## Abstract

We report on a new method for determining function-related conformational entropy changes in proteins. Plexin-B1 RBD dimerization serves as example, and internally mobile N-H bonds serve as probes. S_{k} (entropy in units of k_{B}T) is given by -∫(P_{eq}lnP_{eq})dΩ, where P_{eq} = exp(-u) is the probability density for probe orientation, and u the local potential. Previous slowly relaxing local structure (SRLS) analyses of ^{15}N-H relaxation in proteins determined linear combinations of D00^{2}(Ω) and (D02_{2}(Ω) + D0-2^{2}(Ω)) (D0K_{L}(Ω) represents a Wigner rotation matrix element in uniaxial local medium) as "best-fit" form of u. SRLS also determined the "best-fit" orientation of the related ordering tensor. On the basis of this information the coefficients (in the linear combination) of the terms specified above are determined with molecular dynamics (MD) simulations. With the explicit expression for u thus in hand, S_{k} is calculated. We find that in general S_{k} decreases, i.e., the local order increases, upon plexin-B1 RBD dimerization. The largest decrease in S_{k} occurs in the helices α_{1} and α_{2}, followed by the α_{2}/β_{6} turn. Only the relatively small peripheral β_{2} strand, β_{2}/α_{1} turn, and L3 loop become more disordered. That α-helices dominate ΔS_{k} = S_{k}(dimer) - S_{k}(monomer), a few peripheral outliers partly counterbalance the overall decrease in S_{k}, and the probability density function, P_{eq}, has rhombic symmetry given that the underlying potential function, u, has rhombic symmetry, are interesting features. We also derive S^{2} (the proxy of u in the simple "model-free (MF)" limit of SRLS) with MD. Its conversion into a potential requires assumptions and adopting a simple axial form of u. Ensuing ΔS_{k}(MF) profiles are u-dependent and differ from ΔS_{k}(SRLS). A method that provides consistent, general, and accurate S_{k}, atomistic/mesoscopic in nature, has been developed. Its ability to provide new insights in protein research has been illustrated.

Original language | English |
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Pages (from-to) | 3007-3015 |

Number of pages | 9 |

Journal | Journal of Physical Chemistry B |

Volume | 121 |

Issue number | 14 |

DOIs | |

State | Published - 13 Apr 2017 |

### Bibliographical note

Publisher Copyright:© 2017 American Chemical Society.

### Funding

This work was supported by the Israel Science Foundation (Grant No. 369/15 to E.M.). Part of this work was carried out by Dr. Mirco Zerbetto at Case Western Reserve University, Cleveland, OH, in the group of Prof. Matthias Buck; his hospitality is gratefully acknowledged. We acknowledge fruitful discussions with Prof. Buck, and Prof. Antonino Polimeno of the University of Padova.

Funders | Funder number |
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Università degli Studi di Padova | |

Israel Science Foundation | 369/15 |

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