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On the origin of plasmid-borne, extended-spectrum, antibiotic resistance mutations in bacteria.

Many antibiotic resistance mutations arise in pathogenic bacteria that harbor plasmids (R-plasmids). Resistance to third generation cephalosporins, for instance, largely occurs by one or more point mutations in plasmid bla genes that expand the resistance spectrum of beta-lactamases. Here I review relevant evidence underlying the worldwide emergence of extended spectrum beta-lactamases (ESBLs). The conclusion reached is that the origin of these resistance-conferring mutations cannot be explained by a series of single point mutation and selection events. Instead, highly advantageous stochastic processes might exist that generate alterations in the sequence or the conformation of particular regions in chromosomal or plasmid genomes such as bla, i.e., recombination or mutation. Several explanations for the origin of ESBLs are reviewed but direct experimental evidence to support or to invalidate them is still lacking. The cellular conditions under which ESBLs arise are unknown; however, involvement of nutritional stresses inside natural animal hosts and of plasmid conjugal functions appear likely.

Bacteria↗

Gompertzian mortality originates in the winding-down of the mitotic clock.

UNLABELLED: Gompertz' age-related exponential increase in mortality rate and the obdurately flat mortality trajectory of Drosophila are paradoxical notions for metazoan aging theory. A multiclonal model of Gompertzian organisms provides a resolution by assuming that (a) conception initiates a stochastic process producing a train of replications of fixed length (the Hayflick limit); (b) unique stem cells arise early on to generate multiple vital clones; (c) life continues until one such clone critically depletes its replicative potential. Lifespan is thus governed by the time it takes to reach the terminal branches of the mitotic tree. Although these times are not independent, asymptotic independence can be justified. This clears the way for asymptotic extreme-value theory to guarantee: (1) a non-increasing failure rate, under unlimited replicability; (2) an exponentially increasing failure rate, under limited replicability. However, to obtain an exact fit to the human force-of-mortality function also requires the inclusion of the phenomenon of mitotic deceleration (implemented with a lognormal model of replication). CONCLUSION: the sine qua non of Gompertzian mortality is cellular aging, expressed through these two mitotic phenomena. Conversely, those metazoa with unlimited cellular replicability, by staving off clonal failure would succumb only to catastrophic, age-independent events, yielding a constant mortality rate, the signature of a mitotic clock that does not run down.

Animals↗

A stochastic model for the rapid emergence of specific vertebrate immunity incorporating horizontal transfer of systems enabling duplication and combinational diversification.

Recent molecular data indicate that the antigen-specific combinatorial immune response is restricted to jawed vertebrates where it is found in representatives of all class from cartilagenous fishes to mammals. Here, we analyse the relatively rapid emergence of the combinatorial system terms of three stochastic process, with the system reaching essentially full capacity in immunoglobulin recognition elements and diversification and recombination of gene segments in an evolutionary span of time of less than 20 million years. The mechanisms for inducibility were coopted from ancient and widely spread processes in phylogeny for regulation of cell division. The proposed process of formation entailed the evolution of unknown ancestral genes into those specifying bona fide immunoglobulin domains, and the generation of multiple copies of these via a series of events facilitated by horizontal transfer of site-specific recombinases and recombination signal sequences most probably from microbial and fungal sources. The second process is one of rapid "decay" (evolution) which occurred in about 10 million year under stringent selective conditions to generate proper conserved canonical sequences. The third process is that of the long term evolution of these characteristic immunoglobulin domains over the 450 million years since their emergence. As a first approximation the rates of these three processes were computed using first order differential equations. The rate of formation has a magnitude of 10-7 substitutions per site per year, and that of rapid modifications is 10-8 substitutions per site per year. The long term rate of immunoglobulin evolution is comparable to that of other moderately conserved proteins, (1-3) x 10-9 substitutions per site per year). This model is testable by searching for "footprints" of microbial and fungal DNA processing enzymes and recombination mechanisms. The hypothesis raises the general concept that horizontal transfer of genes facilitating rearrangement and duplication can catalyse major steps of macroevolution.

Animals↗

Pattern formation in a patch occupancy metapopulation model: a cellular automata approach.

The explicit consideration of space in ecological research is of paramount importance to understand the structure and functioning of ecological systems. In this paper we develop a simple spatially explicit metapopulation model in which colonization is constant and independent of the number of occupied patches (i.e. propagule-rain effect, Gotelli, 1991). Extinction, on the other hand, is modelled as a stochastic process whose intensity depends on the number of occupied patches in the neighborhood of each focal patch. Our model is the CA counterpart of two classical patch occupancy metapopulation models. We analytically prove this by showing that our CA converges to the differential equation in the mean-field approximation. The asymptotic behaviour of the system, expressed as the proportion of occupied patches, agrees with the equilibrium proportion of patches derived by using ODEs. In both models, the existence of a rescue-effect increases the range of extinction and colonization parameters over which the system attains complete occupancy of patches. However, in our model this result is strongly influenced by the degree of coupling among patches and is apparent only for local interactions. With local interactions and particular parameter values of colonization and extinction, self-organized spatio-temporal patterns emerge with a fractal-like clustering, even though the environment is spatially homogeneous. Our results point out that the importance of being spatial and discrete (Durrett & Levin, 1994a) in our model is a result of local interactions.

