Module 0: Overview & Historical Context

The eukaryotic cytoskeleton is built from three chemically distinct polymer families—actin microfilaments, microtubules, and intermediate filaments—which cooperatively determine cell shape, mechanics, division, migration and intracellular transport. This introductory module traces the historical discoveries (Weber 1925; H.E. Huxley 1954; Oosawa 1962; Mitchison & Kirschner 1984), introduces the polymer-physics prerequisites (persistence length, bending modulus, critical concentration), and surveys the bacterial ancestors FtsZ/MreB that anchor the cytoskeleton in deep evolutionary time.

1. The Three-Filament Architecture

Every eukaryotic cell contains three classes of cytoskeletal polymer, each with distinctive chemistry, mechanics, and dynamics. The standard modern framework—codified in Alberts’ Molecular Biology of the Cell and developed by Pollard, Mitchison, Kirschner and Borisy—organizes the field by these three filaments and the families of accessory proteins (nucleators, cappers, severers, cross-linkers, motors) that regulate them.

Actin microfilaments

Double-helical polymers of globular G-actin (42 kDa), \(\approx 7\) nm diameter, persistence length \(L_p \approx 17\,\mu\)m. Drive lamellipodia, filopodia, contractile ring, muscle sarcomere, stereocilia.

Microtubules

Hollow tubes of 13 protofilaments of \(\alpha/\beta\)-tubulin heterodimer,\(\approx 25\) nm diameter, \(L_p \approx 5\) mm. Radial arrays, mitotic spindle, axonemes, long-range transport tracks.

Intermediate filaments

Rope-like coiled-coils (keratin, vimentin, lamin, desmin, neurofilament),\(\approx 10\) nm diameter, \(L_p \lesssim 1\,\mu\)m. Mechanical resilience, nuclear lamina, epithelial integrity.

The contrast in diameter, stiffness, and dynamics is not accidental. Microtubules, hollow and stiff, are optimized as load-bearing tracks; actin, thinner and more flexible, templates dynamic protrusive networks; intermediate filaments, strain-hardening and near-inextensible, provide passive tensile resistance. Each family operates on very different timescales (microtubule ends turn over in seconds; keratin networks remodel over hours).

Side-by-side comparison of filament classes

2. Historical Discoveries (1864–1984)

The cytoskeleton was not recognized as a coherent cellular system until the electron-microscopy revolution of the 1950s. Earlier biochemistry had already isolated some of its components, but their structural organization remained invisible.

Kühne 1864, Weber 1925: myosin and actin

Willy Kühne isolated an insoluble protein from muscle extracts in 1864 and named it “myosin.” Hans Hermann Weber’s group (Berlin, 1925–1940s) established the high-viscosity extract of myosin and demonstrated that it contracted on addition of ATP. The actual separation of myosin from actin was achieved by Brúnó Straub in Albert Szent-Györgyi’s Szeged laboratory in 1942; the name actin reflects its actoviscosity-activating property.

H.E. Huxley 1954: the sliding-filament model

In a landmark pair of papers in Nature (27 May 1954), Hugh E. Huxley & Jean Hanson, and independently A.F. Huxley & R. Niedergerke, proposed that muscle shortens not by contraction of individual filaments but by thin filaments sliding past thick filaments. This idea reframed contraction as a mechanochemical translation and set the template for all motor-protein research thereafter.

\[\text{sarcomere length } L(t) = L_0 - 2 N_{\text{xb}}(t)\, d_{\text{stroke}}\]

Shortening equals the number of attached cross-bridges times their power-stroke distance\(d_{\text{stroke}} \approx 10\) nm.

