Accelerating, hyperaccelerating, and decelerating networks

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting accelerating growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from nonstationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value. (c) 2005 Elsevier GmbH. All rights reserved.

Applying network analysis to the conservation of habitat trees in urban environments: a case study from Brisbane, Australia

In Australia more than 300 vertebrates, including 43 insectivorous bat species, depend on hollows in habitat trees for shelter, with many species using a network of multiple trees as roosts, We used roost-switching data on white-striped freetail bats (Tadarida australis; Microchiroptera: Molossidae) to construct a network representation of day roosts in suburban Brisbane, Australia. Bats were caught from a communal roost tree with a roosting group of several hundred individuals and released with transmitters. Each roost used by the bats represented a node in the network, and the movements of bats between roosts formed the links between nodes. Despite differences in gender and reproductive stages, the bats exhibited the same behavior throughout three radiotelemetry periods and over 500 bat days of radio tracking: each roosted in separate roosts, switched roosts very infrequently, and associated with other bats only at the communal roost This network resembled a scale-free network in which the distribution of the number of links from each roost followed a power law. Despite being spread over a large geographic area (> 200 km(2)), each roost was connected to others by less than three links. One roost (the hub or communal roost) defined the architecture of the network because it had the most links. That the network showed scale-free properties has profound implications for the management of the habitat trees of this roosting group. Scale-free networks provide high tolerance against stochastic events such as random roost removals but are susceptible to the selective removal of hub nodes. Network analysis is a useful tool for understanding the structural organization of habitat tree usage and allows the informed judgment of the relative importance of individual trees and hence the derivation of appropriate management decisions, Conservation planners and managers should emphasize the differential importance of habitat trees and think of them as being analogous to vital service centers in human societies.

Network topology and the evolution of dynamics in an artificial genetic regulatory network model created by whole genome duplication and divergence

Topological measures of large-scale complex networks are applied to a specific artificial regulatory network model created through a whole genome duplication and divergence mechanism. This class of networks share topological features with natural transcriptional regulatory networks. Specifically, these networks display scale-free and small-world topology and possess subgraph distributions similar to those of natural networks. Thus, the topologies inherent in natural networks may be in part due to their method of creation rather than being exclusively shaped by subsequent evolution under selection. The evolvability of the dynamics of these networks is also examined by evolving networks in simulation to obtain three simple types of output dynamics. The networks obtained from this process show a wide variety of topologies and numbers of genes indicating that it is relatively easy to evolve these classes of dynamics in this model. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Effect of free ammonia and free nitrous acid concentration on the anabolic and catabolic processes of an enriched Nitrosomonas culture

The effects of free ammonia (FA; NH3) and free nitrous acid (FNA; HNO2) concentrations on the metabolisms of an enriched ammonia oxidizing bacteria (AOB) culture were investigated using a method allowing the decoupling of growth and energy generation processes. A lab-scale sequencing batch reactor (SBR) was operated for the enrichment of an AOB culture. Fluorescent in-situ hybridization (FISH) analysis showed that 82% of the bacterial population in the SBR bound to the NEU probe specifically designed for Nitrosomonas europaea. Batch tests were carried out to measure the oxygen and ammonium consumption rates by the culture at various FA and FNA levels, in the presence or absence of inorganic carbon (CO2, HCO3, and CO32-). It was revealed that FA of up to 16.0 mgNH(3)-N (.) L-1, which was the highest concentration used in this study, did not have any inhibitory effect on either the catabolic or anabolic processes of the Nitrosomonas culture. In contrast, FNA inhibited both the growth and energy production capabilities of the Nitrosomonas culture. The inhibition on growth initiated at approximately 0.10 mgHNO(2)-(NL-1)-L-., and the data suggested that the biosynthesis was completely stopped at an FNA concentration of 0.40 mgHNO(2)-N (.) L-1. The inhibition on energy generation initiated at a slightly lower level but the Nitrosomonas culture was still oxidizing ammonia at half of the maximum rate at an FNA concentration of 0.50-0.63 mgHNO(2)-N (.) L-1. The affinity constant of the Nitrosomonas culture with respect to ammonia was determined to be 0.36 mgNH3-N (.) L-1, independent of the presence or absence of inorganic carbon. (c) 2006 Wiley Periodicals, Inc.