Ecology↗

Individual-based perspectives on R(0).

Without doubt the basic reproductive ratio, R(0), is the most widely used quantity in epidemic theory. Standard compartmental models show how R(0)is related to the average age of infection, vaccination thresholds for eradication and equilibrium solutions. However, many of the basic formulae for R(0)break down when we consider transmission of infection to be a stochastic process involving discrete individuals. This paper clarifies why and when these differences arise and predicts when individual-based considerations are likely to be important in modelling infection dynamics.

Disease Outbreaks↗

Language dynamics in finite populations.

Any mechanism of language acquisition can only learn a restricted set of grammars. The human brain contains a mechanism for language acquisition which can learn a restricted set of grammars. The theory of this restricted set is universal grammar (UG). UG has to be sufficiently specific to induce linguistic coherence in a population. This phenomenon is known as "coherence threshold". Previously, we have calculated the coherence threshold for deterministic dynamics and infinitely large populations. Here, we extend the framework to stochastic processes and finite populations. If there is selection for communicative function (selective language dynamics), then the analytic results for infinite populations are excellent approximations for finite populations; as expected, finite populations need a slightly higher accuracy of language acquisition to maintain coherence. If there is no selection for communicative function (neutral language dynamics), then linguistic coherence is only possible for finite populations.

Humans↗

Three distinct mechanisms facilitate genetic isolation of sympatric wheat streak mosaic virus lineages.

Cross-protection and vector transmission bottlenecks have been proposed as mechanisms facilitating genetic isolation of sympatric viral lineages. Molecular markers were used to monitor establishment and resolution of mixed infections with genetically defined strains of wheat streak mosaic virus (WSMV). Two closely related WSMV strains from the U.S. (Type and Sidney 81) exhibited reciprocal cross-protection in wheat, confirming this classic phenomenon as a mechanism of genetic isolation. In contrast, cross-protection between either U.S. strain and the divergent El Batán 3 strain from Mexico was unilateral, erratic, and only partially effective. Distribution of WSMV strains within individual leaves of plants supporting a mixed infection of Type and Sidney 81 was spatially nonuniform. Strain distribution among individual tillers of coinfected plants also was heterogeneous, with some containing either Type or Sidney 81 alone and some containing both. Transmission by wheat curl mites, acquiring virus from source plants simultaneously infected with both Type and Sidney 81, often resulted in test plants bearing only a single WSMV strain. Spatial subdivision of virus strains within coinfected plants likely contributed to vector transmission bottlenecks during acquisition. Collectively, these three distinct mechanisms enhance genetic isolation of individual viral lineages, and together with stochastic processes, may explain generation and maintenance of genetic diversity in field populations.

Animals↗

Evaluation of cancer prevention strategies by computerized simulation model: an approach to lung cancer.

A computerized simulation model was developed to evaluate the potential impact of primary and secondary prevention on lung cancer mortality in Japan. The natural history of lung cancer was modeled as a Markovian stochastic process from cancer-free to preclinical, clinical, and finally to terminal states. The increase in mortality rate of lung cancer among males aged 75 to 79 years has been the major force of increase in the total number of lung cancer deaths in Japan. The simulation showed that this tendency would continue until the late 1990s, presumably due to the increase in the proportion of ever-smokers in that cohort, who started smoking at an earlier age than did prior generations. It was shown that the number of lung cancer deaths can be reduced either by smoking cessation or screening programs, and that the reduction is proportional to the increase in the annual smoking-cessation rate and to the annual increment in the screening rate. However, only two to three percent reduction of lung cancer deaths in the year 2001 can be expected when the annual smoking-cessation rate is raised from the current value of 0.46 percent to five percent during the period from 1991 to 2000 or when the screening rate is increased by three percent annually for the same period.

Adult↗

Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories.

