具有分离扩散的两种群Lotka—Volterra模型的持久性

本文考虑具有分离扩散的捕食-被捕食系统的持续性。此模型由两种群组成,其中被捕食种群可在两个生态环境中生存,而捕食种群仅能在一个生态环境中生存,两种群的动态行为都用Lotka－Volterra模型来描述。得到了系统强持续的充分必要条件,并证明了无论无扩散时系统是共存的,还是主导的都可以适当选择分离扩散系数使整个系统强持续。     

Evolvability and Single-Genotype Fluctuation in Phenotypic Properties: A Simple Heteropolymer Model

Experiment showed that the response of a genotype to mutation, i.e., the magnitude of mutational change in a phenotypic property, can be correlated with the extent of phenotypic fluctuation among genetic clones. To address a possible statistical mechanical basis for such phenomena at the protein level, we consider a simple hydrophobic-polar lattice protein-chain model with an exhaustive mapping between sequence (genotype) and conformational (phenotype) spaces. Using squared end-to-end distance, R_N², as an example conformational property, we study how the thermal fluctuation of a sequence's R_N² may be predictive of the changes in the Boltzmann average 〈R_N²〉 caused by single-point mutations on that sequence. We found that sequences with the same ground-state (R_N²)₀ exhibit a funnel-like organization under conditions favorable to chain collapse or folding: fluctuation (standard deviation σ) of R_N² tends to increase with mutational distance from a prototype sequence whose 〈R_N²〉 deviates little from its (R_N²)₀. In general, large mutational decreases in 〈R_N²〉 or in σ are only possible for some, though not all, sequences with large σ values. This finding suggests that single-genotype phenotypic fluctuation is a necessary, though not sufficient, indicator of evolvability toward genotypes with less phenotypic fluctuations.     

A New Coarse-Grained Model for E. coli Cytoplasm: Accurate Calculation of the Diffusion Coefficient of Proteins and Observation of Anomalous Diffusion

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

The Spermatid Nucleus in Two Species of Grasshopper

The nuclear changes accompanying spermatid elongation have been studied in two species of grasshopper, Dissosteira carolina and Melanoplus femur-rubrum. Testes were fixed in 1 per cent buffered OsO₄, imbedded in butyl methacrylate, and examined as thin sections in the electron microscope. In both species nuclear changes during spermatid development involve (1) an early period, during which the nuclear contents are predominately fibrous; (2) a middle period, characterized by the lateral association of the nuclear fibers to form plates or lamellae which are oriented longitudinally in the major axis of the elongated nucleus; and (3) a late period, involving coalescence of the lamellae into a crystalline body which eventually becomes so dense that all resolvable detail is lost. The fibers seen in the early spermatid nucleus are about 150 A in diameter and so are similar to fibers described from other types of nuclei. The thickness of the lamellae varies from about 150 A when first formed to 70 A during the later stages. The lack of evident chromosomal boundaries in the spermatid nucleus makes it difficult to relate either the fibers or lamellae to more familiar aspects of chromosome structure. We see no apparent reason to consider that the fiber alignment described here is related to conventional chromosome pairing.     

Localization of Cholesterol and Fatty Acid in a Model Lipid Membrane: A Neutron Diffraction Approach

The intercellular lipid matrix of the skin’s stratum corneum serves to protect the body against desiccation and simultaneously limits the passage of drugs and other xenobiotics into the body. The matrix is made up of ceramides, free fatty acids, and cholesterol, which are organized as two coexisting crystalline lamellar phases. In studies reported here, we sought to use the technique of neutron diffraction, together with the device of isotopic (H/D) substitution, to determine the molecular architecture of the lamellar phase having a repeat distance of 53.9 ± 0.3 Å. Using hydrogenous samples as well as samples incorporating perdeuterated (C24:0) fatty acids and selectively deuterated cholesterol, the diffraction data obtained were used to construct neutron scattering length density profiles. By this means, the locations within the unit cell were determined for the cholesterol and fatty acids. The cholesterol headgroup was found to lie slightly inward from the unit cell boundary and the tail of the molecule located 6.2 ± 0.2 Å from the unit cell center. The fatty acid headgroups were located at the unit cell boundary with their acyl chains straddling the unit cell center. Based on these results, a molecular model is proposed for the arrangement of the lipids within the unit cell.     

