TCB Publications

Juxtaposing density matrix and ensemble-averaged wave packet dynamics.

Mortaza Aghtar, Jörg Liebers, Johan Strümpfer, Klaus Schulten, and Ulrich Kleinekathöfer. Juxtaposing density matrix and ensemble-averaged wave packet dynamics. Journal of Chemical Physics, 2012. In press.

In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behaviour in the wave packet simulations is probed and an improvement is proposed.

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Mutation of conserved histidines alters the tertiary structure and nanomechanics of consensus ankyrin repeats.

Whasil Lee, Johan Strümpfer, Vann Bennett, Klaus Schulten, and Piotr E. Marszalek. Mutation of conserved histidines alters the tertiary structure and nanomechanics of consensus ankyrin repeats. Journal of Biological Chemistry, 2012. In press.

The conserved TPLH tetrapeptide motif of ankyrin repeats (ARs) plays an important role in stabilizing AR proteins, and histidine (TPLH) to arginine (TPLR) mutations in this motif have been associated with a hereditary human anemia, spherocytosis (HS). Here, we used a combination of Atomic Force Microscopy (AFM)-based single-molecule force spectroscopy and molecular dynamics (MD) simulations to examine the mechanical effects of HR substitutions in TPLH motifs in a model ankyrin repeat protein, NI6C. Our MD results show that the mutated protein is less mechanically stable than the wild-type (WT). Our AFM results indicate that the mechanical energy input necessary to fully unfold the mutated protein is only half of that necessary to unfold the WT protein (53 kcal/mol vs. 106 kcal/mol). In addition, the ability of the mutant to generate refolding forces is also reduced. Moreover, the mutant protein subjected to cyclic stretch-relax measurements displays mechanical fatigue, which is absent in the WT. Taken together, these results indicate that the HR substitutions in TPLH motifs compromise mechanical properties of ARs and suggest that the origin of HS may be related to mechanical failure of ankyrin repeats.

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Structural characterization of λ-repressor folding from all-atom molecular dynamics simulations.

Yanxin Liu, Johan Strümpfer, Peter L. Freddolino, Martin Gruebele, and Klaus Schulten. Structural characterization of λ-repressor folding from all-atom molecular dynamics simulations. Journal of Physical Chemistry Letters, 3:1117-1123, 2012.

The five-helix bundle -repressor fragment is a fast-folding protein. A length of 80 amino acid residues puts it on the large end among all known microsecond folders and its size poses a computational challenge for molecular dynamics (MD) studies. We simulated the folding of a novel -repressor fast-folding mutant (-HG) in explicit solvent using an all-atom description. By means of a recently developed tempering method, we observed reversible folding and unfolding of -repressor in a 10- microsecond trajectory. The folding kinetics was also investigated through a set of MD simulations run at different temperatures that together covered more than 125 microseconds. The protein was seen to fold into a native-like topology at intermediate temperature and a slow-folding pathway was identified. The simulations suggest new experimental observables for better monitoring the folding process, and a novel mutation expected to accelerate -repressor folding.

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Fast visualization of Gaussian density surfaces for molecular dynamics and particle system.

Michael Krone, John E. Stone, Thomas Ertl, and Klaus Schulten. Fast visualization of Gaussian density surfaces for molecular dynamics and particle system. In Proceedings of EuroVis 2012, 2012. In press.

We present an efficient algorithm for computation of surface representations enabling interactive visualization of large dynamic particle data sets. Our method is based on a GPU-accelerated data-parallel algorithm for computing a volumetric density map from Gaussian weighted particles. The algorithm extracts an isovalue surface from the computed density map, using fast GPU-accelerated volume rendering techniques such as marching cubes and ray casting. This approach enables interactive display rates for molecular dynamics simulations consisting of hundreds of thousands to millions of atoms. The user can interactively adjust the display of structural detail on a continuous scale, ranging from atomistic detail for in-depth analysis, to reduced detail visual representations suitable for viewing the overall architecture of molecular complexes. The extracted surface is useful for interactive visualization, and provides a basis for structure analysis methods. Although our method is intended to be used for molecular graphics, we show that it is also applicable to other particle data sets, for example coarse-grained whole cell simulations and smoothed particle hydrodynamics simulations.

