Rudolf Podgornik

Chinese Academy of Sciences | CAS · School of Physical Sciences

Our understanding of the “long range” electrodynamic, electrostatic, and polar interactions that dominate the organization of small objects at separations beyond an interatomic bond length is reviewed. From this basic-forces perspective, a large number of systems are described from which one can learn about these organizing forces and how to modula...

We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counterion-only system in the presence of macroscopic, uniformly charged boundaries, whe...

Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems with finite dimensions. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nan...

In this chapter we review the electrostatic properties of charged membranes in aqueous solutions, with or without added salt, employing simple physical models. The equilibrium ionic profiles close to the membrane are governed by the well-known Poisson-Boltzmann (PB) equation. We analyze the effect of different boundary conditions, imposed by the me...

We review approaches aimed at deciphering the physical mechanisms responsible for viral structure and assembly. We discuss the basic principles of condensed matter physics, macroscopic electrostatics and elastomechanics as they apply to nanosized two-dimensional biomolecular shells with spherical topology and icosahedral symmetry, as well as their...

DOI:https://doi.org/10.1103/PhysRevLett.132.199901

Motivation Charged amino acid residues on the spike protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have been shown to influence its binding to different cell surface receptors, its non-specific electrostatic interactions with the environment, and its structural stability and conformation. It is therefore important to obtain...

We present a derivation of the screening length for a solution containing a charge-regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the “uncertainty relation” of the Legendre transform, which connects the Hessians or the local...

Understanding the principles governing protein arrangement in viral capsids and structurally similar protein shells can enable the development of new antiviral strategies and the design of artificial protein cages for...

Motivation Charged amino acid residues on the spike protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have been shown to influence its binding to different cell surface receptors, its non-specific electrostatic interactions with the environment, and its structural stability and conformation. It is therefore important to obtain...

Myriad viruses use positive-strand RNA molecules as their genomes. Far from being only a repository of genetic material, viral RNA performs numerous other functions mediated by its physical structure and chemical properties. In this chapter, we focus on its structure and discuss how long RNA molecules can be treated as branched polymers through pla...

We analyze the changes in the vicinal acidity (pH) at a spherical amphiphilic membrane. The membrane is assumed to contain solvent accessible, embedded, dissociable, charge-regulated moieties. Basing our approach on the linear Debye-Hückel approximation, as well as on the nonlinear Poisson-Boltzmann theory, together with the general Frumkin-Fowler-...

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from t...

We theoretically investigate the combined effects of the chirality and the finite total thickness of nematic cholesteric liquid crystals on the Casimir-Lifshitz torque. We find that the larger the thickness, the more sinusoidal the angular dependence of the torque becomes. We use a Fourier decomposition to quantify this result. The general directio...

Unlike in other viruses, in Cypoviruses the genome is doubly protected since their icosahedral capsids are embedded into a perfect polyhedrin crystal. Current experimental methods cannot resolve the resulting interface structure and we propose a symmetry-based approach to predict it. We reveal a remarkable match between the surfaces of Cypovirus an...

The spike protein of SARS-CoV-2 is responsible for target recognition, cellular entry, and endosomal escape of the virus. At the same time, it is the part of the virus which exhibits the greatest sequence variation across the many variants which have emerged during its evolution. Recent studies have indicated that with progressive lineage emergence...

We theoretically investigate the combined effects of the chirality and the finite total thickness of nematic cholesteric liquid crystals on the Casimir-Lifshitz torque. We find that, the larger the thickness, the more sinusoidal the angular dependence of the torque becomes. We use a Fourier decomposition to quantify this result. The general directi...

We analyze the changes in the vicinal acidity (pH) at a spherical amphiphilic membrane. The membrane is assumed to contain solvent accessible, embedded, dissociable, charge regulated moieties. Basing our approach on the linear Debye-H\"uckel as well as the non-linear Poisson-Boltzmann theory, together with the general Frumkin-Fowler-Guggenheim adso...

Electrostatic-elastic coupling in colloidal crystals, composed of a mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloids, is studied on the continuum level in order to analyze the lattice-mediated interactions between mobile charges. The linearized, Debye-H\" uckel-like mean-field equations allow for an analytic...

