An SRLS Study of 2H Methyl-Moiety Relaxation and Related

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Article 2

An SRLS Study of H Methyl-Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLC1C SH2 #

Oren Tchaicheeyan, and Eva Meirovitch J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08264 • Publication Date (Web): 13 Sep 2016 Downloaded from http://pubs.acs.org on September 13, 2016

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The Journal of Physical Chemistry

Figure 1. Ribbon diagram of PLCγ1C SH2 bound to the peptide Y1021, according to PDB accession code 2ple. 593x532mm (96 x 96 DPI)

ACS Paragon Plus Environment


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3

T17

A21

A33

V36’

A14

c

I81’

I55

L95’

a

A19

2.5 2 0

A46 A51

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L25

V28

2

L35 L16 I55’

1.5

I99’ M93

A5

M24

1

M26

M68

L16

800 τ2 , ps 600

L95 A51 L35

A21 A19

400

V60 T66

V67’ V78

A33 L25

200

A14 A5

00

b

V28 L95’

T17

V36’ M24

M26

I55’ A46

M68

I81’

M93

I99’

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

methyl ACS Paragon Plus Environment

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Saxis

free

a

peptide-bound

c

0.8

S 20 0.4

Saxis 13

S20

0

0

d

b

400 τ 2, ps τ2, ps τ e, ps 200

methyl



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a

free SH2

0.8 2

9 (S 02 )

0.4 2 Saxis

0

b

SH2/peptide complex

0.8 2

9 ( S 02 )

∆

0.4 2 Saxis

0 L35

L35’ V36 A46

L95

0.1

9 ( S 20 )

∆S

M93

2

0

2 axis

c

V67

V67’ L69

L77

V36’ T66

L95’ L69’ L77’

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45


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∆ (S )

2 2 0

I81g2

free-bound

a

0

∆ 9(S 02 ) 2

T17

-0.1 2 ∆ Saxis

L95d1

V60g2

55.6 kHz 167 kHz

V36 L35

L35’

b

bound-free

0

∆S u(SRLS) u(cone)

-0.5

S axis (cone)

-1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45



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0.05

M68

-T∆S = -0.3 kJ mol -1

L16d1

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I81g2 L80d2

-T∆S = -3.2 kJ mol

-1

∆S

L89d2

A21 L89d1

L69d2 L77d2 V60g1 T66

0 A5 A14

L77d1 L69d1

M24 M26 V28g2 A33

A19

I55g2 I47d1

L25d1

-0.05

V67g2 V67g1

A51

V36g2 T17

V78g1 I81d1 L95d2

V78g2 L80d1

V28g1 M93

-0.1

I99d1

I55d1

V36g1

V60g2

L95d1

A46

L35d1

-0.15

L35d2

0 1 2 3 4 5 6 7 8 9 10 1112 1314 15 16 17 18 19 20 2122 2324 25 26 27 28 29 30 3132 3334 3536 37 38 39 40 4142 43 44 4546 47


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An SRLS Study of 2H Methyl-Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLCγ1C SH2

Oren Tchaicheeyan and Eva Meirovitch*

The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, RamatGan 52900 Israel

*Corresponding author: [email protected], phone: 972-3-531-8049

1



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Abstract 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, 𝑆. This version of SRLS is applied to deuterium relaxation from the C−CDH2 bonds of free and peptide-bound PLC 1C SH2. Local C−CDH2 motion is described by a γ

τ2, and a Maier-Saupe potential, u. On average τ2, which largely fulfills τ2 0.01 the SRLS global-motional eigenvalue digresses from 6×D1/D2 and the SRLS global-motional weighting factor digresses from (𝑆3) )) . This is a consequence of mode-coupling of the 2nd-type also coming into play. Interestingly, the global motion is being slowed down and its relative weight is increased; this is consistent with it and the main local-motional eigenmode rotating in opposite sense. On the other hand, the main local-motional eigenvalue is increased and its relative weight is decreased; this is consistent with it being coupled dynamically not only to the global-motional eigenmode but also to the fast eigenmodes included in the 𝐽1tu QvwxK term. For a time-scale separation of 0.1 Table 1 shows that ignoring mode-coupling of both types implies 9% (4.3%) overestimation (underestimation) of the SRLS global (local) motional eigenvalue and 2.3% (25%) underestimation (overestimation) of the 15



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SRLS global (local) motional weighting factor by the respective MF counterparts. These are substantial differences.

