Special Issue: 18th Congress of the Polish Biophysical Society.

The 18th Congress of the Polish Biophysical Society took place at the Faculty of Physics of the University of Warsaw in Warsaw, Poland, in September 2022. In total, 111 attendees (Attendance Profile: 107 in-person, 4 remote; Italy 1, Lithuania 1, Poland 104, United Kingdom 1, United States 4) participated in the event. The authors of lectures and posters at the Congress were invited to prepare their presentations in the form of articles in this special issue of the European Biophysics Journal. The 11 articles published in this special issue present a limited sampling of the subjects of the conference presentations. Nevertheless, they showcase excellence in Polish biophysics across a wide range of topics, using both theoretical and experimental approaches: mechanisms of receptor-ligand interactions, medical applications of proteins and nucleic acids, non-linear dynamics/molecular dynamics of protein systems, hydrodynamics and biosensing. We hope to improve on the representation of the international Polish biophysical community after the next Congress in 2025.

On the possibility of the existence of orienting hydrodynamic steering effects in the kinetics of receptor-ligand association.

In the vast majority of biologically relevant cases of receptor-ligand complex formation, the binding site of the receptor is a small part of its surface, and moreover, formation of a biologically active complex often requires a specific orientation of the ligand relative to the binding site. Before the formation of the initial form of the complex, only long-range, electrostatic and hydrodynamic interactions can act between the ligand approaching the binding site and the receptor. In this context, the question arises whether as a result of these interactions, there is a pre-orientation of the ligand towards the binding site, which to some extent would accelerate the formation of the complex. The role of electrostatic interactions in the orientation of the ligand relative to the binding site of the receptor is well documented. The analogous role of hydrodynamic interactions, although assessed as very significant by Brune and Kim (PNAS 91, 2930-2934, (1994)), is still debatable. In this article, I present the current state of knowledge on this subject and consider the possibilities of demonstrating the orienting effect of hydrodynamic interactions in the processes of receptor-ligand association, in an experimental way supported by computer simulations.

Kinetics of Structural Transitions Induced by Sodium Dodecyl Sulfate in α-Chymotrypsin.

The temporal changes in circular dichroism at 222 and 260 nm were recorded by using stopped-flow spectroscopy after mixing α-chymotrypsin solutions with sodium dodecyl sulfate solutions. Simultaneously with the circular dichroism signal, the fluorescence emission was recorded. Changes in the secondary and tertiary structures of chymotrypsin induced by sodium dodecyl sulfate are characterized by either three or four one-way reactions with relaxation amplitudes and times precisely determined by an advanced numerical procedure of Kuzmic. Quantitatively, transitions within the secondary and tertiary structures of the protein are significantly different. Moreover, changes in the tertiary structure depend on the type of recorded signal (either circular dichroism or fluorescence) and the wavelength of the incident radiation. The latter observation is particularly interesting as it indicates that the contributions of protein's different tryptophans to the total recorded fluorescence depend on the excitation wavelength. We present several results justifying this hypothesis.

Effective screening of Coulomb repulsions in water accelerates reactions of like-charged compounds by orders of magnitude.

The reaction kinetics between like-charged compounds in water is extremely slow due to Coulomb repulsions. Here, we demonstrate that by screening these interactions and, in consequence, increasing the local concentration of reactants, we boost the reactions by many orders of magnitude. The reaction between negatively charged Coenzyme A molecules accelerates ~5 million-fold using cationic micelles. That is ~104 faster kinetics than in 0.5 M NaCl, although the salt is ~106 more concentrated. Rate enhancements are not limited to micelles, as evidenced by significant catalytic effects (104-105-fold) of other highly charged species such as oligomers and polymers. We generalize the observed phenomenon by analogously speeding up a non-covalent complex formation-DNA hybridization. A theoretical analysis shows that the acceleration is correlated to the catalysts' surface charge density in both experimental systems and enables predicting and controlling reaction rates of like-charged compounds with counter-charged species.

Circular Dichroism Spectra of α-Chymotrypsin-SDS Solutions Depend on the Procedure of Their Preparation.

