During an epidemic outbreak in a human population, susceptibility to infection can be reduced by raising awareness of the disease. In this paper, we investigate the effects of three forms of awareness (i.e., contact, local, and global) on the spread of a disease in a random network. Connectivity-correlated transmission rates are assumed. By using the mean-field theory and numerical simulation, we show that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot, which mirrors the recent results of Wu et al. The obtained results point out that individual behaviors in the presence of an infectious disease has a great influence on the epidemic dynamics. Our method enriches mean-field analysis in epidemic models.
Epidemic spread; Complex network; Behavioral response; Heterogeneous transmission; 92D30; 34D20
Though the maximum sustainable yield (MSY) approach has been legally adopted for the management of world fisheries, it does not provide any guarantee against from species extinction in multispecies communities. In the present article, we describe the appropriateness of the MSY policy in a Holling–Tanner prey–predator system with different types of functional responses. It is observed that for both type I and type II functional responses, harvesting of either prey or predator species at the MSY level is a sustainable fishing policy. In the case of combined harvesting, both the species coexist at the maximum sustainable total yield (MSTY) level if the biotic potential of the prey species is greater than a threshold value. Further, increase of the biotic potential beyond the threshold value affects the persistence of the system.
Harvesting; Combined fishing effort; Maximum sustainable total yield (MSTY); Holling-type response function; Volterra’s first principle
Exposure of cell membranes to an electromagnetic field (EMF) in the millimeter wave band (30–300 GHz) can produce a variety of responses. Further, many of the vibrational modes in complex biomolecules fall in the 1–100 GHz range. In addition to fundamental scientific interest, this may have applications in the development of diagnostic and therapeutic medical applications. In the present work, lipid vesicles of different size were used to study the effects of exposure to radiation at 52–72 GHz, with incident power densities (IPD) of 0.0035–0.010 mW/cm2, on the chemical-physical properties of cell membranes. Large unilamellar vesicles (LUVs) were used to study the effect of the radiation on the physical stability of vesicles by dynamic light scattering. An inhibition of the aging processes (Ostwald ripening), which usually occur in these vesicles because of their thermodynamic instability, resulted. Giant unilamellar vesicles (GUVs) were used to study the effect of the radiation on membrane water permeability under osmotic stress by phase contrast microscopy. In this case, a decrease in the water membrane permeability of the irradiated samples was observed. We advance the hypothesis that both the above effects may be explained in terms of a change of the polarization states of water induced by the radiation, which causes a partial dehydration of the membrane and consequently a greater packing density (increased membrane rigidity).
Electronic supplementary material The online version of this article (doi:10.1007/s10867-012-9296-2) contains supplementary material, which is available to authorized users.
Unilamellar vesicles; Lipid membrane; Physical stability; Permeability change; Millimeter waves; Biological effects; Non-ionizing radiation
Neurofilaments are essential cytoskeletal filaments that impart mechanical stability to axons. They are mostly assembled from three neurofilament proteins that form the core of the filament and its sidearms. Adjacent neurofilaments interact with each other through their apposing sidearms and attain unique conformations depending on the ionic condition, phosphorylation state, and interfilament separations. To understand the conformational properties of apposing sidearms under various conditions and gain insight into interfilament interactions, we performed Monte Carlo simulations of neurofilament pairs. We employed a sequence-based coarse-grained model of apposing NF sidearms that are end-tethered to cylindrical geometries according to the stoichiometry of the three neurofilament subunits. Monte Carlo simulations were conducted under different conditions such as phosphorylation state, ionic condition, and interfilament separations. Under salt-free conditions, apposing sidearms are found to adopt mutually excluding stretched but bent away conformations that are reminiscent of a repulsive type of interaction. Under physiological conditions, apposing sidearms are found to be in a coiled conformation, suggesting a short-range steric repulsive type of interaction. Increased sidearm mutual interpenetration and a simultaneous decrease in the individual brush heights were observed as the interfilament separation was reduced from 60 to 40 nm. The observed conformations suggest entropic interaction as a likely mechanism for sidearm-mediated interfilament interactions under physiological conditions.
