characterizing-multiscale-mechanical-properties-brain-tissue-using

Characterizing Multiscale Mechanical Properties of Brain Tissue Using Atomic Force Microscopy, Impact Indentation, and Rheometry

To design and engineer materials inspired by the properties of the brain, whether for mechanical simulants or for tissue regeneration studies, the brain ...

high-resolution-imaging-nuclear-dynamics-live-cells-under-uniaxial

High-resolution Imaging of Nuclear Dynamics in Live Cells under Uniaxial Tensile Strain

Extracellular mechanical strain is known to elicit cell phenotypic responses and has physiological relevance in several tissue systems. To capture the ...

Massachusetts Institute of Technology

Singapore-MIT Alliance for Research and Technology, CREATE

The N-terminal cysteine-rich somatomedin B (SMB) domain (residues 1-44) of the human glycoprotein vitronectin contains the high-affinity binding sites for plasminogen activator inhibitor-1 (PAI-1) and the urokinase receptor (uPAR). We previously showed that the eight cysteine residues of recombinant SMB (rSMB) are organized into four disulfide bonds in a linear uncrossed pattern (Cys(5)-Cys(9), Cys(19)-Cys(21), Cys(25)-Cys(31), and Cys(32)-Cys(39)). In the present study, we use an alternative method to show that this disulfide bond arrangement remains a major preferred one in solution, and we determine the solution structure of the domain using NMR analysis. The solution structure shows that the four disulfide bonds are tightly packed in the center of the domain, replacing the traditional hydrophobic core expected for a globular protein. The few noncysteine hydrophobic side chains form a cluster on the outside of the domain, providing a distinctive binding surface for the physiological partners PAI-1 and uPAR. The hydrophobic surface consists mainly of side chains from the loop formed by the Cys(25)-Cys(31) disulfide bond, and is surrounded by conserved acidic and basic side chains, which are likely to contribute to the specificity of the intermolecular interactions of this domain. Interestingly, the overall fold of the molecule is compatible with several arrangements of the disulfide bonds. A number of different disulfide bond arrangements were able to satisfy the NMR restraints, and an extensive series of conformational energy calculations performed in explicit solvent confirmed that several disulfide bond arrangements have comparable stabilization energies. An experimental demonstration of the presence of alternative disulfide conformations in active rSMB is provided by the behavior of a mutant in which Asn(14) is replaced by Met. This mutant has the same PAI-1 binding activity as rVN1-51, but its fragmentation pattern following cyanogen bromide treatment is incompatible with the linear uncrossed disulfide arrangement. These results suggest that active forms of the SMB domain may have a number of allowed disulfide bond arrangements as long as the Cys(25)-Cys(31) disulfide bond is preserved.

Disulfide bonding arrangements in active forms of the somatomedin B domain of human vitronectin.

We assessed the correlation between charge distribution and conformation of flexible peptides by comparing the theoretically calculated potentiometric-titration curves of two model peptides, Ac-Lys5-NHMe (a model of poly-L-lysine) and Ac-Lys-Ala11-Lys-Gly2-Tyr-NH2 (P1) in water and methanol, with the experimental curves. The calculation procedure consisted of three steps: (i) global conformational search of the peptide under study using the electrostatically driven Monte Carlo (EDMC) method with the empirical conformational energy program for peptides (ECEPP)/3 force field plus the surface-hydration (SRFOPT) or the generalized Born surface area (GBSA) solvation model as well as a molecular dynamics method with the assisted model building and energy refinement (AMBER)99/GBSA force field; (ii) reevaluation of the energy in the pH range considered by using the modified Poisson-Boltzmann approach and taking into account all possible protonation microstates of each conformation, and (iii) calculation of the average degree of protonation of the peptide at a given pH value by Boltzmann averaging over conformations. For Ac-Lys5-NHMe, the computed titration curve agrees qualitatively with the experimental curve of poly-L-lysine in 95% methanol. The experimental titration curves of peptide P1 in water and methanol indicate a remarkable downshift of the first pK(a) value compared to the values for reference compounds (n-butylamine and phenol, respectively), suggesting the presence of a hydrogen bond between the tyrosine hydroxyl oxygen and the H(epsilon) proton of a protonated lysine side chain. The theoretical titration curves agree well with the experimental curves, if conformations with such hydrogen bonds constitute a significant part of the ensemble; otherwise, the theory predicts too small a downward pH shift.

