Multiconformation Continuum Electrostatics Research Articles

Computing the Relative Affinity of Chlorophylls a and b to Light-Harvesting Complex II.

In plants and algae, the primary antenna protein bound to photosystem II is light-harvesting complex II (LHCII), a pigment-protein complex that binds eight chlorophyll (Chl) a molecules and six Chl b molecules. Chl a and Chl b differ only in that Chl a has a methyl group (-CH3) on one of its pyrrole rings, while Chl b has a formyl group (-CHO) at that position. This blue-shifts the Chl b absorbance relative to Chl a. It is not known how the protein selectively binds the right Chl type at each site. Knowing the selection criteria would allow the design of light-harvesting complexes that bind different Chl types, modifying an organism to utilize the light of different wavelengths. The difference in the binding affinity of Chl a and Chl b in pea and spinach LHCII was calculated using multiconformation continuum electrostatics and free energy perturbation. Both methods have identified some Chl sites where the bound Chl type (a or b) has a significantly higher affinity, especially when the protein provides a hydrogen bond for the Chl b formyl group. However, the Chl a sites often have little calculated preference for one Chl type, so they are predicted to bind a mixture of Chl a and b. The electron density of the spinach LHCII was reanalyzed, which, however, confirmed that there is negligible Chl b in the Chl a-binding sites. It is suggested that the protein chooses the correct Chl type during folding, segregating the preferred Chl to the correct binding site.

Proton exit pathways surrounding the oxygen evolving complex of photosystem II

Photosystem II allows water to be the primary electron source for the photosynthetic electron transfer chain. Water is oxidized to dioxygen at the Oxygen Evolving Complex (OEC), a Mn4CaO5 inorganic core embedded on the lumenal side of PSII. Water-filled channels surrounding the OEC must bring in substrate water molecules, remove the product protons to the lumen, and may transport the product oxygen. Three water-filled channels, denoted large, narrow, and broad, extend from the OEC towards the aqueous surface more than 15 Å away. However, the role of each pathway in the transport in and out of the OEC is yet to be established. Here, we combine Molecular Dynamics (MD), Multi Conformation Continuum Electrostatics (MCCE) and Network Analysis to compare and contrast the three potential proton transfer paths. Hydrogen bond network analysis shows that near the OEC the waters are highly interconnected with similar free energy for hydronium at all locations. The paths diverge as they move towards the lumen. The water chain in the broad channel is better connected than in the narrow and large channels, where disruptions in the network are observed approximately 10 Å from the OEC. In addition, the barrier for hydronium translocation is lower in the broad channel. Thus, a proton released from any location on the OEC can access all paths, but the likely exit to the lumen passes through PsbO via the broad channel.

Poor Person's pH Simulation of Membrane Proteins.

pH conditions are central to the functioning of all biomolecules. However, implications of pH changes are nontrivial on a molecular scale. Though a rigorous microscopic definition of pH exists, its implementation in classical molecular dynamics (MD) simulations is cumbersome, and more so in large integral membrane systems. In this chapter, an integrative pipeline is described that combines Multi-Conformation Continuum Electrostatics (MCCE) computations with MD simulations to capture the effect of transient protonation states on the coupled conformational changes in transmembrane proteins. The core methodologies are explained, and all the software required to set up this pipeline are outlined with their key parameters. All associated analyses of structure and function are provided using two case studies, namely those of bioenergetic complexes: NADH dehydrogenase (complex I) and Vo domain of V-type ATPase. The hybrid MCCE-MD pipeline has allowed the discovery of hydrogen bond networks, ligand binding pathways, and disease-causing mutations.

Identification of a Na+-Binding Site near the Oxygen-Evolving Complex of Spinach Photosystem II.

The oxygen-evolving complex (OEC) of photosystem II (PSII) is an oxomanganese cluster composed of four redox-active Mn ions and one redox-inactive Ca2+ ion, with two nearby bound Cl- ions. Sodium is a common counterion of both chloride and hydroxide anions, and a sodium-specific binding site has not been identified near the OEC. Here, we find that the oxygen-evolution activity of spinach PSII increases with Na+ concentration, particularly at high pH. A Na+-specific binding site next to the OEC, becomes available after deprotonation of the D1-H337 amino acid residue, is suggested by the analysis of two recently published PSII cryo-electron microscopy maps in combination with quantum mechanical calculations and multiconformation continuum electrostatics simulations.