Effect of temperature and free ammonia on nitrification and nitrite accumulation in landfill leachate and analysis of its nitrifying bacterial community by FISH

The cause of seasonal failure of a nitrifying municipal landfill leachate treatment plant utilizing a fixed biofilm was investigated by wastewater analyses and batch respirometric tests at every treatment stage. Nitrification of the leachate treatment plant was severely affected by the seasonal temperature variation. High free ammonia (NH3-N) inhibited not only nitrite oxidizing bacteria (NOB) but also ammonia oxidizing bacteria (AOB). In addition, high pH also increased free ammonia concentration to inhibit nitrifying activity especially when the NH4-N level was high. The effects of temperature and free ammonia of landfill leachate on nitrification and nitrite accumulation were investigated with a semi-pilot scale biofilm airlift reactor. Nitrification rate of landfill leachate increased with temperature when free ammonia in the reactor was below the inhibition level for nitrifiers. Leachate was completely nitrified up to a load of 1.5 kg NH4-N m(-3) d(-1) at 28 degrees C. The activity of NOB was inhibited by NH3-N resulting in accumulation of nitrite. NOB activity decreased more than 50% at 0.7 mg NH3-N L-1. Fluorescence in situ hybridization (FISH) was carried out to analyze the population of AOB and NOB in the nitrite accumulating nitrifying biofilm. NOB were located close to AOB by forming small clusters. A significant fraction of AOB identified by probe Nso1225 specifically also hybridized with the Nitrosonlonas specific probe Nsm156. The main NOB were Nitrobacter and Nitrospira which were present in almost equal amounts in the biofilm as identified by simultaneous hybridization with Nitrobacter specific probe Nit3 and Nitrospira specific probe Ntspa662. (c) 2005 Elsevier Ltd. All rights reserved.

The inhibitory effects of free nitrous acid on the energy generation and growth processes of an enriched Nitrobacter culture

The inhibitory effects of nitrite (NO2-)/free nitrous acid (HNO2-FNA) on the metabolism of Nitrobacter were investigated using a method allowing the decoupling of the growth and energy generation processes. A lab-scale sequencing batch reactor was operated for the enrichment of a Nitrobacter culture. Fluorescent in situ hybridization (FISH) analysis showed that 73% of the bacterial population was Nitrobacter. Batch tests were carried out to assess the oxygen and nitrite consumption rates of the enriched culture at low and high nitrite levels, in the presence or absence of inorganic carbon. It was observed that in the absence of CO2, the Nitrobacter culture was able to oxidize nitrite at a rate that is 76% of that in the presence of CO2, with an oxygen consumption rate that is 85% of that measured in the presence of CO2. This enabled the impacts of nitrite/FNA on the catabolic and anabolic processes of Nitrobacter to be assessed separately. FNA rather than nitrite was likely the actual inhibitor to the Nitrobacter metabolism. It was revealed that FNA of up to 0.05 mg HNO2-N center dot L-1 (3.4 mu M), which was the highest FNA concentration used in this study, did not have any inhibitory effect on the catabolic processes of Nitrobacter. However, FNA initiated its inhibition to the anabolic processes of Nitrobacter at approximately 0.011 mg HNO2-N center dot L-1 (0.8 mu M), and completely stopped biomass synthesis at a concentration of approximately 0.023 mg HNO2-N center dot L-1 (1.6 mu M). The inhibitory effect could be described by an empirical inhibitory model proposed in this paper, but the underlying mechanisms remain to be revealed.