We study the effects of charge-regulated acid/base equilibrium on the swelling of polyelectrolyte gels, by considering a combination of the Poisson-Boltzmann theory and a two-site charge-regulation model based on the Langmuir adsorption isotherm. By exploring the volume change as a function of salt concentration for both nano-gels and micro-gels, w...

We explore how the stability of RNA viruses depends on genome topology and interactions between RNA and the capsid proteins. RNA is modeled as a branched polymer with 12 attractive sites (packaging signals) that can form bonds with 12 icosahedrally distributed capsid sites. The genome topology is encoded as a graph by mapping pairs of adjacent pack...

Recent experiments have indicated that at least a part of the osmotic pressure across the giant unilamellar vesicle (GUV) membrane was balanced by the rapid formation of the monodisperse daughter vesicles inside the GUVs through an endocytosis-like process. Therefore, we investigated a possible osmotic role played by these daughter vesicles for the...

The spike protein of SARS-CoV-2 is responsible for target recognition, cellular entry, and endosomal escape of the virus. At the same time, it is the part of the virus which exhibits the greatest sequence variation across the many variants which have emerged during its evolution. Recent studies have indicated that with progressive lineage emergence...

The spike protein (S-protein) is a crucial part of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), with its many domains responsible for binding, fusion, and host cell entry. In this review we use the density functional theory (DFT) calculations to analyze the atomic-scale interactions and investigate the consequences of mutations...

We develop a comprehensive continuum model capable of treating both electrostatic and structural interactions in liquid dielectrics. Starting from a two-order parameter description in terms of charge density and polarization, we derive a field-theoretic model generalizing previous theories. Our theory explicitly includes electrostatic and structura...

The emergence of Omicron SARS-CoV-2 subvariants (BA.1, BA.2, BA.4, and BA.5) with an unprecedented number of mutations in their receptor-binding domain (RBD) of the spike-protein has fueled a new surge of COVID-19 infections, posing a major challenge to the efficacy of existing vaccines and monoclonal antibody (mAb) therapeutics. Here, a thorough a...

Myriad viruses use positive-strand RNA molecules as their genomes. Far from being only a repository of genetic material, viral RNA performs numerous other functions mediated by its physical structure and chemical properties. In this chapter, we focus on its structure and discuss how long RNA molecules can be treated as branched polymers through pla...

Using recent Zika virus structural data we reveal a hidden symmetry of protein order in immature and mature flavivirus shells, violating the Caspar-Klug paradigmatic model of capsid structures. We show that proteins of the outer immature shell layer exhibit trihexagonal tiling, while proteins from inner and outer layers conjointly form a double-she...

A particle driven by active self-propulsion can be subject to inhomogeneous potential fields, steering its orientation and leading to confinement and eventual trapping. Analytical treatment of capture and/or release dynamics for general steering potentials presents a challenge due to its coupling between external potential fields and intrinsic acti...

Significance Unlike common viscosities associated with dissipation, a nondissipative “odd viscosity,” producing transverse stresses, can emerge in isotropic fluids with broken time-reversal and parity symmetries, e.g., electronic Hall systems and chiral active fluids consisting of self-driven spinners. The odd viscosity has been repeatedly reported...

The attachment of the spike protein in SARS-CoV-2 to host cells and the initiation of viral invasion are two critical processes in the viral infection and transmission in which the presence of unique furin (S1/S2) and TMPRSS2 (S2′) cleavage sites play a pivotal role. We provide a detailed analysis of the impact of the BA.1 Omicron mutations vicinal...

Understanding the principles of protein packing and the mechanisms driving morphological transformations in virus shells (capsids) during their maturation can be pivotal for the development of new antiviral strategies. Here, we study how these principles and mechanisms manifest themselves in icosahedral viral capsids assembled from identical symmet...

The receptor-binding domain (RBD) is the essential part in the Spike-protein (S-protein) of SARS-CoV-2 virus that directly binds to the human ACE2 receptor, making it a key target for many vaccines and therapies. Therefore, any mutations at this domain could affect the efficacy of these treatments as well as the viral-cell entry mechanism. We intro...

