STRC Research

Recipe — Profilin Thymosin-β4 Monomer Pool Partitioning

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Recipe — Profilin / Thymosin-β4 Monomer Pool Partitioning

P1 recipe. Future agents should use this rather than re-deriving from scratch when an h09 (or any actin-bundling) model needs the free actin monomer concentration [A]_free in a cell. All inputs are sourced from [[2026-04-23-pollard-2016-actin-review-cshpb]] §6.

Inputs (all from Pollard 2016 §5–6)

SymbolMeaningDefault valueCitation
[A]_tottotal cellular actin50–200 µM (use 100 µM as canonical)[Pollard 2016, p.2]
f_unpunpolymerized fraction0.5 (range 0.25–0.5)[Pollard 2016, p.2]
[A]_unp = f_unp · [A]_totunpolymerized monomer pool50 µMderived
[P]_totprofilin total50–100 µM (use 50 µM)[Pollard 2016, p.2]
[T]_totthymosin-β4 total> 100 µM (use 100 µM, or 0 if non-mammalian / non-leukocyte)[Pollard 2016, p.2]
K_d^Pprofilin × ATP-actin0.1 µM[Pollard 2016, p.2]
K_d^Tthymosin-β4 × Mg-ATP-actin~1 µM[Pollard 2016, p.2]

Both proteins compete for the same monomer (mutually exclusive binding).

Algorithm

Three-state partitioning of the unpolymerized pool:

A_free + P  ⇌  AP     K_d^P
A_free + T  ⇌  AT     K_d^T

Conservation:

[A]_unp = [A]_free + [AP] + [AT]
[P]_tot = [P]_free + [AP]
[T]_tot = [T]_free + [AT]

Mass-action:

[AP] = [A]_free · [P]_free / K_d^P
[AT] = [A]_free · [T]_free / K_d^T

This is a 3-unknown nonlinear system (3 equations, after eliminating [P]_free and [T]_free). Solve numerically (Brent’s method on a single variable [A]_free, since [P]_free and [T]_free can each be expressed as functions of [A]_free).

Python skeleton

import numpy as np
from scipy.optimize import brentq
 
def free_monomer(A_unp, P_tot, T_tot, Kd_P=0.1e-6, Kd_T=1.0e-6):
    """All concentrations in molar. Returns [A]_free in M.
 
    Source: Pollard 2016 CSHPB §5–6.
    See [[Recipe — Profilin Thymosin-β4 Monomer Pool Partitioning]].
    """
    def f(A):
        # P_free = P_tot / (1 + A/Kd_P)  ; AP = P_tot - P_free
        P_free = P_tot / (1 + A / Kd_P)
        T_free = T_tot / (1 + A / Kd_T)
        AP = P_tot - P_free
        AT = T_tot - T_free
        return A + AP + AT - A_unp
 
    # Bracket: A=0 gives -A_unp (negative), A=A_unp gives positive
    return brentq(f, 1e-12, A_unp)
 
# Default cellular case (Pollard 2016 numerics)
A_free = free_monomer(A_unp=50e-6, P_tot=50e-6, T_tot=100e-6)
print(f"[A]_free ≈ {A_free*1e6:.3f} µM")  # → expect sub-µM

Pollard 2016 (p.2 §6) states verbally: “most of the actin monomers are bound to either profilin or thymosin-β4, leaving a low (submicromolar) concentration of free actin monomers.” The recipe above should reproduce this qualitatively (~0.1–0.5 µM [A]_free in the canonical case).

When to use this recipe

  • h09 hydrogel WH2 bundling models — the rate of WH2-driven actin bundling depends on [A]_free, not [A]_tot. Using [A]_tot (100 µM) overestimates monomer flux by ~100×.
  • Stereocilia tip elongation models — the rate of tip subunit incorporation depends on [A]_free near the tip. Espin/EPS8 may locally exclude profilin (literature unclear); fall back to [A]_unp only if a reference supports it.
  • Sequestration math for therapeutic synthetic actin binders — if a peptide is engineered to bind the barbed-end groove (WH2-like), it will compete with profilin and Tβ4 — incorporate as a 4th species in the partitioning.

When NOT to use this recipe

  • Acanthamoeba / yeast — thymosin-β4 is animal-specific. Set T_tot = 0.
  • Plant cells — profilin Kd may differ; literature retrieval required before using 0.1 µM.
  • Local concentration gradients (lamellipodium tip, stereocilia tip, contractile ring) — the bulk-cellular concentrations don’t apply. Use spatially-resolved literature if available.

Anti-fabrication notes

  • Profilin Kd 0.1 µM is for ATP-actin (the dominant species). Profilin Kd for ADP-actin is different (Vinson 1998); not in Pollard 2016 verbatim. Don’t substitute.
  • Thymosin-β4 Kd is reported as “micromolar” in Pollard 2016 (no exact value given) — 1 µM is the canonical literature value (Safer 1991; Xue 2014) but should be confirmed against those primary sources before use in a production model.
  • Profilin can bind PIP₂; cellular profilin available for actin binding may be < [P]_tot. Use the full [P]_tot only for first-pass models.

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