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Entropy Calculation of HIV-1 Env gp120, its Receptor CD4, and their Complex: An Analysis of Configurational Entropy Changes upon Complexation

Shang-Te D. Hsu ^*, Christine Peter , Wilfred F. van Gunsteren  and Alexandre M. J. J. Bonvin ^*

^* Bijvoet Center for Biomolecular Research, Utrecht University, Utrecht, The Netherlands; and Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, Zürich, Switzerland

Correspondence: Address reprint requests to Alexandre M. J. J. Bonvin, Tel.: 31-30-253-3859; Fax: 31-30-253-7623; E-mail: a.m.j.j.bonvin{at}chem.uu.nl.

The HIV-1 gp120/CD4 interaction shows a large, unprecedented entropy/enthalpy compensation, with the capacity to fine-tune recognition over a broad range of affinity. The intermolecular interaction involves stable hydrophobic contacts with a unique protruding CD4-Phe⁴³ structure surrounded by an intermolecular hydrogen-bond network that covers the hemisphere of the CD4 D1 domain. We have applied a heuristic formula based on the covariance matrix of atom-positional fluctuations to assess the configurational entropy of the gp120/CD4 complex at different levels. The system was dissected into various subsets of atoms to evaluate the entropic contributions of different functional elements. By combining the trajectories of the free and complex forms, further insight into the conformational sampling was extracted. Despite the limited sampling time of 10 ns, the theoretically derived changes in configurational entropy are in fair agreement with the experimentally determined data. The simultaneous evaluation of different interaction modes through a decomposition approach is only feasible with the knowledge of the atomic trajectory of the system. The configurational entropy analysis in terms of combined trajectories presented here shall potentially provide accurate estimations of thermodynamic properties of biomolecules given sufficient sampling of conformational space.