Local Ordering at the N-H Sites of the Rho GTPase Binding

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B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Local Ordering at the N-H Sites of the Rho GTPase Binding Domain of Plexin-B1: the Impact of Dimerization Netanel Mendelman, Mirco Zerbetto, Matthias Buck, and Eva Meirovitch J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b05905 • Publication Date (Web): 30 Aug 2019 Downloaded from pubs.acs.org on August 30, 2019

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The Journal of Physical Chemistry

Local Ordering at the NH Sites of the Rho GTPase Binding Domain of plexin-B1: the Impact of Dimerization

Netanel Mendelman,1 Mirco Zerbetto,2 Matthias Buck3 and Eva Meirovitch1,*

The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, RamatGan 52900 Israel1; Department of Chemical Sciences, University of Padova, Padova 35131, Italy2; Case Western Reserve University. Department of Physiology and Biophysics, Cleveland OH, USA3

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

1 ACS Paragon Plus Environment

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Abstract We have developed a new molecular dynamics (MD)-based method for describing analytically local potentials at mobile NH sites in proteins. Here we apply it to the monomer and dimer of the Rho GTPase Binding Domain (RBD) of the transmembrane receptor plexin-B1 to gain insight into dimerization, which can compete with Rho GTPase binding. In our method the (

)

local potential is given by linear combinations, 𝑢 𝐷𝐿,𝐾 , of the real combinations of the Wigner rotation matrix elements, 𝐷𝐿,𝐾, with L = 14 and appropriate symmetry. The combination that “fits best” the corresponding MD Potential Of Mean Force, 𝑢(𝑀𝐷), is the potential we are seeking, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇). For practical reasons the fitting process involves probability distributions, 𝑃𝑒𝑞  (

)

exp(u), instead of potentials, u. The symmetry of the potential, 𝑢 𝐷𝐿,𝐾 , may be related to the irreducible representations of the D2h point group. The monomer (dimer) potentials have mostly Ag and B2u (B1u and B2u) symmetry. For the monomer the associated probability distributions are generally dispersed in space, shallow, and centered at the “reference NH orientation” (see below for definition); for the dimer many are more concentrated, deep and centered away from the (

)

“reference NH orientation”. The 𝑢 𝐷𝐿,𝐾 functions provide a consistent description of the potential energy landscape at protein NH sites. The L1-loop of the plexin-B1 RBD is not seen in the crystal structure, and many resonances of the L4 loop are missing in the NMR 15N1H HSQC spectrum of the dimer; we suggest reasons for these features. An allosteric signal transmission pathway was reported previously for the monomer. We find that it has shallow NH potentials at its ends, which become deeper as one proceeds toward the middle, complementing structurally the previously derived dynamic picture. Prospects of this study include correlating 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) with MD forcefields, and using them without further adjustment in NMR relaxation analysis schemes. 1. INTRODUCTION 2 ACS Paragon Plus Environment

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Internal protein mobility consists of the collection of structural moieties that experience restricted/locally ordered motions. Two physical methods for studying this important feature emerged as particularly useful: NMR relaxation analysis1 and molecular dynamics (MD) simulations2. The NH bond is a typical probe in both methods.3 A basic property of restricted motions are the spatial restraints exerted at the site of their occurrence, in this case by the close protein surroundings. The slowly relaxing local structure (SRLS) approach46 for NMR relaxation analysis710 is currently the most elaborate theory in the field. In SRLS the local restraints are expressed by a Potential Of Mean Force (POMF), u(,), expanded in the infinite basis-set of the real combinations of the Wigner rotation matrix elements, 𝐷𝐿,𝐾(,), where the angles  and  define the orientation of the NH bond in the protein. The MD POMF, 𝑢(𝑀𝐷), can be obtained (as a histogram) from 𝑃(𝑀𝐷) = 𝑒𝑞

exp ( ― 𝑢(𝑀𝐷)) 𝑍

, where Z is the partition function and 𝑃(𝑀𝐷) is the 𝑒𝑞

orientational NH probability distribution derived directly from the MD trajectory as a histogram.11,12 For a complete picture of the dynamic structure of the protein, in addition to the local ordering one also has to characterize the motion itself in terms of type, rate and geometry. SRLS has been devised to do so. 710 Because of limitations associated with data-sensitivity, the potential entering SRLS analyses comprises only the lowest, L = 2, |K| = 0, 2, terms of the u(,) expansion. This potential has the form 𝐷2,𝐾 = 𝑐2,0𝐷2,0(,) 𝑐2,2𝐷2,2(,).810 Including additional terms could improve substantially the emerging picture of structural dynamics, as the spatial restraints are among the most important elements of the analysis.8,10 One way to make progress on this is to acquire additional experimental data. This is often not practical and/or limited in efficacy by



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considerable increase in experimental noise. One might contemplate using the MD POMF, 𝑢(𝑀𝐷); this is also not practical given that 𝑢(𝑀𝐷) is a histogram. The solution we have suggested and implemented in ref 13 is to devise  independent of SRLS  enhanced local ordering potentials on the basis of the expansion of u(,) in 𝐷𝐿,𝐾. Linear combinations of 𝐷𝐿,𝐾 with L = 14 and K = -L…L, and appropriate symmetry (see below), denoted (

)

(

)

by 𝑢 𝐷𝐿,𝐾 , are devised. For every NH bond we seek that composition of 𝑢 𝐷𝐿,𝐾 which “fits-best” (𝐷𝐿,𝐾)

the corresponding 𝑢(𝑀𝐷). For practical reasons,14 one optimizes 𝑃𝑒𝑞 (

=

(𝐷 ) exp ( ― 𝑢 𝐿,𝐾 ) 𝑍

against 𝑃(𝑀𝐷) 𝑒𝑞

)

instead of optimizing 𝑢 𝐷𝐿,𝐾 against 𝑢(𝑀𝐷). (

)

This yields analytical potentials, 𝑢 𝐷𝐿,𝐾 ― BEST , which are reasonably good approximations to 𝑢(𝑀𝐷), and provide an insightful description of the local ordering. The functions 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) and

𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) 𝑃(𝐷 𝑒𝑞

=

(𝐷 ― 𝐵𝐸𝑆𝑇) exp ( ― 𝑢 𝐿,𝐾 ) 𝑍

may be depicted pictorially, improved, and compared among

sites. 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) may be used without further adjustment in SRLS analyses improving the overall picture not only by better representing the local spatial restraints, but also by allowing for additional parameters to be varied in, i.e., determined by, data-fitting. If all of the 𝐷𝐿,𝐾 functions with L = 14 and K = L…L are considered, there will be 24 terms out of which linear combinations are to be built. To reduce this set we invoke point-groupsymmetry considerations.1517 The 𝐷𝐿,𝐾 functions with L = 1 and 3 belong to the polar irreducible representations Au, B1u, B2u and B3u of the D2h point-group. The 𝐷𝐿,𝐾 functions with L = 2 and 4 belong to the non-polar irreducible representations Ag, B1g, B2g and B3g of the D2h point-group.1517 An NH bond attached physically to the protein experiences polar ordering. In a previous study


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we investigated the role of site-symmetry in the context of the local ordering.17 That study provides strong evidence that (a) odd-L 𝐷𝐿,𝐾 functions adequately represent polar ordering, and (b) it is useful to characterize the local ordering in terms of the irreducible representations of the D2h pointgroup. In view of the various approximations, admixtures also comprising non-polar terms are probably realistic. We use the functions belonging to the irreducible representations Au, B1u, B2u and B3u (polar) and Ag (non-polar). Thereby the number of terms to be considered is reduced from 24 to 15. Symmetry is only one of the criteria we invoke for the characterization of the local (

)

𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) potential, 𝑢 𝐷𝐿,𝐾 ― BEST , and the associated probability distribution, 𝑃(𝐷 . Additional 𝑒𝑞

criteria are the forms of these functions; the minimum of 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) or the maximum of 𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) 𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) ; the degree of spatial dispersion of 𝑃(𝐷 ; and the extent to which these 𝑃(𝐷 𝑒𝑞 𝑒𝑞

functions are centered at the “reference NH orientation” (defined below).13 Here we apply the method developed in ref 13, and briefly described above, to the Rho GTPase Binding Domain (RBD) of the transmembrane receptor plexin-B118 (in short, plexin-B1 RBD) in monomer and dimer form. Plexin-B1 mediates cell signaling by direct interaction with several small GTPases.19 The plexin-B1 RBD prevails in solution predominantly as dimer, which can compete with Rho GTPase binding; its X-ray crystallography structure was determined (PDB code R2O2)20. The monomer has been stabilized in solution by the W90F mutation; its NMR structure was also determined (PDB code 2JPH)21. Working with this monomeric mutant allowed the Buck laboratory to obtain insights into oncogenic mutations at other sites, as well as to study dimerization and GTPase binding.18,22 5 ACS Paragon Plus Environment


Dimerization overall reduces dynamics,23 whereas GTPase-binding to the RBDs of various plexins reduces dynamics in some cases and enhances it in others.24 Dynamical network analysis based on backbone dihedral angle cross-correlation was performed revealing signal-transmission pathways in the monomer structure; transfer entropy calculations were also carried out.23 These findings23,24 rely on MD techniques.

15N1H

NMR relaxation studies with relatively simple

representation of the local ordering were also carried out,11,12,25 providing information on NH bond dynamics in the monomer and the dimer. Thus, extensive information on dynamics-related aspects associated with dimerization is currently available.11,12,2324,25 On the other hand, the effect of this important functional process on the potential energy landscape of the plexin-B1 RBD, which is a primary structural feature, has not been investigated. The present study fills this gap, focusing on NH sites. The MD trajectories employed in refs 11, 12 and 23 for other purposes are used here to derive 𝑃(𝑀𝐷) histograms for 𝑒𝑞 orientational NH bond distributions. As delineated above, these histograms serve as target for yielding by optimization the functions 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) (analytical approximation to 𝑢(𝑀𝐷)) and 𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) (analytical approximation to 𝑃(𝑀𝐷) 𝑃(𝐷 𝑒𝑞 ). By comparing corresponding functions between 𝑒𝑞

the monomer and the dimer, insight into the effect of dimerization on the local structure is gained. The fold of the plexin-B1 RBD is similar to that of ubiquitin whereas its loops are much longer than those of ubiquitin.20,21 The biological functions of these two proteins are very different. It is of interest to link the dynamic structure of the loops in plexin-B1 RBD to its functions. The L1-loop (Figure 1) fulfils no currently known biological role. Nevertheless, in the present context it has very different (and quite unique) character in the monomer as compared to the dimer. The differences detected help understand why is this loop absent in the 2R2O crystal structure of the


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dimer20. The L2-loop is likely associated with interdomain interactions,26 and the L3-loop is known to be central to Rho GTPase binding.20,24 For both of these loops differences are revealed between 𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) in the monomer, and their counterparts in the dimer; likely reasons 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) and 𝑃(𝐷 𝑒𝑞

are provided for these differences. The L4-loop interfaces the two monomer units in the dimer. As one would expect, it rigidifies upon dimer formation. Here we quantify this feature in terms of the extent of spatial 𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) dispersion, and the population-patterns, exhibited by 𝑃(𝐷 . This helps understand why a 𝑒𝑞

sizable part of this loop is absent in the NMR 15N1H HSQC spectrum of the dimer12,25. Finally, the shortest signal transmission pathway detected previously in the monomer23 is characterized here in terms of the local potentials, and the orientational probability distributions, prevailing at the constituent NH sites. This study and refs 11, 12 and 23 employed the same MD trajectories, although for different purposes (see above). This is an indication that previously unrevealed information is still inherent in MD trajectories.

2. THEORETICAL BACKGROUND 2.1. Local potentials. In general, for a uniaxial local director the local potential, 𝑈(,), is expanded in the full basis-set of the Wigner rotation matrix elements 𝐷𝐿0𝐾(,):2729

𝑈(,) = ― ∑𝐿,𝐾𝑐𝐿0𝐾𝐷𝐿0𝐾(,), where 𝐿 = 1… and 𝐾 = ― 𝐿…𝐿.

The real potential in units of kT is given by: 13


(1)


𝑢(,) = ―

𝑈 (,  ) 𝑘𝑇



𝐿

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―𝐿

= ― ∑𝐿 = 1[∑𝐾 = 0(𝑐𝐿,𝐾𝐷𝐿,𝐾(,)) + ∑𝐾 =

(𝑐𝐿, ― 𝐾𝐷𝐿, ― 𝐾(,))

―1

(2)

where the 𝐷𝐿,𝐾 (,) = 2Re(𝐷𝐿0𝐾) and 𝐷𝐿, ― 𝐾(,) = 2𝑖𝐼𝑚𝑎𝑔(𝐷𝐿0𝐾). The derivation of the 𝐷𝐿,𝐾 functions from the 𝐷𝐿0𝐾 functions is described in the Supporting Information (SI).

2.2. Local order parameters. For L = 2, the SRLS potential is given by: 𝐷2,𝐾(, ) = ―𝑐2.0 𝐷2,0(,) ― 𝑐2,2𝐷2,2(,).

(3)

In general, five order parameters in irreducible tensor notation may be defined in terms of the 𝐷2,𝐾 potential. They are given by:6

〈𝐷2,𝐾(,)〉 = {∫sin 𝑑 𝑑𝐷2,𝐾(,)exp [ ―𝑢(,)]}/∫sin 𝑑 𝑑 exp [ ― 𝑢(,)], (4)

where K = –2,…2. For at least three-fold (C3v point-group) symmetry around the local director and at least two-fold symmetry (D2h point-group) around the main ordering axis, only 𝑆2,0  𝑆20 = ⟨𝐷200( ,)⟩ and 𝑆2,2 2  𝑆2 = ⟨𝐷202(,) + 𝐷20 ― 2(,)⟩ survive in the PAS of the ordering tensor, S (usually the designations

𝑆20 and 𝑆22 are used).2729 The order parameters associated with L  2 are defined by analogy, with eqs 2 and 3 featuring 𝐷𝐿,𝐾

(,) instead of 𝐷2,𝐾(,).


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2.3 Potential of Mean Force from MD. The POMF, 𝑢(,), is related to the atomistic internal energy 𝑢(,,𝑥) (where x denotes coordinates of the 3D protein structure other than the angles  and ), in terms of the relation 𝑃𝑒𝑞(,) = (∫𝐼𝑑𝑥 exp(–𝑢(,, 𝑥)))/Z = exp(–𝑢(,))/Z (I – integration domain). Solving this integral is problematic. MD can provide an approximation to 𝑢(,); this is 𝑢(𝑀𝐷)(, ), (𝑀𝐷) defined in terms of the estimate for the Boltzmann distribution, 𝑃(𝑀𝐷) (, ))/𝑍. Using 𝑒𝑞 (,) = exp(𝑢 13 a relatively long unbiased simulations, one derives 𝑃(𝑀𝐷) 𝑒𝑞 (,) from the MD trajectory as a histogram.

Thus, the potential, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), determined with our method is an approximation to 𝑢(,, 𝑥). Via the collective coordinate “x” not only the immediate, but also the relatively close, stereo-chemical features of the protein surroundings have a significant effect. However, this effect is implicit. It can be derived explicitly at the atom level with high specificity and in a detailed manner with MD methods, as illustrated in ref 30. A future prospect of interest is to integrate these different approaches.

