36 research outputs found
(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
<sup>15</sup>NāH-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 NāH bonds serve as probes. <i>S</i><sub>k</sub> (entropy in units of <i>k</i><sub>B</sub><i>T</i>) is given by āā«(<i>P</i><sub>eq</sub>ln<i>P</i><sub>eq</sub>)<i>d</i>Ī©, where <i>P</i><sub>eq</sub> = expĀ(ā<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 <sup>15</sup>NāH relaxation in proteins determined linear combinations
of <i>D</i><sub>00</sub><sup>2</sup>(Ī©) and (<i>D</i><sub>02</sub><sup>2</sup>(Ī©) + <i>D</i><sub>0ā2</sub><sup>2</sup>(Ī©))
(<i>D</i><sub>0<i>K</i></sub><sup>L</sup>(Ī©) represents a Wigner rotation matrix element
in uniaxial local medium) as ābest-fitā form of <i>u</i>. SRLS also determined the ābest-fitā 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><sub>k</sub> is calculated. We find that in general <i>S</i><sub>k</sub> decreases, i.e., the local order increases, upon plexin-B1
RBD dimerization. The largest decrease in <i>S</i><sub>k</sub> occurs in the helices Ī±<sub>1</sub> and Ī±<sub>2</sub>, followed by the Ī±<sub>2</sub>/Ī²<sub>6</sub> turn. Only
the relatively small peripheral Ī²<sub>2</sub> strand, Ī²<sub>2</sub>/Ī±<sub>1</sub> turn, and L3 loop become more disordered.
That Ī±-helices dominate Ī<i>S</i><sub>k</sub> = <i>S</i><sub>k</sub>(dimer) ā <i>S</i><sub>k</sub>(monomer), a few peripheral outliers partly counterbalance
the overall decrease in <i>S</i><sub>k</sub>, and the probability
density function, <i>P</i><sub>eq</sub>, has rhombic symmetry
given that the underlying potential function, <i>u</i>,
has rhombic symmetry, are interesting features. We also derive <i>S</i><sup>2</sup> (the proxy of <i>u</i> in the simple
āmodel-free (MF)ā limit of SRLS) with MD. Its conversion
into a potential requires assumptions and adopting a simple axial
form of <i>u</i>. Ensuing Ī<i>S</i><sub>k</sub>(MF) profiles are <i>u</i>-dependent and differ
from Ī<i>S</i><sub>k</sub>(SRLS). A method that provides
consistent, general, and accurate <i>S</i><sub>k</sub>,
atomistic/mesoscopic in nature, has been developed. Its ability to
provide new insights in protein research has been illustrated
An SRLS Study of <sup>2</sup>H Methyl-Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLC<sub>Ī³</sub>1C 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>SĢ</i>. This
version of SRLS is applied to deuterium relaxation from the CāCDH<sub>2</sub> bonds of free and peptide-bound PLC<sub>Ī³</sub>1C SH2.
Local CāCDH<sub>2</sub> motion is described by a correlation
time for local diffusion, Ļ<sub>2</sub>, and a MaierāSaupe
potential, <i>u</i>. On average, Ļ<sub>2</sub>, which
largely fulfills Ļ<sub>2</sub> āŖ Ļ<sub>1</sub> (Ļ<sub>1</sub> - correlation time for global tumbling), is 270 Ā± 41
ps and <i>u</i> is 2 Ā± 0.1 <i>k</i><sub>B</sub><i>T</i>. The PLC<sub>Ī³</sub>1C 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 Ļ<sub>2</sub> āŖ
Ļ<sub>1</sub> and simple local geometry. Despite these conditions
being fulfilled, we find here that Ļ<sub>2</sub> 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 Ī<i>SĢ</i>, the conformational entropy difference between the peptide-bound
and free PLC<sub>Ī³</sub>1C SH2 forms. We find that Ī<i>SĢ</i> is rendered inaccurate in MF because factors a
and b above impair the accuracy of <i>S</i><sub>axis</sub>, the parameter on which the calculation of Ī<i>SĢ</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 <sup>2</sup>H relaxation parameters from methyl moieties
in protein with accuracy commensurate with data sensitivity
Conformational Entropy from Slowly Relaxing Local Structure Analysis of <sup>15</sup>NāH Relaxation in Proteins: Application to Pheromone Binding to MUPāI in the 283ā308 K Temperature Range
