Phase Coexistence in Small, Out-of-Equilibrium Cells

Finite-size corrections and nonequilibrium analysis of biomolecular condensate phase behavior

55.3% Gap Reduction at N=50 152% NEQ Deviation Da = 41.7 Equilibrium: Invalid

Finite-Size Gap Reduction

ATP Rate vs Gap Deviation

Separation Probability vs System Size

Nonequilibrium Concentration Fluctuations

Finite-Size Analysis

N	Eq Gap	Eff Gap	Reduction (%)	Sep Prob
50	0.020	0.009	55.3	0.332
100	0.020	0.015	23.0	0.273
500	0.020	0.019	2.8	0.106
1,000	0.020	0.020	1.1	0.049
5,000	0.020	0.020	0.1	0.002
10,000	0.020	0.020	0.05	0.0003

Timescale Analysis

Timescale	Value
Cell diffusion	4.17 s
Condensate diffusion	0.042 s
Synthesis	0.10 s
Degradation	100 s
Da (synthesis)	41.7
Equilibrium valid?	No

ATP Rate Sweep

ATP Rate (s^-1)	Gap	Deviation (%)	Dilute Fluct
0	0.020	0.0	0.000
10	0.024	20.9	0.003
50	0.037	85.7	0.013
100	0.064	221.1	0.027
500	0.186	829.1	0.153
1,000	0.260	1,200.0	0.166
5,000	0.270	1,247.7	0.215

Critical Chi Corrections

System Size	χ_c	Shift
Equilibrium	0.651	---
N = 10,000	0.714	+0.062
N = 1,000	0.785	+0.133
N = 100	0.936	+0.285