C\bar lr and C\bar ls subcomponents of human complement: Two serine proteinases lacking the ‘histidine-loop’ disulphide bridge

The N-terminal amino acid sequence of human C \(\bar l\) s b chain has been extended to 52 residues. The histidine residue involved in the charge-relay system is located at position 38, whereas the ‘histidine-loop’ disulphide bridge is missing. So far, human complement subcomponents C \(\bar l\) r and C \(\bar l\) s are the only known mammalian serine proteinases lacking this disulphide bridge.     

Kinetic models of coupling between H+ and Na+-translocation and ATP synthesis/hydrolysis by F0F1-ATPases: Can a cell utilize both\Delta \bar \mu _{H^ + } and\Delta \bar \mu _{Na^ + } for ATP synthesis underin vivo conditions using the same enzyme?

Kinetic models of the F₀F₁-ATPase able to transport H⁺ or/and Na⁺ ions are proposed. It is assumed that (i) H⁺ and Na⁺ compete for the same binding sites, (ii) ion translocation through F₀ is coupled to the rate-limiting step of the F₁-catalyzed reaction. The main characteristics of the dependences of ATP synthesis and hydrolysis rates on Δφ, ΔpH, and ΔpNa are predicted for various versions of the coupling model. The mechanism of the switchover from \(\Delta \bar \mu _{H^ + } \) -dependent synthesis to the \(\Delta \bar \mu _{Na^ + } \) -dependent one is demonstrated. It is shown that even with a drastic drop in \(\Delta \bar \mu _{H^ + } \) , ATP hydrolysis by the proton mode of catalysis can be effectively inhibited by Δφ and ΔpNa. The results obtained strongly support the possibility that the same F₀F₁-ATPase in bacterial cells can utilize both \(\Delta \bar \mu _{H^ + } \) and \(\Delta \bar \mu _{Na^ + } \) for ATP synthesis underin vivo conditions.     

Age,smoking habits,heat stress,and their interactive effects with carbon monoxide and peroxyacetylnitrate on man's aerobic power

Metabolic, body temperature, and cardiorespiratory responses of 16 healthy middle-aged (40–57 years) men, 9 nonsmokers and 7 smokers, were obtained during tests of maximal aerobic power at ambient environmental temperatures of 25 ± 0.5 and 35 ± 0.5°C and 20% relative humidity under four conditions: (a) filtered air, FA; (b) 50 ppm carbon monoxide in filtered air, CO; (c) 0.27 ppm peroxyacetylnitrate in filtered air, PAN; and (d) a combination of all three mixtures, PANCO. There was no significant change in maximum aerobic power \(\left( {\dot VO2max} \right)\) related to the presence of air pollutants, although total working time was lowered in the 25°C environment while breathing CO. Older nonsmokers did have a decrement in \(\left( {\dot VO2max} \right)\) while breathing 50 ppm CO, while older smokers failed to show any change. This difference was related to the initial COHb levels of the smokers, who, when breathing this level of ambient CO, had only a 14% increase in COHb over their initial levels in contrast to the 200% increase in the nonsmokers. Smoking habits were the most influential factor affecting the cardiorespiratory responses of these older men to maximal exercise. Regardless of ambient conditions, smokers had a significantly lower (27%) aerobic power than nonsmokers, were breathing closer to their maximal breathing capacities throughout the walk, and had a higher respiratory exchange ratio. While the \(\left( {\dot VO2max} \right)\) of nonsmokers was only 6% less than that of younger nonsmoking males ( \(\bar x\) age = 25 years) working under similar conditions, the aerobic power of the older smokers was 26% lower than that of young smokers ( \(\bar x\) age = 24 years).     