Electronic supplementary material The online version of this article (doi:10.1007/s10867-012-9293-5) contains supplementary material, which is available to authorized users.
Neurofilament sidearms; Phosphorylation; Monte Carlo simulation; Neurofilament brush model; Polyampholytes
We consider a modified energy depot model in the overdamped limit using an asymmetric energy conversion rate, which consists of linear and quadratic terms in an active particle’s velocity. In order to analyze our model, we adopt a system of molecular motors on a microtubule and employ a flashing ratchet potential synchronized to a stochastic energy supply. By performing an active Brownian dynamics simulation, we investigate effects of the active force, thermal noise, external load, and energy-supply rate. Our model yields the stepping and stalling behaviors of the conventional molecular motor. The active force is found to facilitate the forwardly processive stepping motion, while the thermal noise reduces the stall force by enhancing relatively the backward stepping motion under external loads. The stall force in our model decreases as the energy-supply rate is decreased. Hence, assuming the Michaelis–Menten relation between the energy-supply rate and the an ATP concentration, our model describes ATP-dependent stall force in contrast to kinesin-1.
Active Brownian particle; Overdamped motion; Flashing ratchet; Molecular motor
Transmembrane acid–base fluxes affect the intracellular pH and unstirred layer pH around a superfused biological preparation. In this paper the factors influencing the unstirred layer pH and its gradient are studied. An analytical expression of the unstirred layer pH gradient in steady state is derived as a function of simultaneous transmembrane fluxes of (weak) acids and bases with the dehydration reaction of carbonic acid in equilibrium. Also a multicompartment computer model is described consisting of the extracellular bulk compartment, different unstirred layer compartments and the intracellular compartment. With this model also transient changes and the influence of carbonic anhydrase (CA) can be studied. The analytical expression and simulations with the multicompartment model demonstrate that in steady state the unstirred layer pH and its gradient are influenced by the size and type of transmembrane flux of acids and bases, their dissociation constant and diffusion coefficient, the concentration, diffusion coefficient and type of mobile buffers and the activity and location of CA. Similar principles contribute to the amplitude of the unstirred layer pH transients. According to these models an immobile buffer does not influence the steady-state pH, but reduces the amplitude of pH transients especially when these are fast. The unstirred layer pH provides useful information about transmembrane acid–base fluxes. This paper gives more insight how the unstirred layer pH and its transients can be interpreted. Methodological issues are discussed.
Computer model; Unstirred layer pH; Intracellular pH; Proton transport; Buffer; Carbonic anhydrase; Disequilibrium pH; pH
The sequence dependence of DNA-protein interactions that allows proteins to find the correct reaction site also slows down the 1D diffusion of the protein along the DNA molecule, leading to the so-called “speed-stability paradox,” wherein fast diffusion along the DNA molecule is seemingly incompatible with stable targeting of the reaction site. Here, we develop diffusion-reaction models that use discrete and continuous Gaussian random 1D diffusion landscapes with or without a high-energy cut-off, and two-state models with a transition to and from a “searching” mode in which the protein diffuses rapidly without recognizing the target. We show the conditions under which such considerations lead to a predicted speed-up of the targeting process, and under which the presence of a “searching” mode in a two-state model is nearly equivalent to the existence of a high-energy cut-off in a one-state model. We also determine the conditions under which the search is either diffusion-limited or reaction-limited, and develop quantitative expressions for the rate of successful targeting as a function of the site-specific reaction rate, the roughness of the DNA-protein interaction potential, and the presence of a “searching” mode. In general, we find that a rough landscape is compatible with a fast search if the highest energy barriers can be avoided by “hopping” or by the protein transitioning to a lower-energy “searching” mode. We validate these predictions with the results of Brownian dynamics, kinetic Metropolis, and kinetic Monte Carlo simulations of the diffusion and targeting process, and apply these concepts to the case of T7 RNA polymerase searching for its target site on T7 DNA.
Electronic supplementary material The online version of this article (doi:10.1007/s10867-013-9310-3) contains supplementary material, which is available to authorized users.
