Theoretical Investigation of Distributions of Run Lengths for Biological Molecular Motors

Communication between DNA and nucleotide binding sites facilitates stepping by the RecBCD helicase

Double-strand DNA breaks are the severest type of genomic damage, requiring rapid response to ensure survival. RecBCD helicase in prokaryotes initiates processive and rapid DNA unzipping, essential for break repair. The energetics of RecBCD during translocation along the DNA track are quantitatively not defined. Specifically, it's essential to understand the mechanism by which RecBCD switches between its binding states to enable its translocation. Here, we determine, by systematic affinity measurements, the degree of coupling between DNA and nucleotide binding to RecBCD. In the presence of ADP, RecBCD binds weakly to DNA that harbors a double overhang mimicking an unwinding intermediate. Consistently, RecBCD binds weakly to ADP in the presence of the same DNA. We did not observe coupling between DNA and nucleotide binding for DNA molecules having only a single overhang, suggesting that RecBCD subunits must both bind DNA to 'sense' the nucleotide state. On the contrary, AMPpNp shows weak coupling as RecBCD remains strongly bound to DNA in its presence. Detailed thermodynamic analysis of the RecBCD reaction mechanism suggests an 'energetic compensation' between RecB and RecD, which may be essential for rapid unwinding. Our findings provide the basis for a plausible stepping mechanism' during the processive translocation of RecBCD.

Processivity and Velocity for Motors Stepping on Periodic Tracks

Processive molecular motors enable cargo transportation by assembling into dimers capable of taking several consecutive steps along a cytoskeletal filament. In the well-accepted hand-over-hand stepping mechanism, the trailing motor detaches from the track and binds the filament again in the leading position. This requires fuel consumption in the form of ATP hydrolysis and coordination of the catalytic cycles between the leading and the trailing heads. Alternate stepping pathways also exist, including inchworm-like movements, backward steps, and foot stomps. Whether all the pathways are coupled to ATP hydrolysis remains to be determined. Here, to establish the principles governing the dynamics of processive movement, we present a theoretical framework that includes all of the alternative stepping mechanisms. Our theory bridges the gap between the elemental rates describing the biochemical and structural transitions in each head and the experimentally measurable quantities such as velocity, processivity, and probability of backward stepping. Our results, obtained under the assumption that the track is periodic and infinite, provide expressions that hold regardless of the topology of the network connecting the intermediate states, and are therefore capable of describing the function of any molecular motor. We apply the theory to myosin VI, a motor that takes frequent backward steps and moves forward with a combination of hand-over-hand and inchworm-like steps. Our model quantitatively reproduces various observables of myosin VI motility reported by four experimental groups. The theory is used to predict the gating mechanism, the pathway for backward stepping, and the energy consumption as a function of ATP concentration.

Role of AAA3 Domain in Allosteric Communication of Dynein Motor Proteins

Cytoplasmic dynein, an AAA+ motif containing motor, generates force and movement along the microtubule to execute important biological functions including intracellular material transport and cell division by hydrolyzing ATP. Among the six AAA+ domains, AAA1 is the primary ATPase site where a single ATP hydrolysis generates a single step. Nucleotide states in AAA3 gate dynein's activity, suggesting that AAA3 acts as a regulatory switch. However, the comprehensive structural perspective of AAA3 in dynein's mechanochemical cycle remains unclear. Here, we explored the allosteric transition path of dynein involving AAA3 using a coarse-grained structure-based model. ATP binding to the AAA1 domain creates a cascade of conformational changes through the other domains of the ring, which leads to the pre-power stroke formation. The linker domain, which is the mechanical element of dynein, shifts from a straight to a bent conformation during this process. In our present study, we observe that AAA3 gates the allosteric communication from AAA1 to the microtubule binding domain (MTBD) through AAA4 and AAA5. The MTBD is linked to the AAA+ ring via a coiled-coil stalk and a buttress domain, which are extended from AAA4 and AAA5, respectively. Further analysis also uncovers the role of AAA3 in the linker movement. The free energy calculation shows that the linker prefers the straight conformation when AAA3 remains in the ATP-bound condition. As AAA3 restricts the motion of AAA4 and AAA5, the linker/AAA5 interactions get stabilized, and the linker cannot move to the pre-power stroke state that halts the complete structural transition required for the mechanochemical cycle. Therefore, we suggest that AAA3 governs dynein's mechanochemical cycle and motility by controlling the AAA4 and AAA5 domains that further regulate the linker movement and the power stroke formation.

