Asymptotic results for a multi-type contact birth-death process and related SIS epidemic

Exact results concerning the asymptotic speed of propagation of infection have recently been obtained for the multi-type SIS epidemic in continuous space when the contact distributions are assumed to be symmetric with the Laplace transforms finite for all entries. There is a link between the equations for this epidemic and the equations for a multi-type contact birth-death process. This enables methods developed for the epidemic to be used to obtain the asymptotic speed of translation for the contact birth-death process. Symmetry of the contact distributions is required but no existence constraint is placed on their Laplace transforms. The method for removing this constraint may also be used for the SIS epidemic. Results are given for both processes when the basic reproduction ratio is at most one.     

Pandemic bounds for an epidemic on an infinite lattice

Exact results have previously been obtained concerning the spread of infection in continuous space contact models describing a class of multi-type epidemics. Pandemic lower and upper bounds were obtained for the spatial final size. Pandemic results have also been obtained for a discrete space model on the integer lattice using an infinite matrix formulation of the final size equations. However, the proof required restrictive constraints to be placed on the model parameters which do not hold in general and will not be valid when infection modifies behaviour. The purpose of this paper is to remove these constraints and give a general proof of the pandemic results for the multi-type epidemic on the lattice Z(N).     

RS domain-splicing signal interactions in splicing of U12-type and U2-type introns

Serine-arginine (SR) proteins are general metazoan splicing factors that contain an essential arginine/serine-rich (RS) domain. On typical U2-type introns, RS domains contact the branchpoint and 5' splice site to promote base-pairing with U small nuclear RNAs (snRNAs). Here we analyze the role of SR proteins in splicing of U12-type introns and in the second step of U2-type intron splicing. We show that RS domains contact the branchpoint and 5' splice site of a U12-type intron. On a U2-type intron, we find that the RS domain contacts the site of the U6 snRNA-5' splice site interaction during the first step of splicing and shifts to contact the site of the U5 snRNA-exon 1 interaction during the second step. Our results reveal alternative interactions between the RS domain and 5' splice site region that coincide with remodeling of the spliceosome between the two catalytic steps.     

Uncovering epidemiological dynamics in heterogeneous host populations using phylogenetic methods

Host population structure has a major influence on epidemiological dynamics. However, in particular for sexually transmitted diseases, quantitative data on population contact structure are hard to obtain. Here, we introduce a new method that quantifies host population structure based on phylogenetic trees, which are obtained from pathogen genetic sequence data. Our method is based on a maximum-likelihood framework and uses a multi-type branching process, under which each host is assigned to a type (subpopulation). In a simulation study, we show that our method produces accurate parameter estimates for phylogenetic trees in which each tip is assigned to a type, as well for phylogenetic trees in which the type of the tip is unknown. We apply the method to a Latvian HIV-1 dataset, quantifying the impact of the intravenous drug user epidemic on the heterosexual epidemic (known tip states), and identifying superspreader dynamics within the men-having-sex-with-men epidemic (unknown tip states).     

The effect of progressive hypoxia on swimming activity and schooling in Atlantic herring

Schools of herring exposed to progressive hypoxia show a peak in velocity during severe hypoxia, at 15–34% oxygen saturation, followed by a decrease in swimming speed until school disruption occurred. The observed increase in swimming speed during severe hypoxia reveals a graded response, since the lower the fish's swimming speed prior to severe hypoxia ( U ₉₅₋₅₀, the speed at oxygen saturations between 95 and 50%), the greater the relative increase in swimming speed. The oxygen saturations at which both peak velocity and school disruption occurred were lower for fish with lowest U ₉₅₋₅₀, suggesting that the fish with the slowest speed U ₉₅₋₅₀ reach their critical P_O2 (at which there is respiratory distress) last, i.e. at lower oxygen saturation. At a functional level, it is suggested that herring encountering hypoxia increase their speed in order to find more favourable conditions, and the magnitude of this increase is modulated by their respiratory distress. It is also hypothesised that the observed increase in speed may be related to an increase in the rate of position shifting within the school. Since the oxygen saturation at which the response to hypoxia occurs and the magnitude of the response are related to the fish's preferred speed prior to severe hypoxia, it is suggested that such a preferred speed should be measured in experiments testing the effect of hypoxia on fish behaviour.     