The receptor-binding domain (RBD) is the essential part in the Spike-protein (S-protein) of SARS-CoV-2 virus that directly binds to the human ACE2 receptor, making it a key target for many vaccines and therapies. Therefore, any mutations at this domain could affect the efficacy of these treatments as well as the viral-cell entry mechanism. We intro...

Aqueous dielectrics are ubiquitous in soft- and bio-nano matter systems. The theoretical description of such systems in terms of continuum (“macroscopic”) theory remains a serious challenge. In this perspective we first review the existing continuum phenomenological approaches that have been developed in the past decades. In order to describe a pat...

A particle driven by active self-propulsion can be subject to inhomogeneous potential fields, steering its orientation and leading to confinement and eventual trapping. Analytical treatment of capture and/or release dynamics for general steering potentials presents a challenge due to its coupling between external potential fields and intrinsic acti...

We develop a comprehensive continuum model capable of treating both electrostatic and structural interactions in liquid dielectrics. Starting from a two-order parameter description in terms of charge density and polarization, we derive a field-theoretic model generalizing previous theories. Our theory explicitly includes electrostatic and structura...

By using a recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn-Overbeek-type theories, that remains valid also in the cases where the entropy of the charged component(s) is not given by the ideal gas form as in the Debye-Hu ̈ckel theory. The scree...

The attachment of the Spike-protein in SARS-CoV-2 to host cells and the initiation of viral invasion are two critical processes in the viral infection and transmission processes in which the presence of unique furin (S1/S2) and TMPRSS2 (S2') cleavage sites play a pivotal role. In this study, we provide detailed analysis of the impact of the BA.1 Om...

Aequous dielectrics are ubiquitous in soft- and bio-nano matter systems. The theoretical description of such systems in terms of continuum (`macroscopic') theory remains a serious challenge. In this perspective we first review the existing continuum phenomenological approaches that have been developed in the past decades. In order to describe a pat...

The emergence of new SARS-CoV-2 Omicron variant of concern (OV) has exacerbated the COVID-19 pandemic because of a large number of mutations in the spike protein, particularly in the receptor-binding domain (RBD), resulting in highly contagious and/or vaccine-resistant strains. Herein, we present a systematic analysis based on detailed molecular dy...

We develop a field-theoretic approach for the treatment of both the nonlocal and the nonlinear response of structured liquid dielectrics. Our systems of interest are composed of dipolar solvent molecules and simple salt cations and anions. We describe them by two independent order parameters, the polarization field for the solvent and the charge-de...

Diffusion of colloidal particles in microchannels has been extensively investigated, where the channel wall is either a no-slip or a slip-passive boundary. However, in the context of active fluids, driving boundary walls are ubiquitous and are expected to have a substantial effect on the particle dynamics. By mesoscale simulations, we study the dif...

We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-Hückel (DH) and the non-line...

The most recent Omicron variant of SARS-CoV-2 has caused global concern and anxiety. The only thing certain about this strain, with a large number of mutations in the spike protein, is that it spreads quickly, seems to evade immune defense, and mitigates the benefits of existing vaccines. Based on the ultra-large-scale ab initio computational model...

Locomotion in segmented animals, such as annelids and myriapods (centipedes and millipedes), is generated by a coordinated movement known as metameric locomotion, which can be also implemented in robots designed to perform specific tasks. We introduce a theoretical model, based on an active directional motion of the head segment and a passive trail...

The SARS-CoV-2 Delta variant is emerging as a globally dominant strain. Its rapid spread and high infection rate are attributed to a mutation in the spike protein of SARS-CoV-2 allowing for the virus to invade human cells much faster and with an increased efficiency. In particular, an especially dangerous mutation P681R close to the furin cleavage...

Emergence of new SARS-CoV-2 Omicron VOC ( OV ) has exacerbated the COVID-19 pandemic due to a large number of mutations in the spike-protein, particularly in the receptor-binding domain (RBD), resulting in highly contagious and/or vaccine-resistant strain. Herein, we present a systematic analysis based on detailed molecular dynamics (MD) simulation...