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Cryo-EM modeling by the molecular dynamics flexible fitting method.

Kwok-Yan Chan, Leonardo G. Trabuco, Eduard Schreiner, and Klaus Schulten. Cryo-EM modeling by the molecular dynamics flexible fitting method. Biopolymers, 2012. In press.

The increasing power and popularity of cryo-electron (cryo-EM) microscopy in structural biology is accompanied by the development of several hybrid methods, which permit the interpretation of cryo-EM density maps beyond their nominal resolution in terms of atomic models. The Cryo-EM Modeling Challenge 2010 is the first community effort to bring together developers of hybrid methods as well as cryo-EM experimentalists. Participating in the challenge, the molecular dynamics flexible fitting (MDFF) method was applied to a number of cryo-EM density maps. The results are described here. The description places emphasis on three aspects of MDFF use: first, the use of symmetry-based restraints to improve the quality of atomic models derived from density maps of symmetric complexes; second, a comparison of the stereochemical quality of atomic models resulting from different hybrid methods participating in the challenge; third, the first proof-of-principle application of MDFF to electron crystallography data.

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Structural characterization of mRNA-tRNA translocation intermediates.

Xabier Agirrezabala, Hstau Liao, Eduard Schreiner, Jie Fu, Rodrigo Ortiz-Meoz, Klaus Schulten, Rachel Green, and Joachim Frank. Structural characterization of mRNA-tRNA translocation intermediates. Proceedings of the National Academy of Sciences, USA, 109:6094-6099, 2012.

Analysis of a wild-type E. coli pre-translocational sample competent for unimpaired forward translocation by cryo-EM, classification, and single-particle reconstruction has revealed the presence of previously unseen intermediate substates of the bacterial ribosome during the first phase of translocation, characterized by intermediate intersubunit rotations, L1 stalk positions, and tRNA configurations. Furthermore, we have described the domain rearrangements in quantitative terms, which has allowed us to define the processivity and coordination of the conformational reorganization of the ribosome, along with the associated changes in tRNA ribosome-binding configuration. The observed occupancies of substates also allowed a profile of the free-energy landscape to be reconstructed. The results are consistent with the view of the ribosome as a molecular machine employing Brownian motion to reach a functionally productive state (�macrostate II�) via a series of substates with incremental changes in conformation.

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Reaction kinetics and mechanism of magnetic field effects in cryptochrome.

Ilia A. Solov'yov and Klaus Schulten. Reaction kinetics and mechanism of magnetic field effects in cryptochrome. Journal of Physical Chemistry B, 116:1089-1099, 2012.

Creatures as varied as mammals, fish, insects, reptiles, and birds have an intriguing �sixth� sense that allows them to orient themselves in the Earth�s magnetic field. Despite decades of study, the physical basis of this magnetic sense remains elusive. A likely mechanism is furnished by magnetically sensitive radical pair reactions occurring in the retina, the light- sensitive part of animal eyes. A photoreceptor, cryptochrome, has been suggested to endow birds with magnetoreceptive abilities as the protein has been shown to exhibit the biophysical properties required for an animal magnetoreceptor to operate properly. Here, we propose a theoretical analysis method for identifying cryptochrome�s signaling reactions involving comparison of measured and calculated reaction kinetics in cryptochrome. Application of the method yields an exemplary light-driven reaction cycle, supported through transient absorption and electron-spin-resonance observations together with known facts on avian magnetoreception. The reaction cycle permits one to predict magnetic field effects on cryptochrome activation and deactivation. The suggested analysis method gives insight into structural and dynamic design features required for optimal detection of the geomagnetic field by cryptochrome and suggests further experimental and theoretical studies.

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How quantum coherence assists photosynthetic light harvesting.

Johan Strumpfer, Melih Sener, and Klaus Schulten. How quantum coherence assists photosynthetic light harvesting. Journal of Physical Chemistry Letters, 3:536-542, 2012.