We recorded the far- and near-UV circular dichroism (CD) spectra of solutions of α-chymotrypsin and sodium dodecyl sulfate (SDS) with the final surfactant concentration significantly above the critical micellization concentration. Solutions were prepared using three different procedures. The reference procedure was to mix the chymotrypsin solution with the SDS solution once, immediately achieving the final SDS concentration. In alternative procedures, the protein solutions initially contained some SDS and were mixed with pure SDS solutions at a concentration to provide the same final surfactant as the reference mixing. We demonstrate that the supplementation to the selected final concentration of SDS of the pure chymotrypsin solution leads to different CD spectra than the supplementation to this final concentration of SDS in the chymotrypsin solution containing a small concentration of a few millimolar SDS. These differences disappear when the initial concentration of SDS in the protein solution, which we then supplement to the indicated final concentration, is higher. This suggests the irreversibility of the processes caused by the addition of SDS to chymotrypsin and the influence of the initial amount of this surfactant on the processes occurring with its further addition to the solution. For quantitative analysis of far-UV CD spectra in terms of populations of protein secondary structure elements, we used four well-established software packages. All programs consistently indicate that the observed differences in the far-UV CD spectra can be explained by the differences in the increase in the population of helical forms in chymotrypsin under the influence of SDS.

Searching for Hydrodynamic Orienting Effects in the Association of Tri-N-acetylglucosamine with Hen Egg-White Lysozyme.

Using stopped-flow fluorometry, we determined rate constants for the formation of diffusional encounter complexes of tri-N-acetylglucosamine (NAG3) with hen egg-white lysozyme (kaWT) and its double mutant Asp48Asn/Lys116Gln (kaMT). We defined binding anisotropy, κ ≡ (kaWT - kaMT)/(kaWT + kaMT), and determined its ionic strength dependence. Our goal was to check if this ionic strength dependence provides information about the orienting hydrodynamic effects in the ligand-binding process. We also computed ionic strength dependence of the binding anisotropy from Brownian dynamics simulations using simple models of the lysozyme-NAG3 system. The results of our experiments indicate that in the case of lysozyme and NAG3 such hydrodynamic orienting effects are rather negligible. On the other hand, the results of our Brownian dynamics simulations prove that there exist molecular systems for which such orienting effects are substantial. However, the ionic strength dependence of the rate constants for the wild-type and modified systems do not exhibit any qualitative features that would allow us to conclude the presence of hydrodynamic orienting effects from stopped-flow experiments alone. Nevertheless, the results of our simulations suggest the presence of hydrodynamic orienting effects in the receptor-ligand association when the anisotropy of binding depends on the solvent viscosity.

Constant-pH Brownian Dynamics Simulations of a Protein near a Charged Surface.

We have developed a rigid-body Brownian dynamics algorithm that allows for simulations of a globular protein suspended in an ionic solution confined by a charged planar boundary, with an explicit treatment of pH-dependent protein protonation equilibria and their couplings to the electrostatic potential of the plane. Electrostatic interactions are described within a framework of the continuum Poisson-Boltzmann model, whereas protein-plane hydrodynamic interactions are evaluated based on analytical expressions for the position- and orientation-dependent near-wall friction tensor of a spheroid. The algorithm was applied to simulate near-surface diffusion of lysozyme in solutions having pH in the range 4-10 and ionic strengths of 10 and 150 mM. As a reference, we performed Brownian dynamics simulations in which the protein is assigned a fixed, most probable protonation state, appropriate for given solution conditions and unaffected by the presence of the charged plane, and Brownian dynamics simulations in which the protein probes possible protonation states with the pH-dependent probability, but these variations are not coupled to the electric field generated by the boundary. We show that electrostatic interactions with the negatively charged plane substantially modify probabilities of different protonation states of lysozyme and shift protonation equilibria of both acidic and basic amino acid side chains toward higher pH values. Consequently, equilibrium energy distributions, equilibrium position-orientation distributions, and functions that characterize rotational dynamics, which for a protein with multiple ionization sites, such as lysozyme, in the presence of a charged obstacle are pH-dependent, are significantly affected by the approach taken to incorporate the solution pH into simulations.

Effects of Hydrodynamic Interactions on the Near-Surface Diffusion of Spheroidal Molecules.

We investigated diffusion of spheroidal molecules near a planar surface, accounting for spatially dependent translational and rotational mobilities of molecules resulting from their hydrodynamic interactions with the plane. Rigid-body Brownian dynamics simulations of prolate ellipsoids of revolution of an axial ratio in the range of 1.5 to 3.0, suspended in a viscous fluid, with a no-slip flat boundary confining the suspension were employed. Mobility tensor matrices of molecules were evaluated as functions of spheroids' distance and orientation with respect to the plane. Hydrodynamic interactions with the surface lead to substantial changes of spheroids' translational diffusion coefficients both in the direction perpendicular and parallel to the plane when compared with the values characterizing the bulk diffusion. Moreover, the short-time translational diffusion of molecules, measured in the laboratory frame, both in an unbounded fluid and under the confinement, is non-Gaussian, with much larger deviations from Gaussianity observed in the latter case. In an unbounded fluid, distributions of translational displacements of molecules deviate from those expected for a simple Brownian motion as a result of shape anisotropy. In the presence of the plane, spheroids experience an additional anisotropic drag, and consequently, their mobilities depend on their positions and orientations. Therefore, anomalies in the short-time dynamics observed under confinement can be explained in terms of the so-called diffusing-diffusivity mechanism. Our findings have implications for understanding of a wide range of biological and technological processes that involve diffusion of anisotropic molecules near surfaces of natural and model cell membranes, biosensors and nanosensors, and electrodes.