Interplay of charge distribution and conformation in peptides: comparison of theory and experiment.

We compared the ability of two theoretical methods of pH-dependent conformational calculations to reproduce experimental potentiometric titration curves of two models of peptides: Ac-K5-NHMe in 95% methanol (MeOH)/5% water mixture and Ac-XX(A)7OO-NH2 (XAO) (where X is diaminobutyric acid, A is alanine, and O is ornithine) in water, methanol (MeOH), and dimethyl sulfoxide (DMSO), respectively. The titration curve of the former was taken from the literature, and the curve of the latter was determined in this work. The first theoretical method involves a conformational search using the electrostatically driven Monte Carlo (EDMC) method with a low-cost energy function (ECEPP/3 plus the SRFOPT surface-solvation model, assumming that all titratable groups are uncharged) and subsequent reevaluation of the free energy at a given pH with the Poisson-Boltzmann equation, considering variable protonation states. In the second procedure, molecular dynamics (MD) simulations are run with the AMBER force field and the generalized Born model of electrostatic solvation, and the protonation states are sampled during constant-pH MD runs. In all three solvents, the first pKa of XAO is strongly downshifted compared to the value for the reference compounds (ethylamine and propylamine, respectively); the water and methanol curves have one, and the DMSO curve has two jumps characteristic of remarkable differences in the dissociation constants of acidic groups. The predicted titration curves of Ac-K5-NHMe are in good agreement with the experimental ones; better agreement is achieved with the MD-based method. The titration curves of XAO in methanol and DMSO, calculated using the MD-based approach, trace the shape of the experimental curves, reproducing the pH jump, while those calculated with the EDMC-based approach and the titration curve in water calculated using the MD-based approach have smooth shapes characteristic of the titration of weak multifunctional acids with small differences between the dissociation constants. Nevertheless, quantitative agreement between theoretically predicted and experimental titration curves is not achieved in all three solvents even with the MD-based approach, which is manifested by a smaller pH range of the calculated titration curves with respect to the experimental curves. The poorer agreement obtained for water than for the nonaqueous solvents suggests a significant role of specific solvation in water, which cannot be accounted for by the mean-field solvation models.

Assessment of two theoretical methods to estimate potentiometric titration curves of peptides: comparison with experiment.

Parametrization and testing of a new all-atom force field for organic molecules and peptides with fixed bond lengths and bond angles are described. The van der Waals parameters for both the organic molecules and the peptides were taken from J. Phys. Chem. B 2003, 107, 7143 and J. Phys. Chem. B 2004, 108, 12181. First, the values of the 1-4 nonbonded and electrostatic scale factors appropriate to the new force field were determined by computing the conformational energies of six model molecules, namely, ethanol, ethylamine, propanol, propylamine, 1,2-ethanediol, and 1,3-propanediol with different values of these factors. The partial atomic charges of these molecules were obtained by fitting to the electrostatic potentials calculated with the HF/6-31G quantum-mechanical method. Two different charge models (single- and multiple-conformation-derived) were also considered. We demonstrated that the charge model has a stronger effect on the conformational energies than the 1-4 scaling. The choice of a charge model affected the conformational energies of even the smallest molecules considered, whereas the effect of the 1-4 electrostatic or nonbonded scaling was apparent only for 1,3-propanediol. The best agreement with high-level ab initio data was obtained with the multiple-conformation-derived charges and with no scaling of the 1-4 nonbonded or electrostatic interactions (scale factors of 1.0). Next, the torsional parameters of a large number of neutral and charged organic molecules, assumed to be models of the side chains of the 20 naturally occurring amino acids, were computed by fitting to rotational energy profiles obtained from ab initio MP2/6-31G calculations. The quality of the fits was high with average errors for torsional profiles of less than 0.2 kcal/mol. To derive the torsional parameters for the peptide backbone, the partial atomic charges of the 20 neutral and charged amino acids were obtained by fitting to the electrostatic potentials of terminally blocked amino acids using the HF/6-31G quantum-mechanical method. Then, the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe were computed using MP2/6-31G//HF/6-31G quantum-mechanical methods. The phi-psi energy map of Ac-Ala-NMe was used for refinement of the nonbonded parameters for the backbone nitrogen and hydrogen bonded to it. Subsequently, the main-chain torsional parameters were obtained by fitting the molecular mechanics energies to the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe. The transferability of the entire force field was demonstrated by reproducing the main energy minima of terminally blocked Ala3 from the literature. The performance of the force field was also evaluated by simulating crystal structures of small peptides. By comparison of simulated and experimental data, examination of the torsional-angle and atom-positional root-mean-square deviations of the energy-minimized crystal structures from the corresponding X-ray model structures demonstrated high accuracy of the force field.

