dynamic processes of disease and development from terabytes of multidimensional image data? Here I describe a collaborative approach to extracting meaning from biological imaging data. The collaboration consists of teams of biologists and engineers working together. Custom computational tools are built to best exploit application-specific knowledge in order to visualize and analyze large and complex data sets. The image data are summarized, extracting and modeling the features that capture the objects and relationships in the data. The summarization is validated, the results visualized, and errors corrected as needed. Finally, the customized analysis and visualization tools together with the image data and the summarization results are shared. This Perspective provides a brief guide to the mathematical ideas that rigorously quantify the notion of extracting meaning from biological image, and to the practical approaches that have been used to apply these ideas to a wide range of applications in cell and tissue optical imaging.     

Hopping and stalling of processive molecular motors

When a two-headed molecular motor such as kinesin is attached to its track by just a single head in the presence of an applied load, thermally activated head detachment followed by rapid re-attachment at another binding site can cause the motor to ‘hop’ backwards. Such hopping, on its own, would produce a linear force-velocity relation. However, for kinesin, we must incorporate hopping into the motor's alternating-head scheme, where we expect it to be most important for the state prior to neck-linker docking. We show that hopping can account for the backward steps, run length and stalling of conventional kinesin. In particular, although hopping does not hydrolyse ATP, we find that the hopping rate obeys the same Michaelis-Menten relation as the ATP hydrolysis rate. Hopping can also account for the reduced processivity observed in kinesins with mutations in their tubulin-binding loop. Indeed, it may provide a general mechanism for the breakdown of perfect processivity in two-headed molecular motors.     

Head-head coordination is required for the processive motion of cytoplasmic dynein, an AAA+ molecular motor

Cytoplasmic dynein is an AAA(+)-type molecular motor whose major components are two identical heavy chains containing six AAA(+) modules in tandem. It moves along a single microtubule in multiple steps which are accompanied with multiple ATP hydrolysis. This processive sliding is crucial for cargo transports in vivo. To examine how cytoplasmic dynein exhibits this processivity, we performed in vitro motility assays of two-headed full-length or truncated single-headed heavy chains. The results indicated that four to five molecules of the single-headed heavy chain were required for continuous microtubule sliding, while approximately one molecule of the two-headed full-length heavy chain was enough for the continuous sliding. The ratio of the stroking time to the total ATPase cycle time, which is a quantitative indicator of the processivity, was approximately 0.2 for the single-headed heavy chain, while it was approximately 0.6 for the full-length molecule. When two single-headed heavy chains were artificially linked by a coiled-coil of myosin, the processivity was restored. These results suggest that the two heads of a single cytoplasmic dynein communicate with each other to take processive steps along a microtubule.     

Three phase model of the processive motor protein kinesin

Kinesin is a stepping motor that successively produces forward and backward 8-nm steps along microtubules. Under physiological conditions, the steps powering kinesin's motility are biased in one direction and drive various biological motile processes. So far, the physical mechanism underlying the unidirectional bias of the kinesin is not fully understood. Recently, Martin Bier have provided a stepper model [Martin Bier, 2003, Processive motor protein as an overdamped Brownian stepper, Phys. Rev. Lett. 91, 148104], in which the stepping cycle of kinesin includes two distinguished phases: (i) a power stroke phase and (ii) a ratcheted diffusion phase which is characterized as a "random diffusional search". At saturating ATP level, this model can fit the experimental results accurately. In this paper, we'll provide a modified Brownian stepper model, in which the dependence of ATP concentration is considered. In our model, the stepping cycle of kinesin is distinguished into three phases: an ATP-binding phase, a power stroke phase and a ratcheted diffusion phase. This modified model can reconstruct most of the experimental results accurately.     

Engineering the processive run length of the kinesin motor

Conventional kinesin is a highly processive molecular motor that takes several hundred steps per encounter with a microtubule. Processive motility is believed to result from the coordinated, hand-over-hand motion of the two heads of the kinesin dimer, but the specific factors that determine kinesin's run length (distance traveled per microtubule encounter) are not known. Here, we show that the neck coiled-coil, a structure adjacent to the motor domain, plays an important role in governing the run length. By adding positive charge to the neck coiled-coil, we have created ultra-processive kinesin mutants that have fourfold longer run lengths than the wild-type motor, but that have normal ATPase activity and motor velocity. Conversely, adding negative charge on the neck coiled-coil decreases the run length. The gain in processivity can be suppressed by either proteolytic cleavage of tubulin's negatively charged COOH terminus or by high salt concentrations. Therefore, modulation of processivity by the neck coiled-coil appears to involve an electrostatic tethering interaction with the COOH terminus of tubulin. The ability to readily increase kinesin processivity by mutation, taken together with the strong sequence conservation of the neck coiled-coil, suggests that evolutionary pressures may limit kinesin's run length to optimize its in vivo function.     