2.4. Symmetry considerations. The 𝐷𝐿,𝐾 functions belong to the irreducible representations of the D2h point-group (Character Table given in the SI).15 They are polar (change sign upon inversion, “ungerade”-type designated “u”) for odd-L and non-polar (invariant upon inversion, “gerade”-type designated “g”) for even-L. As indicated, in accordance to the nature of the probe we use the 𝐷𝐿,𝐾 functions with L = 14 which correspond to the irreducible representations Ag, Au, B1u, B2u and B3u.

𝑳,𝑲) (,) against 𝑷(𝑴𝑫) 2.5. Optimization of 𝑷(𝑫 𝒆𝒒 (,). The objective is to determine for 𝒆𝒒

every NH bond the particular linear combinations of 𝐷𝐿,𝐾 functions with L = 14 and appropriate (

)

13 symmetry for which 𝑃𝑒𝑞𝐷𝐿,𝐾 (,) “fits best” 𝑡he corresponding 𝑃(𝑀𝐷) 𝑒𝑞 (,) histogram. For that

we used the “Sequential Quadratic Programming (SQP)” iterative method for constrained non9 ACS Paragon Plus Environment


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linear least-squares optimization from the “Global Optimum Solution MultiStart” MATLAB functionality.31 The expression:

(𝑫𝑳,𝑲) 𝜒2 = ∑(𝜃,𝜑) (𝑃(𝑀𝐷) (𝜃,𝜑)𝑖)2 𝑒𝑞 (𝜃,𝜑)𝑖 ― 𝑃𝑒𝑞 𝑖

(5)

is minimized in this algorithm. Further details appear in the SI.

3. RESULTS AND DISCUSSION Figure 1 shows the ribbon diagram of the plexin-B1 RBD monomer (part a) and dimer (part b) used in this study.23 The “monomer” represents the least-restraint-violations conformation of the NMR structure (PDB code 2JPH)21; the “dimer” has been modeled by fusing two 2JPH units to the mini--sheet (comprising the two anti-parallel -strands W90R92) of the crystal structure of the dimer (PDB code 2R2O)20. The long loops of the plexin-B1 RBD ascribe to this protein notable static and dynamic orientational disorder. In this study we focus on the static disorder at its NH sites, quantified in terms of the form of the local potential and the associated orientational NH probability distribution.

3.1. The “reference NH orientation”. For every NH bond the local potential is defined in terms of the coordinates that describe the relative orientation of the local ordering frame, denoted by OF, with respect to the local director frame, denoted by VF. The OF frame is defined in the NH bond; it varies with respect to the VF frame, which is fixed in the protein. When the local potential is zero the NH bond is at equilibrium. This NH position corresponds to the most probable OF frame; we call it the “reference NH orientation”. 10 ACS Paragon Plus Environment

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The most probable OF frame depends on the form of the potential. In ref 13 the local SRLS potential has the form 𝐷2,𝐾 = 𝑐2,0𝐷2,0(,) 𝑐2,2𝐷2,2(,). Its minimum (as well as the maximum 2,𝐾) of 𝑃(𝐷 ) is obtained when (, ) = (90o, 90o). These coordinates specify the orientation of the 𝑒𝑞

most probable OF frame with respect to the VF frame; the reverse transformation (VF-to-OF) is given by the Euler angles 𝛺VF ― OF = (0, 90o, 90o). Previous work has shown that ZOF is pointing along the CC axis, and aligns preferentially perpendicular to the (uniaxial) local director.813 Figure 2a illustrates the VF frame, and Figure 2b the most probable OF frame, for the potential 𝐷2,𝐾 . The local potentials, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), which we determine in this study, have generally forms other than 𝐷2,𝐾 in SRLS. Their minima are specific to every NH-bond and differ from (, ) = (90o, 90o); we denote them by (𝑥, 𝑥). The deviation of (𝑥, 𝑥) from (90o, 90o) (designated in Figures 712, 14 and S1S18 by a white crosshair) is as an empirical estimate of protein-shape complexity.

3.2. The functions 𝑫𝑳,𝑲. Let us examine the form of the 𝐷𝐿,𝐾 terms which comprise the best-fit potentials, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇). As indicated, they have the symmetry of the irreducible representation Ag, Au, B1u, B2u and B3u of the D2h point-group.15 The 𝐷𝐿𝐾 functions with K = 0 are axial and those with K  0 are rhombic. Some of the functions with Ag or B1u symmetry are axial and some are rhombic; all of the functions with Au, B2u or B3u symmetry are rhombic (see Character Table of the D2h point-group, SI). The axial functions are shown in Figure 3, and the rhombic functions with B2u symmetry, which we found to make on average the largest contributions to the local potential (see below), are



shown in Figure 4 (we show the real spherical harmonics, 𝑌𝐿,𝐾, which except for a scaling factor are the same as the 𝐷𝐿,𝐾 functions). The regions colored cyan correspond to negative potential, hence high NH-bond population; the regions colored magenta correspond to positive potential, hence low NH-bond population. The functions 𝑌1,0 and 𝑌3.,0 in Figure 3 are polar and the functions 𝑌2,0 and 𝑌4,0 are non-polar; all of them exhibit axial symmetry around z  ZVF. The polar functions 𝑌1,1, 𝑌3,1 and 𝑌3,3 in Figure 4 are invariant to C2-rotation around z, and to reflection across the zy and xy planes (see Character Table of the D2h point-group, SI).

3.3. Symmetry-based analysis. The histograms, 𝑃(𝑀𝐷) 𝑒𝑞 , for the plexin-B1 RBD monomer and dimer, are shown in Figures S1S18 of the SI (except for the disregarded highly flexible N-, and C-terminal segments – see below). Red represents highly, and dark-blue scarcely, NHpopulated regions in conformation space. In general, 𝑃(𝑀𝐷) exhibits greater spatial dispersion for 𝑒𝑞 the monomer than for the dimer. The symmetry is mostly rhombic for both protein forms. We chose for quantitative analysis the 𝑃(𝑀𝐷) histograms of 35 representative residues. 𝑒𝑞 Tables 1 and 2 show the composition of the corresponding best-fit potentials, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇). The 𝐷𝐿,𝐾 terms comprising these functions have been grouped according to their belonging to the irreducible representations Ag, Au, B1u, B2u or B3u of the D2h point-group. The sums of the absolute values of the coefficients of the terms with Ag, B1u, B2u, B3u or Au symmetry, denoted for brevity “symmetry-sum-X”, where X is Ag, B1u, B2u, B3u or Au, have been calculated and depicted in Tables 1a,b for the monomer and Tables 2a,b for the dimer. This empirical representation of the results makes possible determining which symmetries dominate the potentials 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇).


