Hui Lu

Mechanical unfolding intermediates in titin modules

The modular protein titin, which is responsible for the passive elasticity of muscle, is subjected to stretching forces. Previous work on the experimental elongation of single titin molecules has suggested that force causes consecutive unfolding of each domain in an all-or-none fashion. To avoid problems associated with the heterogeneity of the modular, naturally occurring titin, we engineered single proteins to have multiple copies of single immunoglobulin domains of human cardiac titin. Here we report the elongation of these molecules using the atomic force microscope. We find an abrupt extension of each domain by ∼7u2009Å before the first unfolding event. This fast initial extension before a full unfolding event produces a reversible ‘unfolding intermediate’. Steered molecular dynamics simulations show that the rupture of a pair of hydrogen bonds near the amino terminus of the protein domain causes an extension of about 6u2009Å, which is in good agreement with our observations. Disruption of these hydrogen bonds by site-directed mutagenesis eliminates the unfolding intermediate. The unfolding intermediate extends titin domains by ∼15% of their slack length, and is therefore likely to be an important previously unrecognized component of titin elasticity.

Unfolding of Titin Immunoglobulin Domains by Steered Molecular Dynamics Simulation

Titin, a 1-microm-long protein found in striated muscle myofibrils, possesses unique elastic and extensibility properties in its I-band region, which is largely composed of a PEVK region (70% proline, glutamic acid, valine, and lysine residue) and seven-strand beta-sandwich immunoglobulin-like (Ig) domains. The behavior of titin as a multistage entropic spring has been shown in atomic force microscope and optical tweezer experiments to partially depend on the reversible unfolding of individual Ig domains. We performed steered molecular dynamics simulations to stretch single titin Ig domains in solution with pulling speeds of 0.5 and 1.0 A/ps. Resulting force-extension profiles exhibit a single dominant peak for each Ig domain unfolding, consistent with the experimentally observed sequential, as opposed to concerted, unfolding of Ig domains under external stretching forces. This force peak can be attributed to an initial burst of backbone hydrogen bonds, which takes place between antiparallel beta-strands A and B and between parallel beta-strands A and G. Additional features of the simulations, including the position of the force peak and relative unfolding resistance of different Ig domains, can be related to experimental observations.

The mechanical stability of ubiquitin is linkage dependent

Ubiquitin chains are formed through the action of a set of enzymes that covalently link ubiquitin either through peptide bonds or through isopeptide bonds between their C terminus and any of four lysine residues. These naturally occurring polyproteins allow one to study the mechanical stability of a protein, when force is applied through different linkages. Here we used single-molecule force spectroscopy techniques to examine the mechanical stability of N-C–linked and Lys48-C–linked ubiquitin chains. We combined these experiments with steered molecular dynamics (SMD) simulations and found that the mechanical stability and unfolding pathway of ubiquitin strongly depend on the linkage through which the mechanical force is applied to the protein. Hence, a protein that is otherwise very stable may be easily unfolded by a relatively weak mechanical force applied through the right linkage. This may be a widespread mechanism in biological systems.

The key event in force-induced unfolding of Titin's immunoglobulin domains.

Steered molecular dynamics simulation of force-induced titin immunoglobulin domain I27 unfolding led to the discovery of a significant potential energy barrier at an extension of approximately 14 A on the unfolding pathway that protects the domain against stretching. Previous simulations showed that this barrier is due to the concurrent breaking of six interstrand hydrogen bonds (H-bonds) between beta-strands A and G that is preceded by the breaking of two to three hydrogen bonds between strands A and B, the latter leading to an unfolding intermediate. The simulation results are supported by Angstrom-resolution atomic force microscopy data. Here we perform a structural and energetic analysis of the H-bonds breaking. It is confirmed that H-bonds between strands A and B break rapidly. However, the breaking of the H-bond between strands A and G needs to be assisted by fluctuations of water molecules. In nanosecond simulations, water molecules are found to repeatedly interact with the protein backbone atoms, weakening individual interstrand H-bonds until all six A-G H-bonds break simultaneously under the influence of external stretching forces. Only when those bonds are broken can the generic unfolding take place, which involves hydrophobic interactions of the protein core and exerts weaker resistance against stretching than the key event.

Steered molecular dynamics simulations of force‐induced protein domain unfolding

Steered molecular dynamics (SMD), a computer simulation method for studying force‐induced reactions in biopolymers, has been applied to investigate the response of protein domains to stretching apart of their terminal ends. The simulations mimic atomic force microscopy and optical tweezer experiments, but proceed on much shorter time scales. The simulations on different domains for 0.6 nanosecond each reveal two types of protein responses: the first type, arising in certain β‐sandwich domains, exhibits nanosecond unfolding only after a force above 1,500 pN is applied; the second type, arising in a wider class of protein domain structures, requires significantly weaker forces for nanosecond unfolding. In the first case, strong forces are needed to concertedly break a set of interstrand hydrogen bonds which protect the domains against unfolding through stretching; in the second case, stretching breaks backbone hydrogen bonds one by one, and does not require strong forces for this purpose. Stretching of β‐sandwich (immunoglobulin) domains has been investigated further revealing a specific relationship between response to mechanical strain and the architecture of β‐sandwich domains. Proteins 1999;35:453–463.

Steered Molecular Dynamics

Steered molecular dynamics (SMD) induces unbinding of ligands and conformational changes in biomolecules on time scales accessible to molecular dynamics simulations. Time-dependent external forces are applied to a system, and the responses of the system are analyzed. SMD has already provided important qualitative insights into biologically relevant problems, as demonstrated here for applications ranging from identification of ligand binding pathways to explanation of elastic properties of proteins. First attempts to deduce potentials of mean force by discounting irreversible work performed on the system are summarized. The non-equilibrium statistical mechanics underlying analysis of SMD data is outlined.

