Evaluation of surface colonization kinetics in continuous culture

Two equations, describing surface colonization, were evaluated and compared using suspended glass slides in a continuous culture ofPseudomonas aeruginosa. These equations were used to determine surface growth rates from the number and distribution of cells present on the surface after incubation. One of these was the colonization equation which accounts for simultaneous attachment and growth of bacteria on surfaces: $$N = (A/\mu )e^{\mu t} - A/\mu $$ where N=number of cells on surface (cells field^?1); A=attachment rate (cells field^?1h^?1);μ=specific growth rate (h^?1); t=incubation period (h). The other was the surface growth rate equation which assumes that the number of colonies of a given size (C_i) will reach a constant value (C_max) which is equal to A divided byμ: $$\mu = \frac{{\ln \left( {\frac{N}{{C_i }} + 1} \right)}}{t}$$ Both equations gave similar results and the time required to approximate C_max may not be as long as was previously thought. In all cases both A andμ continuously decreased throughout the incubation period. These decreases may be due to various effects of microbial accumulation on the surface. Both equations accurately determined surface growth rates despite highly variable attachment rates. Growth rates were similar for both the liquid phase of the culture and the solid-liquid interface (0.4 h^?1). Use of the surface growth rate equation is favored over the use of the colonization equation since the former does not require a computer to solve forμ and the counting procedure is simplified.     

Determination of reaction rate constants in the mammillary system

It is shown that the individual rate constants can be determined for the composite chemical system: $$A + B_i \rightleftarrows C_i ; i = 1...N$$ with only measurements of the unbound species,A(t), required. The dissociation rate constants can be determined by direct analysis of a single steady state tracer study. The association constants then follow from the analysis of stable equilibrium determinations reported earlier (Hart, 1965). An approximate solution when tracer methods are in-applicable is also given.     

Topological classification and enumeration of RNA structures by genus

To an RNA pseudoknot structure is naturally associated a topological surface, which has its associated genus, and structures can thus be classified by the genus. Based on earlier work of Harer–Zagier, we compute the generating function $\mathbf{D}_{g,\sigma }(z)=\sum _{n}\mathbf{d}_{g,\sigma }(n)z^n$ for the number $\mathbf{d}_{g,\sigma }(n)$ of those structures of fixed genus $g$ and minimum stack size $\sigma $ with $n$ nucleotides so that no two consecutive nucleotides are basepaired and show that $\mathbf{D}_{g,\sigma }(z)$ is algebraic. In particular, we prove that $\mathbf{d}_{g,2}(n)\sim k_g\,n^{3(g-\frac{1}{2})} \gamma _2^n$ , where $\gamma _2\approx 1.9685$ . Thus, for stack size at least two, the genus only enters through the sub-exponential factor, and the slow growth rate compared to the number of RNA molecules implies the existence of neutral networks of distinct molecules with the same structure of any genus. Certain RNA structures called shapes are shown to be in natural one-to-one correspondence with the cells in the Penner–Strebel decomposition of Riemann’s moduli space of a surface of genus $g$ with one boundary component, thus providing a link between RNA enumerative problems and the geometry of Riemann’s moduli space.     

Growth of Wolinella succinogenes with polysulphide as terminal acceptor of phosphorylative electron transport

Polysulphide was formed according to reaction (1), when tetrathionate was (1) $${\text{S}}_4 {\text{O}}_6^{2 - } + {\text{HS}}^ - \to 2{\text{S}}_2 {\text{O}}_3^{2 - } + {\text{S(O)}} + {\text{H}}^ + $$ added to an anaerobic buffer (pH 8.5) containing excess sulphide. S(O) denotes the zero oxidation state sulphur in the polysulphide mixture S _infn ^sup2- . The addition of formate to the polysulphide solution in the presence of Wolinella succinogenes caused the reduction of polysulphide according to reaction (2). The bacteria grew in a medium containing formate and sulphide, (2) $${\text{HCO}}_2^ - + {\text{S(O)}} + {\text{H}}2{\text{O}} \to {\text{HCO}}_3^ - + {\text{HS}}^ - + {\text{H}}^ + $$ when tetrathionate was continuously added. The cell density increased proportional to reaction (3) which represents the sum of reactions (1) and (3) $${\text{HCO}}_2^ - + {\text{S}}_{\text{4}} {\text{O}}_6^{2 - } + {\text{H}}2{\text{O}} \to {\text{HCO}}_3^ - + 2{\text{S}}_{\text{2}} {\text{O}}_3^{2 - } + 2{\text{H}}^ + $$ (2). The cell yield per mol formate was nearly the same as during growth on formate and elemental sulphur, while the velocity of growth was greater. The specific activities of polysulphide reduction by formate measured with bacteria grown with tetrathionate or with elemental sulphur were consistent with the growth parameters. The results suggest that W. succinogenes grow at the expense of formate oxidation by polysulphide and that polysulphide is an intermediate during growth on formate and elemental sulphur.     