3.1.2. Medium-strength local ordering. We generate Table 2 by analogy with Table 1. A medium-strength potential given by 𝑐3) = 6.58, which corresponds to (𝑆3) )) = 0.7, is used as example. For 𝐷1 𝐷) = 0.003 the SRLS global-motional eigenmode (SRLS, GLOBAL) is the same as its MF counterpart (MF, GLOBAL). For 0.003 < 𝐷1 𝐷) ≤ 0.01 the SRLS 6 × 𝐷1/𝐷2 whereas the SRLS weighting factor is 1.4% smaller than (𝑆02)2. For single calculations this is negligible; however, within the scope of data-fitting considerable inaccuracies are likely to emerge. Let us focus on the local motion. Although a main local-motional eigenmode can be identified already for 𝐷1 𝐷) = 0.003 (SRLS, LOCAL), it differs substantially from its MF counterpart given by egv = 6×𝑐3) /2 and wt = [1 − (𝑆3) )) ] (MF, LOCAL). The SRLS eigenvalue (weighting factor) is overestimated by ~15% (30%) by MF. This scenario persists throughout the parameter range of 0.003 ≤ 𝐷1 𝐷) ≤ 0.01. Additional fast local-motional eigenmodes (denoted 𝐽1tu QvwxK in eq 6) contribute 6−7% (columns denoted “local”). For 𝐷1 𝐷) = 0.01 Table 1 shows that the fractional contribution of the local motion is 0.14 with 93% provided by the main local-motional eigenmode whereas Table 2 shows that the fractional contribution of the local motion is 0.29 with 79% provided by the main local-motional eigenmode. Table 2. Eigenmode composition of the SRLS & MF time correlation functions for

16


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𝒄𝟐𝟎 = 𝟔. 𝟓𝟖 and 𝑫𝟏 𝑫𝟐 as shown. SRLS GLOBAL

MF

LOCAL

local

GLOBAL

LOCAL

𝐷1 𝐷)

egv

wt

egv

wt

egv

wt

egv

wt

egv

wt

egv

wt

egv

wt

0.003

0.02

0.70

17.0

0.23

29.6

0.04

32.9

0.02

16.0

0.01

0.02

0.70

19.7

0.30

0.008

0.05

0.71

17.1

0.23

29.8

0.04

33.1

0.01

16.1

0.01

0.05

.

.

.

0.01

0.06

0.71

17.2

0.23

29.8

0.04

33.2

0.01

16.1

0.01

0.06

.

.

.

0.02

0.12

0.71

17.4

0.22

30.0

0.04

16.3

0.02

33.5

0.01

0.12

.

.

.

0.1

0.55

0.74

19.2

0.16

17.9

0.05

31.7

0.03

−

−

0.60

.

.

.

0.2

1.01

0.78

21.6

0.10.

19.7

0.08

34.0

0.03

−

−

1.20

.

.

.

Some of the mixed eigenmodes in Table 2 have larger eigenvalues (i.e., are faster), whereas others have smaller eigenvalues (i.e., are slower) than the renormalized

τren = 19.7. Eigenmodes with faster eigenvalues are consistent with protein and probe rotating in the same sense whereas eigenmodes with slower eigenvalues are consistent with protein and probe rotating in opposite sense. This is an intriguing manifestation of the manner in which the mixed modes of the 1st-type reorient “more with respect to the protein than with respect to the lab frame”.33 For 𝐷1 𝐷) > 0.01 mode-coupling of the 2nd-type also comes into play. Probe dynamics is an intricate process in this case. Table 2 (by itself and in comparison with Table 1) indicates that SRLS and MF differ substantially for local ordering of medium- strength even when the time-scale 17



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separation is very large. Clearly, MF does not describe such scenarios with sufficient accuracy. This important assessment cannot be deduced from the mathematical theory of moments, which underlines eq 7. 3.1.3. Weak local ordering. Table 3 shows the results of SRLS calculations carried out for 𝑐3) = 1.38, which corresponds to (𝑆3) )) = 0.094, as example of weak potential.

