Molecular dynamics simulations of a protein model in uniform and elongational flows

The role of flow in the self-assembly of dragline spider silk proteins

Hydrodynamic flow in the spider duct induces conformational changes in dragline spider silk proteins (spidroins) and drives their assembly, but the underlying physical mechanisms are still elusive. Here we address this challenging multiscale problem with a complementary strategy of atomistic and coarse-grained molecular dynamics simulations with uniform flow. The conformational changes at the molecular level were analyzed for single-tethered spider silk peptides. Uniform flow leads to coiled-to-stretch transitions and pushes alanine residues into β sheet and poly-proline II conformations. Coarse-grained simulations of the assembly process of multiple semi-flexible block copolymers using multi-particle collision dynamics reveal that the spidroins aggregate faster but into low-order assemblies when they are less extended. At medium-to-large peptide extensions (50%-80%), assembly slows down and becomes reversible with frequent association and dissociation events, whereas spidroin alignment increases and alanine repeats form ordered regions. Our work highlights the role of flow in guiding silk self-assembly into tough fibers by enhancing alignment and kinetic reversibility, a mechanism likely relevant also for other proteins whose function depends on hydrodynamic flow.

Rotational Dynamics of a Protein under Shear Flow Studied by the Eckart Frame Formalism

Proteins are natural polymers that play an essential role in both living organisms and biotechnological applications. During certain bioprocessing steps, they can be exposed to significant mechanical stress induced by, for example, shear flow or sonication, resulting in reduced therapeutic efficacy, aggregation, or even a loss of activity. For this reason, there is a need to understand and determine the susceptibility of the protein activity to the experienced mechanical stress. To acquire this knowledge, it is necessary to study the rotational dynamics of the protein. Commonly, the rotational dynamics of soft molecules is interpreted based on a theoretical analysis performed in an inertial laboratory frame. However, the obtained angular velocity mixes pure rotations and vibrations with angular momentum, consequently lacking a clear dynamical interpretation. On the other hand, the use of the noninertial internal Eckart frame allows the determination of pure angular velocity as it minimizes the coupling between the rotational and vibrational degrees of freedom. In the present work, by conducting open-boundary molecular dynamics simulations and exploiting the Eckart frame formalism, we study the rotational dynamics of a small protein under the shear flow of various strengths. Our results show that the angular velocity increases nonlinearly with increasing shear rate. Furthermore, the protein gains vibrational angular momentum at higher shear rates, which is reflected in the higher angular velocity computed by employing the Eckart frame formalism and confirmed by analysis of the contributions to the total kinetic energy of the biomolecule.

Self-Attractive Semiflexible Polymers under an External Force Field

The dynamical response of a tethered semiflexible polymer with self-attractive interactions and subjected to an external force field is numerically investigated by varying stiffness and self-interaction strength. The chain is confined in two spatial dimensions and placed in contact with a heat bath described by the Brownian multi-particle collision method. For strong self-attraction the equilibrium conformations range from compact structures to double-stranded chains, and to rods when increasing the stiffness. Under the external field at small rigidities, the initial close-packed chain is continuously unwound by the force before being completely elongated. For double-stranded conformations the transition from the folded state to the open one is sharp being steeper for larger stiffnesses. The discontinuity in the transition appears in the force-extension relation, as well as in the probability distribution function of the gyration radius. The relative deformation with respect to the equilibrium case along the direction normal to the force is found to decay as the inverse of the applied force.

Accelerating Reaction Rates of Biomolecules by Using Shear Stress in Artificial Capillary Systems

Biomimetics is a design principle within chemistry, biology, and engineering, but chemistry biomimetic approaches have been generally limited to emulating nature's chemical toolkit while emulation of nature's physical toolkit has remained largely unexplored. To begin to explore this, we designed biophysically mimetic microfluidic reactors with characteristic length scales and shear stresses observed within capillaries. We modeled the effect of shear with molecular dynamics studies and showed that this induces specific normally buried residues to become solvent accessible. We then showed using kinetics experiments that rates of reaction of these specific residues in fact increase in a shear-dependent fashion. We applied our results in the creation of a new microfluidic approach for the multidimensional study of cysteine biomarkers. Finally, we used our approach to establish dissociation of the therapeutic antibody trastuzumab in a reducing environment. Our results have implications for the efficacy of existing therapeutic antibodies in blood plasma as well as suggesting in general that biophysically mimetic chemistry is exploited in biology and should be explored as a research area.

Hydrodynamic effects in proteins

Experimental and numerical results pertaining to flow-induced effects in proteins are reviewed. Special emphasis is placed on shear-induced unfolding and on the role of solvent mediated hydrodynamic interactions in the conformational transitions in proteins.

Force induced unfolding of biopolymers in a cellular environment: a model study

Effect of molecular crowding and confinement experienced by protein in the cell during unfolding has been studied by modeling a linear polymer chain on a percolation cluster. It is known that internal structure of the cell changes in time, however, they do not change significantly from their initial structure. In order to model this we introduce the correlation among the different disorder realizations. It was shown that the force-extension behavior for correlated disorder in both constant force ensemble and constant distance ensemble is significantly different than the one obtained in absence of molecular crowding.