A new force field (ECEPP-05) for peptides, proteins, and organic molecules.

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems.

The influences of temperature, friction, and random forces on the folding of protein A have been analyzed. A series of all-atom molecular dynamics folding simulations with the Amber ff99 potential and Generalized Born solvation, starting from the fully extended chain, were carried out for temperatures from 300 to 500 K, using (a) the Berendsen thermostat (with no explicit friction or random forces) and (b) Langevin dynamics (with friction and stochastic forces explicitly present in the system). The simulation temperature influences the relative time scale of the major events on the folding pathways of protein A. At lower temperatures, helix 2 folds significantly later than helices 1 and 3. However, with increasing temperature, the folding time of helix 2 approaches the folding times of helices 1 and 3. At lower temperatures, the complete formation of secondary and tertiary structure is significantly separated in time whereas, at higher temperatures, they occur simultaneously. These results suggest that some earlier experimental and theoretical observations of folding events, e.g., the order of helix formation, could depend on the temperature used in those studies. Therefore, the differences in temperature used could be one of the reasons for the discrepancies among published experimental and computational studies of the folding of protein A. Friction and random forces do not change the folding pathway that was observed in the simulations with the Berendsen thermostat, but their explicit presence in the system extends the folding time of protein A.

Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: all-atom molecular dynamics in implicit solvent.

Current all-atom force fields often fail to recognize the native structure of a protein as the lowest free energy minimum. One possible cause could be the mathematical form of the potential based on the assumption that the conformation of a residue is independent of its neighbors. Here, using quantum mechanical (QM) methods (MP2/6-31g**//HF/6-31g** and MP2/cc-pVDZ//cc-pVDZ//HF/cc-pVDZ), the intrinsic correctness of the gas phase terms (without solvation) of the Amber ff03 and ff99 potentials are examined by testing their ability to reproduce the relative 3(10)-helix versus extended structure stabilities in the gas phase for 1-7-residue alanine, valine, leucine, and isoleucine homopolypeptides. The 3(10)-helix versus extended state stability strongly depends on chain length and less on the amino acid identity. The helical conformation becomes lower in energy than the extended conformation for all tested peptides longer than two residues, and its stability increases with the increase of chain length. The ff03 potential better describes the 3(10)-helix versus extended state energy than ff99 and also reproduces the curvature of the relative helix-extended state energies. Therefore, the mathematical form of the Amber potential is sufficient to describe the local effect of 3(10)-helix versus extended structure stabilization in the gas phase. However, the energy curves are shifted and the backbone geometries differ compared with the QM results. This may cause significant geometric discrepancies between native and predicted structures. Therefore, extant molecular mechanics force fields, such as Amber, need refinement of their parameters to correctly describe helix-extended state energetics and geometry of major conformations.

Origin of intrinsic 3(10)-helix versus strand stability in homopolypeptides and its implications for the accuracy of the Amber force field.

