Mathematical analysis of an integral equation arising from population dynamics

In this paper, we establish the existence of travelling wave solution to an intrinsically non-linear differential–integral equation formed as a result of mathematical modelling of the evolution of an asexual population in a changing environment. This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows us to use the theory of positive matrices to get some very useful estimates and then to confirm the existence of solution. We also exhibit numerical simulation results and explain the biological meaning of the results.     

Evolution of cannibalistic traits: scenarios derived from adaptive dynamics

The evolution of cannibalistic traits in consumer populations is studied in this paper with the approach of adaptive dynamics theory. The model is kept at its minimum complexity by eliminating some environmental characteristics, like heterogeneity and seasonalities, and by hiding the size-structure of the population. Evolutionary dynamics are identified through numerical bifurcation analysis, applied both to the ecological (resident-mutant) model and to the canonical equation of adaptive dynamics. The result is a rich catalog of evolutionary scenarios involving evolutionary stable strategies and branching points both in the monomorphic and dimorphic dynamics. The possibility of evolutionary extinction of highly cannibalistic populations is also ascertained. This allows one to explain why cannibalism can be a transient stage of evolution.     

Molecular dynamics simulations of a fibrillogenic peptide derived from apolipoprotein C-II

The pathway to amyloid fibril formation in proteins involves specific structural changes leading to the combination of misfolded intermediates into oligomeric assemblies. Recent NMR studies showed the presence of “turns” in amyloid peptides, indicating that turn formation may play an important role in the nucleation of the intramolecular folding and possible assembly of amyloid. Fully solvated all-atom molecular dynamics simulations were used to study the structure and dynamics of the apolipoprotein C-II peptide 56 to 76, associated with the formation of amyloid fibrils. The peptide populated an ensemble of turn structures, stabilized by hydrogen bonds and hydrophobic interactions enabling the formation of a strong hydrophobic core which may provide the conditions required to initiate aggregation. Two competing mechanisms discussed in the literature were observed. This has implications in understanding the mechanism of amyloid formation in not only apoC-II and its fragments, but also in other amyloidogenic peptides.     

Metrics from nonlinear dynamics adapted for characterizing the behavior of nonequilibrium enzymatic rate functions

Several metrics from nonlinear dynamics and statistical mechanics have been characterized on computer-generated number series with various signal-to-noise ratios, demonstrating their individual reliability as a function of sample size and their relationships to each other. The root mean square (RMS) evaluates amplitude, and the power spectral density (PSD) provides a visual display of the frequency spectrum; both measures have very high reliability even for an N as low as 50. The Fractal Dimension (D) is shown to converge rapidly and also to be reliable when N is as low as 50. These three measures (RMS, PSD, and D) have been applied to the complex kinetics of tyrosine hydroxylase time courses (50-point curves) at various BH4 concentrations (near physiological, but far from equilibrium levels). Recently developed measures of spectral entropy and the Liapunov Exponent, -lambda are also characterized.     

Conformational dynamics of full-length inducible human Hsp70 derived from microsecond molecular dynamics simulations in explicit solvent

Human 70?kDa heat shock protein (hHsp70) is an ATP-dependent chaperone and is currently an important target for developing new drugs in cancer therapy. Knowledge of the conformations of hHsp70 is central to understand the interactions between its nucleotide-binding domain (NBD) and substrate-binding domain (SBD) and is a prerequisite to design inhibitors. The conformations of ADP-bound (or nucleotide-free) hHsp70 and ATP-bound hHsp70 was investigated by using unbiased all-atom molecular dynamics (MD) simulations of homology models of hHsp70 in explicit solvent on a timescale of .5 and 2.7 μs, respectively. The conformational heterogeneity of hHsp70 was analyzed by computing effective free-energy landscapes (FELs) and distance distribution between selected pair of residues. These theoretical data were compared with those extracted from single-molecule Förster resonance energy transfer (FRET) experiments and to small-angle X-ray scattering (SAXS) data of Hsp70 homologs. The distance between a pair of residues in FRET is systematically larger than the distance computed in MD which is interpreted as an effect of the size and of the dynamics of the fluorescent probes. The origin of the conformational heterogeneity of hHsp70 in the ATP-bound state is due to different binding modes of the helix B of the SBD onto the NBD. In the ADP-bound (or nucleotide-free) state, it arises from the different closed conformations of the SBD and from the different positions of the SBD relative to the NBD. In each nucleotide-binding state, Hsp70 is better represented by an ensemble of conformations on a μs timescale corresponding to different local minima of the FEL.