Effects of molecular crowding on stretching of polymers in poor solvent

We consider a linear polymer chain in a disordered environment modeled by percolation clusters on a square lattice. The disordered environment is meant to roughly represent molecular crowding as seen in cells. The model may be viewed as the simplest representation of biopolymers in a cell. We show the existence of intermediate states during stretching arising as a consequence of molecular crowding. In the constant distance ensemble the force-extension curves exhibit oscillations. We observe the emergence of two or more peaks in the probability distribution curves signaling the coexistence of different states and indicating that the transition is discontinuous unlike what is observed in the absence of molecular crowding.

Role of pulling direction in understanding the energy landscape of proteins

Single-molecule force spectroscopy provide details of the underlying energy surfaces of proteins which are essential to the understanding of their unfolding process. Recently, it has been observed experimentally that by pulling proteins in different directions relative to their secondary structure, one can gain a better understanding of the shape of the energy landscape. We consider simple lattice models which are anisotropic in nature to study the response of a force in unfolding of a polymer. Our analytical solution of the model, supported by extensive numerical calculations, reveal that the force temperature diagrams are very different depending on the direction of the applied force. We find that either unzipping or shearing kind transitions dominate the dynamics of the unfolding process depending solely on the direction of the applied force.

Stretching of proteins in a uniform flow

Stretching of a protein by a fluid flow is compared to that in a force-clamp apparatus. The comparison is made within a simple topology-based dynamical model of a protein in which the effects of the flow are implemented using Langevin dynamics. We demonstrate that unfolding induced by a uniform flow shows a richer behavior than that in the force clamp. The dynamics of unfolding is found to depend strongly on the selection of the amino acid, usually one of the termini, which is anchored. These features offer potentially wider diagnostic tools to investigate structure of proteins compared to experiments based on the atomic force microscopy.

Role of conformational entropy in force-induced biopolymer unfolding

A statistical mechanical description of flexible and semiflexible polymer chains in a poor solvent is developed in the constant force and constant distance ensembles. We predict the existence of many intermediate states at low temperatures stabilized by the force. A unified response to pulling and compressing forces has been obtained in the constant distance ensemble. We show the signature of a crossover length which increases linearly with the chain length. Below this crossover length, the critical force of unfolding decreases with temperature, while above, it increases with temperature. For stiff chains, we report for the first time sawtoothlike behavior in the force-extension curves which has been seen earlier in the case of protein unfolding.

Does changing the pulling direction give better insight into biomolecules?

Single-molecule manipulation techniques reveal that the mechanical resistance of a protein depends on the direction of the applied force. Using a lattice model of polymers, we show that changing the pulling direction leads to different phase diagrams. The simple model proposed here indicates that in one case the system undergoes a transition akin to the unzipping of a beta sheet, while in the other case the transition is of a shearing (slippage) nature. Our results are qualitatively similar to experimental results. This demonstrates the importance of varying the pulling direction since this may yield enhanced insights into the molecular interactions responsible for the stability of biomolecules.

Do protein molecules unfold in a simple shear flow?

Protein molecules typically unfold (denature) when subjected to extremes of heat, cold, pH, solvent composition, or mechanical stress. One might expect that shearing forces induced by a nonuniform fluid flow would also destabilize proteins, as when a protein solution flows rapidly through a narrow channel. However, although the protein literature contains many references to shear denaturation, we find little quantitative evidence for the phenomenon. We have investigated whether a high shear can destabilize a small globular protein to any measurable extent. We study a protein (horse cytochrome c, 104 amino acids) whose fluorescence increases sharply upon unfolding. By forcing the sample through a silica capillary (inner diameter 150-180 microm) at speeds approaching 10 m/s, we subject the protein to shear rates dv(z)/dr as large as approximately 2 x 10(5) s(-1) while illuminating it with an ultraviolet laser. We can readily detect fluorescence changes of <1%, corresponding to shifts of < approximately 0.01 kJ/mol in the stability of the folded state. We find no evidence that even our highest shear rates significantly destabilize the folded protein. A simple model suggests that extraordinary shear rates, approximately 10(7) s(-1), would be required to denature typical small, globular proteins in water.

Force-induced conformational transition in a system of interacting stiff polymers: application to unfolding

We consider a stiff polymer chain in poor solvent and apply a force at one end of the chain. We find that by varying the stiffness parameter, the polymer undergoes a transition from the globule state to the foldedlike state. The conformation of the folded state mimics the beta sheet as seen in the titin molecule. Using the exact enumeration technique, we study the extension-force and force-temperature diagrams of such a system. The force-temperature diagram shows the re-entrance behavior for a flexible chain. However, for a stiff chain this re-entrance behavior is absent and there is an enhancement in theta temperature with the rise of stiffness. We further propose that the internal information about the frozen structure of a polymer can be read from the distribution of end-to-end distance which shows a sawtoothlike behavior.

Nonequilibrium Monte Carlo simulation of lattice block copolymer chains subject to oscillatory shear flow

This paper has extended nonequilibrium Monte Carlo (MC) approach to simulate oscillatory shear flow in a lattice block copolymer system. Phase transition and associated rheological behaviors of multiple self-avoiding chains have been investigated. Stress tensor has been obtained based upon sampled configuration distribution functions. At low temperatures, micellar structures have been observed and the underlying frequency-dependent rheological properties exhibit different initial slopes. The simulation outputs are consistent with the experimental observations in literature. Chain deformation during oscillatory shear flow has also been revealed. Although MC simulation cannot account for hydrodynamic interaction, the highlight of our simulation approach is that it can, at small computing cost, investigate polymer chains simultaneously at different spatial scales, i.e., macroscopic rheological behaviors, mesoscopic self-assembled structures, and microscopic chain configurations.