(15)N-H-Related Conformational Entropy Changes Entailed By Plexin-B1 RBD Dimerization: Combined Molecular Dynamics/NMR Relaxation Approach

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. Sk (entropy in units of kBT) is given by - 2b(PeqlnPeq)d\u3a9, where Peq = 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)(\u3a9) and (D02(2)(\u3a9) + D0-2(2)(\u3a9)) (D0K(L)(\u3a9) 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, Sk is calculated. We find that in general Sk decreases, i.e., the local order increases, upon plexin-B1 RBD dimerization. The largest decrease in Sk occurs in the helices \u3b11 and \u3b12, followed by the \u3b12/\u3b26 turn. Only the relatively small peripheral \u3b22 strand, \u3b22/\u3b11 turn, and L3 loop become more disordered. That \u3b1-helices dominate \u394Sk = Sk(dimer) - Sk(monomer), a few peripheral outliers partly counterbalance the overall decrease in Sk, and the probability density function, Peq, 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 \u394Sk(MF) profiles are u-dependent and differ from \u394Sk(SRLS). A method that provides consistent, general, and accurate Sk, atomistic/mesoscopic in nature, has been developed. Its ability to provide new insights in protein research has been illustrated

¹⁵N–H-Related Conformational Entropy Changes Entailed By Plexin-B1 RBD Dimerization: Combined Molecular Dynamics/NMR Relaxation Approach

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. <i>S</i>_k (entropy in units of <i>k</i>_B<i>T</i>) is given by –∫(<i>P</i>_eqln<i>P</i>_eq)<i>d</i>Ω, where <i>P</i>_eq = exp­(−<i>u</i>) is the probability density for probe orientation, and <i>u</i> the local potential. Previous slowly relaxing local structure (SRLS) analyses of ¹⁵N–H relaxation in proteins determined linear combinations of <i>D</i>₀₀²(Ω) and (<i>D</i>₀₂²(Ω) + <i>D</i>_0–2²(Ω)) (<i>D</i>_0<i>K</i>^L(Ω) represents a Wigner rotation matrix element in uniaxial local medium) as “best-fit” form of <i>u</i>. 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 <i>u</i> thus in hand, <i>S</i>_k is calculated. We find that in general <i>S</i>_k decreases, i.e., the local order increases, upon plexin-B1 RBD dimerization. The largest decrease in <i>S</i>_k occurs in the helices α₁ and α₂, followed by the α₂/β₆ turn. Only the relatively small peripheral β₂ strand, β₂/α₁ turn, and L3 loop become more disordered. That α-helices dominate Δ<i>S</i>_k = <i>S</i>_k(dimer) – <i>S</i>_k(monomer), a few peripheral outliers partly counterbalance the overall decrease in <i>S</i>_k, and the probability density function, <i>P</i>_eq, has rhombic symmetry given that the underlying potential function, <i>u</i>, has rhombic symmetry, are interesting features. We also derive <i>S</i>² (the proxy of <i>u</i> 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 <i>u</i>. Ensuing Δ<i>S</i>_k(MF) profiles are <i>u</i>-dependent and differ from Δ<i>S</i>_k(SRLS). A method that provides consistent, general, and accurate <i>S</i>_k, atomistic/mesoscopic in nature, has been developed. Its ability to provide new insights in protein research has been illustrated

An SRLS Study of ²H Methyl-Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLC_γ1C SH2