An animated interactive 3D complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:30     

Stochastic models for virus and immune system dynamics

New stochastic models are developed for the dynamics of a viral infection and an immune response during the early stages of infection. The stochastic models are derived based on the dynamics of deterministic models. The simplest deterministic model is a well-known system of ordinary differential equations which consists of three populations: uninfected cells, actively infected cells, and virus particles. This basic model is extended to include some factors of the immune response related to Human Immunodeficiency Virus-1 (HIV-1) infection. For the deterministic models, the basic reproduction number, R₀, is calculated and it is shown that if R₀<1, the disease-free equilibrium is locally asymptotically stable and is globally asymptotically stable in some special cases. The new stochastic models are systems of stochastic differential equations (SDEs) and continuous-time Markov chain (CTMC) models that account for the variability in cellular reproduction and death, the infection process, the immune system activation, and viral reproduction. Two viral release strategies are considered: budding and bursting. The CTMC model is used to estimate the probability of virus extinction during the early stages of infection. Numerical simulations are carried out using parameter values applicable to HIV-1 dynamics. The stochastic models provide new insights, distinct from the basic deterministic models. For the case R₀>1, the deterministic models predict the viral infection persists in the host. But for the stochastic models, there is a positive probability of viral extinction. It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding.     

Insight derived from molecular dynamics simulation into dynamics and molecular motions of cuticle-degrading serine protease Ver112

Cuticle-degrading serine protease Ver112, which derived from a nematophagous fungus Lecanicillium psalliotae, has been exhibited to have high cuticle-degrading and nematicidal activities. We have performed molecular dynamics (MD) simulation based on the crystal structure of Ver112 to investigate its dynamic properties and large-scale concerted motions. The results indicate that the structural core of Ver112 shows a small fluctuation amplitude, whereas the substrate binding sites, and the regions close to and opposite the substrate binding sites experience significant conformational fluctuations. The large concerted motions obtained from essential dynamics (ED) analysis of MD trajectory can lead to open or close of the substrate binding sites, which are proposed to be linked to the functional properties of Ver112, such as substrate binding, orientation, catalytic, and release. The significant motion in the loop regions that is located opposite the binding sites are considered to play an important role in modulating the dynamics of the substrate binding sites. Furthermore, the bottom of free energy landscape (FEL) of Ver112 are rugged, which is mainly caused by the fluctuations of substrate binding regions and loops located opposite the binding site. In addition, the mechanism underlying the high flexibility and catalytic activity of Ver112 was also discussed. Our simulation study complements the biochemical and structural studies, and provides insight into the dynamics-function relationship of cuticle-degrading serine protease Ver112.     

Structural reorganization of molecular sheets derived from cellulose II by molecular dynamics simulations

We investigated structural reorganization of two different kinds of molecular sheets derived from the cellulose II crystal using molecular dynamics (MD) simulations, in order to identify the initial structure of the cellulose crystal in the course of its regeneration process from solution. After a one-nanosecond simulation, the molecular sheet formed by van der Waals forces along the () crystal plane did not change its structure in an aqueous environment, while the other one formed by hydrogen bonds along the (1 1 0) crystal plane changed into a van der Waals-associated molecular sheet, such as the former. The two structures that were calculated showed substantial similarities such as the high occupancy of intramolecular hydrogen bonds between O3^H and O5 of over 0.75, few intermolecular hydrogen bonds, and the high occurrence of hydrogen bonding with water. The convergence of the two structures into one denotes that the van der Waals-associated molecular sheet can be the initial structure of the cellulose crystal formed in solution. The main chain conformations were almost the same as those in the cellulose II crystal except for a −16° shift of φ (dihedral angle of O5-C1-O1-C4) and the gauche-gauche conformation of the hydroxymethyl side group appears probably due to its hydrogen bonding with water. These results suggest that the van der Waals-associated molecular sheet becomes stable in an aqueous environment with its hydrophobic inside and hydrophilic periphery. Contrary to this, a benzene environment preferred a hydrogen-bonded molecular sheet, which is expected to be the initial structure formed in benzene.     