Characterizing the Water Wire in the Gramicidin Channel Found by Monte Carlo Sampling Using Continuum Electrostatics and in Molecular Dynamics Trajectories with Conventional or Polarizable Force Fields

Water molecules play a key role in all biochemical processes. They help define the shape of proteins, and they are reactant or product in many reactions and are released as ligands are bound. They facilitate the transfer of protons through transmembrane proton channel, pump and transporter proteins. Continuum electrostatics (CE) force fields used by program Multiconformation CE (MCCE) capture electrostatic interactions in biomolecules with an implicit solvent, which captures the averaged solvent water equilibrium properties. Hybrid CE methods can use explicit water molecules within the protein surrounded by implicit solvent. These hybrid methods permit the study of explicit hydrogen bond networks within the protein and allow analysis of processes such as proton transfer reactions. Yet hybrid CE methods have not been rigorously tested. Here, we present an explicit treatment of water molecules in the Gramicidin A (gA) channel using MCCE and compare the resulting distributions of water molecules and key hydration features against those obtained with explicit solvent Molecular Dynamics (MD) simulations with the nonpolarizable CHARMM36 and polarizable Drude force fields. CHARMM36 leads to an aligned water wire in the channel characterized by a large absolute net water dipole moment; the MCCE and Drude analysis lead to a small net dipole moment as the water molecules change orientation within the channel. The correct orientation is not as yet known, so these calculations identify an open question.

Characterizing the water wire in the Gramicidin channel found by Monte Carlo sampling using continuum electrostatics and in molecular dynamics trajectories with conventional or polarizable force fields

Water molecules play a key role in all biochemical processes. They help define the shape of proteins, and they are reactant or product in many reactions and are released as ligands are bound. They facilitate the transfer of protons through transmembrane proton channel, pump and transporter proteins. Continuum electrostatics (CE) force fields used by program Multiconformation CE (MCCE) capture electrostatic interactions in biomolecules with an implicit solvent, which captures the averaged solvent water equilibrium properties. Hybrid CE methods can use explicit water molecules within the protein surrounded by implicit solvent. These hybrid methods permit the study of explicit hydrogen bond networks within the protein and allow analysis of processes such as proton transfer reactions. Yet hybrid CE methods have not been rigorously tested. Here, we present an explicit treatment of water molecules in the Gramicidin A (gA) channel using MCCE and compare the resulting distributions of water molecules and key hydration features against those obtained with explicit solvent Molecular Dynamics (MD) simulations with the nonpolarizable CHARMM36 and polarizable Drude force fields. CHARMM36 leads to an aligned water wire in the channel characterized by a large absolute net water dipole moment; the MCCE and Drude analysis lead to a small net dipole moment as the water molecules change orientation within the channel. The correct orientation is not as yet known, so these calculations identify an open question.

Identifying the proton loading site cluster in the ba3 cytochrome c oxidase that loads and traps protons

Cytochrome c Oxidase (CcO) is the terminal electron acceptor in aerobic respiratory chain, reducing O2 to water. The released free energy is stored by pumping protons through the protein, maintaining the transmembrane electrochemical gradient. Protons are held transiently in a proton loading site (PLS) that binds and releases protons driven by the electron transfer reaction cycle. Multi-Conformation Continuum Electrostatics (MCCE) was applied to crystal structures and Molecular Dynamics snapshots of the B-type Thermus thermophilus CcO. Six residues are identified as the PLS, binding and releasing protons as the charges on heme b and the binuclear center are changed: the heme a3 propionic acids, Asp287, Asp372, His376 and Glu126B. The unloaded state has one proton and the loaded state two protons on these six residues. Different input structures, modifying the PLS conformation, show different proton distributions and result in different proton pumping behaviors. One loaded and one unloaded protonation states have the loaded/unloaded states close in energy so the PLS binds and releases a proton through the reaction cycle. The alternative proton distributions have state energies too far apart to be shifted by the electron transfers so are locked in loaded or unloaded states. Here the protein can use active states to load and unload protons, but has nearby trapped states, which stabilize PLS protonation state, providing new ideas about the CcO proton pumping mechanism. The distance between the PLS residues Asp287 and His376 correlates with the energy difference between loaded and unloaded states.