This perspective examines how hundreds of pigment molecules in purple bacteria cooperate through quantum coherence to achieve remarkable light harvesting efficiency. Quantum coherent sharing of excitation, which modifies excited state energy levels and combines transition dipole moments, enables rapid transfer of excitation over large distances. Purple bacteria exploit the resulting excitation transfer to engage many antenna proteins in light harvesting, thereby increasing the rate of photon absorption and energy conversion. We highlight here how quantum coherence comes about and plays a key role in the photosynthetic apparatus of purple bacteria.

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Molecular dynamics investigation of the w current in the Kv1.2 voltage sensor domains.

Fatemeh Khalili-Araghi, Emad Tajkhorshid, Benoit Roux, and Klaus Schulten. Molecular dynamics investigation of the w current in the Kv1.2 voltage sensor domains. Biophysical Journal, 102:258-267, 2012.

Voltage sensor domains (VSD) are transmembrane proteins that respond to changes in membrane voltage and modulate the activity of ion channels, enzymes, or in the case of proton channels allow permeation of protons across the cell membrane. VSDs consist of four transmembrane segments, S1-S4, forming an anti-parallel helical bundle. The S4 segment contains several positively charged residues, mainly arginines, located at every third position along the helix. In the voltage-gated Shaker K channel, the mutation of the first arginine of S4 to a smaller uncharged amino acid allows permeation of cations through the VSD. These currents, known as -currents, travel through the VSD and are distinct from K currents passing through the main ion conduction pore. Here we report molecular dynamics simulations of the -current in the resting-state conformation for Kv1.2 and for four of its mutants. The four tested mutants exhibit various degrees of conductivity for K and Cl ions, with a slight selectivity for K over Cl. Analysis of the ion permeation pathway, in the case of a highly-conductive mutant, reveals a negatively charged constriction region near the center of the membrane which might act as a selectivity filter to prevent permeation of anions through the pore. The residues R1 in S4 and E1 in S2 are located at the narrowest region of the -pore for the resting state conformation of the VSD, in agreement with experiments showing that the largest increase in current is produced by the double mutation E1D and R1S.

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Recognition of methylated DNA through methyl-CpG binding domain proteins.

Xueqing Zou, Wen Ma, Ilia Solov'yov, Christophe Chipot, and Klaus Schulten. Recognition of methylated DNA through methyl-CpG binding domain proteins. Nucleic Acids Research, 40:2747-2758, 2012.

DNA methylation is a key regulatory control route in epigenetics, involving gene silencing and chromosome inactivation. It has been recognized that methyl-CpG binding domain (MBD) proteins play an important role in interpreting the genetic information encoded by methylated DNA (mDNA). Although the function of MBD proteins has attracted considerable attention and is well characterized, the mechanism underlying mDNA recognition by MBD proteins is still poorly understood. In this paper, we demonstrate that the methyl-CpG dinucleotides are recognized at the MBD-mDNA interface by two MBD arginines through an interplay of hydrogen bonding and cation- interaction. Through molecular dynamics and quantum-chemistry calculations we investigate the methyl-cytosine recognition process and demonstrate that methylation enhances MBD-mDNA binding by increasing the hydrophobic interfacial area and by strengthening the interaction between mDNA and MBD proteins. Free-energy perturbation calculations also show that methylation yields favorable contribution to the binding free energy for the MBD-mDNA complex.

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A chemical compass for bird navigation.

Ilia A. Solov'yov, P. J. Hore, Thorsten Ritz, and Klaus Schulten. A chemical compass for bird navigation. In Masoud Mohseni, Yasser Omar, Greg Engel, and Martin B. Plenio, editors, Quantum Effects in Biology, chapter 10. Cambridge University Press, 2012. To be published.

Migratory birds travel spectacular distances each year, navigating and orienting by a variety of means, most of which are poorly understood. Among them is a remarkable ability to perceive the intensity and direction of the Earth's magnetic field. Biologically credible mechanisms for the detection of such a weak field (25-65 mT) are scarce and in recent years just two proposals have emerged as frontrunners. One, essentially classical, centers on clusters of magnetic iron-containing particles in the upper beak which appear to act as a magnetometer for determining geographical position. The other relies on the quantum spin dynamics of transient photoinduced radical pairs. Originally suggested by Schulten in 1978 as the basis of the avian magnetic compass sensor, this mechanism gained support from the subsequent observation that the compass is light-dependent. The radical pair hypothesis began to attract increased interest following the proposal in 2000 that free radical chemistry could occur in the bird's retina initiated by photoexcitation of cryptochrome, a specialized photoreceptor protein. In the present paper we review the important physical and chemical constraints on a possible radical-pair-based compass sensor and discuss the suggestion that radical pairs in cryptochromes might provide a biological realization for a magnetic compass.

