# Confinement Effects on the Kinetics and Thermodynamics of Protein Dimerization

### Wei Wang 1, Wei-Xin Xu 1, Y. Levy 2, E. Trizac 3, P. G. Wolynes 4

#### Proceedings of the National Academy of Sciences of the United States of America 106 (2009) 5517-5522

In the cell, protein complexes form relying on specific interactions between their monomers. Excluded volume effects due to molecular crowding would lead to correlations between molecules even without specific interactions. What is the interplay of these effects in the crowded cellular environment? We study dimerization of a model homodimer both when the mondimers are free or tethered to each other. We consider a structured environment: Two monomers first diffuse into a cavity of size $L$ and then fold and bind within the cavity. The folding and binding are simulated using molecular dynamics based on a simplified topology based model. The {\it confinement} in the cell is described by an effective molecular concentration $C \sim L^{-3}$. A two-state coupled folding and binding behavior is found. We show the maximal rate of dimerization occurred at an effective molecular concentration $C^{op}\simeq 1m$M which is a relevant cellular concentration. In contrast, for tethered chains the rate keeps at a plateau when $CC^{op}$. For both the free and tethered cases, the simulated variation of the rate of dimerization and thermodynamic stability with effective molecular concentration agrees well with experimental observations. In addition, a theoretical argument for the effects of confinement on dimerization is also made.

• 1. National Laboratory of Solid State Microstructure and Department of Physics,
Nanjing University
• 2. Department of Structural Biology,
Weizmann Institute
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Department of Chemistry and Biochemistry,
University of California at San Diego