TABLE 1.

Species, reactions, and rate constants used in the simulation

A₁, A₂, A₃, and A₄ represent the actin monomer, dimer, trimer, and tetramer, respectively. E1, E2, and F represent actin monomers incorporated into the various forms of filamentous actin, i.e. the intermediate “young” forms (E1, E2) and the final “mature” F–actin form (F; see Scheme 1). The units for the rate constants are s⁻¹ for monomolecular reactions and ml·nmol⁻¹·s⁻¹ for bimolecular reactions. The actin tetramer A₄ has a dual role in the simulation. It represents an intermediate species during the filament formation; it also represents the number of filaments. For this reason, its formation in reactions 3 and 10 is set to be irreversible. A₄ participates in filament elongation (reaction 4 and as a complex with CaD in reaction 11) as a catalyst; i.e. although it is required for the reactions to proceed, its concentration does not change during these reactions. This simplification makes the rates of filament elongation dependent on the filament count [A₄]. The simulation was performed with the program COPASI (Complex Pathway Simulator) in deterministic mode (27). Whenever possible, we used the rate constants similar to those published in the literature (16, 32). For the reactions that were not previously considered, we tested a range of values for each constant that yields the most reasonable approximation of the experiment. It should be pointed out that the obtained solutions are neither unique nor complete. In particular, we ignored the fact that one molecule of CaD affects the fluorescence, and hence the structure of several actin monomers in both the intermediate and final forms of the actin filament. Because of these simplifications, the presented model and the underlying simulation should be considered as a starting point for further refinement.

	Reaction	Rate constants
		Forward	Reverse
Process
1. Nucleation step 1	A + A = A2	10	1 × 106
2. Nucleation step 2	A2 + A = A3	10	20000
3. Filament formation	A3 + A -> A4	10	0
4. Elongation	A4 + A -> A4 + E1	14	0
5. Maturation 1	E1 -> E2	0.003	0
6. Maturation 2	E2 -> F	0.0003	0
Reactions involving CaD
7. G-actin binding	A + CaD = A-CaD	10	1000
8. Nucleation step 1	A-CaD + A = A2-CaD	10	1 × 105
9. Nucleation step 2	A2-CaD + A = A3-CaD	10	20000
10. Filament formation	A3-CaD + A -> A4-CaD	10	0
11. Elongation	A4-CaD + A -> A4-CaD + E1	3.5	0
12. CaD binding to filament	A4 + CaD = A4-CaD	10	0.1
13. CaD binding to E1	E1 + CaD = E1-CaD	10	0.01
14. CaD binding to E2	E2 + CaD = E2-CaD	10	5
15. CaD binding to F	F + CaD = F-CaD	10	5
16. Maturation 2	E2-CaD -> F-CaD	0.01	0
17. CaD binding to CaM	CaD + CaM = CaD-CaM	10	0.002