The most recent Omicron variant of SARS-CoV-2 has caused global concern and anxiety. The only thing certain about this strain, with large number of mutations in the spike protein, is that it spreads quickly, seems to evade immune defense and mitigates the benefits of existing vaccines. Based on the ultra-large-scale ab initio computational modeling...

We develop of a field-theoretic approach for the treatment of both the non-local and the non-linear response of structured liquid dielectrics. Our systems of interest are composed of dipolar solvent molecules and simple salt cations and anions. We describe them by two independent order parameters, the polarization field for the solvent and the char...

A rational therapeutic strategy is urgently needed for combating SARS-CoV-2 infection. Viral infection initiates when the SARS-CoV-2 receptor-binding domain (RBD) binds to the ACE2 receptor, and thus, inhibiting RBD is a promising therapeutic for blocking viral entry. In this study, the structure of lead antiviral candidate binder (LCB1), which has...

We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-H\"uckel (DH) and the non-li...

SARS-CoV-2 Delta variant is emerging as a globally dominant strain. Its rapid spread and high infection rate are attributed to a mutation in the spike protein of SARS-CoV-2 allowing the virus to invade human cells much faster and with increased efficiency. Particularly, an especially dangerous mutation P681R close to the furin cleavage site has bee...

Brownian motors and self-phoretic microswimmers are two typical micromotors, for which thermal fluctuations play different roles. Brownian motors utilize thermal noise to acquire unidirectional motion, while thermal fluctuations randomize the self-propulsion of self-phoretic microswimmers. Here we perform mesoscale simulations to study a composite...

RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing substr...

We generalize the Kirkwood-Shumaker theory of protonisation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the...

We generalize the Kirkwood-Shumaker theory of protonisation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the...

The structure and properties of the arginine-glycine-aspartate (RGD) sequence of the 1FUV peptide at 0 K and body temperature (310 K) are systematically investigated in a dry and aqueous environment using more accurate ab initio molecular dynamics and density functional theory calculations. The fundamental properties, such as electronic structure,...

The dielectric spectra of complex biomolecules reflect the molecular heterogeneity of the proteins and are particularly important for the calculations of electrostatic (Coulomb) and electrodynamic (van der Waals) interactions in protein physics. The dielectric response of the proteins can be decomposed into different components depending on the siz...

We model a cholesteric liquid crystal as a planar birefringent multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated calculation of the Casimir-Lifshitz torque. Numerical results differ appreciably from the case of nematic liqu...

We generalize the Kirkwood-Shumaker theory of protonisation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the...

We generalize the Kirkwood-Shumaker theory of protonisation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the...

RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing 1 subs...

The spike protein of SARS-CoV-2 binds to the ACE2 receptor via its receptor-binding domain (RBD), with the RBD–ACE2 complex presenting an essential molecular target for vaccine development to stall the virus infection proliferation. The computational analyses at molecular, amino acid (AA), and atomic levels have been performed systematically to ide...

Complex coacervation, known as the liquid–liquid phase separation of solutions with oppositely charged polyelectrolytes, has attracted substantial interest in recent years. We study the effect of the charge regulation (CR) mechanism on the complex coacervation by including short-range interactions between the charged sites on the polymer chains as...

We model a cholesteric liquid crystal as a planar uniaxial multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated calculation of the Casimir-Lifshitz torque. Numerical results differ appreciably from the case of nematic liquid c...

Locomotion in segmented animals, such as annelids and myriapods (centipedes and millipedes), is generated by a coordinated movement known as metameric locomotion, which can be also implemented in robots designed to perform specific tasks. We introduce a theoretical model, based on an active directional motion of the head segment and a passive trail...

We develop a model of interacting zwitterionic membranes with rotating surface dipoles immersed in a monovalent salt and implement it in a field theoretic formalism. In the mean-field regime of monovalent salt, the electrostatic forces between the membranes are characterized by a non-uniform trend: at large membrane separations, the interfacial dip...

p>The spike protein of SARS-CoV-2 binds to ACE2 receptor via its receptor-binding domain (RBD), with the RBD-ACE2 complex presenting an essential molecular target for vaccine development to stall the virus infection proliferation. The computational analysis at molecular, amino acid (AA) and atomic levels have been performed systematically to identi...