Protein–DNA interaction; Sliding; Two-state model; Protein targeting
The mechanical inhomogeneity of the respiratory system is frequently investigated by measuring the frequency dependence of dynamic compliance, but no data are currently available describing the effects of body temperature variations. The aim of the present report was to study those effects in vivo. Peak airway pressure was measured during positive pressure ventilation in eight anesthetized rats while breathing frequency (but not tidal volume) was altered. Dynamic compliance was calculated as the tidal volume/peak airway pressure, and measurements were taken in basal conditions (mean rectal temperature 37.3 °C) as well as after total body warming (mean rectal temperature 39.7 °C). Due to parenchymal mechanical inhomogeneity and stress relaxation-linked effects, the normal rat respiratory system exhibited frequency dependence of dynamic lung compliance. Even moderate body temperature increments significantly reduced the decrements in dynamic compliance linked to breathing rate increments. The results were analyzed using Student’s and Wilcoxon’s tests, which yielded the same results (p < 0.05). Body temperature variations are known to influence respiratory mechanics. The frequency dependence of dynamic compliance was found, in the experiments described, to be temperature-dependent as temperature variations affected parenchymal mechanical inhomogeneity and stress relaxation. These results suggest that body temperature variations should be taken into consideration when the dynamic compliance–breathing frequency relationship is being examined during clinical assessment of inhomogeneity of lung parenchyma in patients.
Body temperature; Dynamic compliance; Frequency of breathing; Mechanical ventilation; Rat; Respiratory mechanics
Human serum albumin (HSA) nanometer or micron particles represent promising drug-carrier systems. The azimuthal and radial variations of a linear polarization-sensitive backscattering Mueller matrix were experimentally studied in two cases: the scattering particle was smaller or larger in size to the probing wavelength of 780 nm. The results show that the twofold and fourfold structures are characteristic of small particle size suspension, whereas the eightfold structure is characteristic of large particle size suspension. Moreover, for both particle size suspensions, the element patterns have strong radial dependence when the suspension concentration and the incident power of laser change. In addition, for both particle size suspensions, the rotational symmetry of each element is lost in the case of oblique incidence but the multifold structure is maintained. Some suggestions for applications of Mueller matrix imaging in biomedical optics are provided.
Backscattering; Linear polarization; Mueller matrix; Turbid media; Human serum albumin
This communication reports the increase in fluorescence resonance energy transfer (FRET) efficiency between two laser dyes in the presence of deoxyribonucleic acid (DNA). Two types of molecular logic gates have been designed where DNA acts as input signal and fluorescence intensity of different bands are taken as output signal. Use of these logic gates as a DNA sensor has been demonstrated.
FRET; DNA; Molecular logic gate; Sensor
Diel vertical migration is a behavioral antipredator defense that is shaped by a trade-off between higher predation risk in surface waters and reduced growth in deeper waters. The strength of migration of zooplankton increases with a rise in the abundance of predators and their exudates (kairomone). Recent studies span multiple trophic levels, which lead to the concept of coupled vertical migration. The migrations that occur at one trophic level can affect the vertical migration of the next lower trophic level, and so on, throughout the food chain. This is called cascading migration. In this paper, we introduce cascading migration in a well-known model (Hastings and Powell, Ecology 73:896–903, 1991). We represent the dynamics of the system as proposed by Hastings and Powell as a phytoplankton–zooplankton–fish (prey–middle predator–top predator) model where fish affect the migrations of zooplankton, which in turn affect the migrations of motile phytoplankton. The system under cascading migration enhances system stability and population coexistence. It is also observed that for a higher rate of cascading migration, the system shows chaotic behavior. We conclude that the observations of Hastings and Powell remain true if the cascading migration rate is high enough.
Kairomone; Inducible defense; Diel vertical migration; Coexistence; Stability; Hopf-bifurcation; Chaos
Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call “structural homology”) can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.
