TABLE I.

Knotting and unknotting as a function of juxtaposition geometry. 𝒥(j)’s are fractions of segment-passage events via a given juxtaposition geometry j that resulted in various transitions among unknotted (U) and knotted (K) states, computed for 3.5 kb DNA circles under ionic strength [NaCl] = 0.154 M in our model. R_K is the knot reduction factor.

Juxtaposition (j)		${𝒥}_{U\to U}^{(j)}$	${𝒥}_{U\to K}^{(j)}$	${𝒥}_{K\to U}^{(j)}$	${𝒥}_{K\to K}^{(j)}$	RK
	hooked	0.858	0.0028	0.1370	0.0023	48.9
	half-hooked	0.914	0.0077	0.0761	0.0025	9.8
	straight	0.954	0.0240	0.0198	0.0021	0.82
	free	0.894	0.1014	0.0027	0.0022	0.027