Does Ionic Screening Lower Activation Barriers for Conformational Transitions in Proteins?

In this work, we investigated the kinetics of binding of hen egg-white lysozyme with tri- N-acetylglucosamine in aqueous solutions, at two values of pH, 3.2 and 11, as a function of ionic strength, by a stopped-flow method with tryptophyl fluorescence observation of the transients. We analyzed registered reaction progress curves by employing numerical integration of appropriate chemical master equations. We discriminated between several binding models and established that the process observed in experiments follows a two-step mechanism, composed of four elementary stages: diffusional formation of an encounter complex, dissociation of the encounter complex, conformational transition of the encounter complex to the final complex, and the reverse transformation, i.e., from the final complex to the encounter complex. We evaluated rate constants of these elementary stages and determined their dependencies on solution ionic strength. Regardless of solution pH, rate constants of both forward and reverse conformational transitions increase with an increasing ionic strength. This suggests that ionic screening of intramolecular electrostatic interactions may act to lower the activation barrier for conformational transition in proteins.

Hydrodynamic Steering in Protein Association Revisited: Surprisingly Minuscule Effects of Considerable Torques.

We investigate the previously postulated hydrodynamic steering phenomenon, resulting from complication of molecular shapes, its magnitude and possible relevance for protein-ligand and protein-protein diffusional encounters, and the kinetics of diffusion-controlled association. We consider effects of hydrodynamic interactions in a prototypical model system consisting of a cleft enzyme and an elongated substrate, and real protein-protein complexes, that of barnase and barstar, and human growth hormone and its binding protein. The kinetics of diffusional encounters is evaluated on the basis of rigid-body Brownian dynamics simulations in which hydrodynamic interactions between molecules are modeled using the bead-shell method for detailed description of molecular surfaces, and the first-passage-time approach. We show that magnitudes of steering torques resulting from the hydrodynamic coupling of associating molecules, evaluated for the studied systems on the basis of the Stokes-Einstein type relations for arbitrarily shaped rigid bodies, are comparable with magnitudes of torques resulting from electrostatic interactions of binding partners. Surprisingly, however, unlike in the case of electrostatic torques that strongly affect the diffusional encounter, overall effects of hydrodynamic steering torques on the association kinetics, while clearly discernible in Brownian dynamics simulations, are rather minute. We explain this result as a consequence of the thermal agitation of the binding partners. Our finding is relevant for the general understanding of a wide spectrum of molecular processes in solution but there is also a more practical aspect to it if one considers the low level of shape detail of models that are usually employed to evaluate hydrodynamic interactions in particle-based Stokesian and Brownian dynamics simulations of multicomponent biomolecular systems. Results described in the current work justify, in part at least, such a low-resolution description.

Effects of Spatially Dependent Mobilities on the Kinetics of the Diffusion-Controlled Association Derived from the First-Passage-Time Approach.

Brownian dynamics (BD) simulations and the first-passage-time approach are applied to investigate diffusion-controlled association in a biologically relevant model system consisting of a fixed receptor with an elongated cavity and a capsule-like ligand that fits this cavity precisely. Before the binding at the receptor cavity, the ligand undergoes translational and rotational diffusion, either free or under the influence of electrostatic interactions with the receptor. The spatial dependence of the translational and rotational mobilities of the ligand resulting from its hydrodynamic interactions (HIs) with the receptor is accounted for in BD simulations, and an accurate numerical approach is applied for the evaluation of the spatially dependent mobility tensor of the ligand. Different magnitudes of electrostatic interactions (either attraction or repulsion) between the ligand and receptor are considered. The effective range of receptor-ligand electrostatic interactions is varied to account for their screening under different conditions of ionic strength. The effects of HIs on the kinetics of the diffusion-controlled association, evaluated for different electrostatic properties of binding partners, are thoroughly analyzed and discussed.

UV-Vis spectroscopy of tyrosine side-groups in studies of protein structure. Part 2: selected applications.