Page 12 of 50

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Table 1a. Structural Elements of the Plexin-B1 RBD Monomer (Column 1) from which the Residues in Column 2 Have Been Taken for Analysis. “symmetry-sum-X” constituents (in Units of kT) of the corresponding 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) potentials with X equal to Ag (Column 3), B1u (Column 4), B2u (Columns 5), B3u (Column 6) and Au (Column 7). Minimum of 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) in Units of kT (Column 8). The Ag, B1u and B2u Contributions Are Depicted in Bold Font. (

Residue

Ag

B1u

B2u

B3u

Au

25

10.4

14.3

0.0

1.5

1.1

-8.4

26

15.8

5.9

8.6

3.7

1.7

-5.8

37

29.6

6.3

27.0

36.3

2.5

-19.0

41

0.0

36.8

13.0

25.3

0.4

-13.5

43

0.0

24.7

11.7

15.3

2.8

-11.6

45

0.0

46.1

12.7

17.6

2.3

-12.5

50

0.0

10.3

7.2

2.2

0.0

-6.5

54

32.2

0.0

12.4

12.1

0.0

-12.8

56*

9.9

6.7

5.1

4.0

1.5

-9.7

61

0.0

3.6

7.7

6.6

0.0

-7.3

63

0.0

22.2

16.4

2.7

2.2

-12.9

65

12.0

8.3

21.5

27.4

0.7

-18.1

69

14.1

26.1

4.1

1.3

1.3

-9.2

70

13.0

1.8

8.6

1.3

2.0

-4.6

71

6.3

1.8

3.7

1.6

0.4

-4.0

72

14.9

15.7

1.6

2.0

1.1

-7.7

L1

α1

L2

β3

L3


)

min [𝑢 𝐷𝐿,|𝐾| ― 𝐵𝐸𝑆𝑇 ]


73

37.7

29.4

3.0

1.6

Page 14 of 50

0.0

-11.8

Table 1b. As in Table 1a, for the structural elements 4, L4, L4/5 and 5 (see left side).

β4

L4

(

Residue

Ag

B1u

B2u

B3u

Au

74

8.5

7.2

4.8

2.7

1.8

-10.0

75

27.6

39.9

46.4

7.9

1.9

-28.2

76

0.0

31.8

14.1

6.8

0.5

-17.9

78

0.0

20.7

8.5

1.6

1.4

-7.5

82

36.2

4.1

17.0

1.3

0.0

-7.5

83

9.6

6.3

2.0

2.7

0.0

-6.1

87

2.6

0.7

1.6

1.6

1.1

-3.6

88

15.8

1.6

13.4

3.3

0.2

-8.3

90

2.4

1.2

1.6

0.7

0.0

-3.2

92

30.2

22.4

0.0

2.2

0.0

-10.2

93

9.9

9.8

24.8

2.7

1.1

-20.0

94

22.9

8.9

1.2

3.3

0.9

-12.3

101

0.0

19.5

11.8

4.9

2.0

-10.7

103

13.4

16.0

34.1

10.6

2.9

-27.4

106

0.0

2.6

10.1

3.1

0.0

-9.2

109

0.0

13.6

16.9

15.4

0.6

-14.9

110

18.6

10.3

13.9

12.3

2.6

-11.4

Turn

β5


)


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Table 2a. Similar to the title of Table 1a, for the dimer. (

Ag

B1u

B2u

B3u

Au

25

23.2

31.5

20.9

16.3

3.5

-29.1

26

33.6

29.0

28.4

6.8

0.0

-25.1

37

0.0

36.1

25.3

11.0

6.0

-23.0

41

0.0

16.4

21.1

36.2

1.2

-22.3

43

0.0

42.4

14.2

28.2

0.7

-16.3

45

0.0

47.6

25.3

6.8

0.4

-24.6

50

0.0

12.1

13.9

12.5

0.0

-13.1

54

0.0

1.4

6.9

2.5

0.1

-6.9

56

0.0

0.3

5.8

5.0

0.2

-6.4

61

0.0

1.3

13.0

2.3

0.0

-12.9

63

0.0

6.6

17.3

16.0

1.2

-15.5

65

0.0

4.1

22.7

3.4

4.1

-20.2

69

0.0

5.1

10.2

3.3

2.2

-10.2

70

0.0

2.3

4.6

5.0

1.1

-5.7

71

0.0

12.9

13.9

6.8

1.0

-19.7

72

9.5

8.7

25.6

6.4

0.9

-22.0

73

13.7

13.2

27.3

1.9

0.0

-23.1

L1

α1

L2

3

L3


)


Residue


Page 16 of 50

Table 2b. Similar to the title of Table 1b, for the dimer. Residue

β4

L4

(

B1u

B2u

B3u

Au

74

0.0

4.3

7.9

0.9

1.4

-7.2

75

0.0

4.6

13.5

3.0

0.9

-11.8

76

0.0

1.2

12.9

2.0

0.1

-12.3

78

0.0

20.8

22.2

9.6

3.6

-21.6

82

0.0

5.4

25.6

11.6

0.0

-23.2

83

0.0

1.7

9.3

32.0

1.0

-10.0

87

0.0

6.0

13.6

3.5

1.8

-13.3

88

0.0

7.1

9.6

2.8

2.0

-9.8

90

0.0

4.1

17.9

9.0

4.7

-18.0

92

0.0

24.9

15.9

17.6

5.1

-15.4

93

0.0

9.6

24.7

35.4

6.6

-21.7

94

0.0

8.8

22.4

15.3

3.5

-21.0

101

0.0

18.8

15.6

8.5

1.0

-14.5

103

0.0

8.6

11.8

27.1

6.8

-12.3

106

0.0

0.6

15.6

7.7

0.0

-14.3

109

0.0

8.9

15.0

5.8

0.0

-14.3

110

0.0

9.1

23.0

9.1

0.0

-20.3

Turn

5


)


Ag

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Tables 1a and 1b indicate that for the monomer the dominant contributions have Ag, B1u or B2u symmetry. Terms with Ag symmetry contribute primarily to loops and terms with B1u or B2u symmetry contribute primarily to secondary structure elements. When there are no terms with Ag symmetry then the “symmetry-sum-B2u” constituent makes the largest contribution. Tables 2a and 2b indicate that for the dimer the “symmetry-sum-B2u” constituent dominates (with a few exceptions associated with the 1-helix and the 2/5 turn, where the “symmetry-sum-B1u” constituent dominates). As indicated above, the N-, and C-terminal segments have been disregarded. In view of extensive flexibility, the pertinent NH bonds feature highly dispersed 𝑃(𝑀𝐷) histograms. Even if 𝑒𝑞 the latter represent properly sampled orientational distributions, approximating them reasonably𝐿,𝐾) well by 𝑃(𝐷 functions will require an unduly large number of constituents in the potentials 𝑒𝑞

𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), rendering the method of limited utility. This assessment applies to any highly flexible chain segment, including the main-chain of intrinsically disordered proteins; in general, it constitutes a qualitative estimate of the range of applicability of the suggested method.

3.4. Empirical assessments. Given the large amount of data in Tables 1 and 2, it is useful to pinpoint trends which provide empirical insight. The minimum of the potential, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), is a useful feature. We examined columns 37 with the aim of identifying “symmetry-sum-X” constituents that might dominate the absolute value of the minimum of 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), called (for compactness) “potential-minimum”.



Page 18 of 50

For all of the 35 residues in Tables 1 and 2, neither the monomer nor the dimer feature “symmetry-sum-X” on the order of “potential-minimum”. However, for 83% of the monomer residues the difference [“symmetry-sum-Ag”  “symmetry-sum-B1u”], or “symmetry-sum-B2u” (when “symmetry-sum-Ag” = 0 or “symmetry-sum-B2u” dominates), correlates well with the “potential-minimum”. This is shown in Figure 5a, together with the linear regression line, which corresponds to a correlation coefficient of 0.87. For 97% of the dimer residues “symmetry-sumB2u” correlates very well with the “potential-minimum”. This is shown in Figure 5b, together with the linear regression line, which corresponds to a correlation coefficient of 0.96. For both protein forms no other “symmetry-sum-X”, or added/subtracted “symmetry-sum-X” values, yielded correlations of similar quality. The “symmetry-sum-Ag” and “symmetry-sum-B1u” terms comprise both axial and rhombic terms. Most differences are expected to comprise at least one rhombic constituent. The “symmetrysum-B2u” term comprises exclusively rhombic constituents. Thus, we find that the minimum of the potential energy landscape at the NH sites of the plexin-B1 RBD (and eventually proteins, in general) has a specific rhombic symmetry. This is an interesting feature to be further investigated. Figure 6a shows the difference between corresponding “potential-minima” of the dimer and the monomer for the 35 residues analyzed quantitatively. In most cases the potential is deeper (and the associated probability distribution more concentrated  cf. Figures S1S18 of the SI), for the dimer. This may be considered to reflect increased overall structural precision implied by dimerization. The exceptions include NH bonds of the 4-strand, the L2-loop, and the 2/5-turn (see below for further discussion). As indicated above, the location (𝑥, 𝑥) is the minimum of 𝑢((𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) and the location (90o, 90o) is the minimum of 𝐷2,𝐾 in SRLS; the quantity Δ𝑑 ― 𝑚 = [(𝑥 ― 90)2 + (𝑥 ― 90)2] 18 ACS Paragon Plus Environment

0.5

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(Figure 6b) is the distance between them. In most cases, Δ𝑑 ― 𝑚 is larger for the dimer than for the monomer. This might be considered to reflect increased structural strain implied by dimerization.