τe = 50 ps methyl group I81γ ;11 with D1 = 2.56×107 𝑠−1 (ref 11) one has 𝐷1𝐷2=0.008. 2

𝑐02 = 1.38 and τ2 = 50 ps appear in the columns of Table 3 denoted “SRLS”. The parameter values selected suit the methionine groups of free and peptide-bound PLCg1C SH2 analyzed with SRLS (cf. Figure 2 below). The global-motional SRLS eigenmode (SRLS, GLOBAL) is the same for 0.008 ≤ 𝐷1 𝐷) ≤ 0.02. It has egv = 6× 𝐷1 𝐷) and wt = 0.1. The corresponding MF eigenmodes (MF, GLOBAL) have egv = 6× 𝐷1 𝐷) and wt = 0.09. Thus, for 𝑐3) = 1.38 the global-motional weighting factor is underestimated by MF by 10% already for 𝐷1 𝐷) = 0.003; this setup persists up to 𝐷1 𝐷) = 0.02. Table 3. Eigenmode composition of the SRLS & MF time correlation functions for 𝒄𝟐𝟎 = 𝟏. 𝟑𝟖 and 𝑫𝟏 𝑫𝟐 as shown*. SRLS GLOBAL

MF

LOCAL

local

GLOBAL

LOCAL

𝐷1 𝐷)

egv

wt

egv

wt

egv

wt

egv

wt

egv

wt

egv

wt

egv

wt

0.003

0.02

0.10

6.12

0.41

5.64

0.25

7.57

0.23

19.6

0.01

0.02

0.09

6

0.91

0.008

0.05

0.10

6.17

0.36

5.69

0.31

7.60

0.22

19.7

0.01

0.05

.

.

.

0.01

0.06

0.10

6.20

0.34

5.71

0.33

7.61

0.21

19.7

0.01

0.06

.

.

.

18


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0.02

0.12

0.10

5.79

0.43

6.34

0.26

7.67

0.20

19.8

0.02

0.12

.

.

.

0.1

0.59

0.12

6.08

0.69

7.59

0.12

8.31

0.06

20.3

0.02

0.60

.

.

.

0.2

1.15

0.14

6.28

0.75

8.51

0.09

20.9

0.02

−

−

1.20

.

.

.

*The best-fit MF parameters for methyl group I81γ2 of the PLC 1C SH2 bound to pY1021 are 𝑆£¤¥¦ ) = γ

𝑆02)2 = 19×0.85= 0.094 and D2 = 1/(6×0.05×109) 𝑠−1 = 3.3×109 𝑠−1 in SRLS. Given that τm = 6.5 ns, i.e., D1 = 2.56×10§ 𝑠 Q1 , the time-scale separation is in this case 𝐷1 𝐷) = 0.008.

For 𝐷1 𝐷) ≤ 0.02 one can distinguish three local-motional eigenmodes (SRLS, LOCAL) which dominate the contribution of the local motion to the SRLS TCF. Let us examine in greater detail the representative 𝐷1 𝐷) = 0.01

scenario. The three

eigenvalues are 6.20, 5.71 and 7.61 and the respective weighting factors are 0.34, 0.33 and 0.21 (combined weight of 0.88). There is an additional fast local-motional eigenmode with egv ~ 20 contributing 1%. This setup exists already for D1/D2 = 0.003; it persists up to 𝐷1 𝐷) = 0.02. One may envision the free-diffusion eigenmode with egv = 6 and wt = 0.9 being “split” into three eigenmodes with egv on the order of 6 and wt on the order of z{. Three

𝐷2,|| and 𝐷2,⊥ of a free-diffusion eigenmode become slightly different. In that case the underlying phenomenon is lowering of symmetry of the local diffusion tensor from spherical to axial; in this case it is mode-coupling. The MF analogue of this intricate local-motional setup is a single eigenmode with 1

eigenvalue 1/τe and weighting factor [1 − (𝑆3) )) ] = [1 − (𝑆%&'( )) ] (MF, LOCAL). The P

global motional weighting factor, which is a particularly important factor in the data19



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fitting process, is underestimated by MF by 10% already for D1/D2 < 0.003. In view of these findings substantial discrepancies between SRLS and MF are likely to emerge within the scope of data-fitting − see Application section. For 𝐷1 𝐷) > 0.02 all of the SRLS eigenmodes are affected by mode-coupling of the 1st-type, as well as mode-coupling of the 2nd-type.