Steered molecular dynamics simulation of conformational changes of immunoglobulin domain I27 interprete atomic force microscopy observations

Abstract Atomic force microscopy and steered molecular dynamics investigations of the response of so-called mechanical proteins like titin, tenascin or their individual immunoglobulin and fibronectin type III domains have lead to qualitative insights about the relationship between the β sandwich domain architecture and the function of this class of proteins. The proteins, linear segments of up to hundreds of domains, through strain induced shape changes, unfolding and refolding, maintain order and elasticity in cellular systems over a nearly tenfold length scale. In this paper we develop a steered molecular dynamics description of the response of the titin immunoglobulin domain I27 at the onset of domain unfolding in quantitative agreement with AFM observations. We show that if forces stronger than 50 pN are applied to the terminal ends the two hydrogen bonds between the antiparallel A and B β strands break with a concomitant 6–7 A elongation of the protein. If forces strong enough to unfold the domain are applied, the protein is halted in this initial extension until the set of all six hydrogen bonds connecting strands A′ and G break simultaneously. This behavior is accounted for by a barrier separating folded and unfolded states, the shape of which is consistent with AFM and chemical denaturation data. We also demonstrate that steered molecular dynamics simulations which induce unfolding through slow pulling (speed 0.1 A/ps) predict unfolding forces that are within a factor of two within force values extrapolated from AFM observations.

Single-molecule force spectroscopy reveals a mechanically stable protein fold and the rational tuning of its mechanical stability

It is recognized that shear topology of two directly connected force-bearing terminal β-strands is a common feature among the vast majority of mechanically stable proteins known so far. However, these proteins belong to only two distinct protein folds, Ig-like β sandwich fold and β-grasp fold, significantly hindering delineating molecular determinants of mechanical stability and rational tuning of mechanical properties. Here we combine single-molecule atomic force microscopy and steered molecular dynamics simulation to reveal that the de novo designed Top7 fold [Kuhlman B, Dantas G, Ireton GC, Varani G, Stoddard BL, Baker D (2003) Science 302:1364–1368] represents a mechanically stable protein fold that is distinct from Ig-like β sandwich and β-grasp folds. Although the two force-bearing β strands of Top7 are not directly connected, Top7 displays significant mechanical stability, demonstrating that the direct connectivity of force-bearing β strands in shear topology is not mandatory for mechanical stability. This finding broadens our understanding of the design of mechanically stable proteins and expands the protein fold space where mechanically stable proteins can be screened. Moreover, our results revealed a substructure-sliding mechanism for the mechanical unfolding of Top7 and the existence of two possible unfolding pathways with different height of energy barrier. Such insights enabled us to rationally tune the mechanical stability of Top7 by redesigning its mechanical unfolding pathway. Our study demonstrates that computational biology methods (including de novo design) offer great potential for designing proteins of defined topology to achieve significant and tunable mechanical properties in a rational and systematic fashion.

Simulated Refolding of Stretched Titin Immunoglobulin Domains

Steered molecular dynamics (SMD) is used to investigate forced unfolding and spontaneous refolding of immunoglobulin I27, a domain of the muscle protein titin. Previous SMD simulations revealed the events leading to stretch-induced unfolding of I27, the rupture of hydrogen bonds bridging beta-strands A and B, and those bridging beta-strands A and G, the latter rupture occurring at an extension of approximately 15 A and preceding the complete unfolding. Simulations are now used to study the refolding of partially unfolded I27 domains. The results reveal that stretched domains with ruptured interstrand hydrogen bonds shrink along the extension direction. Two types of refolding patterns are recognized: for separated beta-strands A and G, in most simulations five of the six hydrogen bonds between A and G stably reformed in 2 ns, whereas for separated beta-strands A and B hydrogen bonds seldom reformed in eight 2-ns simulations. The mechanical stability of the partially refolded intermediates has been tested by re-stretching.

Three Electronic State Model of the Primary Phototransformation of Bacteriorhodopsin

The primary all-trans --> 13-cis photoisomerization of retinal in bacteriorhodopsin has been investigated by means of quantum chemical and combined classical/quantum mechanical simulations employing the density matrix evolution method. Ab initio calculations on an analog of a protonated Schiff base of retinal in vacuo reveal two excited states S1 and S2, the potential surfaces of which intersect along the reaction coordinate through an avoided crossing, and then exhibit a second, weakly avoided, crossing or a conical intersection with the ground state surface. The dynamics governed by the three potential surfaces, scaled to match the in situ level spacings and represented through analytical functions, are described by a combined classical/quantum mechanical simulation. For a choice of nonadiabatic coupling constants close to the quantum chemistry calculation results, the simulations reproduce the observed photoisomerization quantum yield and predict the time needed to pass the avoided crossing region between S1 and S2 states at tau1 = 330 fs and the S1 --> ground state crossing at tau2 = 460 fs after light absorption. The first crossing follows after a 30 degrees torsion on a flat S1 surface, and the second crossing follows after a rapid torsion by a further 60 degrees. tau1 matches the observed fluorescence lifetime of S1. Adjusting the three energy levels to the spectral shift of D85N and D212N mutants of bacteriorhodospin changes the crossing region of S1 and S2 and leads to an increase in tau1 by factors 17 and 10, respectively, in qualitative agreement with the observed increase in fluorescent lifetimes.