(𝑀𝐷) 3.5. Qualitative analysis of 𝑷(𝑴𝑫) 𝒆𝒒 . In general, the probability distribution, 𝑃𝑒𝑞 , changes

upon dimerization to a greater extent in loops as compared to secondary structure elements (Figures S118 of the SI). Figure 7 shows typical 𝑃(𝑀𝐷) pictures for representative residues from 𝑒𝑞 the 1-helix and the four loops L1L4. Figure 7a shows 𝑃(𝑀𝐷) of residue Q39 from the 1-helix. 𝑒𝑞 For both protein forms, the orientational NH probability distribution extends over a limited region of conformation space and is largely centered at the “reference NH orientation”. The shape of is altered somewhat following dimer formation. 𝑃(𝑀𝐷) 𝑒𝑞 Figure 7b shows 𝑃(𝑀𝐷) of residue A21 from the L1-loop. The spatial dispersion is of 𝑒𝑞 medium extent, with dimerization having a considerable effect on the overall picture (note the different location of the minor conformational ensemble). Importantly and uniquely, while in the monomer 𝑃(𝑀𝐷) is centered near the “reference NH orientation”, in the dimer its center is 𝑒𝑞 removed substantially from that position. The implications of the latter feature are discussed below. Figure 7c shows 𝑃(𝑀𝐷) of residue G51 from the L2-loop, which is associated with 𝑒𝑞 interdomain interactions. The spatial dispersions of 𝑃(𝑀𝐷) is substantially more concentrated in the 𝑒𝑞 dimer, and the 𝑃(𝑀𝐷) centers are shifted somewhat from the “reference NH orientation”, in 𝑒𝑞 different directions. It appears that some uniqueness in the local structure is required for the monomer to function as interdomain interaction-partner.



Figure 7d shows 𝑃(𝑀𝐷) of residue V71 from the L3-loop, which is associated with Rho 𝑒𝑞 GTPase binding. Dimerization reduces the spatial dispersion of 𝑃(𝑀𝐷) and shifts its center to some 𝑒𝑞 extent. All of the outliers of substantial magnitude in Figure 6a (which shows the difference in potential minima between the dimer and the monomer) reside in the 4-strand and the 2/5 turn, which are also associated with Rho GTPase binding.19 For these outliers the monomer potential is deeper, and for two residues in the 4-strand and the 2/5-turn it is substantially deeper, than the dimer potential. These deep monomer potentials are associated with concentrated NH probability distributions (cf. SI); conjointly they reflect structural precision. It may be hypothesized that ligand-binding requires local structural precision afforded by the monomer but not afforded by the dimer. Figure 7e shows 𝑃(𝑀𝐷) of residue V82 from the L4-loop, which interfaces the two monomer 𝑒𝑞 units in the dimer structure. The spatial dispersion of 𝑃(𝑀𝐷) is very broad in the monomer and very 𝑒𝑞 narrow in the dimer (actually comparable to the situation in the 1-helix  cf. Figure 7a). The main effect of dimer formation is to improve the precision of the structure of the L4-loop. In this study we quantify this feature, with interesting implications discussed in section 3.6.2.

3.6. Quantitative analysis of 𝑷(𝑴𝑫) 𝒆𝒒 . Probability distributions depends exponentially on the corresponding potentials; hence, they are less sensitive to details than the potentials themselves. To pinpoint major features, we focus on probability distributions; to reveal specific features, we focus on the lower parts of potentials 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇)).

3.6.1. Why is part of the L1-loop not seen in the crystal structure of the dimer20? The 𝑃(𝑀𝐷) 𝑒𝑞 pictures of residues E24 and C26 from the L1-loop are shown in Figure 8 for the monomer and the 20 ACS Paragon Plus Environment

Page 20 of 50

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dimer. As already pointed out for residue A21 which also belongs to this loop (Figure 7b), the main difference between the monomer and the dimer consists of 𝑃(𝑀𝐷) being centered at the 𝑒𝑞 “reference NH orientation” for the monomer, and substantially removed from that position for the dimer. The L1-loop is the only structural element of the dimer exhibiting this feature, and disregarding residues A21, E24 and C26, it represents the only chain segment not seen in its crystal structure 2R2O20. The process of crystal structure determination requires reasonable compatibility with standard local geometry. We suggest that the large deviation of the maximum of 𝑃(𝑀𝐷) from 𝑒𝑞 the “reference NH orientation”, which may be considered to represent standard local geometry, is the main reason for the L1-loop not being seen in the 2R2O20 crystal structure of the dimer. In all of the solution-states studied, the L1-loop exhibits substantial flexibility. Apart from its termini, it is the most dynamic part of the protein. However, the L1-loop is seen in the crystal structure of an RBD dimer bound to Rnd1 (PDB code 2REX), where it has swung around to be near the interaction site with the GTPase.32 It is likely that the L1-loop experiences different crystal contacts in the 2R2O structure as compared to the 2REX structure.

3.6.2. Why a sizable part of the L4-loop is not seen in the 15N1H HSQC spectrum of the dimer12? The 𝑃(𝑀𝐷) pictures of residues V82 and Q87 from the L4-loop are shown in Figure 9 for 𝑒𝑞 the monomer and the dimer. As already shown in Figure 7e for residue V82 of this loop, the main effect of dimerization is substantial reduction in the spatial dispersion of 𝑃(𝑀𝐷) 𝑒𝑞 . Moreover, the monomer ensemble comprises many highly-populated conformations (large red area in 𝑃(𝑀𝐷) 𝑒𝑞 ) whereas the dimer ensemble comprises few, eventually one major, conformation (small red area in 𝑃(𝑀𝐷) 𝑒𝑞 ).



As indicated, a sizable part of the L4-loop is not seen in the 15N1H HSQC spectrum of the dimer.12,24 We suggest that this is due to slow or intermediate exchange between the major conformation and one or more minor conformations. The relative populations are such that only the major conformations are seen. The circumstances (exchange rates and populations) are specific to every NH site. Some major conformation cross-peaks are broadened beyond detection by slow or intermediate exchange. Others are not affected because the contribution to the natural linewidth is negligibly small in view of slow motion and/or small difference between the chemical shifts of the exchanging sites. The findings of ref 33, where NMR is used to identify regions of the plexinB1 RBD backbone that are likely to participate in inter-domain interactions, is in strong support of the interpretation delineated above (in particular, cf. Figure 6 of that article).