The minimal requirements of a physics-based potential that can refine protein structures are the existence of a correlation between the energy with native similarity and the scoring of the native structure as the lowest in energy. To develop such a force field, the relative weights of the Amber ff03 all-atom potential supplemented by an explicit hydrogen-bond potential were adjusted by global optimization of energetic and structural criteria for a large set of protein decoys generated for a set of 58 nonhomologous proteins. The average correlation coefficient of the energy with TM-score significantly improved from 0.25 for the original ff03 potential to 0.65 for the optimized force field. The fraction of proteins for which the native structure had lowest energy increased from 0.22 to 0.90. Moreover, use of an explicit hydrogen-bond potential improves scoring performance of the force field. Promising preliminary results were obtained in applying the optimized potentials to refine protein decoys using only an energy criterion to choose the best decoy among sampled structures. For a set of seven proteins, 63% of the decoys improve, 18% get worse, and 19% are not changed.

Development of a physics-based force field for the scoring and refinement of protein models.

One of the greatest challenges in protein structure prediction is the refinement of low-resolution predicted models to high-resolution structures that are close to the native state. Although contemporary structure prediction methods can assemble the correct topology for a large fraction of protein domains, such approximate models are often not of the resolution required for many important applications, including studies of reaction mechanisms and virtual ligand screening. Thus, the development of a method that could bring those structures closer to the native state is of great importance. We recently optimized the relative weights of the components of the Amber ff03 potential on a large set of decoy structures to create a funnel-shaped energy landscape with the native structure at the global minimum. Such an energy function might be able to drive proteins toward their native structure. In this work, for a test set of 47 proteins, with 100 decoy structures per protein that have a range of structural similarities to the native state, we demonstrate that our optimized potential can drive protein models closer to their native structure. Comparing the lowest-energy structure from each trajectory with the starting decoy, structural improvement is seen for 70% of the models on average. The ability to do such systematic structural refinements by using a physics-based all-atom potential represents a promising approach to high-resolution structure prediction.

Protein model refinement using an optimized physics-based all-atom force field.

A new atomic force microscopy (AFM)-based chemo-mechanical tweezer has been developed that can measure mechanical properties of individual macromolecules in supramolecular assembly and reveal positions of azide-containing polymers. A key feature of the new technology is the use of an AFM tip densely modified with 4-dibenzocyclooctynols (chemo-mechanical tweezer) that can react with multiple azide containing macromolecules of micelles to give triazole "clicked" compounds, which during retracting phases of AFM imaging are removed from the macromolecular assembly thereby providing a surface topographical image and positions of azide-containing polymers. The force-distance curves gave mechanical properties of removal of individual molecules from a supramolecular assembly. The new chemo-mechanical tweezer will make it possible to characterize molecular details of macromolecular assemblies thereby offering new avenues to tailor properties of such assemblies.

A chemo-mechanical tweezer for single-molecular characterization of soft materials.

Myelination and its regenerative counterpart remyelination represent one of the most complex cell-cell interactions in the central nervous system (CNS). The biochemical regulation of axon myelination via the proliferation, migration, and differentiation of oligodendrocyte progenitor cells (OPCs) has been characterized extensively. However, most biochemical analysis has been conducted in vitro on OPCs adhered to substrata of stiffness that is orders of magnitude greater than that of the in vivo CNS environment. Little is known of how variation in mechanical properties over the physiological range affects OPC biology. Here, we show that OPCs are mechanosensitive. Cell survival, proliferation, migration, and differentiation capacity in vitro depend on the mechanical stiffness of polymer hydrogel substrata. Most of these properties are optimal at the intermediate values of CNS tissue stiffness. Moreover, many of these properties measured for cells on gels of optimal stiffness differed significantly from those measured on glass or polystyrene. The dependence of OPC differentiation on the mechanical properties of the extracellular environment provides motivation to revisit results obtained on nonphysiological, rigid surfaces. We also find that OPCs stiffen upon differentiation, but that they do not change their compliance in response to substratum stiffness, which is similar to embryonic stem cells, but different from adult stem cells. These results form the basis for further investigations into the mechanobiology of cell function in the CNS and may specifically shed new light on the failure of remyelination in chronic demyelinating diseases such as multiple sclerosis.