Effects of altered stride frequency and contact time on leg-spring behavior in human running

Many studies have demonstrated that contact time is a key factor affecting both the energetics and mechanics of running. The purpose of the present study was to further explore the relationships between contact time (t(c)), step frequency (f) and leg stiffness (k(leg)) in human running. Since f is a compound parameter, depending on both contact and aerial time, the specific goal of this study was to independently vary f and t(c) and to investigate their respective effects on spring-mass characteristics during running, seeking to determine if the changes in k(leg) observed when running at different f are mainly due to inherent changes in t(c). We compared three types of constant 3.33 m s(-1) running conditions in 10 male subjects: normal running at the subject's freely chosen f, running with decreased and increased f, and decreased and increased t(c) at the imposed freely chosen f. The data from the varied f trials showed that the variation of t(c) was strongly correlated to that of k(leg) (r(2)=0.90), and the variation of f was also significantly correlated to that of k(leg) (r(2)=0.47). Further, changes in t(c) obtained in various t(c) conditions were significantly correlated to changes in k(leg) (r(2)=0.96). These results confirm that leg stiffness was significantly influenced by step frequency variations during constant speed running, as earlier demonstrated, but our more novel finding is that compared to step frequency, the effect of contact time variations appears to be a stronger and more direct determinant of k(leg). Indeed, 90-96% of the variance in k(leg) can be explained by contact time, whether this latter parameter is directly controlled, or indirectly controlled through its close relationship with step frequency. In conclusion, from the comparison of two experimental procedures, i.e. imposing various step frequency conditions vs. asking subjects to intentionally vary contact time at their freely chosen step frequency, it appears that changes in leg stiffness are mainly related to changes in contact time, rather than to those in step frequency. Step frequency appears to be an indirect factor influencing leg stiffness, through its effect on contact time, which could be considered a major determinant of this spring-mass characteristic of human running.     

Statistical optimization of process variables for antibiotic activity of Xenorhabdus bovienii

The production of secondary metabolites with antibiotic properties is a common characteristic to entomopathogenic bacteria Xenorhabdus spp. These metabolites not only have diverse chemical structures but also have a wide range of bioactivities of medicinal and agricultural interests. Culture variables are critical to the production of secondary metabolites of microorganisms. Manipulating culture process variables can promote secondary metabolite biosynthesis and thus facilitate the discovery of novel natural products. This work was conducted to evaluate the effects of five process variables (initial pH, medium volume, rotary speed, temperature, and inoculation volume) on the antibiotic production of Xenorhabdus bovienii YL002 using response surface methodology. A 2(5-1) factorial central composite design was chosen to determine the combined effects of the five variables, and to design a minimum number of experiments. The experimental and predicted antibiotic activity of X. bovienii YL002 was in close agreement. Statistical analysis of the results showed that initial pH, medium volume, rotary speed and temperature had a significant effect (P<0.05) on the antibiotic production of X. bovienii YL002 at their individual level; medium volume and rotary speed showed a significant effect at a combined level and was most significant at an individual level. The maximum antibiotic activity (287.5 U/mL) was achieved at the initial pH of 8.24, medium volume of 54 mL in 250 mL flask, rotary speed of 208 rpm, temperature of 32.0°C and inoculation volume of 13.8%. After optimization, the antibiotic activity was improved by 23.02% as compared with that of unoptimized conditions.     

Influence of Some Potential Predation Risk Factors and Interaction between Predation Risk and Cost of Fleeing on Escape by the Lizard Sceloporus virgatus

Escape theory predicts that flight initiation distance (predator–prey distance when escape begins) increases as predation risk increases and decreases as cost of fleeing increases. Scant information is available about the effects of some putative predation risk factors and about interaction between simultaneously operating risk and cost of fleeing factors on flight initiation distance and distance fled. By simulating an approaching predator, I studied the effects of body temperature (BT), distance to nearest refuge, and eye contact with a predator, as well as simultaneous effects of predator approach speed and female presence/absence on escape behavior by a small ectothermic vertebrate, the lizard Sceloporus virgatus. Flight initiation distance decreased as BT increased, presumably because running speed increases as BT increases, facilitating escape. Distance to nearest refuge was unrelated to BT or flight initiation distance. Substrate temperature was only marginally related, and air temperature was not related to flight initiation distance. Eye contact did not affect flight initiation during indirect approaches that bypassed lizards by a minimum of 1 m, but an effect of eye contact found in other studies during direct approach might occur. Predator approach speed and presence of a female interactively affected flight initiation distance, which increased as speed increased and decreased when a female was present. In the presence of a female, flight initiation distance was far shorter than when no female was present. The high cost of forgoing a mating opportunity accounts for the interaction because the difference between female presence and absence is greater when risk is greater.     