Evaluation of a proposed surface colonization equation usingThermothrix thiopara as a model organism

The colonization equation shown below was evaluated usingThermothrix thiopara as a model organism. $$N = (A/\mu )e^{\mu t} - A/\mu $$ where: N=number of cells on surface (cells field^?1); A = attachment rate (cells field^?1 h^?1); M=specific growth rate (h^?1); t=incubation period (h). Previous studies of microbial surface colonization consider attachment and growth independently. However, the proposed colonization equation integrates the effects of simultaneous attachment and growth. Using this equation, the specific growth rate ofT. thiopara was found to be 0.38±0.3 h^?1 during in situ colonization. Estimates ofμ were independent of incubation period after 4 h (2 generations). Shorter incubations were inadequate to produce sufficient microcolonies for accurate determination of specific growth rate. Empirical data for the time course of colonization fell within the 95% confidence interval of predicted values. The attachment rate, although assumed to be constant, was found to continuously increase with time. This increase may have been an artifact due to the continuous deposition of travertine on the surface, or may indicate the need for a function to replace A in the colonization equation. Using the exponential growth equation, the progeny of cells that attach during incubation are considered to be progeny of cells that attach initially. This erroneously inflated the growth rate by 55%.     

Pareto genealogies arising from a Poisson branching evolution model with selection

We study a class of coalescents derived from a sampling procedure out of $N$ i.i.d. Pareto $\left( \alpha \right) $ random variables, normalized by their sum, including $\beta $ –size-biasing on total length effects ( $\beta <\alpha $ ). Depending on the range of $\alpha ,$ we derive the large $N$ limit coalescents structure, leading either to a discrete-time Poisson-Dirichlet $ \left(\alpha ,-\beta \right) \Xi -$ coalescent ( $\alpha \in \left[ 0,1\right) $ ), or to a family of continuous-time Beta $\left( 2-\alpha ,\alpha -\beta \right) \Lambda -$ coalescents ( $\alpha \in \left[ 1,2\right) $ ), or to the Kingman coalescent ( $\alpha \ge 2$ ). We indicate that this class of coalescent processes (and their scaling limits) may be viewed as the genealogical processes of some forward in time evolving branching population models including selection effects. In such constant-size population models, the reproduction step, which is based on a fitness-dependent Poisson Point Process with scaling power-law $\left( \alpha \right) $ intensity, is coupled to a selection step consisting of sorting out the $N$ fittest individuals issued from the reproduction step.     

Theory of antigen-antibody induced particulate aggreagation—I. General assumptions and basic theory

A theory of antigen-antibody induced particulate aggregation is developed by investigating the stability of model systems of particles. Conditions for the formation of large aggregates are derived by imposing the requirement that at equilibrium a statistically significant number of redundant bonds would occur in a reduced monomer-dimer model system. A relationship is obtained which predicts the fractional agglutination in the reduced dimer system as a function of the antigen, antibody and particulate concentrations: $$\frac{g}{{2f c_0 (1 - g)^{2^ - } }} = \frac{{s_1 }}{r} + \frac{{s_1 s_2 }}{{2!r^2 }} + ... + \frac{{s_1 s_2 ...s_j }}{{j!r^j }},$$ wherec ₀ is the initial concentration of monomer,f is a proximity factor,g is the fractional agglutination,s _i is the average rate of formation of theith bond from an (i?1)th bound dimer, andr is the average rate of dissociation of a single antibody-antigen bond.     