The two-body (protein and probe) coupled-rotator slowly relaxing local structure (SRLS) approach for NMR relaxation in proteins is extended to derive conformational entropy, <i>Ŝ</i>. This version of SRLS is applied to deuterium relaxation from the C–CDH₂ bonds of free and peptide-bound PLC_γ1C SH2. Local C–CDH₂ motion is described by a correlation time for local diffusion, τ₂, and a Maier–Saupe potential, <i>u</i>. On average, τ₂, which largely fulfills τ₂ ≪ τ₁ (τ₁ - correlation time for global tumbling), is 270 ± 41 ps and <i>u</i> is 2 ± 0.1 <i>k</i>_B<i>T</i>. The PLC_γ1C SH2 data were analyzed previously with the model-free (MF) method. SRLS is a generalization of MF, assumed so far to yield the latter for τ₂ ≪ τ₁ and simple local geometry. Despite these conditions being fulfilled, we find here that τ₂ and <i>u</i> differ substantially from their MF counterparts. This is shown to stem from MF (a) disregarding mode-coupling of the first type (see below) and (b) parametrizing the methyl-moiety-related spectral density function (SDF). Our main interest lies in Δ<i>Ŝ</i>, the conformational entropy difference between the peptide-bound and free PLC_γ1C SH2 forms. We find that Δ<i>Ŝ</i> is rendered inaccurate in MF because factors a and b above impair the accuracy of <i>S</i>_axis, the parameter on which the calculation of Δ<i>Ŝ</i> is based. Conformational entropy was obtained previously using various simple system-specific models. SRLS is unique in obtaining this important thermodynamic quantity based on a general physically well-defined local potential. It is also unique in its ability to extract the information inherent in ²H relaxation parameters from methyl moieties in protein with accuracy commensurate with data sensitivity

Conformational Entropy from Slowly Relaxing Local Structure Analysis of ¹⁵N–H Relaxation in Proteins: Application to Pheromone Binding to MUP‑I in the 283–308 K Temperature Range

The slowly relaxing local structure (SRLS) approach is applied to ¹⁵N–H relaxation from the major urinary protein I (MUP-I), and its complex with pheromone 2-<i>sec</i>-butyl-4,5-dihydrothiazol. The objective is to elucidate dynamics, and binding-induced changes in conformational entropy. Experimental data acquired previously in the 283–308 K temperature range are used. The N–H bond is found to reorient globally with correlation time, τ_1,0, and locally with correlation time, τ_2,0, where τ_1,0 ≫ τ_2,0. The local motion is restricted by the potential <i>u</i> = −<i>c</i>₀²<i>D</i>₀₀², where <i>D</i>₀₀² is the Wigner rotation matrix element for <i>L</i> = 2, <i>K</i> = 0, and <i>c</i>₀² evaluates the strength of the potential. <i>u</i> yields straightforwardly the order parameter, ⟨<i>D</i>₀₀²⟩, and the conformational entropy, <i>S</i>_k, both given by <i>P</i>_eq = exp­(−<i>u</i>). The deviation of the local ordering/local diffusion axis from the N–H bond, given by the angle β, is also determined. We find that <i>c</i>₀² ≅ 18 ± 4 and τ_2,0 = 0<i>–</i>170 ps for ligand-free MUP-I, whereas <i>c</i>₀² ≅ 15 ± 4 and τ_2,0 = 20<i>–</i>270 ps for ligand-bound MUP-I. β is in the 0<i>–</i>10° range. <i>c</i>₀² and τ_2,0 decrease, whereas β increases, when the temperature is increased from 283 to 308 K. Thus, SRLS provides physically well-defined structure-related (<i>c</i>₀² and ⟨<i>D</i>₀₀²⟩), motion-related (τ_2,0), geometry-related (β), and binding-related (<i>S</i>_k) local parameters, and their temperature-dependences. Intriguingly, upon pheromone binding the conformational entropy of MUP-I decreases at high temperature and increases at low temperature. The very same experimental data were analyzed previously with the model-free (MF) method which yielded “global” (in this context, “relating to the entire 283–308 K range”) amplitude (<i>S</i>²) and rate (τ_e) of the local motion, and a phenomenological exchange term (<i>R</i>_ex). <i>S</i>² is found to decrease (implying implicitly “global” increase in <i>S</i>_k) upon pheromone binding

Polar Versus Non-polar Local Ordering at Mobile Sites in Proteins: Slowly Relaxing Local Structure Analysis of ¹⁵N Relaxation in the Third Immunoglobulin-Binding Domain of Streptococcal Protein G