Ambulatory estimates of maximal aerobic power from foot -ground contact times and heart rates in running humans.

Seeking to develop a simple ambulatory test of maximal aerobic power (VO(2 max)), we hypothesized that the ratio of inverse foot-ground contact time (1/t(c)) to heart rate (HR) during steady-speed running would accurately predict VO(2 max). Given the direct relationship between 1/t(c) and mass-specific O(2) uptake during running, the ratio 1/t(c). HR should reflect mass-specific O(2) pulse and, in turn, aerobic power. We divided 36 volunteers into matched experimental and validation groups. VO(2 max) was determined by a treadmill test to volitional fatigue. Ambulatory monitors on the shoe and chest recorded foot-ground contact time (t(c)) and steady-state HR, respectively, at a series of submaximal running speeds. In the experimental group, aerobic fitness index (1/t(c). HR) was nearly constant across running speed and correlated with VO(2 max) (r = 0.90). The regression equation derived from data from the experimental group predicted VO(2 max) from the 1/t(c). HR values in the validation group within 8.3% and 4.7 ml O(2) x kg(-1) x min(-1) (r = 0.84) of measured values. We conclude that simultaneous measurements of foot-ground constant times and heart rates during level running at a freely chosen constant speed can provide accurate estimates of maximal aerobic power.     

Contact guidance of Walker carcinosarcoma cells by the underlying normal fibroblasts is inhibited by RGD-containing synthetic peptides

The metastatic spread of malignant neoplasms is associated with active migration of cancer cells. The migration of neoplastic cells during the metastatic process may be affected by various extracellular factors, including chemoattractants, haptotactic signals, electric fields, substrate anisotropy, and cell-to-cell contacts. We examined the effect of homotypic collisions and heterotypic interactions with normal human skin fibroblasts on the motile activity of Walker carcinosarcoma cells. It was found that Walker carcinosarcoma cells moving in a dense population neither show contact inhibition of movement when colliding with one another nor increase their motile activity as a result of contact stimulation of motility. On the other hand, when plated onto the surface of aligned fibroblasts, Walker carcinosarcoma cells migrated mainly along the long axes of underlying fibroblasts as a result of contact guidance. The directional character of movement (but not the speed of migration) of Walker carcinosarcoma cells on the surface of aligned fibroblasts was completely effaced by RGD-containing synthetic peptide at a concentration of 1 mg/ml but not by 5 microM verapamil (selective voltage-gated calcium channel inhibitor) or 10 microM gadolinium chloride (non-specific blocker of mechanosensitive ion channels). The suppression of directional character of migration of tumour cells by RGD-containing peptide was associated with the decrease in the amount of fibronectin macromolecules attached to fibroblasts. This suggests that alignment and anisotropic distribution of fibronectin macromolecules may be responsible for contact guidance of tumour cells moving on the surface of fibroblasts.     

Modelling energetic costs of fish swimming

The oxygen consumption rates of two cyprinid fishes, carp (Cyprinus carpio L.) and roach (Rutilus rutilus (L.)), were analysed for a wide range of body mass and swimming speed by computerized intermittent-flow respirometry. Bioenergetic models were derived, based on fish mass (M) and swimming speed (U), to predict the minimal speed and mass-specific active metabolic rate (AMR) in these fishes (AMR=aMbUc). Mass and speed together explained more than 90% of the variance in total swimming costs in both cases. The derived models show that carp consume far more oxygen at a specific speed and body mass, thus being less efficient in energy use during swimming than roach. It was further found that in carp (AMR=0.02M0.8U0.95) the metabolic increment during swimming is more strongly effected by speed, whereas in roach (AMR=0.02M0.93U0.6) it is more strongly effected by body mass. The different swimming traits of carp and roach are suitable for their respective lifestyles and ecological demands.     