Deciphering the selectivity of inhibitor MKC9989 towards residue K907 in IRE1α; a multiscale in silico approach.

The selectivity of the ligand MKC9989, as inhibitor of the Inositol-Requiring Enzyme 1α (IRE1α) transmembrane kinase/ribonuclease protein, towards the residue K907 in the context of Schiff base formation, has been investigated by employing an array of in silico techniques including Multi-Conformation Continuum Electrostatics (MCCE) simulations, Quantum Mechanics/Molecular Mechanics (QM/MM) calculations, covalent docking, and Molecular Dynamics (MD) simulations. According to the MCCE results, K907 displays the lowest pKa value among all 23 lysine residues in IRE1α. The MMCE simulations also indicate a critical interaction between K907 and D885 within the hydrophobic pocket which increases significantly at low protein dielectric constants. The QM/MM calculations reveal a spontaneous proton transfer from K907 to D885, consistent with the low pKa value of K907. A Potential Energy Surface (PES) scan confirms the lack of energy barrier and transition state associated with this proton transfer reaction. Covalent docking and MD simulations verify that the protein pocket containing K907 can effectively stabilize the inhibitor by strong π–π and hydrogen bonding interactions. In addition, Radial Distribution Function (RDF) analysis shows that the imine group formed in the chemical reaction between MKC9989 and K907 is inaccessible to water molecules and thus the probability of imine hydrolysis is almost zero. The results of the current study explain the high selectivity of the MKC9989 inhibitor towards the K907 residue of IRE1α.

Extensive Assessment of Various Computational Methods for Aspartate's pKa Shift.

A series of computational methods for pKa shift prediction are extensively tested on a set of benchmark protein systems, aiming at identifying pitfalls and evaluating their performance on high variants. Including 19 ASP residues in 10 protein systems, the benchmark set consists of both residues with highly shifted pKa values as well as those varying little from the reference value, with an experimental RMS free energy differences of 2.49 kcal/mol with respect to blocked amino acid, namely the RMS pKa shift being 1.82 pKa units. The constant pH molecular dynamics (MD), alchemical methods, PROPKA3.1, and multiconformation continuum electrostatics give RMSDs of 1.52, 2.58, 1.37, and 3.52 pKa units, respectively, on the benchmark set. The empirical scoring method is the most accurate one with extremely low computational cost, and the pH-dependent model is also able to provide accurate results, while the accuracy of MD sampling incorporating alchemical free energy simulation is prohibited by convergence achievement and the performance of conformational search incorporating multiconformation continuum electrostatics is bad. Former research works did not define statistical uncertainty with care and yielded the questionable conclusion that alchemical methods perform well in most benchmarks. In this work the traditional alchemical methods are thoroughly tested for high variants. We also performed the first application of nonequilibrium alchemical methods to the pKa cases.

Benchmarking pKa prediction methods for Lys115 in acetoacetate decarboxylase.

Three different pKa prediction methods were used to calculate the pKa of Lys115 in acetoacetate decarboxylase (AADase): the empirical method PROPKA, the multiconformation continuum electrostatics (MCCE) method, and the molecular dynamics/thermodynamic integration (MD/TI) method with implicit solvent. As expected, accurate pKa prediction of Lys115 depends on the protonation patterns of other ionizable groups, especially the nearby Glu76. However, since the prediction methods do not explicitly sample the protonation patterns of nearby residues, this must be done manually. When Glu76 is deprotonated, all three methods give an incorrect pKa value for Lys115. If protonated, Glu76 is used in an MD/TI calculation, the pKa of Lys115 is predicted to be 5.3, which agrees well with the experimental value of 5.9. This result agrees with previous site-directed mutagenesis studies, where the mutation of Glu76 (negative charge when deprotonated) to Gln (neutral) causes no change in Km, suggesting that Glu76 has no effect on the pKa shift of Lys115. Thus, we postulate that the pKa of Glu76 is also shifted so that Glu76 is protonated (neutral) in AADase. Graphical abstract Simulated abundances of protonated species as pH is varied.

Who cares for the protons?

