Table 1.

Parameters of Exchange and Dynamics Describing the Interactions of K63- and K48-Linked Ub₂ with LUV and SUV Liposomes at pH 6.8, 25°C and 1:2 Ubiquitin/Lipid Molar Ratio^a,b

	K63-linked Ub2		K48-linked Ub2
parameters	distal	proximal	distal	proximal
$k_{\text{on}}^{\text{app},\text{LUV}}({\mathrm{s}}^{-1})$	21	18	14	13
$k_{\text{on}}^{\text{app},\text{SUV}}({\mathrm{s}}^{-1})$	197–211	116–144	195–239	162–210
koff × 103 (s−1)	32 ±1	40 ±1	36 ±1	55 ± 3
$p_{\mathrm{B}}^{\text{LUV}}(\%)$ c	0.07	0.04	0.04	0.02
$p_{\mathrm{B}}^{\text{SUV}}(\%)$ c	0.65 ± 0.03	0.32 ± 0.04	0.58 ± 0.07	0.35 ± 0.05
${\tau }_{\mathrm{C}}^{\text{LUV}}(\mu \mathrm{s})$ c	25.2 ± 0.8	21.0 ± 0.4	22.5 ± 0.9	16.0 ± 0.8
${\tau }_{\mathrm{C}}^{\text{SUV}}(\mu \mathrm{s})$ c	1.9 ± 0.2	1.9 ± 0.2	1.9 ± 0.2	1.8 ± 0.2
τr (μs)	0.4–0.6	0.4–1.0	1.2–2.0	0.6–1.4
θ (deg)d	102.7 ± 0.7	98.4 ± 0.9	103.9 ± 0.8	93.5 ± 1.2
φ (deg)d	−5.3 ± 0.7	−13.7 ± 0.7	−5.1 ± 0.9	−13.7 ± 1.0
$F_{\text{LUV}}^{\text{iso}}({\mathrm{s}}^{-1})$	1.3 ± 0.1	1.7 ± 0.1	2.1 ± 0.1	1.9 ± 0.1
$F_{\text{SUV}}^{\text{iso}}({\mathrm{s}}^{-1})$	1.3–2.0	1.7–3.0	2.1–4.3	1.9–3.4
RSUVe	4.2	4.1	2.6	3.7

^aAll reported the values are obtained with $S_{\mathrm{w}}^2$ and τ_w fixed at 0.5 and 300 ns, respectively; throughout, the upper bounds reported for $F_{\text{SUV}}^{\text{iso}}$ correspond to the lower bounds for $k_{\text{on}}^{\text{app},\text{SUV}}$ and τ_r values in Ub₂ domains (see the text for details).

^bFor comparison, the values of $k_{\text{on}}^{\text{app},\text{LUV}},k_{\text{on}}^{\text{app},\text{SUV}}$, k_off, τ_r, θ, and φ for Ub₁ are 27 s⁻¹, 347 ± 14 s⁻¹, 52(±1.9) × 10³ s⁻¹, 1.5 ± 0.2 μs, 108.4 ± 1.1°, and −2.5 ± 1.1°, respectively.

^cUncertainties in these parameter values are propagated considering only the uncertainties in k_off. Uncertainties in the values of $p_{\mathrm{B}}^{\text{LUV}}$ are equal to ~0.002.

^dPolar angles θ and φ are specified in the coordinate system of the inertia tensor of ubiquitin (PDB accession code 1ubq).

^eCalculated for Ub₂–SUV complexes using the experimental values of ΔR_2,SUV and the upper bounds of the fitted $F_{\text{SUV}}^{\text{iso}}$ values.