Maciej Długosz

Electrostatically Biased Binding of Kinesin to Microtubules

An electrostatic field rotates, slides, and guides the kinesin head to bind the microtubule at a site a short distance ahead, thus determining the direction of movement of the motor.

Brownian dynamics simulations on CPU and GPU with BD_BOX

There has been growing interest in simulating biological processes under in vivo conditions due to recent advances in experimental techniques dedicated to study single particle behavior in crowded environments. We have developed a software package, BD_BOX, for multiscale Brownian dynamics simulations. BD_BOX can simulate either single molecules or multicomponent systems of diverse, interacting molecular species using flexible, coarse‐grained bead models. BD_BOX is written in C and employs modern computer architectures and technologies; these include MPI for distributed‐memory architectures, OpenMP for shared‐memory platforms, NVIDIA CUDA framework for GPGPU, and SSE vectorization for CPU.

Secondary structures of native and pathogenic huntingtin N-terminal fragments.

Huntingtons disease is a neurodegenerative disorder caused by a polyglutamine (polyQ) expansion in the N-terminal fragment of the Huntingtin (Htt) protein. Structural properties of Htt N-terminal regions and the molecular mechanism leading to protein aggregation have not been fully explained yet. We performed all-atom replica exchange molecular dynamics to investigate the structures of Htt N-terminal parts with polyQ tracts of nonpathogenic and pathogenic lengths. The monomers were composed of the headpiece (17 N-terminal residues), a polyQ tract (polyQ(17) for native and polyQ(55) for pathogenic sequence), and a polyP(11) region, followed by 17 amino acids of mixed sequence. We found that corresponding regions in both fragments fold to similar secondary structures; the headpiece and polyQ stretch adopt mainly α-helical conformations, and polyP(11) forms the PP II-type helix. The native N-terminal fragment is more compact and stabilized by hydrophobic interactions between the surface of polyP(11) and the amphipathic helix of the headpiece. In the pathogenic fragment the headpiece is solvent exposed and does not interact with polyP(11). The predicted structure of the native N-terminal fragment agrees with the X-ray structure of the Htt first exon containing polyQ(17). The structure of the pathogenic fragment adheres to an aggregation model that is mediated by the Htt headpiece.

RedMD—Reduced molecular dynamics package

We developed a software package (RedMD) to perform molecular dynamics simulations and normal mode analysis of reduced models of proteins, nucleic acids, and their complexes. With RedMD one can perform molecular dynamics simulations in a microcanonical ensemble, with Berendsen and Langevin thermostats, and with Brownian dynamics. We provide force field and topology generators which are based on the one‐bead per residue/nucleotide elastic network model and its extensions. The user can change the force field parameters with the command line options that are passed to generators. Also, the generators can be modified, for example, to add new potential energy functions. Normal mode analysis tool is available for elastic or anisotropic network models. The program is written in C and C++ languages and the structure/topology of a molecule is based on an XML format. OpenMP technology for shared‐memory architectures was used for code parallelization. The code is distributed under GNU public licence and available at http://bionano.icm.edu.pl/software/.

Aminoglycoside association pathways with the 30S ribosomal subunit.

Many aminoglycoside antibiotics target bacterial ribosomes and alter their proper functioning as translational machinery leading to bacterial death. To better understand their several inhibitory mechanisms we applied Brownian dynamics and investigated the kinetics and association of paromomycin, an aminoglycoside representative, with the entire 30S ribosomal subunit. We determined that aminoglycoside specific binding at the ribosomal aminoacyl-tRNA site (A-site) begins with antibiotic diffusion toward any point on the 30S subunit and is followed by exploration of the 30S surface. Surprisingly, there is no direct electrostatic steering of the antibiotic to the A-site. Furthermore, we discovered two possible entrances to the A-site around which the mobility of paromomycin is high. The antibiotic also visits binding sites for other drugs targeting the 30S subunit. We found that paromomycin interacts with different sites located along the helix 44 of 16S rRNA, which might explain the recent experimental findings that paromomycins other inhibitory role arises from overstabilizing the ribosomal 70S complex. In addition, our simulations revealed an alternate binding cleft in the 30S subunit that may be important for paromomycins inhibitory effect on translocation. The diffusion limited rate of association was estimated of the order of 10(9) (M.s)(-1) with no dependence on the ionic strength of the solution; the physical origins of this result are explained.