3.2. Application We present below our SRLS analysis of 2H methyl-moiety relaxation in free and pY1021-bound PLC 1C SH2. The experimental data were analyzed with χ2/df (where df γ

denotes the number of degrees of freedom) below 0.05 critical value. C−CDH2 dynamics was analyzed using the partially-averaged quadrupole constant 𝑄 = 55.6 kHz. C−D dynamics was also analyzed and used for specific purposes (see below); in this case 𝑄 = 167 kHz8,43 was used. The SRLS results are rationalized in the light of the predictions emerging from section 3.1, as well as the known structural features of the PLC 1C SH2/peptide binding γ

sites. A pTyr binding-site comprising the BC loop (residues R39−S44) as key element, and a hydrophobic binding-site comprising the EF loop (residues G70 and N71) and the BG loop (residues L89−R96) as key elements,10,11 (Figure 1) are involved in the peptidebinding process.

Experimental data. 15H T1 and T1 of PLC 1C SH2 free and bound to the peptide ρ

γ

pY1021, acquired at 11.7 and 14.1 T and 303 K,11 are shown in Figure S2 of the SI.

20


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Global diffusion. All of the 2H relaxation data were analyzed with SRLS with very good statistics allowing 𝑐3) and D2 to vary, with τ1 fixed at 7.7 ns for free PLC 1C γ

SH2 and at 6.5 ns for peptide-bound PLC 1C SH2. These correlation times were taken γ

from ref 11, where it is indicated that the monomer-dimer exchange in the free PLC 1C γ

SH2 sample (which prevailed in the samples of ref 10) was largely suppressed, with the monomer dominating. The global motional correlation time, 𝜏1 , was determined with 15

N−H relaxation from the very same sample, in particular using 15N T1/T2 ratios, where

T1 (T2) denotes the longitudinal (transverse)

15

N relaxation time.44 To account for

eventual imperfections associated with imprecision in 𝜏1 determination, we increased the errors on the best-fit parameters by 10% relative to the SRLS-analysis-related errors.

SRLS analysis. C−CDH2 dynamics. Figure 2 shows the local potential strength (𝑐3) ), and the τ2), associated with C−CDH2 bond dynamics. The x-axis in Figure 2a depicts the

experimentally accessible methyl groups as they appear along the protein sequence. The γ2 methyl of valine, the δ2 methyl of leucine and the δ1 methyl of isoleucine are denoted with a “prime” symbol. Note that the δ1 methyl of Ile appears before the γ2 methyl. The notation depicted in this figure also applies to Figures 2b and 3−6. Figure 2a shows 𝑐3) of free (red) and peptide-bound (black) PLC 1C SH2 obtained γ

with SRLS analysis of C−CDH2 dynamics. The potential coefficients lie in the 1−3 range. The error, estimated at 5%, is about twice the symbol size. As expected based on side21



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chain length, the alanines (except for A5, which belongs to a flexible end-chain segment) are associated with stronger potentials than the methionines. Several additional methyl groups, including T17, Vγ236, Iγ281, Lδ195 and Lδ295, are also associated with stronger local potentials. The local potential is considerably stronger in peptide-bound PLC 1C SH2 as γ

compared to free PLC 1C SH2 in the vicinity of the BC loop (residues R39−S44) of the γ

pTyr binding-site. The same trend is observed for residues M93, L95δ1 and L95δ2 of the BG loop of the hydrophobic binding-site. We associate tentatively the stiffening of these methyl moieties with the binding process.

τ2, of the C−CDH2 bond for free (red) and peptide-bound (black) PLC 1C SH2. Most τ2 γ

values lie in the 200−400 ps range. The error, estimated at 15%, is about twice the symbol size. The alanines exhibit a wide range of motional rates from A51 moving slowly to A46 moving rapidly. The methionines exhibit invariably fast local motion. M93 and L95’ belong to the BG loop of the hydrophobic binding-site; they exhibit fast local motion. Note that within the scope of SRLS analysis the methyl groups of residues L69

𝑐02 and τ2 values. The SRLS analysis determined τ2 to be on average 270 ps. The authors of ref 39 carried out molecular dynamics (MD) simulations of the methyl-moieties of the SH3 domain of chicken α-spectrin, using eq 8 to parameterize the SDF. They found that most