Sur l'espace topologique lié à une nouvelle théorie de l'apprentissage

There have been two contrasting doctrines concerning learning, more generally about acquisition of knowledge: empiricism and rationalism. The theory of learning in such a field as artificial intelligence seems to fall within the empiricist framework. On the hand, N. Chomsky and his followers have discussed, during the last decade, concerning learning, especially about language learning, from the rationalist point of view (Chomsky, 1965). The main feature in the rationalist approach toward a theory of learning lies in the speculation that in order to acquire knowledge it is indispensable for a learner to be endowed with “innate ideas”, and that “experience” in the external world are merely subsidiary types of information for the learner. If this is acceptable, we can inquire: Under what kind of innate ideas can the learner understand the structure of the external world? In our previous paper (Uesaka, Aizawa, Ebara, and Ozeki, 1973), we formalized this by introducing the mathematical notion of “learnability”, and gave a partial answer to the above inquiry. In this formalization we assumed that the set F of objects to be learned consists of mappings of N to itself, where N is the set of positive integers. Then, constructing a topological space (F, \(\mathcal{O}\) ) by an appropriate family \(\mathcal{O}\) of open sets, we observed that the notion of learnability can be well described in terms of topological properties of the learning space (F, \(\mathcal{O}\) ). Many problems must be solved, however, before we raise the theory to a complete model of the rationalist theory of learning. The topological study of the space (F, \(\mathcal{O}\) ) is, we believe, the first step toward this approach. In this context, we discuss the topological aspects of this space. Now we define \(\mathcal{O}\) as follows: By N ² we mean the direct product of two N's. Let s be a subset of N ². If, for any (x, y), (x′, y′) in s, x=x′ implies y=y′, then we say that s is single-valued. Let f ∈ F, If, for any (x, y) in s, y=f(x), then f is said to be on s, denoted as \(f\underline \supseteq s\) . Let \(\pi \left( s \right) = \left\{ {g;g \in F,g\underline \supseteq s} \right\}\) . A single-valued finite subset of N ² is called datum. Let D denote the family of all data. Let \(\mathcal{O}* = \left\{ \phi \right\} \cup \left\{ {\pi \left( d \right);d \in D} \right\}\) , and \(\mathcal{O}\) denote the family of all subsets of F, each of which is written as \(\mathop \cup \limits_\alpha W_{\alpha }\) , where W _α is in \(\mathcal{O}*\) . Then, it is easily seen that \(\mathcal{O}\) satisfies the axiom of the open system of a topological space. It is shown that the learning space (F, \(\mathcal{O}\) ) has the following properties:

1. It satisfies the first and the second countability axioms.
2. It is separable and is totally disconnected.
3. It is a Hausdorff space and, further, is regular and normal.
4. It is neither compact nor locally compact.
5. It is metrizable, or more precisely there exists a complete but not totally bounded metric space which is homeomorphic to learning space.
6. Any of its subspace can be embedded into its special subspace.

     

Linear and nonlinear stiffness and friction in biological rhythmic movements

Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as $\dot \theta ^3 $ ) and van der Pol (involving terms such as $\theta ^2 \dot \theta $ ), and the nonlinear elastic functions identified by Duffing (involving terms such as $\theta ^3 $ ), constitute elementary nonlinear components for the assembling of self-sustained oscillators. Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as $\theta ^2 \dot \theta ^3 $ and $\theta \dot \theta ^2 $ , and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.     

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.     

A locally convergent rotationally invariant particle swarm optimization algorithm

Several well-studied issues in the particle swarm optimization algorithm are outlined and some earlier methods that address these issues are investigated from the theoretical and experimental points of view. These issues are the: stagnation of particles in some points in the search space, inability to change the value of one or more decision variables, poor performance when the swarm size is small, lack of guarantee to converge even to a local optimum (local optimizer), poor performance when the number of dimensions grows, and sensitivity of the algorithm to the rotation of the search space. The significance of each of these issues is discussed and it is argued that none of the particle swarm optimizers we are aware of can address all of these issues at the same time. To address all of these issues at the same time, a new general form of velocity update rule for the particle swarm optimization algorithm that contains a user-definable function \(f\) is proposed. It is proven that the proposed velocity update rule guarantees to address all of these issues if the function \(f\) satisfies the following two conditions: (i) the function \(f\) is designed in such a way that for any input vector \(\vec {y}\) in the search space, there exists a region \(A\) which contains \(\vec {y}\) and \( f\!\left( {\vec {y}} \right) \) can be located anywhere in \(A\) , and (ii) \(f\) is invariant under any affine transformation. An example of function \(f\) is provided that satisfies these conditions and its performance is examined through some experiments. The experiments confirm that the proposed algorithm (with an appropriate function \(f)\) can effectively address all of these issues at the same time. Also, comparisons with earlier methods show that the overall ability of the proposed method for solving benchmark functions is significantly better.     

On biomass diversity in ecology

We postulate that the biomass distribution function for an ecological population may be derived from the condition that the biomas diversity functional is maximal subject to an energetic constraint on the total biomass. This leads to a biomass distribution of the form \(p(m) = \bar m^{ - 1} \exp ( - m/\bar m)\) , where \(\bar m\) is the mean biomass per individual. The same condition yields a unique value for the biomass diversity functional. These predictions are tested against fishery data and found to be in good agreement. It is argued that the existence of a unique value for biomass diversity may provide a preliminary theoretical foundation for the observed upper limit to species diversity.     