It is tempting to use standard protonation states for the analysis of protein–ligand interactions. Two different pKa calculation methods, PROPKA (protein pKa) and MCCE (multi conformation continuum electrostatics), were applied to challenge this convenient behavior. As data basis, we selected five recently approved drugs for which structural information of the protein–drug complex is available. We analyzed the pKa calculations in terms of a measure termed BIPS (binary protonation states) recently introduced by us. Both methods agree in detecting the majority of the sites with atypical BIPS values. However, when using only one method, some of the atypcial BIPS value would have been missed. Therefore, we recommend using both methods to set such an interpretation on a solid basis.

MCCE analysis of the pKas of introduced buried acids and bases in staphylococcal nuclease

The pK(a)s of 96 acids and bases introduced into buried sites in the staphylococcal nuclease protein (SNase) were calculated using the multiconformation continuum electrostatics (MCCE) program and the results compared with experimental values. The pK(a)s are obtained by Monte Carlo sampling of coupled side chain protonation and position as a function of pH. The dependence of the results on the protein dielectric constant (ε(prot)) in the continuum electrostatics analysis and on the Lennard-Jones non-electrostatics parameters was evaluated. The pK(a)s of the introduced residues have a clear dependence on ε(prot,) whereas native ionizable residues do not. The native residues have electrostatic interactions with other residues in the protein favoring ionization, which are larger than the desolvation penalty favoring the neutral state. Increasing ε(prot) scales both terms, which for these residues leads to small changes in pK(a). The introduced residues have a larger desolvation penalty and negligible interactions with residues in the protein. For these residues, changing ε(prot) has a large influence on the calculated pK(a). An ε(prot) of 8-10 and a Lennard-Jones scaling of 0.25 is best here. The X-ray crystal structures of the mutated proteins are found to provide somewhat better results than calculations carried out on mutations made in silico. Initial relaxation of the in silico mutations by Gromacs and extensive side chain rotamer sampling within MCCE can significantly improve the match with experiment.

Exploring conformational changes coupled to ionization states using a hybrid Rosetta‐MCCE protocol

A hybrid protocol combining Rosetta fullatom refinement and Multi-Conformation Continuum Electrostatics (MCCE) to estimate pK(a) is applied to the blind prediction of 94 mutated residues in Staphylococcal nuclease (SNase), as part of the pK(a)-cooperative benchmark test. The standard MCCE method is limited to sidechain conformational changes. The Rosetta refinement protocol is used to add the backbone conformational changes in pK(a) calculations. The non-electrostatic energy component from Rosetta and the electrostatic energy from MCCE are combined to weight the calculated ionization states. Of 63 measured pK(a)s, the root mean squared deviation (RMSD) between the calculated pK(a)s and the measured values is 4.3, showing an improvement compared to the RMSD of 6.6 in the standard MCCE calculations, using a low protein dielectric constant of 4. The breakdown of pK(a) shift from the solution values (ΔpK(a)) shows that the desolvation energy contributes the most in the standard MCCE calculations. Lowering desolvation penalties and optimizing electrostatic interactions with the Rosetta/MCCE protocol reduces the ΔpK(a) to favor the charged states. Analysis also showed that the Rosetta/MCCE protocol samples conformations with pK(a)s close to the solution values. The question remains whether the correct conformational changes coupled to the ionization changes are found here. Nevertheless, a challenge emerges to accurately estimate the reorganization energy, which is not directly measured from the electrostatic environment of the site of interest. Possible improvements to the protocol are also discussed.

Developing hybrid approaches to predict pKavalues of ionizable groups

Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure and the subtle structural changes be accounted by using dielectric constant larger than two. On another hand, if the change of the charge state is accompanied by a large structural reorganization of the target protein, then the relevant conformational changes have to be explicitly taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups whose ionization is expected to cause large conformational changes, termed "problematic" residues, and then applies a special protocol on them, while the rest of the pK(a)s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for "problematic" groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the titration curves of the "problematic" residues and then the results are averaged to obtain the corresponding pKa.

