Solvent-induced forces

While evidence for hydration forces date back to early work on clays [1], the understanding of these solvent-induced forces was revolutionized by Horn and Israelachvili using the modem surface force apparatus. Here, for the first time, one had a direct measurement of the oscillatory forces between crossed mica cylinders immersed in a solvent, octamethylcyclotetrasiloxane (OMCTS) [67]. 

In order to apply this model to polyatomic solute/solvent systems a procedure for determining the effective diatomic(s) corresponding to the polyatomic solute of interest must be established. In the original work of Schweizer and Chandler (25), polyatomics were treated as a superposition of isolated diatomic bonds. This model completely ignores any shielding of solvent collisions by neighboring bonds in a polyatomic solute. Later studies have modeled the entire polyatomic solute as psuedo-diatomic whose "atoms represents polyatomic units on either side of the bond of interest (25,38). This approach, which is the one we adopt here, is believed to more realistically represent the solvent induced forces along a bond in a polyatomic molecule. 

San Biagio PL, Bulone D, Martorana V, Palma-Vittorelli MB, 49. Palma MU. Physics and biophysics of solvent induced forces hydrophobic interactions and context-dependent hydration. Euro. Biophys. J. 1998 27 183-196. 

This form is useful in the study of forces applied to solutes or to groups in proteins, in aqueous solutions. The first term is referred to as the direct force and the second term as the solvent-induced force. 

As in the case of pure liquids, the solvent-induced force can be attractive or repulsive even in regions where the direct force is negligible. An attractive force corresponds to a positive slope of W(R), or equivalently, to a negative slope of g(R). The locations of attractive and repulsive regions change when the composition of the system changes. Specifically, for xA lwe have the second peak of (R) at about <7 + <7 2. On the other hand, for > 0, the second peak of g iR) is at ss 2.5 Clearly, there are regions that are... 

P.L. San Biagio and M.U. Palma, Solvent-induced Forces and Fluctuations A Novel Comparison of Human Hemoglobin S and A. Comments Theor. Biol, 2,453-470,1992. 

Clearly, there are regions that are attractive for Xa 1 (say 2 < R < 2.5) but become repulsive at xa 0. Therefore when we change the composition of the system continuously, there are regions in which the two terms on the rhs of (6.4.2) produce forces in different directions. The result is a net diminishing of the overall solvent-induced force between the two tagged T-particles. This corresponds to the flattening of g R) or of W R) that we have observed in Fig. 6.4 at x. 0.65. 

The solvent-induced force should be compared with the indirect force of section (3.3.6). Here, we could formally take the gradient with respect to Ri of the integral in the denominator of (7.14.6). But because of the homogeneity of the system, the average force on particle 1 infinitely separated from particle 2 is zero. This is different from the result obtained in section 3.3 where we had two terms in the indirect force [Eq. (3.3.75)]. 

FIGURE 7.18. (a) Two solute particles at infinite separation 00. The solvent-induced force is zero since no water molecule can be simultaneously close to both solutes, (b) Two solutes at a short distance water molecule can be close to both solutes. Hence a solvent-induced force may be realized. 

The solvent-induced force between the two H0O solvatons is (sections 6.4 and 7.14)... 

We see that the work required to perform the same process in the liquid is almost three times larger than in vacuum. Thus the solvent deepens the minimum well. In terms of force we can say that, approaching the minimum at Ri 3.4 A, the solvent-induced force is attractive. It acts to enhance the attraction in that region (say between R 3.4 A and R 5 A). 

The solvent-induced forces operating between any two molecules were discussed in sections 6.4 and 7.14. Here we extend the treatment for two macromolecules, denoted by L and P. These could be two proteins, two DNA molecules, two membranes, or any two walls containing H0I groups on their surfaces. The emphasis here is on the origin of strong and relatively long-range forces induced specifically by water as a solvent. 

The solvent-induced forces are an order of magnitude more difficult to study than the direct forces. Here we need to take into account protein-solvent interactions as well as solvent-solvent interactions. 

As in the case of protein association, the solvent-induced forces can profoundly alter the specificity of the process. In the association process, we have seen how the solvent... 

This is essentially the same result as (7.14.14), except that here the condition R replaces the condition Ri, R2 in (7.14.14). The analysis of the various possible contributions to the solvent-induced force is therefore the same as we have performed in section 7.14. 

In order to obtain a large solvent-induced force we need both factors in the integrand to be large. This is obtained if the water exerts a strong force on 1 [i.e., ViG(Ri, X ) is large] and at the same time the condition R" produces a large excess local density of water molecules at Xy, (see section 7.14 for more details). 

If 1 is a H(f>0 group and the neighboring groups at are also H< 0, then both the force ViC/(Ri, X ) and the local density p(Xh/R 0 are expected to be normal. (By normal we mean here that the forces and the local densities are as in an a polar solvent.) In this case we cannot expect large solvent-induced forces. 

We therefore conclude that the strongest possible solvent-induced forces are expected to operate on H0I groups that also have in their environment H0I groups in appropriate locations and orientations to provide a large local density of solvent molecules (see Appendix D). 

In the simulation of molecules in aqueous solution, treatment of the solvent and solvent ions is particularly demanding both theoretically and computationally. Continuum or implicit solvent models provide a computationally efficient alternative to the inclusion of explicit solvent molecules. These models typically treat electrostatic and nonpolar contributions separately. A popular approach is to treat, respectively, the former with a continuum electrostatics model and the latter with a surface area model. These models often provide free energies and enthalpies to an accuracy that is comparable to, or better than, that of explicit solvent models, but with two or more orders of magnitude less computation. Other properties such as solvent induced forces, solvent structural features and specific hydrogen-bonding interactions are better treated with explicit solvent models... 

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