The mechanical and pharmacological regulation of glioblastoma cell migration in 3D matrices

The invasion of glioblastoma is a complex process based on the interactions of tumor cells and the extracellular matrix. Tumors that are engineered using biomaterials are more physiologically relevant than a two-dimensional (2D) cell culture system. Matrix metalloproteinases and the plasminogen activator generated by tumor cells regulate a tumor’s invasive behavior. In this study, microtumors were fabricated by encapsulating U87 glioma cells in Type I collagen and then glioma cell migration in the collagen hydrogels was investigated. Crosslinking of collagen with 8S-StarPEG increased the hydrogel viscosity and reduced the tumor cell migration speed in the hydrogels. The higher migration speed corresponded to the increased gene expression of MMP-2, MMP-9, urokinase plasminogen activator (uPA), and tissue plasminogen activator (tPA) in glioma cells grown in non-crosslinked collagen hydrogels. Inhibitors of these molecules hindered U87 and A172 cell migration in collagen hydrogels. Aprotinin and tranexamic acid did not inhibit U87 and A172 migration on the culture dish. This study demonstrated the differential effect of pharmacologic molecules on tumor cell motility in either a 2D or three-dimensional culture environment.     

Phosphorylation-dephosphorylation of retinoblastoma protein not necessary for passage through the mammalian cell division cycle

Phosphorylation of the retinoblastoma protein (Rb) during the G1-phase of the mammalian cell division cycle is currently believed to be a controlling element regulating the passage of cells into S-phase. We find, however, that the suspension-grown cell lines U937, L1210, and MOLT-4 contain exclusively hyperphosphorylated Rb. Furthermore, when adherent NIH3T3 cells are grown at very low densities to avoid overgrowth and contact inhibition, they also contain only hyperphosphorylated Rb. NIH3T3 cells exhibit hypophosphorylation when the cells are grown at moderate to high cell densities. We propose that cultures of adherent cells such as NIH3T3, when grown to moderate cell densities, are made up of two populations of cells: (a) cells that are relatively isolated and therefore growing exponentially without contact inhibition, and (b) cells that are growth-inhibited by local cell density or contact inhibition. The common observation in adherent cell lines, that Rb is both hyper- and hypophosphorylated in the G1-phase and only hyperphosphorylated in the S- and G2-phases, is explained by the effects of cell density and contact inhibition. Thus, phosphorylation-dephosphorylation of Rb protein during the G1 phase is not a necessary process during the NIH3T3, L1210, MOLT-4, and U937 division cycles. We propose that phosphorylation-dephosphorylation of Rb is independent of the division cycle and is primarily determined by growth conditions throughout the division cycle.     

Adsorption of methylene blue using green pea peels (Pisum sativum): A cost-effective option for dye-based wastewater treatment

Methylene blue (MB), a common toxic dye, is largely discharged from dyeing processes for acrylic, nylon, silk, and woolen fabrics in textile industries. While application of conventional removal processes like chemical precipitation, ion exchange, commercial activated carbon adsorption, etc often become cost-prohibitive, the adsorption of MB by abundantly available green pea peel (GPP: Pisum sativum) derived and acid-treated carbon (GPP-AC) has proved to be a cost-attractive option in the present study. The physicochemical and morphological characteristics of GPP-AC were examined with the help of XRD, BET surface area, SEM, and Fourier transform infrared spectrophotometry ((FT-IR) analysis. The influences of such adsorption parameters as initial dye concentration, pH, contact time, adsorbent dosage, agitation speed, particle size, and temperature were evaluated and optimized. The equilibrium contact time for maximum adsorption of MB on to GPPAC was found to be 7 h. The equilibrium data of the adsorption process were modeled by using the Langmuir, Freundlich, Temkin, and Dubinin-Raduskevich (D-R) isotherms. However, the adsorption equilibrium data were best described by the Langmuir Isotherm model, with a maximum adsorption capacity of 163.94 mg MB/g GPPAC at 30°C.     