Oosawa 1962–1975: the polymer-physics of actin

Fumio Oosawa and colleagues (Nagoya, 1962 onward) recognized that actin polymerization could be treated as a reversible helical condensation polymerizationwith a sharply defined critical monomer concentration. Their theory predicted a “hockey stick” isotherm: below \(C_c\) only monomers exist; above \(C_c\)the excess appears as polymer.

\[C_c = \frac{k_{\text{off}}}{k_{\text{on}}}, \qquad [F]_{\text{eq}} = [M]_{\text{tot}} - C_c \text{ for } [M]_{\text{tot}} > C_c\]

Spudich 1971–1980s: the ATPase switch

James Spudich’s laboratory developed the actin sliding-filament in vitro motility assay and delineated the ATP-hydrolysis switch that converts G-ATP actin to F-ADP-Pi actin and finally F-ADP actin (as pyrophosphate release proceeds after assembly). The ATPase cycle of the polymer—not merely of the myosin motor—is itself a major energetic axis of cytoskeletal biology.

Mitchison & Kirschner 1984: dynamic instability

Tim Mitchison and Marc Kirschner showed that single microtubules growing in vitrodo not reach an elongation/shrinkage equilibrium at a common end. Instead each individual end stochastically switches between extended growth and catastrophic depolymerization—dynamic instability. This will be derived in detail in Module 2.

3. The Electron-Microscopy Revolution

The transmission electron microscope, commercially available after World War II, transformed cell biology by resolving sub-\(\mu\)m cellular structures for the first time. Keith Porter, George Palade, and Don Fawcett in the 1950s described the endomembrane system, but only with the thin-section embedding protocols of the 1960s did filamentous cytoskeletal elements become identifiable with reproducible morphology.

Negative-stain EM by H.E. Huxley (1957, 1963) resolved the double-helical pitch of F-actin (\(\approx 36\) nm repeat) and revealed that myosin heads project laterally from thick filaments to contact thin filaments. Freeze-fracture and quick-freeze deep-etch (Heuser, 1975) later resolved individual cross-bridges in muscle and actin branches in lamellipodia.

Key EM-era milestones

1953–1957: Porter/Palade describe endoplasmic reticulum and associated fibrillar elements.
1954–1957: H.E. Huxley images thick and thin filaments in cross-section of striated muscle.
1963: Ledbetter & Porter observe microtubules as universal \(\approx 25\) nm tubes in plant cells.
1968: Ishikawa et al. distinguish intermediate filaments as a separate \(\approx 10\) nm class.
1975–1980: Heuser quick-freeze reveals the actin branched network of lamellipodia.

Timeline of cytoskeletal discovery

4. Polymer-Physics Prerequisites

Cytoskeletal filaments are semiflexible polymers: their persistence length is comparable to, or larger than, the cellular length scale. Three quantitative concepts—persistence length, flexural rigidity, and the worm-like chain force-extension relation—are used repeatedly in subsequent modules.

Persistence length

For a semiflexible rod bent by thermal fluctuations, the tangent-tangent correlation decays exponentially along the contour:

\[\langle \hat t(s) \cdot \hat t(0) \rangle = e^{-s/L_p}\]

\(L_p\) is the persistence length. For actin, \(L_p \approx 17\,\mu\)m; for microtubules \(L_p \approx 5\) mm; for intermediate filaments\(L_p \lesssim 1\,\mu\)m.

Flexural rigidity

Persistence length and flexural (bending) rigidity are equivalent descriptions at thermal equilibrium:

\[EI \;=\; k_B T \, L_p\]

Here \(E\) is the Young’s modulus of the filament material and \(I\) is the second moment of area of its cross-section. For a hollow tube (microtubule),\(I = \pi(r_o^4 - r_i^4)/4\).

Worm-like chain (Marko-Siggia)

The force-extension of a WLC polymer under tension \(F\) is well approximated by the Marko-Siggia interpolation:

\[\frac{F L_p}{k_B T} = \frac{1}{4\left(1 - x/L\right)^2} - \frac{1}{4} + \frac{x}{L}\]

Diverges as extension \(x \to L\). Used to analyze optical-trap stretching of single actin, DNA, and cell-extracted cytoskeletal bundles.