In Part 2 we discuss application of several different types of UV-Vis spectroscopy, such as normal, difference, and second-derivative UV absorption spectroscopy, fluorescence spectroscopy, linear and circular dichroism spectroscopy, and Raman spectroscopy, of the side-chain of tyrosine residues in different molecular environments. We review the ways these spectroscopies can be used to probe complex protein structures.

UV-Vis spectroscopy of tyrosine side-groups in studies of protein structure. Part 1: basic principles and properties of tyrosine chromophore.

Spectroscopic properties of tyrosine residues may be employed in structural studies of proteins. Here we discuss several different types of UV-Vis spectroscopy, like normal, difference and second-derivative UV absorption spectroscopy, fluorescence spectroscopy, linear and circular dichroism spectroscopy, and Raman spectroscopy, and corresponding optical properties of the tyrosine chromophore, phenol, which are used to study protein structure.

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.

8-Azapurines as isosteric purine fluorescent probes for nucleic acid and enzymatic research.

The 8-azapurines, and their 7-deaza and 9-deaza congeners, represent a unique class of isosteric (isomorphic) analogues of the natural purines, frequently capable of substituting for the latter in many biochemical processes. Particularly interesting is their propensity to exhibit pH-dependent room-temperature fluorescence in aqueous medium, and in non-polar media. We herein review the physico-chemical properties of this class of compounds, with particular emphasis on the fluorescence emission properties of their neutral and/or ionic species, which has led to their widespread use as fluorescent probes in enzymology, including enzymes involved in purine metabolism, agonists/antagonists of adenosine receptors, mechanisms of catalytic RNAs, RNA editing, etc. They are also exceptionally useful fluorescent probes for analytical and clinical applications in crude cell homogenates.

Evaluation of Proteins' Rotational Diffusion Coefficients from Simulations of Their Free Brownian Motion in Volume-Occupied Environments.

We have investigated the rotational dynamics of hen egg white lysozyme in monodisperse aqueous solutions of concentrations up to 250 mg/mL, using a rigid-body Brownian dynamics method that accurately accounts for anisotropies of diffusing objects. We have examined the validity of the free diffusion concept in the analysis of computer simulations of volume-occupied molecular solutions. We have found that, when as the only intermolecular interaction, the excluded volume effect is considered, rotational diffusion of molecules adheres to the free diffusion model. Further, we present a method based on the exact (in the case of the free diffusion) analytic forms of autocorrelation functions of particular vectors rigidly attached to diffusing objects, which allows one to obtain from results of molecular simulations the three principal rotational diffusion coefficients characterizing rotational Brownian motion of an arbitrarily shaped rigid particle for an arbitrary concentration of crowders. We have applied this approach to trajectories resulting from Brownian dynamics simulations of hen egg white lysozyme solutions. We show that the apparent anisotropy of proteins' rotational motions increases with an increasing degree of crowding. Finally, we demonstrate that even if the hydrodynamic anisotropy of molecules is neglected and molecules are simulated using their average translational and rotational diffusion coefficients, excluded volume effects still lead to their anisotropic rotational dynamics.

Transient Effects of Excluded Volume Interactions on the Translational Diffusion of Hydrodynamically Anisotropic Molecules.

We have investigated effects of excluded volume interactions on the translational diffusion of hydrodynamically anisotropic molecules. For that, we have performed rigid-body Brownian dynamics simulations of aqueous solutions of hen egg-white lysozyme (HEWL), at concentrations ranging from 1.25 mg/mL to 250 mg/mL and evaluated the lysozyme's self-diffusion. In the long time limit (above 1 µs), the protein's translational diffusion is isotropic, regardless the solution concentration. However, on the time scale of the order of up to hundreds of nanoseconds, the anisotropic translational diffusion is observed, with the transition time from the anisotropic to isotropic translational diffusion depending on the lysozyme concentration. The magnitude of the translational diffusion anisotropy in this transient regime is also concentration-dependent and steric interactions enhance the anisotropy. Moreover, steric interactions cause the anisotropy to be a nonmonotonic function of time. When the hydrodynamic anisotropy of the protein is neglected in Brownian dynamics simulations and its diffusion tensor is replaced with average translational and rotational diffusion coefficients, the lysozyme's translational dynamics in the long-time limit is similar to that in the case of the corresponding hydrodynamically anisotropic object. However, such a similarity is not observed below 1 µs and in this time regime the translational dynamics of lysozyme molecules modeled with isotropic diffusion coefficients substantially deviates from that derived from Brownian dynamics simulations of their hydrodynamically anisotropic counterparts.

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.