Kinetics of cellulase production by Chaetomium globosum at different levels of dissolved oxygen tension using oil palm empty fruit bunch fibre as substrate

The effect of different levels of dissolved oxygen tension (d.o.t) at a fixed agitation speed on the production of three major components of extracellular (free) cellulase (FPase, endoglucanase and -glucosidase) by Chaetomium globosum strain 414 was investigated. Oil palm empty fruit bunch (OPEFB) fibre (10g/l) and peptone (6g/l) were used as carbon and nitrogen sources for cellulase production, respectively. Growth of C. globosum and cellulase complex production were modelled using models based on logistic and Luedeking–Piret equations. The calculated data fitted well to the experimental data, indicating that the models were suitable for describing and verifying growth and cellulase complex production at different d.o.t levels. Cell growth and cellulase production were approximately two-fold higher in the stirred tank fermenter as compared with shake flask culture. At d.o.t of between 30–50% saturation, cell growth and cellulase production were higher than those under oxygen-limited conditions (5% saturation) and at high d.o.t (80% saturation). However, the highest activities of FPase (2.5U/ml), CMCase (59.5U/ml) and -glucosidase (12.8U/ml) were obtained at a d.o.t of 50% saturation and these gave the overall productivities of 20.8, 495 and 53.3U/l.h, respectively.     

Multi-type branching models to describe cell differentiation programs

Cell proliferation and differentiation is described by a multi-type branching process, a probability model that defines the inheritance of cell type. Cell type is defined by (i) a repression index related to the time required for S-phase entry and (ii) phenotype as determined by cell markers and division history. The inheritance of cell type is expressed as the expected number and type of progeny cells produced by a mother cell given her type. Expressions for the expected number and type of cells produced by a multi-cellular (bulk culture) system are derived from the general model by making the simplifying assumption that cell generation times are independent. The multi-type Smith-Martin model (MSM) makes the further assumption that cell generation times are lag-exponentially distributed with phenotype transitions occurring just before entry into S-phase. The inheritance-modified MSM (IMSM) model includes the influence of generation time memory so that mother and daughter generation times are correlated. The expansion of human cord blood CD34⁺ cells by haematopoietic growth factors was division tracked in bulk culture using carboxyfluorescein diacetate, succinimidyl ester (CFDA-SE). The MSM model was fitted to division tracking data to indentify cell cycle length, and the rates of CD34 antigen down-regulation and apoptosis. The IMSM model was estimated for mouse granulocyte-macrophage progenitors using live cell imaging data. Multi-type branching models describe cell differentiation dynamics at both single- and multi-cell scales, providing a new paradigm for systematic analysis of stem and progenitor cell development.     

Latent effect of passive static stretching on driver clubhead speed, distance, accuracy, and consistent ball contact in young male competitive golfers

This investigation was conducted to determine the effect of 2 different warm-up treatments over time on driver clubhead speed, distance, accuracy, and consistent ball contact in young male competitive golfers. Two supervised warm-up treatments, an active dynamic warm-up with golf clubs (AD) and a 20-minute total body passive static stretching routine plus an identical AD warm-up (PSS), were applied before each performance testing session using a counterbalanced design on nonconsecutive days. Immediately after the AD treatment, subjects were instructed to hit 3 full swing golf shots with their driver with 1-minute rest between trials. Immediately after the PSS treatment, subjects were instructed to hit 3 full-swing golf shots with their driver at t0 and thereafter at t15, t30, t45, and t60 minutes with 1-minute rest between swing trials to determine any latent effects of PSS on golf driver performance measures. Results of paired t-tests revealed significant (p < 0.05) decreases in clubhead speed at t0 (-4.92%), t15 (-2.59%), and t30 (-2.19%) but not at t45 (-0.95) or t60 (-0.99). Significant differences were also observed in distance at t0 (-7.26%), t15 (-5.19%), t30 (-5.47%), t45 (-3.30%), and t60 (-3.53%). Accuracy was significantly impaired at t0 (61.99%), t15 (58.78%), t30 (59.46%), and t45 (61.32%) but not at t60 (36.82%). Finally, consistent ball contact was significantly reduced at t0 (-31.29%), t15 (-31.29%), t30 (-23.56%), t45 (-27.49%), and t60 (-15.70%). Plausible explanations for observed performance decrements include a more compliant muscle-tendon unit (MTU) and an altered neurological state because of the PSS treatment. Further, the findings of this study provide evidence supporting the theory that the mechanical properties of the MTU may recover at a faster rate than any associated neurological changes. The results of this inquiry strongly suggest that a total-body passive static stretching routine should be avoided before practice or competition in favor of a gradual AD. Athletes with poor mechanics because of lack of flexibility should perform these exercises after a conditioning session, practice, or competition.