We developed recently the slowly relaxing local structure (SRLS) approach for studying restricted motions in proteins by NMR. The spatial restrictions have been described by potentials comprising the traditional <i>L</i> = 2, <i>K</i> = 0, 2 spherical harmonics. However, the latter are associated with non-polar ordering whereas protein-anchored probes experience polar ordering, described by odd-<i>L</i> spherical harmonics. Here we extend the SRLS potential to include the <i>L</i> = 1, <i>K</i> = 0, 1 spherical harmonics and analyze ¹⁵N–¹H relaxation from the third immunoglobulin-binding domain of streptococcal protein G (GB3) with the polar <i>L</i> = 1 potential (coefficients <i>c</i>₀¹ and <i>c</i>₁¹) or the non-polar <i>L</i> = 2 potential (coefficients <i>c</i>₀² and <i>c</i>₂²). Strong potentials, with ⟨<i>c</i>₀¹⟩ ∼ 60 for <i>L</i> = 1 and ⟨<i>c</i>₀²⟩ ∼ 20 for <i>L</i> = 2 (in units of <i>k</i>_B<i>T</i>), are detected. In the α-helix of GB3 the coefficients of the rhombic terms are <i>c</i>₁¹ ∼ <i>c</i>₂² ∼ 0; in the preceding (following) chain segment they are ⟨<i>c</i>₁¹⟩ ∼ 6 for <i>L</i> = 1 and ⟨<i>c</i>₂²⟩ ∼ 14 for <i>L</i> = 2 (⟨<i>c</i>₁¹⟩ ∼ 3 for <i>L</i> = 1 and ⟨<i>c</i>₂²⟩ ∼ 7 for <i>L</i> = 2). The local diffusion rate, <i>D</i>₂, lies in the 5 × 10⁹–1 × 10¹¹ s^–1 range; it is generally larger for <i>L</i> = 1. The main ordering axis deviates moderately from the N–H bond. Corresponding <i>L</i> = 1 and <i>L</i> = 2 potentials and probability density functions are illustrated for residues A26 of the α-helix, Y3 of the β₁-strand, and L12 of the β₁/β₂ loop; they differ considerably. Polar/orientational ordering is shown to be associated with GB3 binding to its cognate Fab fragment. The polarity of the local ordering is clearly an important factor

Electron-spin relaxation and ordering in smectic and supercooled nematic liquid crystals

We report on careful line shape studies of slow motional and orientation dependent ESR spectra of a deuterated liquid\u2010crystal\u2010like spin probe dissolved in a benzilidene\u2010derivative (40,6) and in cyanobiphenyl derivative (S2 and 5CB) liquid crystals. The simulation of the ESR spectra is based on the Lanczos algorithm recently applied by Moro and Freed in a general and efficient formulation of slow motional and ordering effects on ESR line shapes. With 40,6 which exhibits monolayer smectic phases, we find that the main change in the spin relaxation upon passing from the nematic to the smectic A phase consists of changes occuring in ordering attributable to packing forces on functional groups. Such ordering effects appear to be further enhanced in the SB phase with consequent alterations in dynamics. With S2, which exhibits an interpenetrating bilayer smectic A phase, we find unusual ESR spectra in that phase which may be simulated on the basis of a model of cooperative distortions static on the ESR time scale, and superimposed on individual molecular reorientation. This mode is interpreted as a collective chain distortion which affects the orientational distribution of the piperidine ring of the spin probe. A similar phenomenon is observed in the supercooled nematic phase of 5CB, which is aligned by an electric field, and evidence is also found that the reorientational dynamics of this ring are affected by interaction with local cooperative modes in the liquid crystal (i.e., a SRLS mechanism previously proposed by Freed and co\u2010workers). Some microscopic characteristics of liquid crystals revealed by this and previous ESR spin probe studies are discussed