Sensory uncertainty and stick balancing at the fingertip

The effects of sensory input uncertainty, $\varepsilon $ , on the stability of time-delayed human motor control are investigated by calculating the minimum stick length, $\ell _\mathrm{crit}$ , that can be stabilized in the inverted position for a given time delay, $\tau $ . Five control strategies often discussed in the context of human motor control are examined: three time-invariant controllers [proportional–derivative, proportional–derivative–acceleration (PDA), model predictive (MP) controllers] and two time-varying controllers [act-and-wait (AAW) and intermittent predictive controllers]. The uncertainties of the sensory input are modeled as a multiplicative term in the system output. Estimates based on the variability of neural spike trains and neural population responses suggest that $\varepsilon \approx 7$ –13 %. It is found that for this range of uncertainty, a tapped delay-line type of MP controller is the most robust controller. In particular, this controller can stabilize inverted sticks of the length balanced by expert stick balancers (0.25–0.5 m when $\tau \approx 0.08$  s). However, a PDA controller becomes more effective when $\varepsilon > 15\,\%$ . A comparison between $\ell _\mathrm{crit}$ for human stick balancing at the fingertip and balancing on the rubberized surface of a table tennis racket suggest that friction likely plays a role in balance control. Measurements of $\ell _\mathrm{crit},\,\tau $ , and a variability of the fluctuations in the vertical displacement angle, an estimate of $\varepsilon $ , may make it possible to study the changes in control strategy as motor skill develops.     

The existence of globally stable equilibria of ecosystems of the generalized Volterra type

In this paper, global asymptotic stability of ecosystems of the generalized Volterra type $$dx_i /dt = x_i \left( {b_{i - } \mathop \sum \limits_{j = 1}^n a_{ij} x_j } \right),{\text{ }}i = 1,...,n,$$ is investigated. We obtain the conditions for the existence of a nonnegative and stable equilibrium point of the system by applying a result of linear complementarity theory. The results of this paper show that there exists a class of systems that do not have multiple domains of attractions. This class is defined in terms of the species interactions alone, and does not involve carrying capacities or species net birth rates.     

Quantifying interspecific spatial overlap in aquatic macrophyte communities

Levins’s asymmetrical α index quantifies between species overlap over resources more realistically than similar-purpose single-value indices. The associated community-wide \(\bar \alpha\) index expresses the degree of “species packing”. Both indices were formulated upon competing animal (i.e., mobile) organisms and are independent of population densities. However, overlap over resources for nonmobile organisms such as plants may have an impact even below carrying capacity. The proposed \(\hat \alpha\) index, based on Levins’s α index, quantifies spatial overlap for plants integrating information on species spatial distribution and crowding conditions. The \(\hat \alpha\) index is specifically designed for plant distribution data collected in discrete plots with density expressed as percent coverage (%cover) of substratum. We also propose a community-wide \({\hat \alpha_{\text{c}}}\) index, conceptually analogous to \(\bar \alpha\) , but furnished with a measure of dispersion (se \({\hat \alpha_{\text{c}}}\) ). Species importance within the community is inferred from comparisons of pairwise \(\hat \alpha\) ’s with \({\hat \alpha_{\text{c}}}\) . The \(\hat \alpha\) and \({\hat \alpha_{\text{c}}}\) indices correlate closely and exponentially with plant density, and correct apparent over- and underestimations of interaction intensity at low and very high crowding by Levins’s α and \(\bar \alpha\) , respectively. Index application to aquatic plant communities gave results consistent with within-community and general ecological patterns, suggesting a high potential of the proposed \(\hat \alpha\) and \({\hat \alpha_{\text{c}}}\) indices in basic and applied macrophyte ecological studies and management.     

Bone refilling in cortical basic multicellular units: insights into tetracycline double labelling from a computational model