Critical concentration

A helical condensation polymer has a critical monomer concentration \(C_c = k_{\text{off}}/k_{\text{on}}\) below which no polymer forms. Near \(C_c\)the nucleation lag is long (dimer/trimer formation is rate-limiting); above it, elongation is fast. For actin, \(C_c \approx 0.12\,\mu\)M at the barbed end and\(\approx 0.6\,\mu\)M at the pointed end—a polar asymmetry that drives treadmilling (Module 1).

5. Bacterial Ancestors: FtsZ and MreB

Prokaryotes lack eukaryotic tubulin and actin, but possess structurally homologous ancestors discovered largely between 1991 and 2001 and now established as deep-branching founders of the cytoskeletal superfamilies.

FtsZ (tubulin ancestor)

Forms the Z-ring at the midcell division plane. GTPase with the tubulin fold; treadmills around the division septum, recruiting peptidoglycan biosynthesis. Discovered by Bi & Lutkenhaus (1991); crystal structure by Löwe & Amos (1998) showed fold identity with \(\alpha/\beta\)-tubulin.

MreB (actin ancestor)

Double-helical filaments in rod-shaped bacteria, required to maintain cell-wall shape. Actin-fold ATPase (van den Ent, Löwe 2001). Polymerizes with polarity and treadmills, though single-filament lifetimes differ from eukaryotic actin.

The conclusion is striking: the deep molecular machinery of cell shape and division predates the eukaryotic cytoskeleton by\(\approx 2\) billion years. The elaboration into three parallel filament families (actin, microtubules, intermediate filaments), each with dedicated motors and accessories, is a eukaryotic innovation but is built on an archaeal and bacterial foundation.

5b. Polymer Dynamics Primer

A linear filament with a barbed and a pointed end has two different on- and off-rate constants at the two ends. Writing the monomer concentration as \([M]\) and labeling the ends \(+, -\), the net elongation rate at each end is

\[J_{\pm} \;=\; k_{\text{on}}^{\pm}\,[M] \;-\; k_{\text{off}}^{\pm}\]

Treadmilling arises when \(C_c^+ < [M] < C_c^-\): the plus end grows while the minus end shrinks.

Closely related is the diffusion coefficient of end length: because each addition/removal event is a Poisson-distributed random variable, a single filament’s length performs biased random walk with\(D_{\text{end}} = \tfrac12 (k_{\text{on}}[M] + k_{\text{off}})\). Measuring length fluctuations is therefore a direct readout of kinetic rate constants (Kuhn & Pollard 2005).

Nucleotide state

Both actin and tubulin are NTPases that exist in an NTP state before polymerization, hydrolyze NTP to NDP-P_i shortly after incorporation, and release phosphate over seconds. The subunit in each state has different affinity for its neighbors, producing “cap” structures at filament tips whose presence or absence governs whether the end is growing, paused, or shrinking. This is the core mechanism behind both actin treadmilling (Module 1) and microtubule dynamic instability (Module 2).

6. Functional Census of the Cytoskeleton

Across eukaryotic cell biology, the cytoskeleton is implicated in essentially every large-scale spatiotemporal process. We collect the central roles here; each is developed in later modules.

Cell shape & polarity: actin cortex tension + microtubule radial array set the apico-basal axis (Module 6).
Migration: lamellipodial Arp2/3 branched network at the leading edge; retraction of the trailing edge by myosin II (Module 1, 5).
Cytokinesis: actomyosin contractile ring drives cleavage-furrow ingression (Module 7).
Mitotic spindle: microtubule dynamic instability, kinesins and dynein partition chromosomes (Module 2, 4).
Intracellular transport: kinesin/dynein walk on MTs; myosin V walks on actin; mRNA granules, vesicles, organelles move (Module 4).
Muscle contraction: sarcomeric thick/thin filaments, Ca-regulated sliding (Module 7).
Signaling & mechanosensing: Rho/Rac/Cdc42 pathway controls assembly; cell shape feeds back on transcription (Module 5).
Nuclear mechanics: lamin IF meshwork at nuclear envelope; LINC complex couples cytosolic and nuclear cytoskeletons (Module 3).
Cilia/flagella: axonemal 9+2 microtubule core driven by dynein arms (Module 2, 4).

