Multiscale relaxation dynamics and diffusion of myelin basic protein in solution studied by quasielastic neutron scattering

Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586-599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head-tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Signature of functional enzyme dynamics in quasielastic neutron scattering spectra: The case of phosphoglycerate kinase

We present an analysis of high-resolution quasi-elastic neutron scattering spectra of phosphoglycerate kinase which elucidates the influence of the enzymatic activity on the dynamics of the protein. We show that in the active state the inter-domain motions are amplified and the intra-domain asymptotic power-law relaxation ∝t-α is accelerated, with a reduced coefficient α. Employing an energy landscape picture of protein dynamics, this observation can be translated into a widening of the distribution of energy barriers separating conformational substates of the protein.

Variation of Structural and Dynamical Flexibility of Myelin Basic Protein in Response to Guanidinium Chloride

Myelin basic protein (MBP) is intrinsically disordered in solution and is considered as a conformationally flexible biomacromolecule. Here, we present a study on perturbation of MBP structure and dynamics by the denaturant guanidinium chloride (GndCl) using small-angle scattering and neutron spin-echo spectroscopy (NSE). A concentration of 0.2 M GndCl causes charge screening in MBP resulting in a compact, but still disordered protein conformation, while GndCl concentrations above 1 M lead to structural expansion and swelling of MBP. NSE data of MBP were analyzed using the Zimm model with internal friction (ZIF) and normal mode (NM) analysis. A significant contribution of internal friction was found in compact states of MBP that approaches a non-vanishing internal friction relaxation time of approximately 40 ns at high GndCl concentrations. NM analysis demonstrates that the relaxation rates of internal modes of MBP remain unaffected by GndCl, while structural expansion due to GndCl results in increased amplitudes of internal motions. Within the model of the Brownian oscillator our observations can be rationalized by a loss of friction within the protein due to structural expansion. Our study highlights the intimate coupling of structural and dynamical plasticity of MBP, and its fundamental difference to the behavior of ideal polymers in solution.

Dynamical Behavior of Disordered Regions in Disease-Related Proteins Revealed by Quasielastic Neutron Scattering

Background and Objectives: Intrinsically disordered proteins (IDPs) and proteins containing intrinsically disordered regions (IDRs) are known to be involved in various human diseases. Since the IDPs/IDRs are fluctuating between many structural substrates, the dynamical behavior of the disease-related IDPs/IDRs needs to be characterized to elucidate the mechanisms of the pathogenesis of the diseases. As protein motions have a hierarchy ranging from local side-chain motions, through segmental motions of loops or disordered regions, to diffusive motions of entire molecules, segmental motions, as well as local motions, need to be characterized. Materials and Methods: Combined analysis of quasielastic neutron scattering (QENS) spectra with the structural data provides information on both the segmental motions and the local motions of the IDPs/IDRs. Here, this method is applied to re-analyze the QENS spectra of the troponin core domain (Tn-CD), various mutants of which cause the pathogenesis of familial cardiomyopathy (FCM), and α-synuclein (αSyn), amyloid fibril formation of which is closely related to the pathogenesis of Parkinson's disease, collected in the previous studies. The dynamical behavior of wild-type Tn-CD, FCM-related mutant Tn-CD, and αSyn in the different propensity states for fibril formation is characterized. Results: In the Tn-CD, the behavior of the segmental motions is shown to be different between the wild type and the mutant. This difference is likely to arise from changes in the intramolecular interactions, which are suggested to be related to the functional aberration of the mutant Tn-CD. In αSyn, concerted enhancement of the segmental motions and the local motions is observed with an increased propensity for fibril formation, suggesting the importance of these motions in fibril formation. Conclusions: Characterization of the segmental motions as well as the local motions is thus useful for discussing how the changes in dynamical behavior caused by the disease-related mutations and/or environmental changes could be related to the functional and/or behavioral aberrations of these proteins.

Revisiting the modeling of quasielastic neutron scattering from bulk water

Quasi-elastic neutron scattering (QENS) from bulk-water at 300 K, measured on the IRIS backscattering neutron spectrometer (ISIS, UK), is interpreted using the jump diffusion model (JDM), a “minimalistic” multi-timescale relaxation model (MRM) and molecular dynamics simulations (MD). In the case of MRM data analysis is performed in the time domain, where the relaxation of the intermediate scattering function is described by a stretched Mittag-Leffler function, Eα(−(|t|/τ)α). This function displays an asymptotic power law decay and contains the exponential relaxation function as a special case (α = 1). To further compare the two approaches, MD simulations of bulk water were performed using the SPCE force field and the resulting MD trajectories analysed using the nMoldyn software. We show that both JDM and MRM accurately describe the diffusion of bulk water observed by QENS at all length scales, and confirm that MD simulations do not fully describe the quantum effects of jump diffusion.