A new conceptual and theoretical framework for studying the human postural control system is introduced. Mathematical techniques from statistical mechanics are developed and applied to the analysis and interpretation of stabilograms. This work was based on the assumption that the act of maintaining an erect posture could be viewed, in part, as a stochastic process. Twenty-five healthy young subjects were studied under quite-standing conditions. Center-of-pressure (COP) trajectories were analyzed as one-dimensional and two-dimensional random walks. This novel approach led to the extraction of repeatable, physiologically meaningful parameters from stabilograms. It is shown that although individual stabilograms for a single subject were highly variable and random in appearance, a consistent, subject-specific pattern emerged with the generation of averaged stabilogram-diffusion plots (mean square COP displacement vs time interval). In addition, significant inter-subject differences were found in the calculated results. This suggests that the steady-state behavior of the control mechanisms involved in maintaining erect posture can be quite variable even amongst a population of age-matched, anthropometrically similar, healthy individuals. These posturographic analyses also demonstrated that COP trajectories could be modelled as fractional Brownian motion and that at least two control systems-a short-term mechanism and a long-term mechanism-were operating during quit standing. More specifically, the present results suggest that over short-term intervals open-loop control schemes are utilized by the postural control system, whereas over long-term intervals closed-loop control mechanisms are called into play. This work strongly supports the position that much can be learned about the functional organization of the postural control system by studying the steady-state behavior of the human body during periods of undisturbed stance.

Adult↗

The generation of transplasmic Drosophila simulans by cytoplasmic injection: effects of segregation and selection on the perpetuation of mitochondrial DNA heteroplasmy.

Experimental transplasmic Drosophila simulans were obtained through cytoplasm microinjection between eggs carrying different mitochondrial genomes. These genomes (siII and siIII) show a 1.5% difference in their sequences. They produced a large number of heteroplasmic flies in their F1 progeny and several flies were still heteroplasmic at the eighth generation. The distribution of frequencies of mitochondrial genotypes in the offspring of heteroplasmic females suggests that the stochastic processes involved in the evolution of experimental heteroplasmy of multiple nucleotide sites are very similar to those previously described for spontaneous length heteroplasmy. In addition, the siII genome has a noticeable advantage over the siIII genome in both directions of injection. This advantage is estimated at 58% per fly generation and 5% per cell generation.

Animals↗

Stochastic selection in both haplophase and diplophase.

A population genetic model incorporating the evolutionary forces of zygotic selection, gametic selection and non-Mendelian segregation has been analyzed for the case in which all selection coefficients and the segregation parameter are assumed to be random variables that are uncorrelated from generation to generation. The diffusion approximation of the model is developed, and the subsequent analysis shows that one of four limiting outcomes of the stochastic process may obtain--an allele may be fixed or lost almost surely and irrespective of the initial gene frequency, the gene frequency may converge to a unique stationary distribution, or an allele may be fixed or lost with probabilities depending on the initial gene frequency. These outcomes correspond rather closely with the possible outcomes of the deterministic model--fixation or loss of an allele, convergence to a stable equilibrium, or the existence of an unstable equilibrium.

Alleles↗

The frequency of cyclic processes in biological multistate systems.

Cyclic processes in stochastic models of macromolecular biological systems are considered. The diagram solution of the model equations (master equation) gives rise to special functions of the rate constants, called the circuit (or one-way cycle) fluxes. As Hill has shown, these functions are the fundamental theoretical components of the operational fluxes, i.e., of the rates of reaction, of transport, of energy conversion, etc. Evidence recently has been found by Monte Carlo simulations that the circuit fluxes can be interpreted as the frequencies of circuit completions. Making use of the theory of graphs, we prove that this physical interpretation of the circuit fluxes is generally valid.

Kinetics↗

Analysing ion channels with hidden Markov models.

Ion channel current amplitudes (mu) and open probabilities (Po) have been analysed so far by defining a 50% threshold to distinguish between open and closed states of the channels. With this standard method (SM) it is very difficult or even impossible to analyse channels of different size in one membrane patch correctly. A stochastical model, named the hidden Markov model (HMM), separates between observation noise and the stochastic process of opening and closing of ion channels. The HMM allows the independent analysis of mu, Po, and mean dwell times (tau) of different channels in one membrane patch, without defining threshold levels. Using this method errors in the analysis are not summarized like in the SM because all different analysing procedures (e.g. filtering, setting of threshold, fitting processes) are done in one step. Two different K+ channels in excised basolateral membranes of the cortical collecting duct of rat (CCD) were analysed by the SM and the HMM. The mu value of the intermediate-conductance K+ channel (i-K+) was 3.9 +/- 0.1 pA (SM) and 3.8 +/- 0.2 pA (HMM) for 11 observations. The Po value of this channel was 10.2 +/- 4.2% (SM) and 10.1 +/- 4.0% (HMM). The mean tau values were 5.4 +/- 0.6 ms for the open state and 9.6 +/- 2.2 ms and 145 +/- 21 ms for the closed states (SM) and 7.8 +/- 1.1 ms, 7.7 +/- 0.9 ms and 148 +/- 24 ms (HMM), respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Algorithms↗

The size distribution of poly(A) in newly synthesized and old Balbiani ring RNA.