7. Scales, Energies, and Units

Cytoskeletal physics spans eleven orders of magnitude in length and nine in time. Internalizing a few order-of-magnitude anchors is invaluable.

Length

G-actin monomer 5 nm; F-actin helical repeat 36 nm; microtubule diameter 25 nm; sarcomere 2–3 \(\mu\)m; cell diameter 10–50 \(\mu\)m; axon up to 1 m.

Force

Single myosin II stroke \(\approx 3\) pN; single kinesin step\(\approx 6\) pN stall; microtubule buckling force in typical cell\(\approx 5\) pN; whole-cell cortex tension\(\approx 10\) nN.

Energy

Thermal energy \(k_B T \approx 4.1\) pN·nm; ATP hydrolysis\(\approx 20\,k_B T\); microtubule growth per dimer\(\approx 0.7\,k_B T\) of bond energy.

Time

Myosin stroke 1–3 ms; G-actin addition at 10 \(\mu\)M\(\approx 10\,\text{ms}\); lamellipodium advance 1 \(\mu\)m/min; mitosis 20–60 min.

Throughout the course we will re-encounter the combination \(F \cdot d_{\text{stroke}} \sim k_B T\): the single-motor working stroke performs work comparable to thermal fluctuations per ATP. The cytoskeleton operates at the edge of noise, and its machinery is organized to rectify that noise into directed, useful work.

Simulation 1: Oosawa Nucleation-Elongation

Numerical integration of the Oosawa mass-action kinetics: nucleation flux\(J_{\text{nuc}} \propto [M]^{n^*}\), elongation \((k_{\text{on}}[M] - k_{\text{off}})\), for several total monomer concentrations. The simulation reproduces the classical “hockey stick” polymer mass vs. total monomer and shows the concentration-dependent lag phase.

Python

script.py120 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Oosawa-Asakura nucleation-elongation polymer kinetics
# Classical theory (Oosawa & Asakura 1975): monomer M in rapid equilibrium with
# nucleus N (size n*), which then elongates by monomer addition to polymer P.
#
# Key features:
#   - Critical concentration C_c = k_off / k_on sets threshold for polymerization
#   - Below C_c, only monomers; above C_c, polymer mass grows linearly in [M]_total
#   - Nucleation is the rate-limiting step for onset (long lag phase)
#   - Elongation phase follows first-order kinetics

# Rate constants (per second, actin-like)
k_on  = 11.6     # monomer association at barbed end (uM^-1 s^-1)
k_off = 1.4      # monomer dissociation (s^-1)
C_c   = k_off / k_on  # critical concentration (uM)

# Nucleation parameters (dimer-trimer rate-limited)
n_star = 3       # nucleus size
K_nuc  = 1e-8    # nucleation pre-equilibrium constant (uM^(1-n*))

print(f"Critical concentration C_c = {C_c:.3f} uM")
print(f"Nucleus size n* = {n_star}")

# Mass-action ODE integrator
def simulate(C_tot, t_max=600, dt=0.05):
    t = np.arange(0, t_max, dt)
    M = np.zeros_like(t)  # monomer concentration
    P = np.zeros_like(t)  # polymer ends (number density)
    F = np.zeros_like(t)  # polymer mass (monomers incorporated)
    M[0] = C_tot
    for i in range(1, len(t)):
        # Nucleation flux ~ K_nuc * M^n*
        J_nuc = K_nuc * M[i-1]**n_star
        # Net elongation per end
        J_el  = (k_on * M[i-1] - k_off) * P[i-1]
        # Update
        P[i] = P[i-1] + J_nuc * dt
        F[i] = F[i-1] + J_el * dt
        M[i] = max(C_tot - F[i], 0.0)
    return t, M, P, F