Approximation of sojourn-times via maximal couplings: motif frequency distributions

Sojourn-times provide a versatile framework to assess the statistical significance of motifs in genome-wide searches even under non-Markovian background models. However, the large state spaces encountered in genomic sequence analyses make the exact calculation of sojourn-time distributions computationally intractable in long sequences. Here, we use coupling and analytic combinatoric techniques to approximate these distributions in the general setting of Polish state spaces, which encompass discrete state spaces. Our approximations are accompanied with explicit, easy to compute, error bounds for total variation distance. Broadly speaking, if \({\mathsf{T}}_n\) is the random number of times a Markov chain visits a certain subset \({\mathsf{T}}\) of states in its first \(n\) transitions, then we can usually approximate the distribution of \({\mathsf{T}}_n\) for \(n\) of order \((1-\alpha )^{-m}\) , where \(m\) is the largest integer for which the exact distribution of \({\mathsf{T}}_m\) is accessible and \(0\le \alpha \le 1\) is an ergodicity coefficient associated with the probability transition kernel of the chain. This gives access to approximations of sojourn-times in the intermediate regime where \(n\) is perhaps too large for exact calculations, but too small to rely on Normal approximations or stationarity assumptions underlying Poisson and compound Poisson approximations. As proof of concept, we approximate the distribution of the number of matches with a motif in promoter regions of C. elegans. Mathematical properties of the proposed ergodicity coefficients and connections with additive functionals of homogeneous Markov chains as well as ergodicity of non-homogeneous Markov chains are also explored.     

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.     

Chromosomal replication in Drosophila virilis

DNA fiber autoradiography was used to determine parameters underlying the DNA replication of the eukaryotic chromosome in Drosophila diploid brain cells in organ culture. The average rate of fork movement, estimated from 4 different labelling intervals, is 0.35 μm/min at 25 ° C. Of the tandem arrays 93% show patterns which are compatible with bidirectional replication, 7% show unidirectional replication. The unidirectional mode of replication is interpreted as being a consequence of the experimental schedule (using hot-cold pulse labelling) combined with the occurrence of termination signals. — Some autoradiograms showed the expected two grain tracks of different densities; others showed only a high density track. The latter were most prominent in arrays of short replicons (<10 μm) which correlate with replicating satellite sequences. — The majority of replicons fall into size classes < 100 μm. The frequency distribution is skewed towards larger replicon sizes; it spans 2–238 μm, has a mean of ˉx = 35.6 μm and a median of = 21.0 μm. If the distribution is corrected for supposed satellite replicons, the median increases to = 31.0 μm. — In experiments using warmhot pulse labelling, arrays were scored which must have been a consequence of fixed termination signals. Furthermore, grain tracks diverging from weak labelled centers often have different lengths, indicating that these replicons contain two diverging replicating sections of unequal length. Presented to Professor Dr. Wolfgang Beermann on the occasion of his 60th birthday with my best wishes     

N-site Phosphorylation Systems with 2N-1 Steady States

Multisite protein phosphorylation plays a prominent role in intracellular processes like signal transduction, cell-cycle control and nuclear signal integration. Many proteins are phosphorylated in a sequential and distributive way at more than one phosphorylation site. Mathematical models of \(n\) -site sequential distributive phosphorylation are therefore studied frequently. In particular, in Wang and Sontag (J Math Biol 57:29–52, 2008), it is shown that models of \(n\) -site sequential distributive phosphorylation admit at most \(2n-1\) steady states. Wang and Sontag furthermore conjecture that for odd \(n\) , there are at most \(n\) and that, for even \(n\) , there are at most \(n+1\) steady states. This, however, is not true: building on earlier work in Holstein et al. (Bull Math Biol 75(11):2028–2058, 2013), we present a scalar determining equation for multistationarity which will lead to parameter values where a \(3\) -site system has \(5\) steady states and parameter values where a \(4\) -site system has \(7\) steady states. Our results therefore are counterexamples to the conjecture of Wang and Sontag. We furthermore study the inherent geometric properties of multistationarity in \(n\) -site sequential distributive phosphorylation: the complete vector of steady state ratios is determined by the steady state ratios of free enzymes and unphosphorylated protein and there exists a linear relationship between steady state ratios of phosphorylated protein.     

