Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments.

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

The Rise and Fall of Omicron BA.1 Variant as Seen in Wastewater Supports Epidemiological Model Predictions.

The COVID-19 pandemic caused by the SARS-CoV-2 virus has inflicted significant mortality and morbidity worldwide. Continuous virus mutations have led to the emergence of new variants. The Omicron BA.1 sub-lineage prevailed as the dominant variant globally at the beginning of 2022 but was subsequently replaced by BA.2 in numerous countries. Wastewater-based epidemiology (WBE) offers an efficient tool for capturing viral shedding from infected individuals, enabling early detection of potential pandemic outbreaks without relying solely on community cooperation and clinical testing resources. This study integrated RT-qPCR assays for detecting general SARS-CoV-2 and its variants levels in wastewater into a modified triple susceptible-infected-recovered-susceptible (SIRS) model. The emergence of the Omicron BA.1 variant was observed, replacing the presence of its predecessor, the Delta variant. Comparative analysis between the wastewater data and the modified SIRS model effectively described the BA.1 and subsequent BA.2 waves, with the decline of the Delta variant aligning with its diminished presence below the detection threshold in wastewater. This study demonstrates the potential of WBE as a valuable tool for future pandemics. Furthermore, by analyzing the sensitivity of different variants to model parameters, we are able to deduce real-life values of cross-variant immunity probabilities, emphasizing the asymmetry in their strength.

Smart design of universally decorated nanoparticles for drug delivery applications driven by active transport.

Targeting the cell nucleus remains a challenge for drug delivery. Here, we present a universal platform for the smart design of nanoparticle (NP) decoration that is based on: (i) a spacer polymer, commonly biotin-polyethylene-glycol-thiol, whose grafting density and molecular weight can be tuned for optimized performance, and (ii) protein binding peptides, such as cell penetrating peptides (CPPs), cancer-targeting peptides, or nuclear localization signal (NLS) peptides, that are linked to the PEG free-end by universal chemistry. We manifested our platform with two different bromo-acetamide (Br-Ac) modified NLSs. We used cell extract-based and live cell assays to demonstrate the recruitment of dynein motor proteins, which drive the NP active transport toward the nucleus, and the enhancement of cellular and nuclear entry, manifesting the properties of NLS as a CPP. Our control of the NP decoration scheme, and the modularity of our platform, carry great advantages for nano-carrier design for drug delivery applications.

Spatio-temporal spread of COVID-19: Comparison of the inhomogeneous SEPIR model and data from South Carolina.

During the COVID-19 pandemic authorities have been striving to obtain reliable predictions for the spreading dynamics of the disease. We recently developed a multi-"sub-populations" (multi-compartments: susceptible, exposed, pre-symptomatic, infectious, recovered) model, that accounts for the spatial in-homogeneous spreading of the infection and shown, for a variety of examples, how the epidemic curves are highly sensitive to location of epicenters, non-uniform population density, and local restrictions. In the present work we test our model against real-life data from South Carolina during the period May 22 to July 22 (2020). During this period, minimal restrictions have been employed, which allowed us to assume that the local basic reproduction number is constant in time. We account for the non-uniform population density in South Carolina using data from NASA's Socioeconomic Data and Applications Center (SEDAC), and predict the evolution of infection heat-maps during the studied period. Comparing the predicted heat-maps with those observed, we find high qualitative resemblance. Moreover, the Pearson's correlation coefficient is relatively high thus validating our model against real-world data. We conclude that the model accounts for the major effects controlling spatial in-homogeneous spreading of the disease. Inclusion of additional sub-populations (compartments), in the spirit of several recently developed models for COVID-19, can be easily performed within our mathematical framework.

Managing an evolving pandemic: Cryptic circulation of the Delta variant during the Omicron rise.