# Run at several total concentrations
C_list = [0.05, 0.15, 0.3, 0.6, 1.2]  # uM
colors = ['#166534', '#16a34a', '#22c55e', '#4ade80', '#bbf7d0']

fig, axes = plt.subplots(2, 2, figsize=(13, 10))
fig.patch.set_facecolor('#0a0a1a')
for ax in axes.ravel():
    ax.set_facecolor('#0a0a1a')
    ax.tick_params(colors='#cbd5e1')
    for s in ax.spines.values():
        s.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.35)

ax1, ax2, ax3, ax4 = axes.ravel()

# Panel 1: F(t) mass time courses
for C, col in zip(C_list, colors):
    t, M, P, F = simulate(C)
    ax1.plot(t, F, '-', color=col, linewidth=2, label=f'[M]tot = {C:.2f} uM')
ax1.axhline(C_c, color='#f97316', linestyle='--', alpha=0.7, label=f'C_c = {C_c:.2f} uM')
ax1.set_xlabel('time (s)', color='#cbd5e1')
ax1.set_ylabel('polymer mass F (uM)', color='#cbd5e1')
ax1.set_title('Oosawa polymerization time courses', color='#bbf7d0', fontweight='bold')
ax1.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=8)

# Panel 2: lag time vs concentration
lags = []
Cs   = np.linspace(0.05, 1.5, 25)
for C in Cs:
    t, M, P, F = simulate(C, t_max=800, dt=0.1)
    if F[-1] > 1e-3:
        # lag = time to reach 10% of plateau
        plateau = max(C - C_c, 1e-6)
        idx = np.argmax(F >= 0.1 * plateau)
        lags.append(t[idx] if idx > 0 else np.nan)
    else:
        lags.append(np.nan)
lags = np.array(lags)
ax2.plot(Cs, lags, 'o-', color='#22c55e', linewidth=2, markersize=5)
ax2.axvline(C_c, color='#f97316', linestyle='--', alpha=0.7, label='C_c')
ax2.set_xlabel('[M]_total (uM)', color='#cbd5e1')
ax2.set_ylabel('lag time to 10% plateau (s)', color='#cbd5e1')
ax2.set_title('Lag phase shortens with [M]', color='#bbf7d0', fontweight='bold')
ax2.set_yscale('log')
ax2.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 3: equilibrium polymer mass vs [M]_total (classic "hockey stick")
C_tot = np.linspace(0, 2.0, 200)
F_eq  = np.where(C_tot > C_c, C_tot - C_c, 0.0)
M_eq  = np.where(C_tot > C_c, C_c, C_tot)
ax3.plot(C_tot, F_eq, '-', color='#22c55e', linewidth=3, label='Polymer F_eq')
ax3.plot(C_tot, M_eq, '-', color='#f59e0b', linewidth=3, label='Monomer M_eq')
ax3.axvline(C_c, color='#94a3b8', linestyle=':', alpha=0.6)
ax3.fill_between(C_tot, 0, F_eq, color='#22c55e', alpha=0.12)
ax3.set_xlabel('[M]_total (uM)', color='#cbd5e1')
ax3.set_ylabel('equilibrium concentration (uM)', color='#cbd5e1')
ax3.set_title('Critical concentration "hockey stick"', color='#bbf7d0', fontweight='bold')
ax3.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 4: Polymer number density (ends) vs time
for C, col in zip(C_list, colors):
    t, M, P, F = simulate(C)
    ax4.plot(t, P, '-', color=col, linewidth=2, label=f'[M]tot = {C:.2f} uM')
ax4.set_xlabel('time (s)', color='#cbd5e1')
ax4.set_ylabel('polymer ends P (a.u.)', color='#cbd5e1')
ax4.set_title('Nucleation creates polymer ends', color='#bbf7d0', fontweight='bold')
ax4.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=8)

