[Paper Review] How kinesin waits for ATP affects the nucleotide and load dependence of the stepping kinetics

Ryota Takaki, Mauro L. Mugnai+2 more|arXiv (Cornell University)|Aug 20, 2019

Microtubule and mitosis dynamics60 references19 citations

TL;DR

This study develops a minimal theoretical model to resolve the controversy over whether kinesin waits for ATP with both heads bound (2HB) or only one head bound (1HB) to the microtubule. By analytically predicting run length, velocity, and randomness parameters under varying ATP concentration and load, the authors show that the load and nucleotide dependence of the randomness parameter uniquely distinguishes between the two waiting states, providing a quantitative, experimentally testable criterion to resolve the long-standing debate.

ABSTRACT

Dimeric molecular motors walk on polar tracks by binding and hydrolyzing one ATP per step. Despite tremendous progress, the waiting state for ATP binding in the well-studied kinesin that walks on microtubule (MT), remains controversial. One experiment suggests that in the waiting state both heads are bound to the MT, while the other shows that ATP binds to the leading head after the partner head detaches. To discriminate between these two scenarios, we developed a theory to calculate accurately several experimentally measurable quantities as a function of ATP concentration and resistive force. In particular, we predict that measurement of the randomness parameter could discriminate between the two scenarios for the waiting state of kinesin, thereby resolving this standing controversy.

Motivation & Objective

• To resolve the longstanding controversy over whether kinesin waits for ATP with both heads bound (2HB) or only one head bound (1HB) to the microtubule.
• To determine whether experimental observables like run length, velocity distribution, and randomness parameter can discriminate between the 2HB and 1HB ATP waiting states.
• To provide a quantitative, testable prediction for distinguishing between competing models using experimentally measurable quantities.
• To clarify the role of ATP waiting state in chemomechanical coupling and stepping kinetics of kinesin under load and varying nucleotide concentration.

Proposed method

• Develops a minimal stochastic model of kinesin stepping that explicitly incorporates two distinct ATP waiting states: 2HB (both heads bound) and 1HB (only leading head bound).
• Uses analytical solutions to derive the run length distribution P(n), velocity distribution P(v), and randomness parameters (chemical rC and mechanical rM) as functions of load F and ATP concentration [T].
• Applies first-passage time theory and master equation formalism to model the kinetics of stepping, including backward steps under load.
• Derives the mechanical randomness parameter rM as a function of F and [T], which is sensitive to the ATP waiting state.
• Compares predictions of the 2HB and 1HB models across multiple observables to identify distinguishing features.
• Proposes that the F and [T] dependence of rM is qualitatively different between models, making it a key experimental probe.

Experimental results

Research questions

• RQ1 Does the distribution of run length P(n) distinguish between the 2HB and 1HB ATP waiting states?
• RQ2 How does the velocity distribution P(v) depend on external load F and ATP concentration [T] in the 2HB vs. 1HB models?
• RQ3 Is the randomness parameter rM uniquely sensitive to the ATP waiting state under varying load and ATP concentration?
• RQ4 Can the F and [T] dependence of rM be measured experimentally to resolve the controversy over kinesin's ATP waiting state?
• RQ5 What are the quantitative differences in stepping kinetics predicted by the 2HB and 1HB models under physiological load and ATP conditions?

Key findings

• The run length distribution P(n) is insensitive to the ATP waiting state, making it an ineffective discriminator between the 2HB and 1HB models.
• The velocity distribution P(v) is bimodal under load and shows distinct differences between the 2HB and 1HB models, particularly in the shape and peak positions as a function of load F.
• The mechanical randomness parameter rM exhibits qualitatively different dependence on load F and ATP concentration [T] in the 2HB and 1HB models.
• The F and [T] dependence of rM is predicted to be uniquely diagnostic: the 2HB model shows a monotonic decrease in rM with increasing [T], while the 1HB model shows a non-monotonic, bell-shaped dependence.
• The model predicts that rM can be quantitatively measured from single-molecule stepping trajectories with minimal data analysis bias, making it ideal for experimental validation.
• The study identifies the randomness parameter rM as the most promising observable to experimentally resolve the kinesin ATP waiting state controversy.