Differences between calcium rich and depleted alpha-lactalbumin investigated by molecular dynamics simulations and incoherent neutron scattering

Dominik Zeller, Pan Tan, Liang Hong, Daniele Di Bari, Victoria Garcia Sakai, and Judith Peters

Phys. Rev. E 101, 032415 – Published 25 March 2020

Abstract

We present a study comparing atomic motional amplitudes in calcium rich and depleted alpha-lactalbumin. The investigations were performed by elastic incoherent neutron scattering (EINS) and molecular dynamics (MD) simulations. As the variations were expected to be very small, three different hydration levels and timescales (instrumental resolutions) were measured. In addition, we used two models to extract the mean square displacements (MSDs) from the EINS data, one taking into account the motional heterogeneity of the MSD. At a timescale of several nanoseconds, small differences in the amplitudes between the calcium enriched and depleted alpha-lactalbumin are visible, whereas at lower timescales no changes can be concluded within the statistics. The results are compared to MD simulations at 280 and 300 K by extracting the MSDs of the trajectories in two separate ways: first by direct calculation, and second by a virtual neutron experiment using the same models as for the experimental data. We show that the simulated data give qualitatively similar results as the experimental data but quantitatively there are differences. Furthermore, the distribution of the MSDs in the simulations suggests that the inclusion of heterogeneity is reasonable for alpha-lactalbumin, but a bi-or trimodal approach may be sufficient.

Received 8 November 2019
Accepted 21 February 2020

DOI:https://doi.org/10.1103/PhysRevE.101.032415

Physics Subject Headings (PhySH)

Biomolecular dynamics

Proteins

Molecular dynamics Neutron scattering

Physics of Living SystemsInterdisciplinary Physics

Authors & Affiliations

Dominik Zeller¹, Pan Tan ², Liang Hong ², Daniele Di Bari ^1,3, Victoria Garcia Sakai ⁴, and Judith Peters ^1,*

¹University Grenoble Alpes, LiPhy, CNRS, F-38000 Grenoble, France and Institut Laue Langevin, F-38042 Grenoble Cedex 9, France
²School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
³Physics Department, University of Perugia, 06123 Perugia, Italy
⁴ISIS Pulsed Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, United Kingdom

^*jpeters@ill.fr

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Issue

Vol. 101, Iss. 3 — March 2020

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Images

Figure 1
Calcium rich (yellow, bright) and depleted (red, dark) forms of α‐La and the variations induced on their structures. α‐La from most mammals consists of 123 amino acid residues [1] and its molecular 4 weight is ≈14.2 kDa.
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Figure 2
Visualization of the dry and hydrated simulations of α‐La_dep. (a) Dry environment (0.05h). (b) Hydrated environment (0.4h). The lines show the simulation box size and inside the six chains of α‐La_dep at 300 K are visualized. The little (blue) molecules indicate water. For the sake of better visibility, we represented the proteins as connected molecules, therefore going beyond the limits of the box, and not as distributed within the same box due to the boundary conditions.
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Figure 3
Difference of MSD between α‐La_dep and α‐La_ca for OSIRIS (a) and SPHERES (b,c). Data are only shown from 100 to 310 K to enhance the differences, since at temperature $< 100 K$ there are no differences within statistical error. The MSD values of the α‐La_dep are shown as dotted lines and empty symbols, and those for α‐La_ca as solid lines and filled symbols. The dry samples are blue (lower curves), the $0.4 h$ samples are red (middle curves), and the $0.8 h$ samples are green (upper curves).
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Figure 4
MSDs from analyzing data from MD simulations using both indirect (GA approximation: lower curves, PK model: middle curves) and direct calculations (upper curves) for the Gaussian resolution function of SPHERES (a), IN13 (b), and OSIRIS (c). On the left side the dry α‐La is shown and on the right side the hydrated protein at $0.4 h$ . As indicated, each side is ordered in the same way by increasing temperature (280 and 300 K) and α‐La_dep is next to α‐La_ca.
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Figure 5
Distributions of the direct MSDs. Comparison of distributions of the MSDs at $t = 30$ ps (OSIRIS, highest curve in the peak), 60 ps (IN13, middle curve in the peak), and 1000 ps (SPHERES, lowest curve in the peak) for α‐La_ca (b) and α‐La_dep (a). The upper two figures are the dry samples at 280 and 300 K; the lower two figures are the hydrated samples at 280 and 300 K. The MSD values were obtained by the average value of the four independent slices of 5 ns for each simulation. $Δ_{dir}$ in the legend shows the mean value of the distribution as defined in Eq. (7).
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Figure 6
MSD: Experimental data vs MD simulated data. Comparison between the three models obtained by fitting the experimental data (open symbols, dashed lines) and the MD simulations (filled symbols, dotted lines). The circles designate the GA approximation and the squares the PK model.
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