(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) 3.6.3. 𝑃(𝑀𝐷) and 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇). Quite a few 𝑃(𝑀𝐷) pictures along with their 𝑒𝑞 , 𝑃𝑒𝑞 𝑒𝑞 𝐿,𝐾 ― BEST) simulated 𝑃(𝐷 counterparts are shown in ref 13; the fits are good. A similar degree of 𝑒𝑞

agreement has been obtained in the present study. We show below typical examples of the set (𝐷𝐿,𝐾 ― BEST) including 𝑃(𝑀𝐷) and the lower-part of 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇); for simplicity, we use the 𝑒𝑞 , 𝑃𝑒𝑞 𝑠𝑖𝑚 𝑠𝑖𝑚 designations 𝑃𝑀𝐷 , respectively. 𝑒𝑞 , 𝑃𝑒𝑞 and 𝑢

Figure 10 shows the set specified above for residues D64 of the 3-strand (Figure 10a), S78 of the L4 loop (Figure 10b), and Q25 of the L1-loop (Figure 10c), of the dimer. The simulations are very good, with 𝜒2 values of 0.3, 0.2 and 1.5 for residues D64, S78 and Q25, respectively (the average 𝜒2 for the dimer is 0.3). All of the main features of 𝑃𝑀𝐷 𝑒𝑞  shape, extent of dispersion and 𝑠𝑖𝑚 location of the center – are well reproduced by 𝑃𝑠𝑖𝑚 , are deep, with well𝑒𝑞 . All three potentials, 𝑢

defined cup-shaped minima of 17.8, 21.6 and 29.1 kT for D64, S78, and Q25, respectively.


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Figure 11 shows two examples for the monomer, both taken from the L4-loop where 𝑃(𝑀𝐷) 𝑒𝑞 is most intricate, hence more difficult to reproduce. The 𝜒2 values are 2.8 and 2.3 for residue G88 and R92, respectively (the average 𝜒2 for the monomer is 1.5). The fits are good given the complexity and in some cases the multi-site character of 𝑃(𝑀𝐷) 𝑒𝑞 . The potentials are shallow, with the global minimum of the major site equal to 8.3 and 10.2 kT for G88 and R92, respectively. The lower parts of the potential energy landscapes are more trough-shaped than cup-shaped. Further studies, where terms with B1g, B2g and B3g symmetry, and/or higher L-values, will be included, are required to better understand the character of the local ordering at the NH sites of the L4-loop of the monomer. These enhancements are outside the scope of the present study. 𝑠𝑖𝑚 𝑠𝑖𝑚 Our last example is depicted in Figure 12, which illustrates 𝑃𝑀𝐷 for residue 𝑒𝑞 , 𝑃𝑒𝑞 and 𝑢

H74 of the monomer and the dimer. The fits are very good. This residue is exceptional in exhibiting 𝑀𝐷 𝑃𝑀𝐷 𝑒𝑞 pictures of similar character in both protein forms. The spatial dispersion of the 𝑃𝑒𝑞 functions

is moderate, the 𝑃𝑀𝐷 𝑒𝑞 centers are located close to the “reference NH orientation”, and the best-fit potentials, 𝑢𝑠𝑖𝑚, are shallow. Two close minima are featured by 𝑢𝑠𝑖𝑚, with the global minimum being 10.0 kT for the monomer and 7.2 kT for the dimer. In the monomer, residue H74 is located at the intersection of the shortest signal transmission pathway, and the overlapping signal transmission pathways 1 and 2.23 This is illustrated in Figure 13a, where the protein backbone is colored in cyan, the shortest signal transmission pathway in red, and the overlapping signal transmission pathways 1 and 2 in pink. Figure 13b shows the minima of the local potentials of the residues that comprise the shortest signal transmission pathway (orange bars), along with the corresponding minima of the dimer (blue bars). Within the scope of an average error estimated at ±1.5 kT the monomer exhibits a regular trend in the shortest signal transmission pathway. The potentials are shallow at the two 23 ACS Paragon Plus Environment


ends and become systematically deeper as one proceeds toward the middle. At that point, which coincides with the location of residue H74, the potential is again shallow, possibly reflecting diminished structural strain in compensation of increased structural strain at the neighboring constituents of the shortest signal transmission pathway. No regular trend is exhibited by the dimer. That is, the deviations of the potential minima from an illustrative line similar to the one drawn for the monomer would exceed substantially ±1.5 kT. These results are consistent with, and reinforce, the analysis of ref 23, where the signal transmission pathways were devised. That analysis is based on correlational motions derived from dihedral angle cross-correlation matrices. While the monomer experiences such motions the dimer does not do so, in agreement with only the potential minima of the monomer exhibiting a regular trend. The unique status of residue H74 is new information provided by the present study. Figure 14 shows the potentials, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), and the corresponding MD probability distributions, 𝑃(𝑀𝐷) 𝑒𝑞 , for residues F90, N94, H74, L109 and R61 of the shortest signal transmission pathway. The potentials of the end-pathway residues R61 and F90 are shallow and rhombic (see projection on the (, ) surface). The potentials of residues N94 and L109 are deep and rhombic. The potential of the middle residue H74 is shallow and nearly axial. Exceptionally, the H74 potential is shallower for the dimer as compared to the monomer. Connecting these features with atom-level properties of the MD force-field is a future prospect of interest. Another prospect of interest is to use 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) without further adjustment in SRLS analyses where so far the local potential has been adjusted.

4. CONCLUSIONS


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MD-derived POMFs of the amide bonds of the plexin-B1 RBD in monomer and dimer form are reproduced with reasonably good approximation by (analytical) linear combinations of 𝐷𝐿,𝐾 functions with L = 14 and appropriate symmetry. The monomer potentials are dominated by terms with polar (B1u and B2u) and non-polar (Ag) symmetry. They are shallow, exhibit substantial spatial dispersion, and are largely centered at the “reference NH orientation”. The dimer potentials are dominated by polar terms with B1u and B2u symmetry. They are largely deep, exhibit limited spatial dispersion, and in many cases are not centered at the “reference NH orientation”. Interpretations are offered for the L1-loop not being seen in the dimer crystal, and a large portion of the L4-loop not being seen in the NMR 15N1H HSQC spectrum of the dimer. A shortest signal transmission pathway was detected previously in the monomer. We find that the global minima of the pertinent local NH potentials exhibit a regular trend in the monomer but not in the dimer. Prospects of interest are stimulated by these results. The MD trajectories employed here were obtained with unbiased MD simulations, assumed to sample the conformation space satisfactorily. Among others, we offer the location of 𝑃(𝑀𝐷) in 𝑒𝑞 space as physically-relevant structural information. For practical reasons, authors recently prefer to perform biased or otherwise accelerated MD simulations for enhanced sampling. Comparison of 𝑃(𝑀𝐷) maximum from a representative biased simulation with its unbiased counterpart may 𝑒𝑞 serve as convergence criterion.

Supporting Information Available. Derivation of the real 𝐷𝐿,𝐾 functions from the Wigner rotation matrix elements, 𝐷𝐿0𝐾. Character Table of the D2h point-group; procedure for deriving Potential 𝐿,𝐾) (,) against 𝑃(𝑀𝐷) Of Mean Force from MD trajectories; procedure for optimizing 𝑃(𝐷 𝑒𝑞 (,); the 𝑒𝑞

histograms, 𝑃(𝑀𝐷) 𝑒𝑞 , of the NH bonds of the plexin-B1 RBD in monomer and dimer form. 25 ACS Paragon Plus Environment


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Author Information ORCID: Eva Meirovitch: 0000-0001-5117-5079 Matthias Buck: 0000-0002-2958-0403 Acknowledgments. We acknowledge support from the Israel Science Foundation (grant 369/15 to E.M.), and the Binational Israel-U.S.A. Science Foundation (grant 2016097 to E.M. and Jack H. Freed). The work of M. Buck for this project was supported by NIH grant R01GM112491.