τ2. The authors of ref 46 studied phospholamban 2H-labeled at the Ala15, Ala24 and Leu51 positions in phospholipid bilayers to find that side-chain motions other than methyl-rotation affect the 2H lineshapes. Although the corresponding correlation times

22


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τ2. The authors of ref 47 generated a 1 µs long MD trajectory for bovine pancreatic trypsin inhibitor (BPTI). Its analysis showed that the average dynamic content of the

τ2. The following comment is in order. Within the scope of SRLS the scaling factor

1 P

cannot be used to derive the best-fit parameters of J(ω)(C−CDH2) from the best-fit parameters of J(ω)(C−D), because the SRLS J(ω) functions are numerical. We carried out both C−D and C−CDH2 analyses, to find empirically that corresponding trends in u

τ2 are quite similar, with scaling factors of ~3 for u and ~18 for τ2 (the C−CDH2 parameters are larger). Because in displaying the best-fit parameters the focus is primarily on trends, we only show the results of the C−CDH2 analysis. On the other hand, C−D analysis is important in assessing the effect of 1st-type mode-coupling and MF parameterization of the methyl-related-SDF. The latter comprises 𝑆£¤¥¦ associated with C−CDH2 dynamics and 𝜏L associated with C−D dynamics. Hence, to evaluate the implication of the factors mentioned above by comparing analogous SRLS and MF parameters, both C−D dynamics and C−CDH2 dynamics have to be analyzed with SRLS.

SRLS and MF comparison. 𝑆%&'( in MF corresponds formally to 𝑆3) (C−CDH2); z {

𝑆%&'( in MF corresponds formally to and 𝑆3) (C-D) in SRLS; 𝜏K in MF corresponds

formally to 𝜏) (C-D) in SRLS. Figure 3a refers to free PLC 1C SH2. It shows 𝑆3) from SRLS analysis of C−D γ

dynamics (black) and z{𝑆%&'( from MF analysis (red). It can be seen that these two curves 23



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differ substantially. Figure 3a also shows 𝑆3) from SRLS analysis of C−CDH2 dynamics (blue) and 𝑆%&'( from MF analysis (magenta). These two curves also differ substantially. Thus, with regard to local ordering MF does not agree with reasonable accuracy with either of the two stochastic models for treating 2H relaxation from methyl-moieties.

τ2 from SRLS analysis of C−D dynamics (black), τ2 from SRLS analysis of C−CDH2 dynamics (blue), and τe from MF analysis (red) for free PLC 1C SH2. The red and blue γ

curves differ to a very large extent; surely τe in MF does not represent the correlation time for C−CDH2 motion. On the other hand, τe does not agree satisfactorily with the correlation time for methyl rotation either (cf. red and black curves in Figure 3b). Figure 3c is analogous to Figure 3a for peptide-bound PLC 1C SH2 and Figure 3d γ

is analogous to Figure 3b for peptide-bound PLC 1C SH2. γ

The large differences between corresponding SRLS and MF data in Figure 3 indicate that parameterizing the SDF, and disregarding mode-coupling, yield an inaccurate picture based on physically vague parameters. Parameter differences might fare better; let us explore this aspect. The key MF

𝑆axis2. Its formal SRLS analogue in the context of C−D dynamics is 9×(𝑆02)2. Figure 4a (4b) shows these data for free (peptide-bound) PLC 1C SH2. As expected based on γ

Figures 3a and 3c, the SRLS and MF calculations are yielding substantially different

9×(𝑆02)2] is shown in black and Δ𝑆axis2 is shown in red. Even these data differ considerably (88% of the differences between corresponding black and red data in Figure 4c are outside the error margin). Based on the MF rationale Δ𝑆%&'( ) is considered to represent differences in the squared order parameter associated with C−CDH2 dynamics in free and peptide-bound 24


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PLC 1C SH2.11 We show in Figure 5a Δ(𝑆3) )) from SRLS analysis of C−CDH2 dynamics γ

(black) along with Δ𝑆%&'( ) (blue). The differences are substantial (even when the error bar is taken very conservatively to be three times the symbol size). Unlike the usual definition of parameter difference − the free-form-related parameter subtracted from the peptide-bound-form-related parameter − we use here the reversed definition. The purpose of this reversal is to easier follow trends, as increase in squared order parameter difference (shown in Figure 5a) corresponds to decrease in conformational entropy difference (shown in Figure 5b); hence within the scope of the reversed definition of Δ(𝑆3) )) and Δ𝑆%&'( ) in Figure 5a, all of the profiles shown in Figure 5 exhibit similar trends. ∆(𝑆3) ))

from SRLS analysis of C−D dynamics (red). The difference between

(𝑆02)2(C−CDH2) (black) and 9×Δ(𝑆02)2(C−D) (red) is small.