SARS-CoV-2 continued circulation results in mutations and the emergence of various variants. Until now, whenever a new, dominant, variant appeared, it overpowered its predecessor after a short parallel period. The latest variant of concern, Omicron, is spreading swiftly around the world with record morbidity reports. Unlike the Delta variant, previously considered to be the main variant of concern in most countries, including Israel, the dynamics of the Omicron variant showed different characteristics. To enable quick assessment of the spread of this variant we developed an RT-qPCR primers-probe set for the direct detection of Omicron variant. Characterized as highly specific and sensitive, the new Omicron detection set was deployed on clinical and wastewater samples. In contrast to the expected dynamics whereupon the Delta variant diminishes as Omicron variant increases, representative results received from wastewater detection indicated a cryptic circulation of the Delta variant even with the increased levels of Omicron variant. Resulting wastewater data illustrated the very initial Delta-Omicron dynamics occurring in real time. Despite this, the future development and dynamics of the two variants side-by-side is still mainly unknown. Based on the initial results, a double susceptible-infected-recovered model was developed for the Delta and Omicron variants. According to the developed model, it can be expected that the Omicron levels will decrease until eliminated, while Delta variant will maintain its cryptic circulation. If this comes to pass, the mentioned cryptic circulation may result in the reemergence of a Delta morbidity wave or in the possible generation of a new threatening variant. In conclusion, the deployment of wastewater-based epidemiology is recommended as a convenient and representative tool for pandemic containment.

Can one detect intermediate denaturation states of DNA sequences by following the equilibrium open-close dynamic fluctuations of a single base pair?

Melting of DNA sequences may occur through a few major intermediate states, whose influence on the melting curve has been discussed previously, while their effect on the kinetics has not been explored thoroughly. Here, we chose a simple DNA sequence, forming a hairpin in its native (zipped) state, and study it using molecular dynamic (MD) simulations and a model integrating the Gaussian network model with bond-binding energies-the Gaussian binding energy (GBE) model. We find two major partial denaturation states, a bubble state and a partial unzipping state. We demonstrate the influence of these two states on the closing-opening base pair dynamics, as probed by a tagged bond auto-correlation function (ACF). We argue that the latter is measured by fluorescence correlation spectroscopy experiments, in which one base of the pair is linked to a fluorescent dye, while the complementary base is linked to a quencher, similar to the experiment reported by Altan-Bonnet et al. [Phys. Rev. Lett. 90, 138101 (2003)]. We find that tagging certain base pairs at temperatures around the melting temperature results in a multi-step relaxation of the ACF, while tagging other base pairs leads to an effectively single-step relaxation, albeit non-exponential. Only the latter type of relaxation has been observed experimentally, and we suggest which of the other base pairs should be tagged in order to observe multi-step relaxation. We demonstrate that this behavior can be observed with other sequences and argue that the GBE can reliably predict these dynamics for very long sequences, where MD simulations might be limited.

Nano-Particles Carried by Multiple Dynein Motors Self-Regulate Their Number of Actively Participating Motors.

Intra-cellular active transport by native cargos is ubiquitous. We investigate the motion of spherical nano-particles (NPs) grafted with flexible polymers that end with a nuclear localization signal peptide. This peptide allows the recruitment of several mammalian dynein motors from cytoplasmic extracts. To determine how motor-motor interactions influenced motility on the single microtubule level, we conducted bead-motility assays incorporating surface adsorbed microtubules and combined them with model simulations that were based on the properties of a single dynein. The experimental and simulation results revealed long time trajectories: when the number of NP-ligated motors Nm increased, run-times and run-lengths were enhanced and mean velocities were somewhat decreased. Moreover, the dependence of the velocity on run-time followed a universal curve, regardless of the system composition. Model simulations also demonstrated left- and right-handed helical motion and revealed self-regulation of the number of microtubule-bound, actively transporting dynein motors. This number was stochastic along trajectories and was distributed mainly between one, two, and three motors, regardless of Nm. We propose that this self-regulation allows our synthetic NPs to achieve persistent motion that is associated with major helicity. Such a helical motion might affect obstacle bypassing, which can influence active transport efficiency when facing the crowded environment of the cell.