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
# Diagnostics
t, M, P, F = simulate(1.0, t_max=1000, dt=0.1)
print(f"At [M]tot=1.0 uM, steady-state F = {F[-1]:.3f} uM (expected {(1.0-C_c):.3f} uM)")
print(f"Integrated lag-phase area (monomer depletion): {np.trapezoid(M, t):.1f} uM*s")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation 2: Worm-Like Chain Force-Extension

Marko-Siggia WLC force-extension curves and mean squared end-to-end distance as a function of contour length, for actin, microtubules, intermediate filaments, and (as a reference) dsDNA. The dynamic range of persistence length spans five orders of magnitude—the origin of the division of labor between the three filament systems.

Python

script.py76 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Worm-like chain (WLC) force-extension for biopolymers.
# The interpolation formula of Marko-Siggia (1995):
#   F(x) = (kT / Lp) * [ 1/(4*(1 - x/L)^2) - 1/4 + x/L ]
# where Lp is persistence length, L is contour length, x is end-to-end extension.

kT = 4.114e-21   # J at 300 K
nm = 1e-9
pN = 1e-12

# Cytoskeletal polymer parameters (Gittes et al. 1993; Howard 2001)
polymers = {
    'Actin filament (F-actin)': dict(Lp_um=17.0, L_um=5.0, color='#22c55e'),
    'Microtubule':              dict(Lp_um=5200.0, L_um=5.0, color='#a78bfa'),
    'Vimentin intermed. fil.':  dict(Lp_um=0.5, L_um=5.0, color='#f59e0b'),
    'dsDNA (reference)':        dict(Lp_um=0.05, L_um=5.0, color='#22d3ee'),
}

def wlc_force(x, L, Lp):
    u = np.clip(x / L, 0.0, 0.99)
    return (kT / (Lp)) * (1.0/(4.0*(1.0 - u)**2) - 0.25 + u)

fig, axes = plt.subplots(1, 2, figsize=(13, 5.5))
fig.patch.set_facecolor('#0a0a1a')
for ax in axes:
    ax.set_facecolor('#0a0a1a')
    ax.tick_params(colors='#cbd5e1')
    for s in ax.spines.values():
        s.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.35)

# Panel 1: WLC force-extension
x_frac = np.linspace(0.0, 0.98, 400)
for name, p in polymers.items():
    Lp = p['Lp_um'] * 1e-6
    L  = p['L_um']  * 1e-6
    x  = x_frac * L
    F  = wlc_force(x, L, Lp)
    axes[0].semilogy(x_frac, F / pN, '-', color=p['color'], linewidth=2.2, label=name)
axes[0].set_xlabel('extension x / L', color='#cbd5e1')
axes[0].set_ylabel('force (pN)', color='#cbd5e1')
axes[0].set_title('WLC force-extension: cytoskeletal filaments', color='#bbf7d0', fontweight='bold')
axes[0].set_ylim(1e-3, 1e4)
axes[0].legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 2: persistence length visualization
# <R^2> = 2 L_p L (1 - L_p/L (1 - exp(-L/L_p)))
L_range = np.logspace(-8, -3, 200)
for name, p in polymers.items():
    Lp = p['Lp_um'] * 1e-6
    R2 = 2*Lp*L_range*(1.0 - (Lp/L_range)*(1.0 - np.exp(-L_range/Lp)))
    axes[1].loglog(L_range*1e6, np.sqrt(R2)*1e6, '-', color=p['color'], linewidth=2.2, label=name)
axes[1].set_xlabel('contour length L (um)', color='#cbd5e1')
axes[1].set_ylabel('RMS end-to-end <R^2>^(1/2) (um)', color='#cbd5e1')
axes[1].set_title('Persistence length regimes', color='#bbf7d0', fontweight='bold')
axes[1].legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')