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References 1. Ishima, R.; Torchia, D. A. Protein Dynamics by NMR. Nat. Struct. Biol. 2000, 7, 740743. 2. Case, D. A. Molecular Dynamics and NMR Spin Relaxation in Proteins. Acc. Chem. Res. 2002, 35, 325-331. 3. Jarymowycz, V. A.; Stone, M. J. Fast Time Scale Dynamics of Protein Backbones: NMR Relaxation Methods, Applications, and Functional Consequences. Chem. Rev. 2006, 106, 1624-1671. 4. Polimeno, A.; Freed, J. H. A Many-Body Stochastic Approach to Rotational Motions in Liquids. Adv. Chem. Phys. 1993, 83, 89-206. 5. Polimeno, A.; Freed, J. H. Slow Motional ESR in Complex Fluids: The Slowly Relaxing Local Structure Model of Solvent Cage Effects. J. Phys. Chem. 1995, 99, 10995–11006. 6. Liang, Z.; Freed, J. H. An Assessment of the Applicability of Multifrequency ESR to Study the Complex Dynamics of Biomolecules. J. Phys. Chem. B 1999, 103, 6384–6396. 7. Tugarinov, V.; Liang, Z.; Shapiro, Y. E.; Freed, J. H.; Meirovitch, E. A Structural ModeCoupling Approach to

15N

NMR Relaxation in Proteins. J. Am. Chem. Soc. 2001, 123,

3055-3063. 8. Meirovitch, E.; Shapiro, Y. E.; Polimeno, A.; Freed, J. H. Protein Dynamics from NMR: The Slowly Relaxing Local Structure Analysis Compared with Model-Free Analysis. J. Phys. Chem. A. 2006, 110, 8366-8396. 9. Zerbetto, M.; Polimeno, A.; Meirovitch, E. General Theoretical/Computational Tool for Interpreting NMR Spin Relaxation in Proteins. J. Phys. Chem. B. 2009, 113, 1361313625. 27 ACS Paragon Plus Environment


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10. Meirovitch, E.; Shapiro, Yu. E.; Polimeno, A.; Freed, J. H. Structural Dynamics of Biomolecules by NMR: The Slowly Relaxing Local Structure Approach. Prog. NMR Spectrosc. 2010, 56, 360-405. 11. Zerbetto, M.; Buck, M.; Meirovitch, E.; Polimeno, A. Integrated Computational Approach to the Analysis of NMR Relaxation in Proteins: Application to ps-ns Main-Chain 15N-1H and Global Dynamics of the Rho GTPase Binding Domain of Plexin-B1. J. Phys. Chem. B 2011, 115, 376–388. 12. Zerbetto, M.; Anderson, R.; Bouquet-Bonnet, S.; Rech, M.; Zhang, L.; Meirovitch, E.; Polimeno, A.; Buck, M. Analysis of 15N-1H NMR Relaxation in Proteins by a Combined Experimental and Molecular Dynamics Simulation Approach: Picosecond-Nanosecond Dynamics of the Rho GTPase Binding Domain of Plexin-B1 in the Dimeric State Indicates Allosteric Pathways. J. Phys. Chem. B 2013, 117, 174-184. 13. Tchaicheeyan, O.; Mendelman, N.; Zerbetto, M.; Meirovitch, E. Local Ordering at Mobile Sites in Proteins: Combining Perspectives from NMR Relaxation and Molecular Dynamics. J. Phys. Chem. B 2019, 123, 2745-2755. 14. Budil, D. E.; Sale, K. C.; Khairy. K. A.; Fajer, P. G. Calculating Slow-Motional Electron Paramagnetic Resonance Spectra from Molecular Dynamics Using a Diffusion Operator Approach. J. Phys. Chem. A 2006, 110, 3703-3713. 15. e-Chemical

Portal,

D2h

point

group.

http://www.webqc.org/printable-

symmetrypointgroup-d2h.html (accessed May 15, 2019). 16. Zare, R. N. Angular Momentum, John Wiley & Sons Inc., Hoboken, New Jersey, U. S. A. 1988.


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17. Tchaicheeyan, O.; Freed, J. H.; Meirovitch, E. Local Ordering at Mobile Sites in Proteins from Nuclear Magnetic Resonance Relaxation: The Role of Site Symmetry. J. Phys. Chem. B 2016, 120, 2886-2898. 18. Hota, P. K.; Buck, M. Plexin Structures Are Coming: Opportunities for Multilateral Investigations of Semaphorin Guidance Receptors, their Cell Signaling Mechanisms and Functions. Cell. Mol. Like Sci. 2012, 69, 3765-3805. 19. Zhang, L.; Bouguet-Bonnet, S.; Buck, M. Combining NMR and Molecular Dynamics Studies for Insights into the Allostery of Small GTPase-Protein Interactions. Methods Mol. Biol. 2012, 796, 235-259. 20. Tong, Y.; Chugha, P.; Hota, P. K.; Alviani, R. S.; Li, M.; Tempel, W.; Shen, L.; Park, H.W.; Buck, M. Binding of Rac1, Rnd1 and RhoD to a Novel Rho GTPase Interaction Motif Destabilizes Dimerization of the Plexin-B1 Effector Domain. J. Biol. Chem. 2007, 282, 37215-37224. 21. Tong, Y.; Hota, P. K.; Hamaneh, M. B.; Buck, M. Insights into Oncogenic Mutations of Plexin-B1 Based on the Solution Structure of the Rho GTPase Binding Domain. Structure 2008, 16, 246-258. 22. Hota, P. K.; Buck, M. Thermodynamic Characterization of two Homologous Protein Complexes: Associations of the Semaphorin Receptor Plexin-B1 with Rnd1 and Active Rac1. Protein Sci. 2009, 18, 1060-1071. 23. Zhang, L.; Centa, T.; Buck, M. Structure and Dynamics Analysis on Plexin-B1 Rho GTPase Binding Domain as a Monomer and Dimer. J. Phys. Chem. B 2014, 118, 73027311.



24. Zhang, L.; Buck, M. Molecular Dynamics Simulations Reveal Isoform Specific Contact Dynamics between the Plexin Rho GTPase Binding Domain (RBD) and Small Rho GTPases Rac1 and Rnd1. J. Phys. Chem. B 2017, 121, 1485-1498. 25. Bouguet-Bonnet S.; Buck M. Compensatory and Long-Range Changes in PicosecondNanosecond Main-Chain Dynamics Upon Complex Formation: 15N Relaxation Analysis of the Free and Bound States of the Ubiquitin-Like Domain of Human Plexin-B1 and the Small GTPase Rac1. J. Mol. Biol. 2008, 377, 1474-1487. 26. Tong, Y.; Hota, P. K.; Penachioni, J. Y.; Hamaneh, M. B.; Kim, S.; Alviani, R. S.; Shen, L.; He, H.; Tempel, W.; Tamagone, L.; Park, H. W.; Buck, M. Structure and Function of the Intracellular Region of the Plexin-B1 Transmembrane Receptor. J. Biol. Chem. 2009, 284, 35962-72. 27. Polnaszek, C. F.; Freed, J. H. Electron Spin Resonance Studies of Anisotropic Ordering, Spin Relaxation, and Slow Tumbling in Liquid Crystalline Solvents. J. Phys. Chem. 1975, 79, 2283-2306. 28. NMR of Liquid Crystals, edited by J. W. Emsley, Reidel, Dordrecht, 1983. 29. Freed, J. H.; Nayeem, A.; Rananavare, S. B. The Molecular Dynamics of Liquid Crystals, Chapter 12, p 271, edited by Luckhurst, G.R. and Veracini, C. A. Kluwer Academic Publishers, The Netherlands, 1994. 30. Buck, M.; Karplus, M. Internal and Overall Peptide Group Motion in Proteins: Molecular Dynamics Simulations for Lysozyme Compared with Results from X-Ray and NMR Spectroscopy. J. Am. Chem. Soc. 1999, 121, 9645-9658. 31. MATLAB version 9.6; Software and Statistics Toolbox; Mathworks Inc., Natick, Massachusetts, U. S. A.