Pseudorevertants of a Semliki Forest Virus Fusion-Blocking Mutation Reveal a Critical Interchain Interaction in the Core Trimer

Semliki Forest virus (SFV) is an enveloped alphavirus that infects cells by a low-pH-triggered membrane fusion reaction mediated by the viral E1 protein. E1 inserts into target membranes and refolds to a hairpin-like homotrimer containing a central core trimer and an outer layer composed of domain III and the juxtamembrane stem region. The key residues involved in mediating E1 trimerization are not well understood. We recently showed that aspartate 188 in the interface of the core trimer plays a critical role. Substitution with lysine (D188K) blocks formation of the core trimer and E1 trimerization and strongly inhibits virus fusion and infection. Here, we have isolated and characterized revertants that rescued the fusion and growth defects of D188K. These revertants included pseudorevertants containing acidic or polar neutral residues at E1 position 188 and a second-site revertant containing an E1 K176T mutation. Computational analysis using multiconformation continuum electrostatics revealed an important interaction bridging D188 of one chain with K176 of the adjacent chain in the core trimer. E1 K176 is completely conserved among the alphaviruses, and mutations of K176 to threonine (K176T) or isoleucine (K176I) produced similar fusion phenotypes as D188 mutants. Together, our data support a model in which a ring of three salt bridges formed by D188 and K176 stabilize the core trimer, a key intermediate of the alphavirus fusion protein.

Multiconformation Continuum Electrostatics Analysis of the Effects of a Buried Asp Introduced near HemeainRhodobacter sphaeroidesCytochromecOxidase

Cytochrome c oxidase (CcO) reduces O(2) to water via a series of proton-coupled electron transfers, generating a transmembrane electrochemical gradient. Coupling electron and proton transfer requires changing the pK(a) values of buried residues at each stage in the reaction cycle. Heme a is a key cofactor in the CcO electron transfer chain. Mutation of Ser44 to Asp has been reported [Mills, D. A., et al. (2008) Biochemistry 47, 11499-11509], changing the hydrogen bond acceptor from His102, the heme a axial ligand in Rhodobactor sphaeroides CcO. This adds an acidic residue to the CcO interior. The electrochemical behavior of heme a in wild-type and S44D CcO is compared using the continuum electrostatics program MCCE. The introduced, deeply buried Asp remains ionized at physiological pH only when the nearby heme is oxidized. Heme a reduction is now calculated to be strongly coupled to Asp proton binding, while with Ser44, it is weakly coupled to small protonation shifts at multiple sites, increasing the pH dependence in the mutant. At pH 7, the partially ionized Asp 44 is calculated to lower the heme redox potential by 50 mV as expected given the thermodynamics of coupled electron and proton transfers. This highlights an curious finding in the experimental results where a low Asp pK(a) is found together with a stabilized reduced heme. The stabilization of a heme oxidation in a model complex by a hydrogen bond to the axial His ligand calculated with continuum electrostatics and with density functional theory were in good agreement.

The measured and calculated affinity of methyl‐ and methoxy‐substituted benzoquinones for the QAsite of bacterial reaction centers

Quinones play important roles in mitochondrial and photosynthetic energy conversion acting as intramembrane, mobile electron, and proton carriers between catalytic sites in various electron transfer proteins. They display different affinity, selectivity, functionality, and exchange dynamics in different binding sites. The computational analysis of quinone binding sheds light on the requirements for quinone affinity and specificity. The affinities of 10 oxidized, neutral benzoquinones were measured for the high affinity Q(A) site in the detergent-solubilized Rhodobacter sphaeroides bacterial photosynthetic reaction center. Multiconformation Continuum Electrostatics was then used to calculate their relative binding free energies by grand canonical Monte Carlo sampling with a rigid protein backbone, flexible ligand, and side chain positions and protonation states. Van der Waals and torsion energies, Poisson-Boltzmann continuum electrostatics, and accessible surface area-dependent ligand-solvent interactions are considered. An initial, single cycle of GROMACS backbone optimization improves the match with experiment as do coupled-ligand and side-chain motions. The calculations match experiment with an root mean square deviation (RMSD) of 2.29 and a slope of 1.28. The affinities are dominated by favorable protein-ligand van der Waals rather than electrostatic interactions. Each quinone appears in a closely clustered set of positions. Methyl and methoxy groups move into the same positions as found for the native quinone. Difficulties putting methyls into methoxy sites are observed. Calculations using a solvent-accessible surface area-dependent implicit van der Waals interaction smoothed out small clashes, providing a better match to experiment with a RMSD of 0.77 and a slope of 0.97.