Mechanical environment modulates biological properties of oligodendrocyte progenitor cells.

Axon remyelination in the central nervous system requires oligodendrocytes that produce myelin. Failure of this repair process is characteristic of neurodegeneration in demyelinating diseases such as multiple sclerosis, and it remains unclear how the lesion microenvironment contributes to decreased remyelination potential of oligodendrocytes. Here, we show that acidic extracellular pH, which is characteristic of demyelinating lesions, decreases the migration, proliferation, and survival of oligodendrocyte precursor cells (OPCs), and reduces their differentiation into oligodendrocytes. Further, OPCs exhibit directional migration along pH gradients toward acidic pH. These in vitro findings support a possible in vivo scenario whereby pH gradients attract OPCs toward acidic lesions, but resulting reduction in OPC survival and motility in acid decreases progress toward demyelinated axons and is further compounded by decreased differentiation into myelin-producing oligodendrocytes. As these processes are integral to OPC response to nerve demyelination, our results suggest that lesion acidity could contribute to decreased remyelination.

Extracellular acidic pH inhibits oligodendrocyte precursor viability, migration, and differentiation.

A critical open problem in ab initio protein folding is protein energy function design, which pertains to defining the energy of protein conformations in a way that makes folding most efficient and reliable. In this paper, we address this issue as a weight optimization problem and utilize a machine learning approach, learning-to-rank, to solve this problem. We investigate the ranking-via-classification approach, especially the RankingSVM method and compare it with the state-of-the-art approach to the problem using the MINUIT optimization package. To maintain the physicality of the results, we impose non-negativity constraints on the weights. For this we develop two efficient non-negative support vector machine (NNSVM) methods, derived from L2-norm SVM and L1-norm SVMs, respectively. We demonstrate an energy function which maintains the correct ordering with respect to structure dissimilarity to the native state more often, is more efficient and reliable for learning on large protein sets, and is qualitatively superior to the current state-of-the-art energy function.

ArticleTotal : 2	Year
Publication title Cited by 36	2016
Publication title Cited by 1	2019

Article	Year
Disulfide bonding arrangements in active forms of the somatomedin B domain of human vitronectin. Biochemistry\| PubMed ID: 15157085	2004
Interplay of charge distribution and conformation in peptides: comparison of theory and experiment. Biopolymers\| PubMed ID: 15630705	2005
Assessment of two theoretical methods to estimate potentiometric titration curves of peptides: comparison with experiment. The journal of physical chemistry. B\| PubMed ID: 16509748	2006
A new force field (ECEPP-05) for peptides, proteins, and organic molecules. The journal of physical chemistry. B\| PubMed ID: 16526746	2006
Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems. The journal of physical chemistry. B\| PubMed ID: 16852728	2005
Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: all-atom molecular dynamics in implicit solvent. Journal of computational chemistry\| PubMed ID: 17279497	2007
Origin of intrinsic 3(10)-helix versus strand stability in homopolypeptides and its implications for the accuracy of the Amber force field. Journal of computational chemistry\| PubMed ID: 17342701	2007
Development of a physics-based force field for the scoring and refinement of protein models. Biophysical journal\| PubMed ID: 18178653	2008
Protein model refinement using an optimized physics-based all-atom force field. Proceedings of the National Academy of Sciences of the United States of America\| PubMed ID: 18550813	2008
A chemo-mechanical tweezer for single-molecular characterization of soft materials. Chemistry (Weinheim an der Bergstrasse, Germany)\| PubMed ID: 22374886	2012
Mechanical environment modulates biological properties of oligodendrocyte progenitor cells. Stem cells and development\| PubMed ID: 22646081	2012
Extracellular acidic pH inhibits oligodendrocyte precursor viability, migration, and differentiation. PloS one\| PubMed ID: 24098762	2013
Learning Protein Folding Energy Functions. Proceedings / IEEE International Conference on Data Mining. IEEE International Conference on Data Mining\| PubMed ID: 25311546	2011

Anna Jagielska

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