Lysine side-chain dynamics derived from 13C-multiplet NMR relaxation studies on di- and tripeptides

Summary ¹³C NMR relaxation data have been used to determine dipolar auto- and cross-correlation times for the di- and tripeptides GK, KG and GKG, primarily to analyze lysine side-chain motional dynamics. In general, correlation times are largest for backbone positions and decrease on going through the lysine side chain, consistent with the idea of increased mobility at C and C methylenes. Correlation times, however, vary with the peptide ionization state. In the zwitterionic state of GK, for example, both auto-and cross-correlation times are at their maximum values, indicating reduced internal motions probably resulting from intramolecular electrostatic interactions. Modifying the charge state increases motional fluctuations. Activation energies determined from the temperature dependence of CH rotational autocorrelation times at neutral pH are approximately equal for glycine and lysine C and lysine C and C positions (4.1±0.2 to 4.5±0.2 kcal/mol) and tend to decrease slightly for lysine C and C (3.8±0.2 to 4.3±0.2 kcal/mol). The sign of lysine side-chain cross-correlations could not be explained by using any available rotational model, including one parameterized for multiple internally restricted rotations and anisotropic overall tumbling. Molecular and stochastic dynamics calculations were performed to obtain insight into correlated internal rotations and coupled overall tumbling and internal motions. Relatively strong correlations were found for i,i+1 backbone and lysine side-chain internal bond rotations. Stochastic dynamics calculations were more successful at explaining experimentally observed correlation times. In the fully charged state, a preferred conformation was detected with an all-trans lysine side chain.Abbreviations rf radio frequency - GK dipeptide glycine-lysine - KG dipeptide lysine-glycine - GKG tripeptide glycine-lysine-glycine     

Relationships among recent models for insect population dynamics with variable rates of development

A classification scheme for those population models which allow variation in development rates is proposed, based on two ways of modifying standard age-structured models. The resulting classes of models are termed development index models and sojourn time models. General formulations for the two classes of models are developed from two basic balance equations, and numerous specific models from the literature are shown to fit into the scheme. Concepts from competing risks theory are shown to be important in understanding the interplay between mortality and maturation. Relationships among the classes are investigated both for the most general forms of the models and for the simpler forms often used. The scheme can provide guidance in developing appropriate insect population models for specific modelling situations.Contribution 3878871     

Regression equations for estimating stature from long bones of early Holocene European samples

Regression equations for estimating living stature from long bone lengths have been calibrated on a sample of European Neolithic skeletons (33 males and 27 females) by using both least-squares (model I) and major-axis (model II) regression techniques. Stature estimates of the skeletal sample have been made by means of Fully's anatomical method, a procedure based on the sum of all osseous components of height, providing the best approximations to the actual stature. The calculated equations have been tested, along with those generally used to predict stature of earlier European remains, on a small, well-preserved sample including Late Upper Paleolithic, Mesolithic, and Neolithic skeletons. The results indicate that the model II equations are particularly useful when very short or very tall individuals are involved and, at the same time, are among the best predictors of stature in less extreme conditions. © 1996 Wiley-Liss, Inc.     

Stochastic models for phytoplankton dynamics in Mediterranean Sea

In this paper, we review some results obtained from three one-dimensional stochastic models, which were used to analyze picophytoplankton dynamics in two sites of the Mediterranean Sea. Firstly, we present a stochastic advection–reaction–diffusion model to describe the vertical spatial distribution of picoeukaryotes in a site of the Sicily Channel. The second model, which is an extended version of the first one, is used to obtain the vertical stationary profiles of two groups of picophytoplankton, i.e. Pelagophytes and Prochlorococcus, in the same marine site as in the previous case. Here, we include intraspecific competition of picophytoplanktonic groups for limiting factors, i.e. light intensity and nutrient concentration. Finally, we analyze the spatio-temporal behaviour of five picophytoplankton populations in a site of the Tyrrhenian Sea by using a reaction–diffusion–taxis model. The study is performed, taking into account the seasonal changes of environmental variables, obtained starting from experimental findings. The multiplicative noise source, present in all three models, mimics the random fluctuations of temperature and velocity field. The vertical profiles of chlorophyll concentration obtained from the stochastic models show a good agreement with experimental data sampled in the two marine sites considered. The results could be useful to devise a new class of models based on a stochastic approach and able to predict future changes in biomass primary production.     