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Quantum biology of retinal proteins.

Shigehiko Hayashi and Klaus Schulten. Quantum biology of retinal proteins. In Masoud Mohseni, Yasser Omar, Greg Engel, and Martin B. Plenio, editors, Quantum Effects in Biology. Cambridge University Press, 2012. To be published.

Retinal is a biological chromophore ubiquitous in visual reception of higher life forms, but serving also as an antenna in bacterial light energy transformation and photo-taxis. The chromophore, bound as a Schiff base to a lysine amino acid, arises in various retinal proteins, the best known two being the visual receptor rhodopsin and the light-induced proton pump bacteriorhodopsin. Rhodopsin (Rh) resides in the retina of animal eyes. Its extremely fast (200 fs) primary photo-reaction furnishes the visual receptor with very high sensitivity to detect incoming light, matching nearly a single photon counter. The photo- biological mechanism of retinal has been fascinating experimental and theoretical researchers over many decades. In this article, the quantum processes involved in the photo-activation of retinal in Rh, and related proteins are presented.

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Symmetry-restrained flexible fitting for symmetric EM maps.

Kwok-Yan Chan, James Gumbart, Ryan McGreevy, Jean M. Watermeyer, B. Trevor Sewell, and Klaus Schulten. Symmetry-restrained flexible fitting for symmetric EM maps. Structure, 19:1211-1218, 2011.

Many large biological macromolecules have inherent structural symmetry, being composed of a few distinct subunits, repeated in a symmetric array. These complexes are often not amenable to traditional high-resolution structural determination methods, but can be imaged in functionally relevant states using cryo-electron microscopy (cryo-EM). A number of methods for fitting atomic-scale structures into cryo-EM maps have been developed, including the molecular dynamics flexible fitting (MDFF) method. However, quality and resolution of the cryo-EM map are the major determinants of a method's success. In order to incorporate knowledge of structural symmetry into the fitting procedure, we developed the symmetry-restrained MDFF method. The new method adds to the cryo-EM map-derived potential further restraints on the allowed conformations of a complex during fitting, thereby improving the quality of the resultant structure. The benefit of using symmetry-based restraints during fitting, particularly for medium to low-resolution data, is demonstrated for three different systems.

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Oligomerization state of photosynthetic core complexes is correlated with the dimerization affinity of a transmembrane helix.

Jen Hsin, Loren LaPointe, Alla Kazy, Christophe Chipot, Alessandro Senes, and Klaus Schulten. Oligomerization state of photosynthetic core complexes is correlated with the dimerization affinity of a transmembrane helix. Journal of the American Chemical Society, 133:14071-14081, 2011.

In the Rhodobacter (Rba.) species of photosynthetic purple bacteria, a single transmembrane -helix, PufX, is found within the core complex, an essential photosynthetic macromolecular assembly that performs the absorption and the initial processing of light energy. Despite its structural simplicity, many unresolved questions surround PufX, the most important of which is its location within the photosynthetic core complex. One proposed placement of PufX is at the center of a core complex dimer, where two PufX helices associate in the membrane and form a homodimer. Inability for PufX of certain Rba. species to form a homodimer is thought to lead to monomeric core complexes. In the present study, we employ a combination of computational and experimental techniques to test the hypothesized homodimerization of PufX. We carry out a systematic investigation to measure the dimerization affinity of PufX from four Rba. species, using a molecular dynamics-based free-energy method, as well as experimental TOXCAT assays. We found that the four PufX helices have substantially different dimerization affinities. Both computational and experimental techniques demonstrate that species with dimeric core complexes have PufX that can potentially form a homodimer, whereas the one species with monomeric core complexes has a PufX with little to no dimerization propensity. Our analysis of the helix-helix interface revealed a number of positions that may be important for PufX dimerization and the formation of a hydrogen bond network between these GxxxG containing helices. Our results suggest that the different oligomerization states of core complexes in various Rba. species can be attributed, among other factors, to the different propensity of its PufX helix to homodimerize.