Chromatin pairing; Homology; Electrostatics; Shape recognition; Long-range bridging
Phospholipase A2 (PLA2), isolated from Daboia russelli pulchella (Russell’s viper), is enzymatically active as well as induces several pharmacological disorders including neurotoxicity, myotoxicity, cardiotoxicity, anti-coagulant, hemolytic, and platelet effects. Indomethacin reduces the effects of anti-coagulant and pro-inflammatory actions of PLA2. Pyrazolo[3,4-d]pyrimidines constitute a class of naturally occurring fused uracils that posses diverse biological activities. The in-silico docking studies of nine pyrazolo[3,4-d]pyrimidine molecules have been carried out with the X-ray crystal structure of Russell’s viper PLA2 (PDB ID: 3H1X) to predict the binding affinity, molecular recognition, and to explicate the binding modes, using AUTODOCK and GLIDE (Standard precision and Extra precision) modules, respectively. Docking results through each method make obvious that pyrazolo[3,4-d]pyrimidine molecules with trimethylene linker can bind with both anti-coagulation and enzymatic regions of PLA2.
Electronic supplementary material The online version of this article (doi: 10.1007/s10867-013-9299-7) contains supplementary material, which is available to authorized users.
Pyrazolo[3,4-d]pyrimidines; PLA2; Molecular docking; AUTODOCK4.2; Schrödinger; ADME calculatioin
The problem of viral packaging (condensation) and ejection from viral capsid in the presence of multivalent counterions is considered. Experiments show divalent counterions strongly influence the amount of DNA ejected from bacteriophage. In this paper, the strong electrostatic interactions between DNA molecules in the presence of multivalent counterions is investigated. It is shown that experiment results agree reasonably well with the phenomenon of DNA reentrant condensation. This phenomenon is known to cause DNA condensation in the presence of tri- or tetra-valent counterions. For divalent counterions, the viral capsid confinement strongly suppresses DNA configurational entropy, therefore the correlation between divalent counterions is strongly enhanced causing similar effect. Computational studies also agree well with theoretical calculations.
DNA virus; DNA overcharging; Multivalent counterions; Strongly correlated electrostatics
Physical virology seeks to define the principles of physics underlying viral infections, traditionally focusing on the fundamental processes governing virus assembly, maturation, and disassembly. A detailed understanding of virus structure and assembly has facilitated the development and analysis of virus-based materials for medical applications. In this Physical Virology review article, we discuss the recent developments in nanomedicine that help us to understand how physical properties affect the in vivo fate and clinical impact of (virus-based) nanoparticles. We summarize and discuss the design rules that need to be considered for the successful development and translation of virus-based nanomaterials from bench to bedside.
Design rules; Viral nanoparticles; Physical virology; Nanotechnology; Nanomedicine; Drug delivery; Long range interactions
Viruses can be described as biological objects composed mainly of two parts: a stiff protein shell called a capsid, and a core inside the capsid containing the nucleic acid and liquid. In many double-stranded DNA bacterial viruses (aka phage), the volume ratio between the liquid and the encapsidated DNA is approximately 1:1. Due to the dominant DNA hydration force, water strongly mediates the interaction between the packaged DNA strands. Therefore, water that hydrates the DNA plays an important role in nanoindentation experiments of DNA-filled viral capsids. Nanoindentation measurements allow us to gain further insight into the nature of the hydration and electrostatic interactions between the DNA strands. With this motivation, a continuum-based numerical model for simulating the nanoindentation response of DNA-filled viral capsids is proposed here. The viral capsid is modeled as large- strain isotropic hyper-elastic material, whereas porous elasticity is adopted to capture the mechanical response of the filled viral capsid. The voids inside the viral capsid are assumed to be filled with liquid, which is modeled as a homogenous incompressible fluid. The motion of a fluid flowing through the porous medium upon capsid indentation is modeled using Darcy’s law, describing the flow of fluid through a porous medium. The nanoindentation response is simulated using three-dimensional finite element analysis and the simulations are performed using the finite element code Abaqus. Force-indentation curves for empty, partially and completely DNA-filled capsids are directly compared to the experimental data for bacteriophage λ. Material parameters such as Young’s modulus, shear modulus, and bulk modulus are determined by comparing computed force-indentation curves to the data from the atomic force microscopy (AFM) experiments. Predictions are made for pressure distribution inside the capsid, as well as the fluid volume ratio variation during the indentation test.