Conformational entropy. Figure 5b shows differences in conformational entropy, ΔŜ(SRLS), calculated from u of C−CDH2 dynamics using eq 1 (black), and from 𝑆3) of C−CDH2 dynamics using eq 9 (red). It also shows ΔŜ(MF) calculated form 𝑆%&'( using eq 9 (blue). The black and red profiles are virtually the same; this indicates that the diffusion-in-a-cone potential is a good approximation to the MS potential, in agreement with ref 36. The black SRLS profile and the blue MF profile have some common features. However, the MF profile exhibits quite a few unduly large digressions from the mean, which render the overall pictures qualitatively different from the black SRLS profile. We

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did not find independent evidence in support of outstanding properties of the “substantially digressing” methyl groups in the MF profile. Figure 6 shows ΔŜ obtained with SRLS analysis of C−D dynamics (black) and C−CDH2 dynamics (red). With an error estimation of 15% most C−D-associated data lie outside the error margin. The two profiles are similar, with an approximately 11-fold attenuated C−D profile as compared to the C−CDH2 profile. The red ΔŜ values in Figure 6 are mostly negative, indicating that the local ordering/core packing largely increases upon peptide-binding at the C−CDH2 sites of PLC 1C SH2. The increase in local ordering is particularly large for the methyl groups γ

L35δ1, L35δ2, V36γ , V36γ2 and A46, which reside in the chain segments flanking the BC 1

loop of the pTyr binding-site (cf. the relevant blue ellipse). The ΔŜ values of the methyl groups L69δ1 and L69δ2 of the EF loop of the hydrophobic binding-site are within the error margin (cf. the relevant blue ellipse). For the BG loop of the hydrophobic bindingsite, ΔŜ associated with the methyl groups L89δ1 and L89δ increases (i.e., the disorder 2

increases), whereas ΔŜ associated with the methyl groups M93, L95δ and L95δ2 1

decreases (i.e., the order increases), upon peptide binding (cf. the relevant blue ellipse). The methyl groups M68, L80δ and I81γ2 belong to the monomer-dimer interface. 2

At this time there is not enough information to rationalize in physical terms the decrease in 𝑆 upon peptide-binding for these methyl groups. Further studies are required to clarify this point. The overall conformational entropy contribution on the part of the C−CDH2

26


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𝑇∆𝑆 = (−3.2 ± 0.48) kJ/mol. The (very small) contribution of the C−D bonds is estimated at (−0.3 ± 0.05) kJ/mol. It is of interest to discuss in this context the work of Vugmeyster et al.,45 who (among others) studied conformational entropy associated with methyl-moiety dynamics in the solid-state. Deuterated valine and leucine methyl groups of polycrystalline chicken

13×Q by fast methyl-rotation, the C−CD3 motion was modeled in terms of (1) rotameric jumps among one major and three equally-populated minor conformations, and (2) motion on an arc of the 70.5o-tilted C−CD3-centered cone. Order parameters and 𝑆 values were calculated; 𝑆 was plotted as a function of the corresponding order parameter both directly, as well as using eq 9. Poor agreement between corresponding graphs was revealed, leading to the conclusion that eq 9 is a poor approximation for the models considered. Equation 9 is based on diffusion-in-a-cone, which is a simple axial motion. Rotameric jumps and arc motion are asymmetric motional modes. The disagreement is understandable. However, the implications are broader in scope. Equation 9 features the MF generalized order parameter, S (or 𝑆%&'( ), redefined as axial order parameter because only one adjustable parameter (S) is available. This is a simplification appropriate within the scope of single-temperature relaxation analysis (the present case; although it does not mean that S or 𝑆%&'( are accurate), but not within the scope of the substantially more sensitive temperature-dependent slow-motional lineshape analysis.45,48 Reference 48 is our work where we analyzed the experimental lineshapes of ref 45 in terms of a single local motion described by a rhombic local potential and an axial local diffusion tensor.