Metabolic rate estimates for a eutrophic lake from diel dissolved oxygen signals

Estimates of net primary production, community respiration (R'), and gross primary production (P _g) are developed and presented for the productive layers of eutrophic Onondaga Lake, NY, U.S.A., for time scales ranging from diel to several months, based on 4 months of robotic diel profiles of dissolved oxygen (DO) and temperature. Metabolic rate calculations are made through application of a DO mass balance framework that also accommodates inputs and losses of DO mediated by exchange across the air–water interface and across the lower boundary of the productive layers. It is demonstrated that the dynamics of the flux across the air–water interface are important to the metabolic rate estimates, while vertical mixing-based losses to the underlying layers can be ignored. Study average estimates of R' (1.49 g O₂ m^–3 d^–1) and P _g (1.60 g O₂ m^–3 d^–1) obtained by this non-isolated community approach are consistent with levels reported in the literature for similar chlorophyll a concentrations, based on isolated community (bottle experiment) protocols to measure these metabolic rates. The non-isolated community approach is shown to have limited utility for quantifying day-to-day changes in these rates in this lake, apparently because of horizontal exchange with waters of different DO concentrations. However, this approach may support reliable estimates of metabolic rates at intermediate time scales; e.g., several days to a week. The DO mass balance framework is demonstrated to be valuable in resolving the relative roles of various physical and biological processes in regulating the DO pool of the productive layers.     

Neural stem cells isolated from amyloid precursor proteinmutated mice for drug discovery

AIM: To develop an in vitro model based on neural stem cells derived from transgenic animals, to be used in the study of pathological mechanisms of Alzheimer’s disease and for testing new molecules.METHODS: Neural stem cells(NSCs) were isolated from the subventricular zone of Wild type(Wt) and Tg2576 mice. Primary and secondary neurosphere generation was studied, analysing population doubling and the cell yield per animal. Secondary neurospheres were dissociated and plated on MCM Gel Cultrex 2D and after 6 d in vitro(DIVs) in mitogen withdrawal conditions,spontaneous differentiation was studied using specific neural markers(MAP2 and TuJ-1 for neurons, GFAP forastroglial cells and CNPase for oligodendrocytes). Gene expression pathways were analysed in secondary neurospheres, using the QIAGEN PCR array for neurogenesis, comparing the Tg2576 derived cell expression with the Wt cells. Proteins encoded by the altered genes were clustered using STRING web software.RESULTS: As revealed by 6E10 positive staining, all Tg2576 derived cells retain the expression of the human transgenic Amyloid Precursor Protein. Tg2576 derived primary neurospheres show a decrease in population doubling. Morphological analysis of differentiated NSCs reveals a decrease in MAP2- and an increase in GFAP-positive cells in Tg2576 derived cells. Analysing the branching of TuJ-1 positive cells, a clear decrease in neurite number and length is observed in Tg2576 cells.The gene expression neurogenesis pathway revealed11 altered genes in Tg2576 NSCs compared to Wt.CONCLUSION: Tg2576 NSCs represent an appropriate AD in vitro model resembling some cellular alterations observed in vivo, both as stem and differentiated cells.     

川西高寒山地灌丛草甸不同海拔土壤有机碳矿化的季节动态

为探明高寒山地灌丛草甸不同海拔土壤碳矿化潜力,选取折多山3800 m、4000 m、4200 m 3个海拔梯度的灌丛草甸,采用室内培养法测定不同季节土壤累积矿化量和矿化速率,运用一级动力学方程对土壤碳矿化过程进行拟合,并分析不同海拔土壤活性碳组分季节变化及累积矿化量与土壤环境因子的关系。结果表明:土壤累积矿化量及活性碳组分均呈现出0—20 cm土层显著高于20—40 cm土层,且夏季最高的季节变化,而海拔变化趋势不一致,但大体呈现出3800 m灰化土最大。土壤碳矿化速率随着培养时间的推移逐渐降低慢慢趋于平缓,且前21 d降低幅度显著高于后21 d。各海拔C₀和C₀/SOC均夏季最高,表明高寒灌丛草甸夏季土壤固碳能力最低,且3800 m灰化土固碳能力最低。土壤碳矿化与土壤全氮、有机碳、活性碳显著相关,且微生物量碳更能直接影响土壤碳矿化。土壤碳矿化季节性变化受土壤理化性质和环境因素综合影响,这些因子共同作用使得土壤有机碳库各组分发生复杂变化,所以对于高寒灌丛草甸地区植被多样性的保护及夏季牧场的合理控制至关重要。