Low Values of the Scheraga–Mandelkern β parameter for proteins. An explanation based on porous sphere hydrodynamics

Several globular proteins have values of the Scheraga–Mandelkern β parameter significantly below the theoretical minimum value, β₀ = 2.112 × 10⁶, for an impermeable sphere. Using the Felderhof–Deutch generalization of the Debye–Bueche–Brinkman theory of hydrodynamics of porous spheres, we have shown that values of β slightly below this supposed minimum are theoretically expected. A porous sphere of uniform density has a minimum β of 2.084 × 10⁶ at a Debye shielding ratio of 6.5, corresponding, for example, to a sphere radius of 11 Å and an inverse hydrodynamic shielding length of 0.6 Å^?1, values not far from those of small proteins. A two-layer porous sphere model gives similar results. Although this is the first theoretical explanation of values of β below β₀, the theory is incomplete since β values as low as 2.03 × 10⁶ are observed.