Information flow, gating, and energetics in dimeric molecular motors

Figures

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  Fig. 1.. Kinesin stepping and associated transitions. (A) Schematics of a typical optical trap experiment used to monitor stepping on the MT. A resistive force, F, acts on the cargo. (B) Example of transitions for interacting systems with X and Y being the leading and trailing heads, respectively. The CSs associated with X and Y are denoted by circled letters A, B, and C. In this example, the transition in X is described as (x0,y0)=(A,A)→(x1,y0)=(B,A), and the transition in Y is given by (x1,y0)=(B,A)→(x1,y1)=(B,C). Transitions occur at times t1, t2, t3,⋯. (C) Forward stepping cycle for kinesin. The cycle is divided into CS transitions (yellow) and mechanical stepping (green). The CS of the TH is in blue, and that of the LH is shown in red. The nucleotide state T denotes ATP, Φ means the nucleotide state is not bound, D denotes ADP, and DP is the post hydrolyzed state with the trailing containing ADP plus the inorganic phosphate, Pi. The caricatures for the physical states of the motor corresponding to each CS are displayed.

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  Fig. 2.. (A and B) Rates of energy expenditure in kinesin as a function of the external load, F. The rates of work (power) performed by the motor and the rate of heat dissipation calculated from the kinetic network in Fig. 1C are denoted as W˙ and Q˙, respectively. The sum of W˙ (blue dashed line) and Q˙ is Δμ. (green dashed line). The rate of input energy in the single-molecule experiment (41) (black) is Δμ.ex. Insets show the corresponding bare quantities, W (blue dashed line), Q (green dashed line), Δμ (red dashed line), and Δμex (black solid line). (A) [T] = 1 mM, [D] = 0.1 mM, and [Pi] = 1 mM. (B) [T] = 10 µM, [D] = 1 µM, and [Pi] = 1 mM. Under both conditions, Δμ.≈Δμ.ex, which not only validates the theory but also shows that the extracted parameters for kinesin (SI Appendix, Table S1) using different observables are reasonable. (C) Allocation of the input chemical energy for mechanical transition (Δμmc) and chemical transitions (Δμch) as a function of F. The results are obtained theoretically for the kinesin network in Fig. 1C. The black dashed line shows the experimental value, Δμex, which is the energy input. Solid lines are for [T] = 1 mM, [D] = 0.1 mM, [Pi] = 1 mM, and dotted…

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  Fig. 3.. Analysis of the experimental data using theory. (A and B) Contribution of each term in Eqs. 7. and 9; Δμmc is the energy needed for driving the mechanical step, σch is the apparent entropy production in the chemical transitions, Δich is the change in the PMI during chemical transitions, and Δμex = 20.5 kBT is the input chemical energy from the experiment (41). The apparent energy expended to drive the chemical transitions is Δμ˜ch. The gray colors and the corresponding numbers are the three regimes explained in the text. (A) [T] = 1 mM, [D] = 0.1 mM, and [Pi] = 1 mM. (B) [T] = 10 µM, [D] = 1 µM, and [Pi] = 1 mM. In both A and B, the regime corresponding to Δμmc exceeding Δμex is physically not allowed. (C) The probability for the forward step (Pf; blue), the backward step (Pb; yellow), and the fraction (Pb/Pf; black), calculated from ref. 44 (SI Appendix, section III). F=5 pN is highlighted by the gray line where Δich=0. (D) Same as C except the stepping probabilities are calculated using a theory developed elsewhere (10).

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  Fig. 4.. (A) Chemomechanical cycle for myosin V. The diagram shows three cycles, F, ϵ, and M. F is associated with stepping utilizing chemical energy by ATP hydrolysis; ϵ is a futile cycle in which ATP is consumed but the motor does not step; M describes mechanical stepping without ATP hydrolysis. In yellow are the chemical transitions, and the transitions in dashed green are mechanical transitions. Blue and red colors describe the CSs in the two heads of the motor. The cycle is adopted from refs. 44 and 67. (B) The probability for the forward step (Pf), the backward step (Pb), and the fraction (Pb/Pf), digitized from ref. 25. The gray line highlights F≈1 pN where Δich becomes negative. Note that, at all values of F, Pf+Pb≠1, because there are pathways associated with stomping of the LH and TH (25). (C and D) Plots for the terms in Eqs. 7 and 9. for myosin V. Δμmc is the chemical energy allocated to the mechanical stepping, σch is the apparent entropy production during chemical transitions, Δich is the change of PMI during chemical transitions, and Δμ is the chemical energy input at given nucleotide concentrations. Δμ˜ch is the apparent energy spent for chemical transitions. Gray regions…