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Theory and simulation of the environmental effects on FMO electronic transitions.

Carsten Olbrich, Johan Strümpfer, Klaus Schulten, and Ulrich Kleinekathoefer. Theory and simulation of the environmental effects on FMO electronic transitions. Journal of Physical Chemistry Letters, 2:1771-1776, 2011.

Long-lived quantum coherence has been experimentally observed in the Fenna- Matthews-Olson (FMO) light-harvesting complex. It is much debated which role thermal effects play and if the observed low-temperature behavior arises also at physiological temperature. To contribute to this debate we use molecular dynamics simulations to study the coupling between the protein environment and the vertical excitation energies of individual bacteriochlorophyll molecules in the FMO complex of the green sulphur bacterium Chlorobaculum tepidum. The so-called spectral densities, which account for the environmental influence on the excited state dynamics, are determined from temporal autocorrelation functions of the energy gaps between ground and first excited states of the individual pigments. Although the overall shape of the spectral density is found to be rather similar for all pigments, variations in their magnitude can be seen. Differences between the spectral densities for the pigments of the FMO monomer and FMO trimer are also presented.

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Immersive out-of-core visualization of large-size and long-timescale molecular dynamics trajectories.

John E. Stone, Kirby L. Vandivort, and Klaus Schulten. Immersive out-of-core visualization of large-size and long-timescale molecular dynamics trajectories. Lecture Notes in Computer Science, 6939:1-12, 2011.

Atomistic molecular dynamics (MD) simulations of biomolecules provide insight into their physical mechanisms and potential as drug targets. Unfortunately, such simulations are extremely demanding in terms of computation, storage, and visualization. Immersive visualization environments permit fast, intuitive exploration of the pharmacological potential, but add further demands on resources. We describe the design and application of out-of-core visualization techniques for large-size and longtimescale MD simulations involving many terabytes of data, including in particular fast regeneration of molecular representations, atom selection mechanisms, out-of-core optimized MD trajectory file formats, and multithreaded programming techniques. Our approach leverages technological advances in commodity solid state disk (SSD) devices, to enable trajectory animation rates for large structures that were previously unachievable except by in-core approaches, while maintaining full visualization flexibility. The out-of-core visualization techniques are implemented and evaluated in VMD, a widely used molecular visualization tool.

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Cytosine methylation alters DNA mechanical properties.

Philip M.D. Severin, Xueqing Zou, Hermann E. Gaub, and Klaus Schulten. Cytosine methylation alters DNA mechanical properties. Nucleic Acids Research, 39:8740-8751, 2011.

DNA methylation plays an essential role in transcriptional control of organismal development in epigenetics, from turning off a specific gene to inactivation of entire chromosomes. While the biological function of DNA methylation is becoming increasingly clear, the mechanism of methylation-induced gene regulation is still poorly understood. Through single-molecule force experiments and simulation we investigated the effects of methylation on strand separation of DNA, a crucial step in gene expression. Molecular force assay and single-molecule force spectroscopy revealed a strong methylation dependence of strand separation. Methylation is observed to either inhibit or facilitate strand separation, depending on methylation level and sequence context. Molecular dynamics simulations provided a detailed view of methylation effects on strand separation, suggesting the underlying physical mechanism. According to our study, methylation in epigenetics may regulate gene expression not only through mechanisms already known but also through changing mechanical properties of DNA.

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From atomistic modeling to excitation transfer and two-dimensional spectra of the FMO light-harvesting complex.

Carsten Olbrich, Thomas L. C. Jansen, Jörg Liebers, Mortaza Aghtar, Johan Strümpfer, Klaus Schulten, Jasper Knoester, and Ulrich Kleinekathoefer. From atomistic modeling to excitation transfer and two-dimensional spectra of the FMO light-harvesting complex. Journal of Physical Chemistry B, 115(26):8609-8621, 2011.