Capsid nanoindentation; AFM; Darcy’s law; Finite element simulations; Spring constant
We have performed Langevin dynamics simulations of a coarse-grained model of ejection of dsDNA from Φ29 phage. Our simulation results show significant variations in the local ejection speed, consistent with experimental observations reported in the literature for both in vivo and in vitro systems. In efforts to understand the origin of such variations in the local speed of ejection, we have investigated the correlations between the local ejection kinetics and the packaged structures created at various motor forces and chain flexibility. At lower motor forces, the packaged DNA length is shorter with better organization. On the other hand, at higher motor forces typical of realistic situations, the DNA organization inside the capsid suffers from significant orientational disorder, but yet with long orientational correlation times. This in turn leads to lack of registry between the direction of the DNA segments just to be ejected and the direction of exit. As a result, a significant amount of momentum transfer is required locally for successful exit. Consequently, the DNA ejection temporarily slows down exhibiting pauses. This slowing down occurs at random times during the ejection process, completely determined by the particular starting conformation created by prescribed motor forces. In order to augment our inference, we have additionally investigated the ejection of chains with deliberately changed persistence length. For less inflexible chains, the demand on the occurrence of large momentum transfer for successful ejection is weaker, resulting in more uniform ejection kinetics. While being consistent with experimental observations, our results show the nonergodic nature of the ejection kinetics and call for better theoretical models to portray the kinetics of genome ejection from phages.
Genome ejection from phages
Defective interfering (DI) viruses are thought to cause oscillations in virus levels, known as the ‘Von Magnus effect’. Interference by DI viruses has been proposed to underlie these dynamics, although experimental tests of this idea have not been forthcoming. For the baculoviruses, insect viruses commonly used for the expression of heterologous proteins in insect cells, the molecular mechanisms underlying DI generation have been investigated. However, the dynamics of baculovirus populations harboring DIs have not been studied in detail. In order to address this issue, we used quantitative real-time PCR to determine the levels of helper and DI viruses during 50 serial passages of Autographa californica multiple nucleopolyhedrovirus (AcMNPV) in Sf21 cells. Unexpectedly, the helper and DI viruses changed levels largely in phase, and oscillations were highly irregular, suggesting the presence of chaos. We therefore developed a simple mathematical model of baculovirus-DI dynamics. This theoretical model reproduced patterns qualitatively similar to the experimental data. Although we cannot exclude that experimental variation (noise) plays an important role in generating the observed patterns, the presence of chaos in the model dynamics was confirmed with the computation of the maximal Lyapunov exponent, and a Ruelle-Takens-Newhouse route to chaos was identified at decreasing production of DI viruses, using mutation as a control parameter. Our results contribute to a better understanding of the dynamics of DI baculoviruses, and suggest that changes in virus levels over passages may exhibit chaos.
Baculovirus; Bifurcations; Chaos; Defective interfering virus; Experimental evolution
The amount and type of self-entanglement of DNA filaments is significantly affected by spatial confinement, which is ubiquitous in biological systems. Motivated by recent advancements in single DNA molecule experiments based on nanofluidic devices and by the introduction of algorithms capable of detecting knots in open chains, we investigate numerically the entanglement of linear, open DNA chains confined inside nano-slits. The results regard the abundance, type, and length of occurring knots and are compared with recent findings for DNA inside nano-channels. In both cases, the width of the confining region, D, spans the 30 nm–1 μm range and the confined DNA chains are 1–4 μm long. It is found that the knotting probability is maximum for slit widths in the 70–100 nm range. However, over the considered DNA contour lengths, the maximum incidence of knots remains below 20%, while for channel confinement it tops 50%. Further differences of the entanglement are seen for the average contour length of the knotted region, which drops significantly below D ~100 nm for channel-confinement, while it stays approximately constant for slit-like confinement. These properties ought to reverberate in different kinetic properties of linear DNA depending on confinement and could be detectable experimentally or exploitable in nano-technological applications.
