Conventional Kinesin (Kin-1), which is 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 towards 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. For example, how the motor waits for ATP to bind to the leading head has become controversial. Two experiments using a similar protocol, which follow the movement of a large gold nanoparticle attached to one of the motor heads, have arrived at different conclusions. One of them (1) asserts that kinesin waits for ATP in a state with both heads bound to the MT, whereas the other (2) shows that ATP binds to the leading head after the trailing head is detached. In order to discriminate between these two scenarios, we developed a minimal model, which analytically predicts the outcomes of a number of experimental observables quantities, such as the distribution of run length [P (n)], the distribution of velocity [P (v)], and the randomness parameter as a function of an external resistive force (F ) and ATP concentration ([T]). We find that P (n) is insensitive to the waiting state of kinesin. The bimodal velocity distribution P (v) depends on the ATP waiting states of kinesin. The differences in P (v) as a function of F between the two 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 whether ATP waits with both heads bound to the MT or with detached tethered head. 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, thus providing insights into the waiting state of kinesin for ATP. A. Chemical randomness parameter, r C 8 B. Mechanical randomness parameter, r M 9 C. Derivation of mechanical randomness parameter with backward steps 11 IV. Two models for how kinesin waits for ATP 17 V. Variant of 1HB model: k − is independent of [T] 20 VI. Fitting theory to experimental data 21 References 23 2 I. DERIVATION OF THE RUN LENGTH DISTRIBUTION The summation in Eq.(4) in the main text, P (n) = ∞ m,l=0(m + l)! m!l! can be carried out for n > 0, leading to, P (n > 0) =

Condensation of hundreds of mega-base-pair-long human chromosomes in a small nuclear volume is a spectacular biological phenomenon. This process is driven by the formation of chromosome loops. The ATP consuming motor, condensin, interacts with chromatin segments to actively extrude loops. Motivated by real-time imaging of loop extrusion (LE), we created an analytically solvable model, predicting the LE velocity and step size distribution as a function of external load. The theory fits the available experimental data quantitatively, and suggests that condensin must undergo a large conformational change, induced by ATP binding, bringing distant parts of the motor to proximity. Simulations using a simple model confirm that the motor transitions between an open and a closed state in order to extrude loops by a scrunching mechanism, similar to that proposed in DNA bubble formation during bacterial transcription. Changes in the orientation of the motor domains are transmitted over ~50 nm, connecting the motor head and the hinge, thus providing an allosteric basis for LE.

Molecular motors belonging to the kinesin and myosin super family hydrolyze ATP by cycling through a sequence of chemical states. These cytoplasmic motors are dimers made up of two linked identical monomeric globular proteins. Fueled by the free energy generated by ATP hydrolysis, the motors walk on polar tracks (microtubule or filamentous actin) processively, which means that only one head detaches and executes a mechanical step while the other stays bound to the track. Thus, the one motor head must regulate chemical state of the other, referred to as "gating", a concept that is not fully understood. Inspired by experiments, showing that only a fraction of the energy from ATP hydrolysis is used to advance the kinesin motors against load, we demonstrate that additional energy is used for coordinating the chemical cycles of the two heads in the dimer - a feature that characterizes gating. To this end, we develop a general framework based on information theory and stochastic thermodynamics, and establish that gating could be quantified in terms of information flow between the motor heads. Applications of the theory to kinesin-1 and Myosin V show that information flow occurs, with positive cooperativity, at external resistive loads that are less than a critical value, Fc. When force exceeds Fc, effective information flow ceases. Interestingly, Fc, which is independent of the input energy generated through ATP hydrolysis, coincides with force at which the probability of backward steps starts to increase. Our findings suggest that transport efficiency is optimal only at forces less than Fc, which implies that these motors must operate at low loads under in vivo conditions.

No abstract

The condensation of several mega base pair human chromosomes in a small cell volume is a spectacular phenomenon in biology. This process, involving the formation of loops in chromosomes, is facilitated by ATP consuming motors (condensin and cohesin), that interact with chromatin segments thereby actively extruding loops. Motivated by real time videos of loop extrusion (LE), we created an analytically solvable model, which yields the LE velocity as a function of external load acting on condensin. The theory fits the experimental data quantitatively, and suggests that condensin must undergo a large conformational change, triggered by ATP binding and hydrolysis, that brings distant parts of the motor to proximity. Simulations using a simple model confirm that a transition between an open and closed states is necessary for LE. Changes in the orientation of the motor domain are transmitted over ∼ 50 nm, connecting the motor head and the hinge, thus providing a plausible mechanism for LE. The theory and simulations are applicable to loop extrusion in other structural maintenance complexes.How chromosomes are structurally organized in the tight cellular space is a long standing problem in biology. Remarkably, these information carrying polymers in humans containing more than 100 million base pairs, depending on the chromosome number, are densely packed (apparently with negligible knots) in the 5 − 10 µm cell nucleus [1,2]. In order to accomplish this herculean feat nature has evolved a family of SMCs (Structural Maintenance of Chromosomes) complexes [3,4] (bacterial SMC, cohesin, and condensin) to facilitate large scale compaction of chromosomes in all living systems. Compaction is thought to occur by active generation of a large array of loops, which are envisioned to form by extrusion of the genomic material [5,6] driven by ATPconsuming motors. The SMC complexes have been identified as a major component of the loop extrusion (LE) process [3,4].Of interest here is condensin, which has motor activity as it translocates on DNA [7], resulting in active extrusion loops in an ATP-dependent manner [8]. We first provide a brief description of the architecture of condensin (drawn schematically in Fig.1) because the theory is based on this picture. Condensin is a ring shaped dimeric motor to which a pair of SMC proteins (Smc2 and Smc4) are attached. Smc2 and Smc4, which have coiled coil (CC) structures, are connected at the hinge domain. The ATP binding domains are in the motor heads [4,9]. The CCs have kinks roughly in the middle of the CCs [9]. The relative flexibility in the elbow region (located near the kinks) could be the key to the conformational transitions in the CC that are powered by ATP binding and hydrolysis [4,10]. At present, there is no direct experimental evidence that this is so.Previous studies using simulations [6,11,12], which build on the pioneering insights by Nasmyth [5], suggested that multiple condensins concertedly translocate * dave.thirumalai@gmail.com along the chromosome extruding loops of increas...