A key future-oriented theme for much of the modeling work in this dissertation is the need to understand the organization and dynamics of the cytoskeleton because it plays a key role in cell function. In 2013, I produced models for Dr. Sira Sriswasdi, who was then a student working with David Spicher at the Wistar institute. The goal of this project was to generate a molecular model of minispectrin in order to provide detail to crosslinking experiments. Spectrin is large, flexible molecule that exists primarily as a heterotetramer of various isoforms, and forms a large part of the “membrane skeleton”, a two-dimensional network on the inner leaflet of the plasma membrane [205].
Cross-linking experiments coupled with mass spectrometry can resolve the motion of spectrin, which is otherwise too large for crystallography or NMR experiments [320]. Our simulations sought to test the accuracy of homology models for the protein by comparing their motions to that observed by crosslinking. Specifically, we sought to predict whether particular residues would move close enough to crosslink in hour-long duration of a typical experiment.
Molecular simulations Molecular dynamics simulations were used to investigate the
flexibility of mini-spectrin subunits in order to provide additional insight into the dynamics mini-spectrin flexibility. Theα2 subunit was simulated for 100 ns using the
CHARMM27 all-atom molecular dynamics force field [207] in GROMACS (version 4.5.5)
[342]. The starting structure, derived from homology models provided by the Spicher lab, was minimized, solvated with water, neutralized with counter-ions, and relaxed under constant volume (NVT) simulation for 100 ps before switching to a constant- pressure (NPT) for a production run lasting 100 ns. All simulation parameters were set as per the standard method [37] with a temperature of 300K and at least 20 Å of water between the protein and the periodic boundary condition.
This simulation procedure was also used to refine the structures of the wild-type mini-spectrin dimer, the L207P mutant dimer, and mini-spectrin tetramer. These simulations contained up to 1.8 million atoms. These simulations showed a root mean-squared deviation (RMSD) of up to 11 Å from the homology models.
Principal component analysis To connect these simulations to cross-linking experi-
ments, principal component analysis (PCA) was used to estimate the energy barrier necessary to bring key residues within the 12 Å cross-linking distance in a simulation of a single subunit. In this method, the motion of backboneα-carbon atoms is measured by a covariance matrix of atomic positions. For a system of N particles, diagonal- ization of the covariance matrix gives a set of eigenvalues and eigenvectors which
Figure 7.3: Structure of the minispectrin tetramer used in atomistic simulations described in this section. Spectrin is made from similar, heterogeneous repeating units of these filaments.
provide the amplitudes and directions of independent motions in the 3N-dimensional configuration space. The largest eigenvalues correspond to delocalized, low-frequency motions and are often sufficient to describe much of the protein fluctuations. Similar methods have been used to characterize protein structure and function in a variety of systems [7, 19, 35].
Invoking the quasiharmonic approximation to estimate the minimum energy re- quired to bring key residues within the 12 Å cross-linking distance, we project a set of eigenvectors onto the average protein structure, each of which is scaled by a chosen amplitude δi requiring an energy equal to Ui(δi) = 21kiδi2 where ki is an effec-
tive spring constant for the ith mode. The spring constants are estimated using the
equipartition theorem, according to which, each harmonic mode has a stiffness given by ki = kBT/ λi where λi is the eigenvalue corresponding to the ith mode and kB is
Boltzmann’s constant. By projecting a linear combination of these scaled eigenvec- tors onto the protein’s average structure, we calculate the corresponding inter-residue distance.
The total energy to bring the residues to this distance is then the sum of the corresponding Ui(δi). The Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization
algorithm implemented in NumPy (version 1.6.2) [343] was used to search for the lowest-energy combination of eigenvectors subject to a harmonic restraint which set a preferred intra-residue gap distance.
Assuming a molecular vibrational frequency of kBT/h = 6×1012s−1 we estimate
(using transition state theory) that it would be possible to cross an energy barrier of roughly 36 kBT during an hour-long cross-linking experiment. This suggests that the
and third links will reach 18.8 Å and 22.4 Å within one hour. The average inter-residue distances for these links were observed to be 15.3 Å, 28.2 Å and 31.3 Å, respectively during the 100 ns simulation.
While estimates of the time-to-crosslink were reasonable when analyzed one-at-a- time, they failed to produce aconsistent description of the crosslinking. For example, comparing the projection of the simulation trajectories onto the long-mode fluctu- ations suggested that the structure was not well-equilibrated. Moreover, the PCA calculation showed high uncertainty across segments of the trajectory. This is likely a consequence of the rugged energy landscape that proteins explore.
There is much to be learned by extrapolating molecular simulations to timescales accessible by modern experiments. In the future it may be possible to more closely link atomistic simulations with the results of crosslinking experiment, particularly since zero-length crosslinks are now available [321].