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32. Wang, H.; Hota, P. K.; Shen, L.; Nedyalkova, L.; Borthkur, S.; Kim, S.; Buck, M.; Park, H. W. Structural Basis of Rnd1 Binding to Plexin Rho GTPase Binding Domains (RBDs). J. Biol. Chem. 2011, 286, 26093-106. 33. Tong, Y.; Hughes, D.; Placanica, L.; Buck, M. When Monomers Are Preferred: A Strategy for the Identification and Disruption of Weakly Oligomerized Proteins. Structure 2005, 13, 7-15.



Figure captions Figure 1. Ribbon diagram of the monomer (a) and dimer (b) used in the MD simulations that yielded the 𝑢(𝑀𝐷) histograms. Reproduced with permission from ref 23. Copyright (2014) American Chemical Society.

Figure 2. Local director frame, VF (a), and most probably local ordering frame, OF (b), for the SRLS potential 𝐷2,𝐾. The angle between the NH bond and the CC axis in Figure 2a is 101.3o.8

Figure 3. The axial real spherical harmonics (proportional to the corresponding 𝐷𝐿,𝐾 functions) 𝑌1,0, 𝑌2,0, 𝑌3,0 and 𝑌4,0 with B1u, Ag, B1u and Ag symmetry, respectively. Reproduced with permission from ref 13. Copyright (2019) American Chemical Society.

Figure 4. The rhombic real spherical harmonics 𝑌1,1, 𝑌3,1 and 𝑌3,3 with B2u symmetry. Reproduced with permission from ref 13. Copyright (2019) American Chemical Society.

Figure 5. [“symmetry-sum-Ag” – “symmetry-sum-B1u”], or “symmetry-sum-B2u” when “symmetry-sum-Ag” is zero, as a function of “potential-minimum” for the monomer (a). “symmetry-sum-B2u” as a function of “potential-minimum” for the dimer (b). “symmetry-sum-X” is the sum of the absolute values of the coefficients of the terms with symmetry X, where X is one of the irreducible representations Ag, Au, B1u, B2u or B3u of the D2h point-group.


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Figure 6. (a) Difference between the minimum of 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) for the dimer and its counterpart for the monomer for the 35 residues of plexin-B1 RBD subjected to quantitative analysis. (b) Distance Δ𝑑 ― 𝑚 = [(𝑥 ― 90)2 + (𝑥 ― 90)2]

0.5

between the minimum of the

potential, 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), located at (𝑥, 𝑥), and the minimum of the potential, 𝑢(𝐷2,𝐾), located at (90o, 90o), for the residues shown in part a. Figure 7. 𝑃(𝑀𝐷) histogram for residue Q39 of the α1-helix (a); residue A21 of the L1 loop 𝑒𝑞 (b); residue G51 of the L2-loop (c); residue V71 of the L3-loop (d); and residue V82 of the L4loop (e), for the monomer and the dimer of the plexin-B1 RBD.

Figure 8. 𝑃(𝑀𝐷) histograms for residues A24 (a) and G26 (b) of the L1-loop, for the 𝑒𝑞 monomer and the dimer of the plexin-B1 RBD.

Figure 9. 𝑃(𝑀𝐷) histograms for residues V82 (a) and Q87 (b) of the L4-loop, for the 𝑒𝑞 monomer and the dimer of the plexin-B1 RBD.

Figure 10. 𝑃(𝑀𝐷) histogram denoted by 𝑃MD 𝑒𝑞 eq (upper picture, left), its simulated counterpart, (𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) 𝐿,𝐾 ― 𝐵𝐸𝑆𝑇) , denoted by 𝑃sim , denoted by 𝑢𝑠𝑖𝑚 𝑃(𝐷 eq (lower picture, left), and the potential, 𝑢 𝑒𝑞

which corresponds to 𝑃sim eq (picture on the right), for residues D64 of the 3-strand (a), S78 of the L4-loop (b), and Q25 of the L1-loop (c) of the plexin-B1 RBD dimer. Similar designations apply to Figures 11 and 12.



sim Figure 11. 𝑃MD eq (upper picture, left), its simulated counterpart, 𝑃eq (lower picture, left),

and the potential, 𝑢𝑠𝑖𝑚, which corresponds to 𝑃sim eq (picture on the right), for residues G88 (a) and R92 (b) of the L4-loop of the plexin-B1 RBD monomer.

sim Figure 12. 𝑃MD eq (upper picture, left), its simulated counterpart, 𝑃eq (lower picture, left),

and the potential, 𝑢𝑠𝑖𝑚, which corresponds to 𝑃sim eq (picture on the right), for residue H74 of the β4 strand for the monomer and the dimer of plexin-B1 RBD.

Figure 13. RBD backbone (cyan), overlapping signal transmission pathways 1 and 2 (pink) and shortest signal transmission pathway (red) of the monomer (part a). Reproduced with permission from ref 23. Copyright (2014) American Chemical Society. Minimum energy of the residues comprising the shortest signal transmission pathway for the monomer (orange bars) and the dimer (blue bars) (part b). The shortest signal transmission pathway comprises (from the Nterminus toward the C-terminus) the residues F90, R92, N94, I37, H74, V65, L109, L63 and R61.

Figure 14. The potentials 𝑢(𝐷𝐿,𝐾 ― 𝐵𝐸𝑆𝑇), their minima, and the corresponding MD POMFs, 𝑃(𝑀𝐷) 𝑒𝑞 , for residues F90, N94, H74, L109 and R61 of the shortest signal transmission pathway in the monomer, shown in Figure 13a.


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TOC Graphic



a

ACS Paragon Plus Environment

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b

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The Journal of Physical Chemistry 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

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a

b

(kT)


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a

L1

α1

L2

β3

L3

β4

𝐊 −𝐁𝐄𝐒𝐓 ∆𝐝−𝐦 (𝐮𝐃𝐋, ) 𝐦𝐢𝐧

kT

b

Δd-m ([(θx-90)2+(φx-90)2]0.5)


residue

L4

α2/β5

β5

C-term


monomer

Page 42 of 50

dimer

a α1 39

θ

b L1 21 22 22 22 2x xx L2 xx 51 xx 22 xx xx xx xx L3 xx 71 xx 22 xx ggg g xx xx xx L4 xx 82 xx xx xx xx xx xx xx

θ

c θ

d θ

e θ

φ

φ


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monomer

dimer

a L1 24

θ

b L1 26

θ

φ

φ



monomer

Page 44 of 50

dimer

a L4 82

θ

b L4 87

θ

φ


φ

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dimer

a θ

3, res 64

kT

θ

ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww ww w

θ

θ

θ

θ

φ

b

L4, res78

kT

θ

φ

c

kT

L1, res 25

θ θ

φ

φ



Page 46 of 50

monomer

a θ

L4, res 88

kT

θ θ

φ

b θ

L4, res 92

kT

θ

φ

1111 θ 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 Plus Environment ACS Paragon 1111 1111

φ

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4, res 74

a θ kT

monomer

θ θ

φ

b θ

kT

dimer θ θ

φ ϕ


φ


a

b residue

kT


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F90

kT

=

R61

L109

N94

H74

7.6

= 3.0

13.9

12.3 10.3



monomer

dimer

u, kT







H74




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Local Ordering at the N-H Sites of the Rho GTPase Binding

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