Membrane proteins carry great importance in cellular functions, such as nutrient uptake, transport of membrane-impermeable molecules, ion balance, etc. These make membrane proteins the prime drug targets. In fact, 50% of modern medicines target helical membrane proteins. However, despite the biological importance, membrane proteins are notoriously difficult to study. Because it is difficult to obtain high-resolution structures, membrane proteins are greatly under-represented in Protein Data Bank. The scarcity of available structures makes it even harder to obtain information of the dynamic behaviors of membrane proteins. The topic lying at the heart of the problem is how transmembrane proteins fold. Observation of how bacteriorhodopsin (bR) folds in vitro leads to a two-stage thermodynamic model, which was brought up in 1990. In the first stage, unfolded chain forms helices on the surface of the membrane and the helices spontaneously insert into the bilayer. In the second stage, the transmembrane helices assemble into a well-functional tertiary structure. To study the folding in terms of a thermodynamic model is meaningful because in vivo fold- ing must proceed within the thermodynamic context. The importance of understanding the two-stage model is that the two stages are controlled by different forces. The first stage is driven mainly by the hydrophobic effect, whereas the second stage is mediated by various weak interactions. There are several factors that add to the difficulty of studying the folding of transmembrane proteins computationally. First, the structures of transmembrane proteins are in nature complex. Ideally, the transmembrane protein consists of several transmembrane helices, each of which is hydrophobically stabe and spans the lipid bilayer, such as bR. However, exceptions happen all the time. Re-entrant helices enter and exit the bilayer on the same side; interfacial helices lie on the interface of the membrane; and there are kinks and coils in the middle of a transmembrane helix. Moreover, sometimes the transmembrane helix is not hydrophobically stable by itself but via the association with neighboring helices. Second, the folding and stability of transmembrane proteins are dictated by a delicate balance of various weak interactions, such as van der Waals forces, H-bonding, salt-bridge, and weakly polar interactions. The interplay between the protein and the lipid bilayer also plays an important role. Besides, multiple functional conformations exist. The energy minimum may only correlate to one of them. Thus, developing a force field, which describes the balance of those weak interactions well and is able to distinguish native-like structures from non-native structures, is the prerequisite for computational study. Third, it is hard to mimic the realistic protein/membrane complex, as the complex is highly heterogeneous and composed of a variety of biomolecules at different concentrations. Lastly, it is usually very expensive to simulate membrane proteins. The size of the system is typically larger than 100,000 atoms, including the protein, lipids, ligands, water molecules and ions, and the timescale required for obtaining physically meaningful results is usually microsecond or longer. To circumvent these problems or to look at the problem from a different angle, people unfold membrane proteins by force and obtain the folding energetics by extrapolating the applied force back to zero. Experimentally, single-molecule force spectroscopy (SMFS), such as atomic force spectroscopy (AFM) and magnetic tweezers, allows scientists to manipulate biomolecules on the single-molecule level. SMFS has proven beneficial in detecting sparsely populated intermediates and yielding kinetic insights into the unfolding pathways of membrane proteins. To put it all together, before my study, Dr. John Jumper in our group has developed a fast, atomic-level coarse-grained model, Upside, which is capable of de novo folding of proteins shorter than 100 residues in cpu-hours. Upside is a non-Go, physics based model with five atoms per residue (N, Cα, C, H, O), a side chain bead and with residue- and neighbor-dependent Ramachandran maps. The energy function includes H-bonds, side chain- side chain and side chain-backbone interactions (including helix capping), and a solvation term. At each step, the side chain bead is first decorated to each of the residues. The positions of the side chain beads are determined based on the joint probability of all side chain beads which gives the lowest global free energy for all side chains. The force is computed using the joint probability. Then, the side chain beads are undecorated while the forces are applied to the backbone atoms. I have incorporated Upside with my new knowledge-based membrane burial potential as the implicit solvent for membrane proteins, which dynamically calculates the degree of side chain exposure to lipids during the simulations and includes energies for unsatisfied H-bond donors and acceptors in the membrane. Hence, I am able to perform fast, atomic-level simulations on membrane proteins. In specific, I choose to study the forced unfolding of membrane proteins by SMFS. I have developed an accurate and fast atomic-level simulation that allows me to conduct hundreds of unfolding simulations to characterize the folding energy surface under force. The algorithm reproduces many of the experiment features of SMFS studies for the unfolding of bR and GlpG. I find that the mode of force application alters the perception of the folding landscape. For GlpG unfolding using a weaker spring to mimic a magnetic tweezers measurement, the force remains nearly constant after the initial unfolding event and few if any intermediates are observed, as found in experiment. With a stiff cantilever, however, the force drops to near-zero after each major unfolding event and numerous intermediates are observed. Notably, the application of constant force, whether intentionally or as a result of force being applied through a weak spring constant, as with magnetic tweezers or after a substantial portion of the protein is unfolded, reduces the probability of observing intermediates while increasing the apparent unfolding cooperativity as compared to the use of stiffer cantilevers with short attachment handles. Our method can assist experimental studies by helping convert force extension curves to structures, pathways, and energies, which can be challenging. Moreover, our method can be employed to simulate complicated thought experiments beyond current experimental capabilities such as pulling on multiple sites in multiple directions with different strength springs with either membrane or soluble proteins.




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