Extracellular pH and Regulation of Integrin-Ligand Interactions

In the tumor and wound microenvironments, the extracellular matrix often exhibits acidic extracellular pH. It is well known that acidic pH can strongly affect processes such as cell adhesion and migration. However, the molecular mechanisms governing these effects have not been established. Here, we consider the hypothesis that acidic extracellular pH directly alters the interactions between cell surface integrin receptors and ECM ligands, which are critical to cell adhesion and migration. We employed Multi-Conformation Continuum Electrostatics to predict amino acid pKa values in the integrin avb3 headpiece, and conducted molecular dynamics simulations at acidic and physiological pH to examine the effect of pH on integrin conformational states. Our results suggest that acidic pH promotes opening of the avb3 headpiece, an important step in activation that can enable more effective ligand-receptor association interactions. This has important implications for downstream cell processes in the cancer and wound environments. We also conducted molecular-level experimental approaches, including flow cytometry and atomic force microscope-enabled force spectroscopy, to further examine the role of pH in regulating integrin-ligand interactions. These molecular-level results are connected to cell-level measurements of adhesion and migration at different pH levels, providing a detailed, multi-scale understanding of how acidic extracellular pH affects cell behavior.

MCCE2: improving protein pKa calculations with extensive side chain rotamer sampling.

Multiconformation continuum electrostatics (MCCE) explores different conformational degrees of freedom in Monte Carlo calculations of protein residue and ligand pK(a)s. Explicit changes in side chain conformations throughout a titration create a position dependent, heterogeneous dielectric response giving a more accurate picture of coupled ionization and position changes. The MCCE2 methods for choosing a group of input heavy atom and proton positions are described. The pK(a)s calculated with different isosteric conformers, heavy atom rotamers and proton positions, with different degrees of optimization are tested against a curated group of 305 experimental pK(a)s in 33 proteins. QUICK calculations, with rotation around Asn and Gln termini, sampling His tautomers and torsion minimum hydroxyls yield an RMSD of 1.34 with 84% of the errors being <1.5 pH units. FULL calculations adding heavy atom rotamers and side chain optimization yield an RMSD of 0.90 with 90% of the errors <1.5 pH unit. Good results are also found for pK(a)s in the membrane protein bacteriorhodopsin. The inclusion of extra side chain positions distorts the dielectric boundary and also biases the calculated pK(a)s by creating more neutral than ionized conformers. Methods for correcting these errors are introduced. Calculations are compared with multiple X-ray and NMR derived structures in 36 soluble proteins. Calculations with X-ray structures give significantly better pK(a)s. Results with the default protein dielectric constant of 4 are as good as those using a value of 8. The MCCE2 program can be downloaded from http://www.sci.ccny.cuny.edu/~mcce.

Extracellular pH and Regulation of Integrin Activation

It is well established that chemomechanical properties of the extracellular matrix (ECM) can have a profound effect on cell processes such as adhesion, migration, and differentiation. To understand and modulate such complex processes, it is crucial to have a detailed understanding of the feedback between a cell and the adjacent microenvironment. This is particularly important in the tumor and wound environments, where the ECM often exhibits altered characteristics such as acidic extracellular pH. This microenvironmental property could significantly alter the interactions between cell surface integrin receptors and ECM ligands, which are critical to downstream cell behaviors such as adhesion, migration, and signaling. Here, we use molecular dynamics simulations to examine the role of acidic extracellular pH in regulating integrin activation. The simulation system is the headpiece domains of integrin αvβ3 in complex with a cyclic RGD peptide. Multi Conformation Continuum Electrostatics was used to predict pKa values for all titratable residues in the system, and results were used to select residues for protonation in order to represent an effective acidic extracellular pH. Molecular dynamics simulations at acidic and physiological pH were compared to examine the effect of pH on αvβ3-RGD conformational states. Our results suggest that acidic pH promotes integrin headpiece opening, which is one of the steps in integrin activation, and we propose a possible mechanism for this effect. This finding is consistent with experimental data from the literature, and has important implications for cell adhesion and migration in cancer and wound healing.