The size distribution of newly synthesized and old poly(A) sequences on transcripts of the giant tissue specific puffs, Balbiani rings in salivary glands of Chironomus tentans has been determined. After labeling with [3H]adenosine, poly(A) containing Balbiani ring RNA(75S RNA) was selectively collected by means of a recently developed technique. This combines electrophoretic fractionation and affinity chromatography in one run by insertion of poly(U) immobilized in glass fiber filters in an agarose gel slab. The majority of short-term labeled poly(A) chains released from poly(A) containing 75S RNA molecules is distributed within a narrow size range migrating as one peak with a mean value of 103 +/- 2 nucleotides, which is probably the initial length of poly(A). The labeling pattern of ribonuclease resistant poly(A) stretches after chase with unlabeled adenosine displays a relatively broad and heterogeneous size spectrum from at least 20 to more than 100 nucleotides. The main peak of labeled adenylate core in newly formed poly(A) containing RNA of non-Balbiani ring origin is dispersed within a broader size range than that of Balbiani ring RNA and possesses an average value of 94 +/- 2 nucleotides. During chase conditions, the relative frequency of occurrence of poly(A) chains of 75S RNA in the size range of 100 nucleotides exhibits a significant decrease in parallel with a rather uniform gain in the size classes between 20--50 nucleotides. However, the results are inconsistent with the existence of an age-dependent shortening of poly(A) chains in the balbiani ring RNA. A significant portion of 75S RNA molecules remain associated with poly(A) segments which are essentially of original size even after 21 hr in the presence of unlabeled adenosine. This finding provides support for the possibility that the initiation of the poly(A) shortening in 75S RNA is a stochastic process.

Animals↗

Generalizations of current status data with applications.

In estimation of a survival function, current status data arises when the only information available on individuals is their survival status at a single monitoring time. Here, we briefly review extensions of this form of data structure in two directions: (i) doubly censored current status data, where there is incomplete information on the origin of the failure time random variable, and (ii) current status information on more complicated stochastic processes. Simple examples of these data forms are presented for motivation.

HIV Infections↗

Monitoring international migration flows in Europe. Towards a statistical data base combining data from different sources.

"The paper reviews techniques developed in demography, geography and statistics that are useful for bridging the gap between available data on international migration flows and the information required for policy making and research. The basic idea of the paper is as follows: to establish a coherent and consistent data base that contains sufficiently detailed, up-to-date and accurate information, data from several sources should be combined.... The issues may be tackled more easily if the statistics that are being compiled are viewed as different outcomes or manifestations of underlying stochastic processes governing migration. The link between the processes and their outcomes is described by models, the parameters of which must be estimated from the available data.... The paper discusses the experience of the U.S. Bureau of the Census in combining migration data from several sources. It also summarizes the many efforts in Europe to establish a coherent and consistent data base on international migration." (SUMMARY IN FRE)

Americas↗

Cellular lung dosimetry for inhaled radon decay products as a base for radiation-induced lung cancer risk assessment. II. Microdosimetric calculations.

Lung dose calculations for inhaled radon decay products presented in part I have revealed that mean basal cell doses are significantly dependent on various personal and environmental factors. Whereas these macroscopic dosimetric methods have been applied with great success to radiation protection problems, the interpretation of radiobiological effects, such as lung cancer incidence, needs some refinement of these methods. Energy deposition at the microscopic level as the physical input quantity and radiation carcinogenesis as the biological endpoint are by nature stochastic processes. Therefore, a microdosimetric model was developed taking into consideration the randomness of physical and biological parameters involved, Part II of the paper presents results on specific energy distributions in lung cells, demonstrating that single event density distributions together with the number of cells receiving single hits represent more appropriate parameters than mean radiation doses.

Alpha Particles↗

[Significance of clinical and laboratory chemical parameters for the course and prognosis of non-Hodgkin's lymphomas].

Using a regression model, the prognostic significance of clinical and biochemical parameters as well as of histology was analyzed in a group of 336 patients with Non-Hodgkin's lymphoma. A stochastic process model was used for evaluation of the course of disease. With respect to overall survival, serum-LDH-activity, performance status, and the histologically defined grade of malignancy were found to be the most important prognostic parameters, as well as age, though that to a lesser extent. In the course of disease, stage was the most relevant factor for achievement of a complete remission. In patients without remission, survival was determined mainly by histology and serum-LDH-activity; the latter was also of importance for duration of remission. Our study shows that histology is not the only prognostic factor in NHL but that other parameters, mainly serum-LDH-activity and performance status, also have to be considered in comparing different groups of patients.

Age Factors↗