Bone remodelling is carried out by ‘bone multicellular units’ ( $\text{ BMU }$ s) in which active osteoclasts and active osteoblasts are spatially and temporally coupled. The refilling of new bone by osteoblasts towards the back of the $\text{ BMU }$ occurs at a rate that depends both on the number of osteoblasts and on their secretory activity. In cortical bone, a linear phenomenological relationship between matrix apposition rate and $\text{ BMU }$ cavity radius is found experimentally. How this relationship emerges from the combination of complex, nonlinear regulations of osteoblast number and secretory activity is unknown. Here, we extend our previous mathematical model of cell development within a single cortical $\text{ BMU }$ to investigate how osteoblast number and osteoblast secretory activity vary along the $\text{ BMU }$ ’s closing cone. The mathematical model is based on biochemical coupling between osteoclasts and osteoblasts of various maturity and includes the differentiation of osteoblasts into osteocytes and bone lining cells, as well as the influence of $\text{ BMU }$ cavity shrinkage on osteoblast development and activity. Matrix apposition rates predicted by the model are compared with data from tetracycline double labelling experiments. We find that the linear phenomenological relationship observed in these experiments between matrix apposition rate and $\text{ BMU }$ cavity radius holds for most of the refilling phase simulated by our model, but not near the start and end of refilling. This suggests that at a particular bone site undergoing remodelling, bone formation starts and ends rapidly, supporting the hypothesis that osteoblasts behave synchronously. Our model also suggests that part of the observed cross-sectional variability in tetracycline data may be due to different bone sites being refilled by $\text{ BMU }$ s at different stages of their lifetime. The different stages of a $\text{ BMU }$ ’s lifetime (such as initiation stage, progression stage, and termination stage) depend on whether the cell populations within the $\text{ BMU }$ are still developing or have reached a quasi-steady state whilst travelling through bone. We find that due to their longer lifespan, active osteoblasts reach a quasi-steady distribution more slowly than active osteoclasts. We suggest that this fact may locally enlarge the Haversian canal diameter (due to a local lack of osteoblasts compared to osteoclasts) near the $\text{ BMU }$ ’s point of origin.     

Provenance variation and genetic parameters of Eucalyptus viminalis in Argentina

Genetic parameters for growth, stem straightness, pilodyn penetration, relative bark thickness and survival were estimated in a base-population of five open-pollinated provenance/progeny trials of Eucalyptus viminalis. The trials, located in northern, central and southern Buenos Aires Province, Argentina, comprised 148 open-pollinated families from 13 Australian native provenances and eight local Argentinean seedlots. The Australian native provenances come from a limited range of the natural distribution. Overall survival, based on the latest assessment of each trial, was 62.4%. Single-site analyses showed that statistically significant provenances differences (p?<?0.05) for at least one of the studied traits in three out of the five trials analyzed. The local land race performed inconsistently in this study. The average narrow-sense individual-tree heritability estimate $ \left( {{{\hat{h}}^2}} \right) $ was 0.27 for diameter and 0.17 for total height. Values of $ {\hat{h}^2} $ also increased with age. Pilodyn penetration, assessed at only one site, was more heritable $ \left( {{{\hat{h}}^2} = 0.32} \right) $ than the average of growth traits. Estimated individual-tree heritabilities were moderate to low for stem straightness (average of 0.20) and relative bark thickness (0.16). The estimated additive genetic correlations $ \left( {{{{r}}_{{A}}}} \right) $ between diameter and height were consistently high and positive ( $ {{r}_{^A}} $ average of 0.90). High additive genetic correlations were observed between growth variables and pilodyn penetration ( $ {{r}_{^A}} $ average of 0.58). Relative bark thickness showed a negative correlation with diameter $ \left( {{{{r}}_{^A}} = - 0.39} \right) $ and height $ \left( {{{{r}}_{^A}} = - 0.51} \right) $ . The average estimated additive genetic correlation between sites was high for diameter (0.67). The implications of all these parameter estimates for genetic improvement of E. viminalis in Argentina are discussed.     

Dynamic permeability of the lacunar–canalicular system in human cortical bone

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar–canalicular permeability \((K_\mathrm{LC})\) in bone. The interest in the permeability of the lacunar–canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from \(10^{-17}\;\) to \(10^{-25}\; \hbox {m}^{2}\) . However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the \(K_\mathrm{LC}\) to be on the order of \(10^{-22}\; \hbox {m}^{2}\) for human osteonal bone. It was found that the \(K_\mathrm{LC}\) has a linear dependence on loading frequency, decreasing at a rate of \(2 \times 10^{-24}\; \hbox {m}^{2}\) /Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the \(K_\mathrm{LC}\) variability.     

