Maximum entropy reconstruction of joint φ, ψ-distribution with a coil-library prior: the backbone conformation of the peptide hormone motilin in aqueous solution from φ and ψ-dependent J-couplings

Abstract

In this paper, we present a new method for structure determination of flexible "random-coil" peptides. A numerical method is described, where the experimentally measured 3J(H(alpha)Nalpha) and [3J(H(alpha)Nalpha+1 couplings, which depend on the phi and psi dihedral angles, are analyzed jointly with the information from a coil-library through a maximum entropy approach. The coil-library is the distribution of dihedral angles found outside the elements of the secondary structure in the high-resolution protein structures. The method results in residue specific joint phi,psi-distribution functions, which are in agreement with the experimental J-couplings and minimally committal to the information in the coil-library. The 22-residue human peptide hormone motilin, uniformly 15N-labeled was studied. The 3J(H(alpha)-N(i+1)) were measured from the E.COSY pattern in the sequential NOESY cross-peaks. By employing homodecoupling and an in-phase/anti-phase filter, sharp H(alpha)-resonances (about 5 Hz) were obtained enabling accurate determination of the coupling with minimal spectral overlap. Clear trends in the resulting phi,psi-distribution functions along the sequence are observed, with a nascent helical structure in the central part of the peptide and more extended conformations of the receptor binding N-terminus as the most prominent characteristics. From the phi,psi-distribution functions, the contribution from each residue to the thermodynamic entropy, i.e., the segmental entropies, are calculated and compared to segmental entropies estimated from 15N-relaxation data. Remarkable agreement between the relaxation and J-couplings based methods is found. Residues belonging to the nascent helix and the C-terminus show segmental entropies, of approximately -20 J K(-1) mol(-1) and -12 J K(-1) mol(-1), respectively, in both series. The agreement between the two estimates of the segmental entropy, the agreement with the observed J-couplings, the agreement with the CD experiments, and the assignment of population to sterically allowed conformations show that the phi,psi-distribution functions are indeed meaningful and useful descriptions of the conformational preferences for each residue in this flexible peptide.

Just a Flexible Linker? The Structural and Dynamic Properties of CBP-ID4 Revealed by NMR Spectroscopy

“…The 3 J HN-Ha coupling constants (46) (Fig. 3) provide complementary information to detect a contingent residual structural propensity along the polypeptide chain, and therefore are often used in structural characterizations of chemically unfolded proteins or IDPs (76)(77)(78)(79)(80). The obtained average value of~7 Hz is similar to values obtained for flexible proteins and other disordered peptides (79,80).…”

Population distribution of flexible molecules from maximum entropy analysis using different priors as background information: application to the ϕ, ψ-conformational space of the α-(1→2)-linked mannose disaccharide present in N- and O-linked glycoproteins

“…For continuous distributions the information entropy is defined relative to a prior, P, in order to avoid an invariance problem. 50 (3) When the base two logarithm is used the information entropy is a direct measure of how many bits of information one needs in order to transform the prior, P(f,y ), into the distribution, r(f,y ). The information entropy is zero if r(f,y ) is identical to P(f,y ) and negative otherwise.…”

Molecular simulations minimally restrained by experimental data

“…12 suggests that the restrained ensemble simulations generate the same distribution as the maximum entropy method if the number of replicas satisfies the following inequality 1 ≪ N ≪ min(eigenvalues of K · Σ λ ). (14) This condition is the generalization of the condition N ≪ K derived for the special case of harmonic potentials 16 . Under this condition, (I + N K −1 Σ −1 λ ) −1 ≈ I, the corresponding single-replica distribution becomes…”

“…The restrained simulations should be no more biased by the restraints than is necessary, which is a principle that motivated the alternative maximum entropy method, which seeks a distribution that reproduces the experimental values of the observables and is minimally perturbed from the unbiased distribution [11][12][13][14] . It has been established that in some limit of infinite number a) Correspondence to huafeng.xu@silicontx.com of replicas and infinitely strong restraints, restrained ensemble simulations generate a statistically equivalent distribution as the maximum entropy method 10,[15][16][17] .…”