The experimental observation of long-lived quantum coherences in the Fenna-Matthews- Olson (FMO) light-harvesting complex at low temperatures has challenged general intuition in the field of complex molecular systems and provoked considerable theoretical effort in search for explanations. Here we report on room-temperature calculations of the excited-state dynamics in FMO using a combination of molecular dynamics simulations and electronic structure calculations. Thus we obtain trajectories for the Hamiltonian of this system which contains time-dependent vertical excitation energies of the individual bacteriochlorophyll molecules and their mutual electronic couplings. The distribution of energies and couplings are analyzed together with possible spatial correlations. It is found that in contrast to frequent assumptions the site energy distribution is non-Gaussian. In a subsequent step, averaged wave packet dynamics is used to determine the exciton dynamics in the system. Finally, with the time-dependent Hamiltonian linear and two- dimensional spectra are determined. The thus obtained linear absorption lineshape agrees well with experimental observation and is largely determined by the non-Gaussian site energy distribution. The two-dimensional spectra are in line with what one would expect by extrapolation of the experimental observations at lower temperatures and indicate almost total loss of long-lived coherences.

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Cytoplasmic domain filter function in the mechanosensitive channel of small conductance.

Ramya Gamini, Marcos Sotomayor, Christophe Chipot, and Klaus Schulten. Cytoplasmic domain filter function in the mechanosensitive channel of small conductance. Biophysical Journal, 101:80-89, 2011.

Mechanosensitive (MS) channels, inner membrane proteins of bacteria, open and close in response to mechanical stimuli such as changes in membrane tension during osmotic stress. In bacteria, these channels act as safety valves preventing cell lysis upon hypoosmotic cell swelling: the channels open under membrane tension to release osmolytes along with water. The MS channel of small conductance, MscS, consists, beside the transmembrane channel, of a large cytoplasmic domain (CD) that features a balloon-like, water filled chamber opening to the cytoplasm through seven side pores and a small distal pore. The CD is apparently a molecular sieve covering the channel, that optimizes loss of osmolytes during osmoadaptation. We employ diffusion theory and molecular dynamics simulations to explore the transport kinetics of Glu and K as representative osmolytes. We suggest that the CD indeed acts as a filter that actually balances passage of Glu and K, and possibly other positive and negative osmolytes, to yield a largely neutral efflux and, thereby, reduce cell depolarization in the open state and conserve to a large degree the essential metabolite Glu.

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Stereochemical errors and their implications for molecular dynamics simulations.

Eduard Schreiner, Leonardo G. Trabuco, Peter L. Freddolino, and Klaus Schulten. Stereochemical errors and their implications for molecular dynamics simulations. BMC Bioinformatics, 12:190, 2011.

Background: Biological molecules are often asymmetric with respect to stereochemistry, and correct stereochemistry is essential to their function. Molecular dynamics simulations of biomolecules have increasingly become an integral part of biophysical research. However, stereochemical errors in biomolecular structures can have a dramatic impact on the results of simulations.

Results: Here we illustrate the effects that chirality and peptide bond configuration flips may have on the secondary structure of proteins throughout a simulation. We also analyze the most common sources of stereochemical errors in biomolecular structures and present software tools to identify, correct, and prevent stereochemical errors in molecular dynamics simulations of biomolecules.

Conclusions: Use of the tools presented here should become a standard step in the preparation of biomolecular simulations.

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Extension of a three-helix bundle domain of myosin VI and key role of calmodulins.

Yanxin Liu, Jen Hsin, HyeongJun Kim, Paul R Selvin, and Klaus Schulten. Extension of a three-helix bundle domain of myosin VI and key role of calmodulins. Biophysical Journal, 100:2964-2973, 2011.

The molecular motor protein myosin VI, upon dimerization, moves towards the minus end of actin filaments with a step size of 30-36 nm. Such large step size either drastically limits the degree of complex formation between dimer subunits to leave enough length for the lever arms, or requires an extension mechanism of the lever arms' crystallographically observed structure. Recent experimental work proposed that myosin VI dimerization triggers the unfolding of the protein's proximal tail domain which acts as a lever arm extension. Here, we demonstrate through steered molecular dynamics simulation the feasibility of such extension arising from turning a three-helix bundle into a long alpha-helix. A key role is played by known calmodulin binding that facilitates the extension through altering the strain path; even more remarkable, new calmodulin binding sites open up that may mechanically strengthen the extended lever arms.

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