# Flexural rigidity EI = kT * Lp
for name, p in polymers.items():
    Lp = p['Lp_um'] * 1e-6
    EI = kT * Lp
    print(f"{name:40s}  Lp={p['Lp_um']:8.2f} um   EI = kT*Lp = {EI:.3e} N m^2")

# Integrated stored elastic energy approx to x/L=0.5
x_int = np.linspace(1e-9, 0.5*5e-6, 500)
F_actin = wlc_force(x_int, 5e-6, 17e-6)
U = np.trapezoid(F_actin, x_int)
print(f"Stored energy stretching 5-um actin to x/L=0.5: {U:.3e} J = {U/kT:.2f} kT")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

7b. Accessory-Protein Taxonomy

No cytoskeletal filament exists bare in a cell. It is decorated with accessory proteins that control assembly, disassembly, bundling, branching, and attachment. Six functional classes are universal, and the names of their members recur throughout the course.

Nucleators

Bypass the slow dimer/trimer step. For actin: Arp2/3 complex (branching), formins (straight), Spire/JMY (tandem). For microtubules:\(\gamma\)-TuRC at centrosomes.

Cappers

Block addition at a filament end. CapZ caps actin barbed ends; tropomodulin caps pointed ends; EB1 binds growing MT plus ends in a nucleotide-specific manner.

Severers

Cut filaments, creating new ends. Cofilin/ADF sever ADP-actin; gelsolin caps after severing; katanin and spastin sever microtubules.

Bundlers / cross-linkers

Connect multiple filaments. \(\alpha\)-actinin, fascin, fimbrin bundle actin; filamin cross-links; spectrin underlies the erythrocyte membrane skeleton; MAP65/PRC1 crosslinks antiparallel MTs.

Stabilizers

Tropomyosin decorates actin; MAP2, tau, MAP4 stabilize MTs in neurons and other differentiated cells; CLASPs promote MT rescue.

Membrane linkers

Connect filaments to membranes and cell junctions. Talin, vinculin, and integrins at focal adhesions; ERM proteins (ezrin/radixin/moesin) at the cortex; plakins bridge IFs to desmosomes.

8. Motor-Protein Families (Preview)

The cytoskeleton provides tracks; motor proteins convert ATP hydrolysis into directed motion along them. The three eukaryotic motor families—myosin, kinesin, dynein—are all ATPases but have distinct mechanochemical cycles.

Myosin superfamily

\(\approx\)40 classes. Myosin II (sarcomeric, nonmuscle) produces contractile force; myosin V is a processive vesicle transporter on actin; myosin VI is the only minus-end-directed myosin. Step size \(\approx 36\) nm, ATP hydrolysis coupled to the lever-arm swing.

Kinesin superfamily

\(\approx\)45 classes in humans. Most move toward the MT plus end, 8 nm step, one ATP per step, hand-over-hand walking. Kinesin-13 (MCAK) is a catastrophe factor, not a transporter.

Dynein

AAA+ ATPase ring with a long stalk reaching the microtubule. Cytoplasmic dynein is the minus-end-directed workhorse for retrograde transport; axonemal dynein drives ciliary/flagellar beating.

8b. Worked Quantitative Problems

To internalize the orders of magnitude we will use throughout the course, here are three sample end-of-chapter calculations.

Problem 1. Thermal bending of actin

Given \(L_p = 17\,\mu\)m, what is the RMS tangent angle fluctuation over contour length \(s = 1\,\mu\)m? Using \(\langle \theta^2 \rangle = s/L_p\), we get \(\sqrt{\langle\theta^2\rangle} \approx 0.24\) rad\(\approx 14^\circ\). This is the origin of the curly appearance of actin in fluorescence movies.