Dictyostelium myosin-5b is a conditional processive motor

Dictyostelium myosin-5b is the gene product of myoJ and one of two closely related myosin-5 isoenzymes produced in Dictyostelium discoideum. Here we report a detailed investigation of the kinetic and functional properties of the protein. In standard assay buffer conditions, Dictyostelium myosin-5b displays high actin affinity in the presence of ADP, fast ATP hydrolysis, and a high steady-state ATPase activity in the presence of actin that is rate limited by ADP release. These properties are typical for a processive motor that can move over long distances along actin filaments without dissociating. Our results show that a physiological decrease in the concentration of free Mg(2+)-ions leads to an increased rate of ADP release and shortening of the fraction of time the motor spends in the strong actin binding states. Consistently, the ability of the motor to efficiently translocate actin filaments at very low surface densities decreases with decreasing concentrations of free Mg(2+)-ions. In addition, we provide evidence that the observed changes in Dd myosin-5b motor activity are of physiological relevance and propose a mechanism by which this molecular motor can switch between processive and non-processive movement.     

A DNA-translocating Snf2 molecular motor: Saccharomyces cerevisiae Rdh54 displays processive translocation and extrudes DNA loops

We have used total internal reflection fluorescence microscopy (TIRFM) to investigate the characteristics of the yeast homologous recombination factor Rdh54 on DNA. Our results demonstrate translocation of Rdh54 on DNA and extrusion of DNA loops by Rdh54 in an ATP hydrolysis-dependent manner. The translocating Rdh54 was highly processive and displayed a variety of behavior, including variations in translocation rate and distance, pauses, and reversals. We provide evidence that the DNA loops generated encompass an average of 6 kb, and Rdh54 often abruptly releases the extruded DNA. Rdh54 forms a multimeric complex, which we speculate has at least two functionally distinct DNA-binding sites, one of which enables translocation while the other remains anchored to another DNA locale. Our work, together with other recent studies, suggests that translocation-coupled DNA loop extrusion is a common mechanistic feature among the Snf2-family of chromatin-remodeling proteins.     

Extracting multi-way chromatin contacts from Hi-C data

There is a growing realization that multi-way chromatin contacts formed in chromosome structures are fundamental units of gene regulation. However, due to the paucity and complexity of such contacts, it is challenging to detect and identify them using experiments. Based on an assumption that chromosome structures can be mapped onto a network of Gaussian polymer, here we derive analytic expressions for n-body contact probabilities (n > 2) among chromatin loci based on pairwise genomic contact frequencies available in Hi-C, and show that multi-way contact probability maps can in principle be extracted from Hi-C. The three-body (triplet) contact probabilities, calculated from our theory, are in good correlation with those from measurements including Tri-C, MC-4C and SPRITE. Maps of multi-way chromatin contacts calculated from our analytic expressions can not only complement experimental measurements, but also can offer better understanding of the related issues, such as cell-line dependent assemblies of multiple genes and enhancers to chromatin hubs, competition between long-range and short-range multi-way contacts, and condensates of multiple CTCF anchors.     

Extracting dynamics from static cancer expression data

Static expression experiments analyze samples from many individuals. These samples are often snapshots of the progression of a certain disease such as cancer. This raises an intriguing question: Can we determine a temporal order for these samples? Such an ordering can lead to better understanding of the dynamics of the disease and to the identification of genes associated with its progression. In this paper we formally prove, for the first time, that under a model for the dynamics of the expression levels of a single gene, it is indeed possible to recover the correct ordering of the static expression datasets by solving an instance of the traveling salesman problem (TSP). In addition, we devise an algorithm that combines a TSP heuristic and probabilistic modeling for inferring the underlying temporal order of the microarray experiments. This algorithm constructs probabilistic continuous curves to represent expression profiles leading to accurate temporal reconstruction for human data. Applying our method to cancer expression data we show that the ordering derived agrees well with survival duration. A classifier that utilizes this ordering improves upon other classifiers suggested for this task. The set of genes displaying consistent behavior for the determined ordering are enriched for genes associated with cancer progression.