Linear DNA; Knots; Spatial confinement; Nanochannels; Nanoslits
From the analysis of sizes of approximately 130 small icosahedral viruses we find that there is a typical structural capsid protein, having a mean diameter of 5 nm and a mean thickness of 3 nm, with more than two thirds of the analyzed capsid proteins having thicknesses between 2 nm and 4 nm. To investigate whether, in addition to the fairly conserved geometry, capsid proteins show similarities in the way they interact with one another, we examined the shapes of the capsids in detail. We classified them numerically according to their similarity to sphere and icosahedron and an interpolating set of shapes in between, all of them obtained from the theory of elasticity of shells. In order to make a unique and straightforward connection between an idealized, numerically calculated shape of an elastic shell and a capsid, we devised a special shape fitting procedure, the outcome of which is the idealized elastic shape fitting the capsid best. Using such a procedure we performed statistical analysis of a series of virus shapes and we found similarities between the capsid elastic properties of even very different viruses. As we explain in the paper, there are both structural and functional reasons for the convergence of protein sizes and capsid elastic properties. Our work presents a specific quantitative scheme to estimate relatedness between different proteins based on the details of the (quaternary) shape they form (capsid). As such, it may provide an information complementary to the one obtained from the studies of other types of protein similarity, such as the overall composition of structural elements, topology of the folded protein backbone, and sequence similarity.
Capsid; Virus; Geometry; Icosahedron; Faceting; Elasticity
Morphological changes in the polyhedra of the Bombyx mori L. nuclear polyhedrosis virus (BmNPV), a baculovirus causing the deadly grasserie disease in silkworms, brought about by mixing with lipophilically capped amorphous silica nanoparticles (LASN, average size 10 ± 2 nm) were studied with scanning electron microscopy (SEM) and Fourier transform infrared (FTIR) spectroscopy. SEM shows that the regular octagonal polyhedra facets are replaced by a larger number of newly formed irregular ones. The average number of facets reveals a nonlinear growth pattern with nanoparticle (NP) concentration, where an initial linear region ends in a plateau. IR bands corresponding to vibration modes of the capping show (a) a saturation of the area under the band with NP concentration, indicating a correlation with attachment to viral polyhedra and (b) a narrowing of the band per NP from the linear to the plateau portions of the distortion curve, suggesting non-equilibrium and equilibrium situations, respectively.
Silica nanoparticle; Baculovirus polyhedra; Morphological deformity; Boltzmann equation
Single-stranded RNAs of simple viruses seem to be topologically more compact than other types of single-stranded RNA. It has been suggested that this has an evolutionary purpose: more compact structures are more easily encapsulated in the limited space that the cavity of the virus capsid offers. We employ a simple Flory theory to calculate the optimal amount of polymers confined in a viral shell. We find that the free energy gain or more specifically the efficiency of RNA encapsidation increases substantially with topological compactness. We also find that the optimal length of RNA encapsidated in a capsid increases with the degree of branching of the genome even though this effect is very weak. Further, we show that if the structure of the branching of the polymer is allowed to anneal, the optimal loading increases substantially.
Virus assembly; Self-assembly; Branched polymers; Flory theory
Double-stranded DNA bacteriophage genomes are packaged into their icosahedral capsids at the highest densities known so far (about 50 % w:v). How the molecule is folded at such density and how its conformation changes upon ejection or packaging are fascinating questions still largely open. We review cryo-TEM analyses of DNA conformation inside partially filled capsids as a function of the physico-chemical environment (ions, osmotic pressure, temperature). We show that there exists a wide variety of DNA conformations. Strikingly, the different observed structures can be described by some of the different models proposed over the years for DNA organisation inside bacteriophage capsids: either spool-like structures with axial or concentric symmetries, or liquid crystalline structures characterised by a DNA homogeneous density. The relevance of these conformations for the understanding of DNA folding and unfolding upon ejection and packaging in vivo is discussed.
Bacteriophage; DNA packaging; DNA ejection; Cryo-electron microscopy