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.     

Anomalous Diffusion Reports on the Interaction of Misfolded Proteins with the Quality Control Machinery in the Endoplasmic Reticulum

A multitude of transmembrane proteins enters the endoplasmic reticulum (ER) as unfolded polypeptide chains. During their folding process, they interact repetitively with the ER's quality control machinery. Here, we have used fluorescence correlation spectroscopy to probe these interactions for a prototypical transmembrane protein, VSVG ts045, in vivo. While both folded and unfolded VSVG ts045 showed anomalous diffusion, the unfolded protein had a significantly stronger anomaly. This difference subsided when unfolded VSVG ts045 was in a complex with its chaperone calnexin, or when a mutant form of VSVG ts045 with only one glycan was used. Our experimental data and accompanying simulations suggest that the folding sensor of the quality control (UGT1) oligomerizes unfolded VSVG ts045, leading to a more anomalous/obstructed diffusion. In contrast, calnexin dissolves the oligomers, rendering unfolded VSVG ts045 more mobile, and hence prevents poisoning of the ER.     

Oxygen Diffusion from the Roots of Woody Species

Application of the‘polarographic’ technique for studying oxygen diffusion from roots has provided preliminary results which establish that oxygen passes through the woody species Salix atrocinerea Brot., Salix fragilis L., Salix repens L., and Myrica gale L., in the gaseous phase as it does in other wetland species. Entry into the shoots occurs through the bark directly above the water table and in the willow cuttings the effective length of shoot for gas intake was the basal three centimetres above the water table. The length of shoot involved was longer in Myrica gale and the roots were of the normal (un-nodulated) type. Trials on Alnus glutinosa (L.) Gaertn. provided no conclusive results and it is thought that this was perhaps because measurements were on nodulated roots only.     

Ensembles of Breathing Nucleosomes: A Computational Study

About three-fourths of the human DNA molecules are wrapped into nucleosomes, protein spools with DNA. Nucleosomes are highly dynamic, transiently exposing their DNA through spontaneous unspooling. Recent experiments allowed to observe the DNA of an ensemble of such breathing nucleosomes through x-ray diffraction with contrast matching between the solvent and the protein core. In this study, we calculate such an ensemble through a Monte Carlo simulation of a coarse-grained nucleosome model with sequence-dependent DNA mechanics. Our analysis gives detailed insights into the sequence dependence of nucleosome breathing observed in the experiment and allows us to determine the adsorption energy of the DNA bound to the protein core as a function of the ionic strength. Moreover, we predict the breathing behavior of other potentially interesting sequences and compare the findings to earlier related experiments.     

Nucleosome Assembly Depends on the Torsion in the DNA Molecule: A Magnetic Tweezers Study

We have used magnetic tweezers to study nucleosome assembly on topologically constrained DNA molecules. Assembly was achieved using chicken erythrocyte core histones and histone chaperone protein Nap1 under constant low force. We have observed only partial assembly when the DNA was topologically constrained and much more complete assembly on unconstrained (nicked) DNA tethers. To verify our hypothesis that the lack of full nucleosome assembly on topologically constrained tethers was due to compensatory accumulation of positive supercoiling in the rest of the template, we carried out experiments in which we mechanically relieved the positive supercoiling by rotating the external magnetic field at certain time points of the assembly process. Indeed, such rotation did lead to the same nucleosome saturation level as in the case of nicked tethers. We conclude that levels of positive supercoiling in the range of 0.025-0.051 (most probably in the form of twist) stall the nucleosome assembly process.     

两毒素环境中具有分离扩散的种群动力系统的持久性

本文是文「５」在ｎ＝２时更进一步的讨论,模型由一个种群构成,此种群可在两个毒素环境中生存,且种群扩散仅与其所在自下而上环境中的（数量）密度决定,得到了比文「５」更精细的结论。