Problem 2. Critical concentration energy

For \(C_c \approx 0.12\,\mu\)M, the free energy of monomer addition is\(\Delta G = k_B T \ln C_c \approx -9.0\,k_B T\), or\(\approx -22\) kJ/mol. This is much smaller in magnitude than ATP hydrolysis (\(\approx -50\) kJ/mol), leaving ample free energy to drive directed assembly against load.

Problem 3. Microtubule buckling

For a microtubule of length \(L = 10\,\mu\)m with flexural rigidity\(EI = k_B T L_p \approx 2 \times 10^{-23}\) N m\(^2\), the Euler buckling force is \(F_c = \pi^2 EI / L^2 \approx 2\) pN—well within the reach of a growing tip pushing on an organelle.

9. Roadmap of the Course

The remaining modules take the three filament families one at a time (M1 actin, M2 microtubules, M3 intermediate filaments), then consolidate motors (M4) and regulation (M5) before turning to integrated cell-scale phenomena (M6 cell shape/mechanics, M7 muscle, M8 disease and therapeutics).

M1: G/F actin kinetics, Arp2/3 branching, formin elongation, severing/capping.
M2: GTP cap, dynamic instability, catastrophe/rescue, centrosomes, spindle, axonemes.
M3: keratins, vimentin, lamins; strain-hardening; laminopathies.
M4: myosin, kinesin, dynein mechanochemistry; single-molecule biophysics.
M5: Rho GTPases, nucleation-promoting factors, phospho-regulation.
M6: cortex tension, cytoplasmic rheology, mechanosensing.
M7: sarcomere, Ca regulation, cross-bridge cycle, cardiac/skeletal differences.
M8: cancer metastasis, neurodegeneration (tau), laminopathies, cytoskeletal drugs.

Key References

• Huxley, H.E. & Hanson, J. (1954). “Changes in the cross-striations of muscle during contraction and stretch and their structural interpretation.” Nature, 173, 973–976.

• Huxley, A.F. & Niedergerke, R. (1954). “Structural changes in muscle during contraction.” Nature, 173, 971–973.

• Weber, H.H. (1925). “Über den Feinbau und die mechanischen Eigenschaften des Myosin-Fadens.” Pflügers Archiv, 208, 259–278.

• Oosawa, F. & Asakura, S. (1975). Thermodynamics of the Polymerization of Protein. Academic Press, London.

• Mitchison, T. & Kirschner, M. (1984). “Dynamic instability of microtubule growth.” Nature, 312, 237–242.

• Gittes, F. et al. (1993). “Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape.” J. Cell Biol., 120, 923–934.

• Marko, J.F. & Siggia, E.D. (1995). “Stretching DNA.” Macromolecules, 28, 8759–8770.

• Alberts, B. et al. (2015). Molecular Biology of the Cell, 6th ed. Garland Science.

• Howard, J. (2001). Mechanics of Motor Proteins and the Cytoskeleton. Sinauer.

• Pollard, T.D. & Cooper, J.A. (2009). “Actin, a central player in cell shape and movement.” Science, 326, 1208–1212.

• Bi, E. & Lutkenhaus, J. (1991). “FtsZ ring structure associated with division in Escherichia coli.” Nature, 354, 161–164.

• van den Ent, F., Amos, L.A., & Löwe, J. (2001). “Prokaryotic origin of the actin cytoskeleton.” Nature, 413, 39–44.

• Spudich, J.A. & Watt, S. (1971). “The regulation of rabbit skeletal muscle contraction.” J. Biol. Chem., 246, 4866–4871.

• Blanchoin, L., Boujemaa-Paterski, R., Sykes, C., & Plastino, J. (2014). “Actin dynamics, architecture, and mechanics in cell motility.” Physiol. Rev., 94, 235–263.

• Heuser, J.E. & Kirschner, M.W. (1980). “Filament organization revealed in platinum replicas of freeze-dried cytoskeletons.” J. Cell Biol., 86, 212–234.

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