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That analysis48 is based on the microscopic-order-macroscopic-disorder (MOMD) approach, which is the limit of SRLS for “frozen” protein. The primary quantity to be used in deriving 𝑆 is clearly the potential (or directly Peq). This is the approach adopted by us and by the authors of ref 45, with the SRLS potential being general and extendable. Using order parameters instead of potentials will be appropriate if they feature the same symmetry, and the order parameters are defined in terms of the potential. Calculating Peq from MD trajectories is more accurate; however, this is

based on an atomistic perspective. Mesoscopic approaches still have currently several important advantages over atomistic approaches.35

Conclusions The SRLS approach, enhanced to calculate conformational entropy, was applied to 2H methyl-moiety relaxation in free and pY1021-bound PLC 1C SH2. Both C−D and γ

C−CDH2 dynamics are properly described by a Maier-Saupe potential, u, and a correlation time for local diffusion, 𝜏) . Conformational entropy, 𝑆, is calculated from u based on the definition of 𝑆. On average, at the C−D and C−CDH2 sites u is (0.7 ± 0.04) and (2 ± 0.1) kBT,

𝜏2 is (15 ± 2.3) and (270 ± 41) ps, respectively; and −𝑇∆𝑆 is (−0.3 ± 0.05) and (−3.2 ± 0.48) kJ/mol, respectively. The relatively slow C−CDH2 motions are supported by independent studies. Our SRLS results have been compared with previous MF results obtained from the same data. 𝑆 was not provided by the earlier MF analysis. We calculated it from the MF parameter 𝑆%&'( using a specific analytical expression based on diffusion-in-a-cone as 28


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dynamic model connecting 𝑆%&'( and 𝑆. Corresponding SRLS and MF parameters were found to differ substantially. This is shown to stem from (i) mode-coupling of the 1st-type being unaccounted for in MF, and (ii) the fact that MF parameterizes the methyl-related spectral density. The ∆𝑆 profiles from SRLS and MF also differ substantially. This stems from factors (i) and (ii) affecting adversely the accuracy of 𝑆%&'( . Mode-coupling of the 1st-type, caused by the restrictions on probe motion being exerted by a moving body (the protein), exists even when the local motion is fast and the local geometry is simple. Its effect has been investigated here in depth for the first time. With regard to the binding aspect, SRLS reveals stronger potentials at the pTyrbinding-site and specific changes in potential strength and local-motional rates otherwise, in the peptide-bound form of PLC 1C SH2. Based on 𝑆%&'( ) data MF finds that the order γ

at the pTyr-binding-site increases upon peptide binding whereas the hydrophobic binding-site experiences substantial disorder in both PLC 1C SH2 forms. γ

Acknowledgments This work was supported by the Israel Science Foundation (Grant No. 369/15 to E.M.).

Supporting Information Available: A summary of the slowly relaxation local structure approach is provided (section I of the SI). 2H T1 and T1 of PLC 1C SH2 free and ρ

γ

bound to the peptide pY1021, acquired at 11.7 and 14.1 T and 303 K,11 are shown in Figure S2 of the SI (section II of the SI). Several SRLS-related aspects appear in section

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III of the SI. This material is available free of charge via the internet at http://pubs.acs.org.