Brownian dynamics study of the association between the 70S ribosome and elongation factor G

Protein synthesis on the ribosome involves a number of external protein factors that bind at its functional sites. One key factor is the elongation factor G (EF-G) that facilitates the translocation of transfer RNAs between their binding sites, as well as advancement of the messenger RNA by one codon. The details of the EF-G/ribosome diffusional encounter and EF-G association pathway still remain unanswered. Here, we applied Brownian dynamics methodology to study bimolecular association in the bacterial EF-G/70S ribosome system. We estimated the EF-G association rate constants at 150 and 300 mM monovalent ionic strengths and obtained reasonable agreement with kinetic experiments. We have also elucidated the details of EF-G/ribosome association paths and found that positioning of the L11 protein of the large ribosomal subunit is likely crucial for EF-G entry to its binding site.

Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems

Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne-Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne-Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead-shell molecular models, using either the analytical Rotne-Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies.

Effects of pH on kinetics of binding of mRNA-cap analogs by translation initiation factor eIF4E.

Abstract. Stopped-flow spectrofluorimetry and a theoretical method for predicting protonation equilibria in polyelectrolytes were combined in an analysis of the pH dependence of the kinetics of binding of analogues of the 5′-mRNA cap to the cap binding protein eIF4E. The computer simulations and available experimental data indicate that there are two titratable groups in the binding site of the protein and two titratable groups on the ligands directly involved in the binding, in addition to stacking interactions described by other groups. The observed pH dependencies of the rate constants obtained from the stopped-flow experiments are consistent with this finding. In particular, it is concluded that binding of both forms of the cap analogs regarding protonation at the N1 position of the guanine ring is efficient, and the shift to a predominantly protonated form of the ring takes place after formation of the complex.

Hydrodynamic effects on the relative rotational velocity of associating proteins.

Hydrodynamic steering effects on the barnase-barstar association were studied through the analysis of the relative rotational velocity of the proteins. We considered the two proteins approaching each other in response to their electrostatic attraction and employed a method that accounts for the long-range and many-body character of the hydrodynamic interactions, as well as the complicated shapes of the proteins. Hydrodynamic steering effects were clearly seen when attractive forces were applied to the geometric centers of the proteins (resulting in zero torques) and the attraction acted along the line that connects centers of geometry of proteins in their crystallographic complex. When we rotated barstar relative to barnase around this line by an angle in the range from -90° to 60°, the rotational velocity arising solely from hydrodynamic interactions restored the orientation of the proteins in the crystal structure. However, because, in reality, both electrostatic forces and torques act on the proteins and these forces and torques depend on the protein-protein distance and the relative orientation of the binding partners, we also investigated more realistic situations employing continuum electrostatics calculations based on atomistic protein models. Overall, we conclude that hydrodynamic interactions aid barnase and barstar in assuming a proper relative orientation upon complex formation.

Contributions of Far-Field Hydrodynamic Interactions to the Kinetics of Electrostatically-Driven Molecular Association

We simulated the diffusional encounters in periodic systems of model isotropic and anisotropic molecules using Brownian dynamics. We considered the electrostatic, excluded volume, and far-field hydrodynamic forces between diffusing molecules. Our goal was to estimate to what extent the hydrodynamic interactions influence the association kinetics when the associating partners are oppositely charged and their direct electrostatic interactions are screened by small mobile ions of dissolved salt. Overall, including hydrodynamic interactions decreases the association rate constants. The relative magnitude of this decrease does not depend on the ionic strength for the association of isotropic charged objects. This also holds true for nonspecific association (i.e., without restrictions regarding the relative orientation of binding partners in an encounter complex) of anisotropic objects. However, such dependence is visible for orientation-specific association of anisotropic objects. Moreover, we observe that some orientations of anisotropic molecules are hydrodynamically favorable during their mutual approach, and that such molecules can be hydrodynamically steered toward a particular relative orientation. This hydrodynamic orientational steering is impeded in case of strong electrostatic interactions or steric hindrance.