Run length distribution of dimerized kinesin-3 molecular motors: comparison with dimeric kinesin-1

Kinesin-3 and kinesin-1 molecular motors are two families of the kinesin superfamily. It has been experimentally revealed that in monomeric state kinesin-3 is inactive in motility and cargo-mediated dimerization results in superprocessive motion, with an average run length being more than 10-fold longer than that of kinesin-1. In contrast to kinesin-1 showing normally single-exponential distribution of run lengths, dimerized kinesin-3 shows puzzlingly Gaussian distribution of run lengths. Here, based on our proposed model, we studied computationally the dynamics of kinesin-3 and compared with that of kinesin-1, explaining quantitatively the available experimental data and revealing the origin of superprocessivity and Gaussian run length distribution of kinesin-3. Moreover, predicted results are provided on ATP-concentration dependence of run length distribution and force dependence of mean run length and dissociation rate of kinesin-3.

How kinesin waits for ATP affects the nucleotide and load dependence of the stepping kinetics

Conventional kinesin, responsible for directional transport of cellular vesicles, takes multiple nearly uniform 8.2-nm steps by consuming one ATP molecule per step as it walks toward the plus end of the microtubule (MT). Despite decades of intensive experimental and theoretical studies, there are gaps in the elucidation of key steps in the catalytic cycle of kinesin. How the motor waits for ATP to bind to the leading head is controversial. Two experiments using a similar protocol have arrived at different conclusions. One asserts that kinesin waits for ATP in a state with both the heads bound to the MT, whereas the other shows that ATP binds to the leading head after the trailing head detaches. To discriminate between the 2 scenarios, we developed a minimal model, which analytically predicts the outcomes of a number of experimental observable quantities (the distribution of run length, the distribution of velocity [[Formula: see text]], and the randomness parameter) as a function of an external resistive force (F) and ATP concentration ([T]). The differences in the predicted bimodality in [Formula: see text] as a function of F between the 2 models may be amenable to experimental testing. Most importantly, we predict that the F and [T] dependence of the randomness parameters differ qualitatively depending on the waiting states. The randomness parameters as a function of F and [T] can be quantitatively measured from stepping trajectories with very little prejudice in data analysis. Therefore, an accurate measurement of the randomness parameter and the velocity distribution as a function of load and nucleotide concentration could resolve the apparent controversy.

Theoretical Analysis of Run Length Distributions for Coupled Motor Proteins

Motor proteins, also known as biological molecular motors, play important roles in various biological processes. In recent years, properties of single-motor proteins have been intensively investigated using multiple experimental and theoretical tools. However, in real cellular systems biological motors typically function in groups, but the mechanisms of their collective dynamics remain not well understood. Here we investigate theoretically distributions of run lengths for coupled motor proteins that move along linear tracks. Our approach utilizes a method of first-passage processes, which is supplemented by Monte Carlo computer simulations. Theoretical analysis allowed us to clarify several aspects of the cooperativity mechanisms for coupled biological molecular motors. It is found that the run length distribution for two motors, in contrast to single motors, is nonmonotonic. In addition, the transport efficiency of two-motor complexes might be strongly increased. We also argue that the degree of cooperativity is influenced by several characteristics of motor proteins such as the strength of intermolecular interactions, stall forces, dissociations constants, and the detachment forces. The application of our theoretical analysis for several motor proteins is also discussed.

Anomalous Dynamics of in Vivo Cargo Delivery by Motor Protein Multiplexes

Vesicle transport conducted by motor protein multiplexes (MPMs), which is ubiquitous among eukaryotes, shows anomalous and stochastic dynamics qualitatively different from the dynamics of thermal motion and artificial active matter; the relationship between in vivo vesicle-delivery dynamics and the underlying physicochemical processes is not yet quantitatively understood. Addressing this issue, we perform accurate tracking of individual vesicles, containing upconverting nanoparticles, transported by kinesin-dynein-multiplexes along axonal microtubules. The mean-square-displacement of vesicles along the microtubule exhibits unusual dynamic phase transitions that are seemingly inconsistent with the scaling behavior of the mean-first-passage time over the travel length. These paradoxical results and the vesicle displacement distribution are quantitatively explained and predicted by a multimode MPM model, developed in the current work, where ATP-hydrolysis-coupled motion of MPM has both unidirectional and bidirectional modes.