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23. Ward, J. M.; Gorenstein, N. M.; Tian, J; Martin, S. F.; Post, C. B. Constraining Binding Hot Spots: NMR and Molecular Dynamics Provide a Structural Explanation for Enthalpy-Entropy Compensation in SH2-Ligand Binding. J. Am. Chem. Soc. 2010, 132, 11058-11070. 24. Akke, M. Conformational Dynamics and Thermodynamics of Protein-Ligand Binding Studies by NMR Relaxation. Biochem. Soc. Trans. 2012, 40, 419-423. 25. Lipari, G.; Szabo, A. Model-Free Approach to the Interpretation of Nuclear Magnetic Resonance Relaxation in Macromolecules. 1. Theory and Range of Validity. J. Am. Chem. Soc. 1982, 104, 4546-4559. 26. Lipari, G.; Szabo, A. Model-Free Approach to the Interpretation of Nuclear Magnetic Resonance Relaxation in Macromolecules. 2. Analysis of Experimental Results. J. Am. Chem. Soc. 1982, 104, 4559-4570. 27. Clore, G. M.; Szabo, A.; Bax, A.; Kay, L. E.; Driscoll, P. C.; Gronenborn, A. M. Deviations from the Simple Two-Parameter Model-Free Approach to the Interpretation of Nitrogen-15 Nuclear Magnetic Relaxation of Proteins. J. Am. Chem. Soc. 1990, 112, 4989-4991. 28. Lee, A. L.; Sharp, K. A.; Kranz, J. K.; Song, X. J.; Wand, A. J. TemperatureDependence of the Internal Dynamics of a Calmodulin-Peptide Complex. Biochemistry 2002, 41, 13814-13825. 29. Polimeno, A.; Freed, J. H. A Many-Body Stochastic Approach to Rotational Motions in Liquids. Adv. Chem. Phys. 1993, 83, 89-204

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Figure Captions Figure 1. Ribbon diagram of PLC 1C SH2 bound to the peptide Y1021, according γ

to PDB accession code 2ple.

𝑐02 (part a) and τ2 (part b) obtained with SRLS analysis of C−CDH2 dynamics for free PLC 1C SH2 (red) and peptide-bound PLC 1C SH2 (black). A quadrupole constant of 55.6 γ

γ

kHz was used. The x-axis in Figure 2a depicts the experimentally accessible methyl groups as they appear along the protein sequence. The γ2 methyl of valine, the δ2 methyl of leucine and the δ1 methyl of isoleucine are denoted with a “prime” symbol. The δ1 methyl of isoleucine appears before the γ2 methyl. The notation depicted in this figure also applies to Figures 2b and 3−6. In Figure 2a the errors are estimated at 5%, which is approximately twice the symbol size. In Figure 2b they are estimated at 15%, which is approximately twice the symbol size.

Figure 3. Part a: 𝑆3) from C−D dynamics (black), 𝑆3) from C−CDH2 dynamics

13𝑆axis (red) and 𝑆axis (magenta) for free PLC 1C SH2. Part b: τ2, ps, from C−D γ

τ2, ps, from C−CDH2 dynamics (blue), and τe, ps from MF analysis (red) for free PLC 1C γ

SH2. Part c: 𝑆3) from C−D dynamics (black), 𝑆3) from C−CDH2 dynamics (blue), z{𝑆%&'(

𝑆axis (magenta) for peptide-bound PLC 1C SH2. Part d: τ2, ps, from C−D dynamics γ

τ2, ps, from C−CDH2 dynamics (blue), and τe, ps from MF analysis (red) for peptidebound PLC 1C SH2. The average error is 2.5 times the symbol size. γ

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Figure 4. 9(𝑆3) )) from SRLS analysis of C−D dynamics (black) and 𝑆%&'( ) from MF analysis (red) for free PLC 1C SH2 (part a) and peptide-bound PLC 1C SH2 (part b). γ

γ

(𝑆02)2] and Δ𝑆axis2 calculated from parts a and b (part c). The average error is 2.5 times the symbol size.

Figure 5. Part a: Δ(𝑆3) )) from SRLS analysis of C−CDH2 dynamics (black), Δ(𝑆3) )) from SRLS analysis of C−D dynamics multiplied by 9 (red), and Δ𝑆%&'( ) (blue). Any given parameter for peptide-bound PLC 1C SH2 was subtracted from the γ

corresponding parameter for free PLC 1C SH2. Part b: ΔŜ from u obtained with SRLS γ

analysis of C−CDH2 dynamics using eq 1 (black); ΔŜ from 𝑆3) obtained with SRLS analysis of C−CDH2 dynamics using eq 9 (red); ΔŜ from 𝑆%&'( using eq 9 (blue). Any given parameter for free PLC 1C SH2 was subtracted from the corresponding parameter γ

for peptide-bound PLC 1C SH2. The average error is 2.5 times the symbol size. γ

Figure 6. Conformational entropy difference, ΔŜ, obtained with SRLS analysis of C−CDH2 dynamics and C−D dynamics using eq 1. The average error is 2.5 times the symbol size.

39


An SRLS Study of 2H Methyl-Moiety Relaxation and Related

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