The slowly relaxing
local structure (SRLS) approach is applied to <sup>15</sup>NāH
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
283ā308 K temperature range are used. The NāH bond is
found to reorient globally with correlation time, Ļ<sub>1,0</sub>, and locally with correlation time, Ļ<sub>2,0</sub>, where
Ļ<sub>1,0</sub> ā« Ļ<sub>2,0</sub>. The local motion
is restricted by the potential <i>u</i> = ā<i>c</i><sub>0</sub><sup>2</sup><i>D</i><sub>00</sub><sup>2</sup>, where <i>D</i><sub>00</sub><sup>2</sup> is the Wigner rotation matrix element for <i>L</i> = 2, <i>K</i> = 0, and <i>c</i><sub>0</sub><sup>2</sup> evaluates the
strength of the potential. <i>u</i> yields straightforwardly
the order parameter, āØ<i>D</i><sub>00</sub><sup>2</sup>ā©, and the conformational
entropy, <i>S</i><sub>k</sub>, both given by <i>P</i><sub>eq</sub> = expĀ(ā<i>u</i>). The deviation of
the local ordering/local diffusion axis from the NāH bond,
given by the angle Ī², is also determined. We find that <i>c</i><sub>0</sub><sup>2</sup> ā
18 Ā± 4 and Ļ<sub>2,0</sub> = 0<i>ā</i>170 ps for ligand-free MUP-I, whereas <i>c</i><sub>0</sub><sup>2</sup> ā
15 Ā±
4 and Ļ<sub>2,0</sub> = 20<i>ā</i>270 ps for
ligand-bound MUP-I. Ī² is in the 0<i>ā</i>10Ā°
range. <i>c</i><sub>0</sub><sup>2</sup> and Ļ<sub>2,0</sub> decrease, whereas
Ī² increases, when the temperature is increased from 283 to 308
K. Thus, SRLS provides physically well-defined structure-related (<i>c</i><sub>0</sub><sup>2</sup> and āØ<i>D</i><sub>00</sub><sup>2</sup>ā©), motion-related (Ļ<sub>2,0</sub>), geometry-related (Ī²), and binding-related (<i>S</i><sub>k</sub>) 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 āglobalā (in this
context, ārelating to the entire 283ā308 K rangeā)
amplitude (<i>S</i><sup>2</sup>) and rate (Ļ<sub>e</sub>) of the local motion, and a phenomenological exchange term (<i>R</i><sub>ex</sub>). <i>S</i><sup>2</sup> is found
to decrease (implying implicitly āglobalā increase in <i>S</i><sub>k</sub>) upon pheromone binding
Polar Versus Non-polar Local Ordering at Mobile Sites in Proteins: Slowly Relaxing Local Structure Analysis of <sup>15</sup>N 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 <sup>15</sup>Nā<sup>1</sup>H relaxation from the
third immunoglobulin-binding domain of streptococcal protein G (GB3)
with the polar <i>L</i> = 1 potential (coefficients <i>c</i><sub>0</sub><sup>1</sup> and <i>c</i><sub>1</sub><sup>1</sup>) or the non-polar <i>L</i> = 2 potential (coefficients <i>c</i><sub>0</sub><sup>2</sup> and <i>c</i><sub>2</sub><sup>2</sup>). Strong potentials, with āØ<i>c</i><sub>0</sub><sup>1</sup>ā© ā¼
60 for <i>L</i> = 1 and āØ<i>c</i><sub>0</sub><sup>2</sup>ā© ā¼
20 for <i>L</i> = 2 (in units of <i>k</i><sub>B</sub><i>T</i>), are detected. In the Ī±-helix of
GB3 the coefficients of the rhombic terms are <i>c</i><sub>1</sub><sup>1</sup> ā¼ <i>c</i><sub>2</sub><sup>2</sup> ā¼ 0; in the preceding (following) chain segment they are
āØ<i>c</i><sub>1</sub><sup>1</sup>ā© ā¼ 6 for <i>L</i> =
1 and āØ<i>c</i><sub>2</sub><sup>2</sup>ā© ā¼ 14 for <i>L</i> = 2 (āØ<i>c</i><sub>1</sub><sup>1</sup>ā© ā¼ 3 for <i>L</i> =
1 and āØ<i>c</i><sub>2</sub><sup>2</sup>ā© ā¼ 7 for <i>L</i> =
2). The local diffusion rate, <i>D</i><sub>2</sub>, lies
in the 5 Ć 10<sup>9</sup>ā1 Ć 10<sup>11</sup> s<sup>ā1</sup> range; it is generally larger for <i>L</i> = 1. The main ordering axis deviates moderately from the NāH
bond. Corresponding <i>L</i> = 1 and <i>L</i> =
2 potentials and probability density functions are illustrated for
residues A26 of the Ī±-helix, Y3 of the Ī²<sub>1</sub>-strand,
and L12 of the Ī²<sub>1</sub>/Ī²<sub>2</sub> 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