Epidemiological model for the inhomogeneous spatial spreading of COVID-19 and other diseases.

We suggest a novel mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume uniform (random) encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. However, in human population, especially under different levels of mobility restrictions, this assumption is likely to fail. Splitting the geographic region under study into areal nodes, and assuming infection kinetics within nodes and between nearest-neighbor nodes, we arrive into a continuous, "reaction-diffusion", spatial model. To account for COVID-19, the model includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic. Our model accounts for the spreading evolution of infectious population domains from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. For instance, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the populated area. Predicted infection "heat-maps" show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas-such as those underway in a few countries.

Kinetics of actin networks formation measured by time resolved particle-tracking microrheology.

Actin is one of the most studied cytoskeleton proteins showing a very rich span of structures and functions. For example, adenosine triphosphate (ATP)-assisted polymerization of actin is used to push protrusions forward in a mechanism that enables cells to crawl on a substrate. In this process, the chemical energy released from the hydrolysis of ATP is what enables force generation. We study a minimal model system comprised of actin monomers in an excess of ATP concentration. In such a system polymerization proceeds in three stages: nucleation of actin filaments, elongation, and network formation. While the kinetics of filament growth was characterized previously, not much is known about the kinetics of network formation and the evolution of networks towards a steady-state structure. In particular, it is not clear how the non-equilibrium nature of this ATP-assisted polymerization manifests itself in the kinetics of self-assembly. Here, we use time-resolved microrheology to follow the kinetics of the three stages of self-assembly as a function of initial actin monomer concentration. Surprisingly, we find that at high enough initial monomer concentrations the effective elastic modulus of the forming actin networks overshoots and then relaxes with a -2/5 power law. We attribute the overshoot to the non-equilibrium nature of the polymerization and the relaxation to rearrangements of the network into a steady-state structure.

Directional Stepping Model for Yeast Dynein: Longitudinal- and Side-Step Distributions.

Motor proteins are biological machines that convert chemical energy stored in ATP to mechanical work. Kinesin and dynein are microtubule (MT)-associated motor proteins that, among other functions, facilitate intracellular transport. Here, we focus on dynein motility. We deduce the directional step distribution of yeast dynein motor protein on the MT surface by combing intrinsic features of the dynein and MTs. These include the probability distribution of the separation vector between the two microtubule-binding domains, the angular probability distribution of a single microtubule-binding domain translation, the existence of an MT seam defect, MT-binding sites, and theoretical extension that accounts for a load force on the motor. Our predictions are in excellent accord with the measured longitudinal step size distributions at various load forces. Moreover, we predict the side-step distribution and its dependence on longitudinal load forces, which shows a few surprising features. First, the distribution is broad. Second, in the absence of load, we find a small right-handed bias. Third, the side-step bias is susceptible to the longitudinal load force; it vanishes at a load equal to the motor stalling force and changes to a left-hand bias above that value. Fourth, our results are sensitive to the ability of the motor to explore the seam several times during its walk. Although available measurements of side-way distribution are limited, our findings are amenable to experimental check and, moreover, suggest a diversity of results depending on whether the MT seam is viable to motor sampling.

Membrane undulations in a structured fluid: Universal dynamics at intermediate length and time scales.

The dynamics of membrane undulations inside a viscous solvent is governed by distinctive, anomalous, power laws. Inside a viscoelastic continuous medium these universal behaviors are modified by the specific bulk viscoelastic spectrum. Yet, in structured fluids the continuum limit is reached only beyond a characteristic correlation length. We study the crossover to this asymptotic bulk dynamics. The analysis relies on a recent generalization of the hydrodynamic interaction in structured fluids, which shows a slow spatial decay of the interaction toward the bulk limit. For membranes which are weakly coupled to the structured medium we find a wide crossover regime characterized by different, universal, dynamic power laws. We discuss various systems for which this behavior is relevant, and delineate the time regime over which it may be observed.

