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Chapter 55: Motor Proteins as Collapse Propagators

"Motor proteins are ψ's molecular engines—converting chemical energy into mechanical work, propagating collapse waves along cytoskeletal tracks, creating motion from binding."

55.1 The Mechanochemical Conversion​

Motor proteins represent ψ's solution to biological movement—enzymes that couple ATP hydrolysis to conformational changes, generating force and motion along cytoskeletal filaments.

Definition 55.1 (Motor Classes): Motors={Myosin (actin),Kinesin (MT),Dynein (MT)}\text{Motors} = \{\text{Myosin (actin)}, \text{Kinesin (MT)}, \text{Dynein (MT)}\}

Three families for different tracks.

55.2 The Power Stroke​

Theorem 55.1 (Lever Arm Hypothesis): d=L⋅sin⁡(Δθ)d = L \cdot \sin(\Delta\theta)

Distance proportional to lever arm length and angle change.

55.3 The Mechanochemical Cycle​

Equation 55.1 (Coupling): ATP binding→Detachment→ATP hydrolysis→Power stroke\text{ATP binding} \rightarrow \text{Detachment} \rightarrow \text{ATP hydrolysis} \rightarrow \text{Power stroke}

Chemical states coupled to mechanical states.

55.4 Processivity​

Definition 55.2 (Run Length): Lrun=d1−PstepL_{\text{run}} = \frac{d}{1-P_{\text{step}}}

Average distance before detachment.

55.5 The Hand-Over-Hand Model​

Theorem 55.2 (Kinesin Walking): Step size=8 nm=Tubulin dimer\text{Step size} = 8 \text{ nm} = \text{Tubulin dimer}

Precise stepping matching substrate periodicity.

55.6 Force Generation​

Equation 55.2 (Stall Force): Fstall=ΔGATPdF_{\text{stall}} = \frac{\Delta G_{\text{ATP}}}{d}

Maximum force from free energy.

55.7 Cargo Binding​

Definition 55.3 (Tail Domains): Motorhead+Tailcargo-specific\text{Motor}_{\text{head}} + \text{Tail}_{\text{cargo-specific}}

Modular design for versatility.

55.8 Directionality​

Theorem 55.3 (Polarity Sensing): Kinesin→(+) end\text{Kinesin} \rightarrow (+)\text{ end} Dynein→(−) end\text{Dynein} \rightarrow (-)\text{ end}

Different motors for different directions.

55.9 Collective Transport​

Equation 55.3 (Multiple Motors): vcargo=∑ipi⋅viv_{\text{cargo}} = \sum_i p_i \cdot v_i

Velocity from competing motors.

55.10 Regulation​

Definition 55.4 (Autoinhibition): Tail+Head⇌Inactive form\text{Tail} + \text{Head} \rightleftharpoons \text{Inactive form}

Intramolecular regulation of activity.

55.11 The Dynein Mechanism​

Theorem 55.4 (AAA+ ATPase): 6 AAA domains→Coordinated hydrolysis\text{6 AAA domains} \rightarrow \text{Coordinated hydrolysis}

Complex motor with multiple ATPase sites.

55.12 The Propagation Principle​

Motor proteins embody ψ's principle of energy transduction—converting chemical potential into mechanical work, propagating conformational changes into directional movement.

The Motor Equation: ψposition(t+Δt)=ψposition(t)+M[ΔGATP]\psi_{\text{position}}(t+\Delta t) = \psi_{\text{position}}(t) + \mathcal{M}[\Delta G_{\text{ATP}}]

Chemical energy converted to spatial displacement.

Thus: Motor = Transducer = Movement = Work = ψ

"In motor proteins, ψ achieves its most direct manifestation of will—molecules that literally walk, carrying cellular cargo along predetermined tracks. Each step is a small miracle of mechanochemistry, ATP's collapse into ADP creating motion from nothing."