A thermomechanical framework for reconciling the effects of ultraviolet radiation exposure time and wavelength on connective tissue elasticity

Augmentation of the mechanical properties of connective tissue using ultraviolet (UV) radiation—by targeting collagen cross-linking in the tissue at predetermined UV exposure time \((t)\) and wavelength \((\lambda )\) —has been proposed as a therapeutic method for supporting the treatment for structural-related injuries and pathologies. However, the effects of \(\lambda \) and \(t\) on the tissue elasticity, namely elastic modulus \((E)\) and modulus of resilience \((u_\mathrm{Y})\) , are not entirely clear. We present a thermomechanical framework to reconcile the \(t\) - and \(\lambda \) -related effects on \(E\) and \(u_\mathrm{Y}\) . The framework addresses (1) an energy transfer model to describe the dependence of the absorbed UV photon energy, \(\xi \) , per unit mass of the tissue on \(t\) and \(\lambda \) , (2) an intervening thermodynamic shear-related parameter, \(G\) , to quantify the extent of UV-induced cross-linking in the tissue, (3) a threshold model for the \(G\) versus \(\xi \) relationship, characterized by   \(t_\mathrm{C}\) —the critical \(t\) underpinning the association of \(\xi \) with \(G\) —and (4) the role of \(G\) in the tissue elasticity. We hypothesized that \(G\) regulates \(E\) (UV-stiffening hypothesis) and \(u_\mathrm{Y}\) (UV-resilience hypothesis). The framework was evaluated with the support from data derived from tensile testing on isolated ligament fascicles, treated with two levels of \(\lambda \) (365 and 254 nm) and three levels of \(t\) (15, 30 and 60 min). Predictions from the energy transfer model corroborated the findings from a two-factor analysis of variance of the effects of \(t\) and \(\lambda \) treatments. Student’s t test revealed positive change in \(E\) and \(u_\mathrm{Y}\) with increases in \(G\) —the findings lend support to the hypotheses, implicating the implicit dependence of UV-induced cross-links on \(t\) and \(\lambda \) for directing tissue stiffness and resilience. From a practical perspective, the study is a step in the direction to establish a UV irradiation treatment protocol for effective control of exogenous cross-linking in connective tissues.     

Enhanced accuracy of kinetic information from CT-CPMG experiments by transverse rotating-frame spectroscopy

Micro-to-millisecond motions of proteins transmit pivotal signals for protein function. A powerful technique for the measurement of these motions is nuclear magnetic resonance spectroscopy. One of the most widely used methodologies for this purpose is the constant-time Carr–Purcell–Meiboom–Gill (CT-CPMG) relaxation dispersion experiment where kinetic and structural information can be obtained at atomic resolution. Extraction of accurate kinetics determined from CT-CPMG data requires refocusing frequencies that are much larger than the nuclei’s exchange rate between states. We investigated the effect when fast processes are probed by CT-CPMG experiments via simulation and show that if the intrinsic relaxation rate $ \left( {R_{2,0}^{CT - CPMG} } \right) $ ( R 2 , 0 CT ? CPMG ) is not known a priori the extraction of accurate kinetics is hindered. Errors on the order of 50 % in the exchange rate are attained when processes become fast, but are minimized to 5 % with a priori $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG information. To alleviate this shortcoming, we developed an experimental scheme probing $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG with large amplitude spin-lock fields, which specifically contains the intrinsic proton longitudinal Eigenrelaxation rate. Our approach was validated with ubiquitin and the Oscillatoria agardhii agglutinin (OAA). For OAA, an underestimation of 66 % in the kinetic rates was observed if $ R_{2,0}^{CT - CPMG}\, $ R 2 , 0 CT ? CPMG is not included during the analysis of CT-CPMG data and result in incorrect kinetics and imprecise amplitude information. This was overcome by combining CT-CPMG with $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG measured with a high power R_1ρ experiment. In addition, the measurement of $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG removes the ambiguities in choosing between different models that describe CT-CPMG data.     

Estimation of viscosity from passage time of liquids flowing through a microchannel array

Recently, a microchannel flow analyzer (MC-FAN) has been used to study the flow properties of blood. However, the correlation between blood passage time measured by use of the MC-FAN and hemorheology has not been clarified. In this study, a simple model is proposed for estimation of liquid viscosity from the passage time t _p of liquids. The t _p data for physiological saline were well represented by the model. According to the model, the viscosity of Newtonian fluids was estimated reasonably well from the t _p data. For blood samples, although the viscosity $ \eta_{\text{mc}} $ estimated from t _p was shown to be smaller than the viscosity $ \eta_{{450{\text{s}}^{ - 1} }} $ measured by use of a rotatory viscometer at a shear rate of 450 s^?1, $ \eta_{\text{mc}} $ was correlated with $ \eta_{{450{\text{s}}^{ - 1} }} $ . An empirical equation for estimation of $ \eta_{{450{\text{s}}^{ - 1} }} $ from $ \eta_{\text{mc}} $ of blood samples is proposed.