Manipulation of double-stranded DNA melting by force.

By integrating elasticity-as described by the Gaussian network model-with bond binding energies that distinguish between different base-pair identities and stacking configurations, we study the force induced melting of a double-stranded DNA (dsDNA). Our approach is a generalization of our previous study of thermal dsDNA denaturation [J. Chem. Phys. 145, 144101 (2016)JCPSA60021-960610.1063/1.4964285] to that induced by force at finite temperatures. It allows us to obtain semimicroscopic information about the opening of the chain, such as whether the dsDNA opens from one of the ends or from the interior, forming an internal bubble. We study different types of force manipulation: (i) "end unzipping," with force acting at a single end base pair perpendicular to the helix, (ii) "midunzipping," with force acting at a middle base pair perpendicular to the helix, and (iii) "end shearing," where the force acts at opposite ends along the helix. By monitoring the free-energy landscape and probability distribution of intermediate denaturation states, we show that different dominant intermediate states are stabilized depending on the type of force manipulation used. In particular, the bubble state of the sequence L60B36, which we have previously found to be a stable state during thermal denaturation, is absent for end unzipping and end shearing, whereas very similar bubbles are stabilized by midunzipping, or when the force location is near the middle of the chain. Ours results offer a simple tool for stabilizing bubbles and loops using force manipulations at different temperatures, and may implicate on the mechanism in which DNA enzymes or motors open regions of the chain.

Sufficient minimal model for DNA denaturation: Integration of harmonic scalar elasticity and bond energies.

We study DNA denaturation by integrating elasticity - as described by the Gaussian network model - with bond binding energies, distinguishing between different base pairs and stacking energies. We use exact calculation, within the model, of the Helmholtz free-energy of any partial denaturation state, which implies that the entropy of all formed "bubbles" ("loops") is accounted for. Considering base pair bond removal single events, the bond designated for opening is chosen by minimizing the free-energy difference for the process, over all remaining base pair bonds. Despite of its great simplicity, for several known DNA sequences our results are in accord with available theoretical and experimental studies. Moreover, we report free-energy profiles along the denaturation pathway, which allow to detect stable or meta-stable partial denaturation states, composed of bubble, as local free-energy minima separated by barriers. Our approach allows to study very long DNA strands with commonly available computational power, as we demonstrate for a few random sequences in the range 200-800 base-pairs. For the latter, we also elucidate the self-averaging property of the system. Implications for the well known breathing dynamics of DNA are elucidated.

Temperature-induced unfolding behavior of proteins studied by tensorial elastic network model.

Motivated by single molecule experiments and recent molecular dynamics (MD) studies, we propose a simple and computationally efficient method based on a tensorial elastic network model to investigate the unfolding pathways of proteins under temperature variation. The tensorial elastic network model, which relies on the native state topology of a protein, combines the anisotropic network model, the bond bending elasticity, and the backbone twist elasticity to successfully predicts both the isotropic and anisotropic fluctuations in a manner similar to the Gaussian network model and anisotropic network model. The unfolding process is modeled by breaking the native contacts between residues one by one, and by assuming a threshold value for strain fluctuation. Using this method, we simulated the unfolding processes of four well-characterized proteins: chymotrypsin inhibitor, barnase, ubiquitein, and adenalyate kinase. We found that this step-wise process leads to two or more cooperative, first-order-like transitions between partial denaturation states. The sequence of unfolding events obtained using this method is consistent with experimental and MD studies. The results also imply that the native topology of proteins "encrypts" information regarding their unfolding process. Proteins 2016; 84:1767-1775. © 2016 Wiley Periodicals, Inc.

Multimotor Driven Cargos: From Single Motor under Load to the Role of Motor-Motor Coupling.