Metabolism and thermoregulation in desert and montane grasshoppers

Temperature regulation and oxygen consumption were examined in two species of grasshoppers: Melanoplus sanguinipes from cold alpine tundra at elevation 3,800 m, and Trimerotropis pallidipennis from hot desert habitats at elevation 250 m. Both species utilized behavioral thermoregulation to keep body temperature (T _b ) more constant than environmental temperatures (T _e ) during the day. The difference in average T _b in the two species was much less than the difference in T _e 's. Microclimate measurements indicate that temperature regulation is not difficult for M. sanguinipes, but T. pallidipennis must restrict activity for much of the day to avoid heat stress and can easily overheat if it moves into sunlit areas. Oxygen consumption ( \(\dot V{\text{O}}_{\text{2}} \) ) at average T _b and total daily energy expenditures are higher in M. sanguinipes than in T. pallidipennis, as is the Q₁₀ for \(\dot V{\text{O}}_{\text{2}} \) . These differences may be related to different strategies for energy utilization and predator avoidance.     

Interdependency and hierarchy of exact and approximate epidemic models on networks

Over the years numerous models of \(SIS\) (susceptible \(\rightarrow \) infected \(\rightarrow \) susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general motif-based models. We illustrate how the different models can be derived from one another and, where this is not possible, discuss extensions to established models that enables this derivation. We also derive a general result for the exact differential equations for the expected number of an arbitrary motif directly from the Kolmogorov/master equations and conclude with a comparison of the performance of the different closed systems of equations on networks of varying structure.     

Transmission dynamics for vector-borne diseases in a patchy environment

In this paper, a mathematical model is derived to describe the transmission and spread of vector-borne diseases over a patchy environment. The model incorporates into the classic Ross–MacDonald model two factors: disease latencies in both hosts and vectors, and dispersal of hosts between patches. The basic reproduction number \(\mathcal{R }_0\) is identified by the theory of the next generation operator for structured disease models. The dynamics of the model is investigated in terms of \(\mathcal{R }_0\) . It is shown that the disease free equilibrium is asymptotically stable if \(\mathcal{R }_0<1\) , and it is unstable if \(\mathcal{R }_0>1\) ; in the latter case, the disease is endemic in the sense that the variables for the infected compartments are uniformly persistent. For the case of two patches, more explicit formulas for \(\mathcal{R }_0\) are derived by which, impacts of the dispersal rates on disease dynamics are also explored. Some numerical computations for \(\mathcal{R }_0\) in terms of dispersal rates are performed which show visually that the impacts could be very complicated: in certain range of the parameters, \(\mathcal{R }_0\) is increasing with respect to a dispersal rate while in some other range, it can be decreasing with respect to the same dispersal rate. The results can be useful to health organizations at various levels for setting guidelines or making policies for travels, as far as malaria epidemics is concerned.     

Consumption and utilization of a soyflour-wheat germ diet by larvae of the tobacco budworm parasitized by the tachinidEucelatoria sp

The number ( \(\bar X\) =2.4) ofEucelatoria sp. maggots that completed development in 4th- or 5th-instar larvae of the tobacco budworm (TBW),Heliothis virescens (F.), was significantly greater (P<0.05) than the number ( \(\bar X\) =1.2) that completed development in 3rd-instar larvae. Maggot development time decreased with increasing number of maggots per host larva. It also decreased with advancing larval instars. The range was 6.9±1.1 days in early 3rd-instar TBW larvae and 5.0±0.8 days in early 5th-instar TBW larvae. Unparasitized 3rd- or 4th-instar TBW larvae consumed significantly more food than did similar aged larvae parasitized byEucelatoria sp., but larvae parasitized during the early 5th-instar consumed more food than did similar aged unparasitized larvae. Consumption by 4th- or 5th-instar larvae increased significantly as maggot densities increased from 1 to 3 per host larva, but decreased at a density of 4 or more maggots per host larva. Although body weight gain and consumption were both significantly reduced 48 and 120 h after parasitization of late 3rd-instar larvae (6 days old), the approximate digestibility (AD) value was significantly greater for parasitized than for unparasitized larvae. Unparasitized larvae were more efficient in converting digested food to body substance (ECD) than parasitized larvae, but the efficiency in conversion of ingested food to body substance (ECI) was similar for both parasitized and unparasitized larvae.     

Individual-Based Model for Quorum Sensing with Background Flow

Quorum sensing is a wide-spread mode of cell–cell communication among bacteria in which cells release a signalling substance at a low rate. The concentration of this substance allows the bacteria to gain information about population size or spatial confinement. We consider a model for \(N\) cells which communicate with each other via a signalling substance in a diffusive medium with a background flow. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration \(u\) of the signalling substance, coupled with \(N\) ODEs for the masses \(a_i\) of the substance within each cell. The cells are balls of radius \(R\) in \(\mathbb {R} ^3\) , and under some scaling assumptions we formally derive an effective system of \(N\) ODEs describing the behaviour of the cells. The reduced system is then used to study the effect of flow on communication in general, and in particular for a number of geometric configurations.