While almost any kind of face mask offers some protection against particles and pathogens of different sizes, the most efficient ones make use of a layered structure where one or more layers are electrically charged. These electret layers are essential for the efficient filtration of difficult-to-capture small particles, yet the exact nature of ele...

p>The protein dielectric constant reflects the molecular heterogeneity of the proteins and can be decomposed into different components depending on the size, structure, composition, locality, and environment of the protein in general. The long history of its computation and measurement attest to the vital importance of electrostatic interactions in...

We develop a model of interacting zwitterionic membranes with rotating surface dipoles immersed in a monovalent salt, and implement it in a field theoretic formalism. In the mean-field regime of monovalent salt, the electrostatic forces between the membranes are characterized by a non-uniform trend: at large membrane separations, the interfacial di...

Complex coacervation, known as the liquid-liquid phase separation of solutions with oppositely charged polyelectrolytes, has attracted substantial interest in recent years. We study the effect of charge regulation (CR) mechanism on the complex coacervation, by including short-range interactions between the charged sites on the polymer chains, as we...

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson–Boltzm...

The COVID-19 pandemic poses a severe threat to human health with an unprecedented social and economic disruption. Spike (S) glycoprotein of the SARS-CoV-2 virus is pivotal in understanding the virus anatomy, since it initiates the first contact with the ACE2 receptor in the human cell. We report results of ab initio computation of the spike protein...

In its original formulation, the seminal Deryaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability seemed like a simple but realistic description of the world of colloid interactions in electrolyte solutions. It is based on a straightforward superposition of the mean-field Poisson-Boltzmann (PB) electrostatics with the electrodynamic va...

Liquid-liquid phase separation has emerged as one of the important paradigms in the chemical physics as well as biophysics of charged macromolecular systems. We elucidate an equilibrium phase separation mechanism based on charge regulation, i.e., protonation-deprotonation equilibria controlled by pH, in an idealized macroion system which can serve...

By using the recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn-Overbeek type theories, that remains valid also in the cases where the entropy is not given by the ideal gas form as in the Debye-Huckel theory. The screening length consistent with...

While almost any kind of face mask offers some protection against particles and pathogens of different sizes, the most efficient ones make use of a layered structure where one or more layers are electrically charged. This electret layer is essential to efficient filtration of difficult-to-capture small particles, yet the exact nature of electrostat...

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-...

p>The COVID-19 pandemic poses a severe threat to human health with an unprecedented social and economic disruption. Spike (S) glycoprotein of the SARS-CoV-2 virus is pivotal in understanding the virus anatomy, since it initiates the first contact with the ACE2 receptor in the human cell. We report results of ab initio computation of the spike prote...

Orientational ordering driven by mechanical distortion of soft substrates plays a major role in material transformation processes such as elastocapillarity and surface anchoring. We present a theoretical model of the orientational response of anisotropic rods deposited onto a surface of a soft, elastic substrate of finite thickness. We show that an...

Liquid-liquid phase separation has emerged as one of the important paradigms in the chemical physics as well as biophysics of charged macromolecular systems. We elucidate an equilibrium phase separation mechanism based on charge regulation, i.e., protonation-deprotonation equilibria controlled by pH, in an idealized macroion system which can serve...

Research in the field of nanoplasmonic metamaterials is moving towards more and more interesting and, potentially useful, applications. In this paper we focus on a class of such metamaterials formed by voltage controlled self-assembly of metallic nanoparticale at electrochemical solid |liquid interfaces. We perform a simplified, comprehensive analy...

Understanding the physicochemical processes occurring in viruses during their maturation is of fundamental importance since only mature viruses can infect the host cells. Here we consider the irreversible and reversible morphological changes that occur with dodecahedral φ6 procapsid during sequential packaging of 3 RNA segments forming the viral ge...