Motor proteins constitute an essential part of the cellular machinery. They have been the subject of intensive studies in the past two decades. Yet, when several motors simultaneously carry a single cargo, the effect of motor-motor coupling, such as mutual stalling and jamming, remains unclear. We commence by constructing a general model for single motor motion, which is a product of a derived load-dependent expression and a phenomenological motor specific function. Forming the latter according to recent single molecule measurements for a given load, the model correctly predicts the motor full step-size distribution for all other measured loads. We then use our proposed model to predict transport properties of multimotor complexes, with particular attention to 1-dimensional constructs with variable flexibility, motor density, and number of motors: (i) a chain of motors connected by springs, a recently studied construction of a pair, and (ii) an array of motors all connected by identical springs to a stiff rod, which is essentially a mirror image of standard gliding motility assays. In both systems, and for any number of carrying motors, we find that, while low flexibility results in a strongly damped velocity, increased flexibility renders an almost single motor velocity. Comparing our model based simulations to recent gliding assays we find remarkable qualitative agreement. We also demonstrate consistency with other multimotor motility assays. In all cases, the characteristic spring constant, that controls the crossover behavior between high and low velocity regimes, is found to be the stalling force divided by the mean step size. We conjecture that this characteristic spring constant can serve as a tool for engineering multimotor complexes.

N-terminal-mediated oligomerization of DnaA drives the occupancy-dependent rejuvenation of the protein on the membrane.

DnaA, the initiator of chromosome replication in most known eubacteria species, is activated once per cell division cycle. Its overall activity cycle is driven by ATP hydrolysis and ADP-ATP exchange. The latter can be promoted by binding to specific sequences on the chromosome and/or to acidic phospholipids in the membrane. We have previously shown that the transition into an active form (rejuvenation) is strongly co-operative with respect to DnaA membrane occupancy. Only at low membrane occupancy is DnaA reactivation efficiently catalysed by the acidic phospholipids. The present study was aimed at unravelling the molecular mechanism underlying the occupancy-dependent DnaA rejuvenation. We found that truncation of the DnaA N-terminal completely abolishes the co-operative transformation between the high and low occupancy states (I and II respectively) without affecting the membrane binding. The environmentally sensitive fluorophore specifically attached to the N-terminal cysteines of DnaA reported on occupancy-correlated changes in its vicinity. Cross-linking of DnaA with a short homobifunctional reagent revealed that state II of the protein on the membrane corresponds to a distinct oligomeric form of DnaA. The kinetic transition of DnaA on the membrane surface is described in the present study by a generalized 2D condensation phase transition model, confirming the existence of two states of DnaA on the membrane and pointing to the possibility that membrane protein density serves as an on-off switch in vivo. We conclude that the DnaA conformation attained at low surface density drives its N-terminal-mediated oligomerization, which is presumably a pre-requisite for facilitated nt exchange.

Protein unfolding from free-energy calculations: integration of the Gaussian network model with bond binding energies.

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

Nucleus-targeted drug delivery: theoretical optimization of nanoparticles decoration for enhanced intracellular active transport.

A rational design for a nanoparticle is suggested, which will maximize its arrival efficiency from the plasma membrane to the nuclear surrounding. The design is based on grafting the particle surface with polymer spacers, each ending with a motor protein associating molecule, for example, nuclear localization signal peptide. It is theoretically shown that the spacer polymer molecular weight can be adjusted to significantly increase the effective particle processivity time. This should lead to appreciable enhancement of active transport of the nanocarrier, and consequently drug delivery, to the nucleus.

Cooperativity in thermal and force-induced protein unfolding: integration of crack propagation and network elasticity models.

We investigate force-induced and temperature-induced unfolding of proteins using the combination of a gaussian network model and a crack propagation model based on "bond"-breaking independent events. We assume the existence of threshold values for the mean strain and strain fluctuations that dictate bond rupture. Surprisingly, we find that this stepwise process usually leads to a few cooperative, first-order-like, transitions in which several bonds break simultaneously, reminiscent of the "avalanches" seen in disordered networks.