Unusual dynamics of extinction in a simple ecological model.

Studies on natural populations and harvesting biological resources have led to the view, commonly held, that (i) populations exhibiting chaotic oscillations run a high risk of extinction; and (ii) a decrease in emigration/exploitation may reduce the risk of extinction. Here we describe a simple ecological model with emigration/depletion that shows behavior in contrast to this. This model displays unusual dynamics of extinction and survival, where populations growing beyond a critical rate can persist within a band of high depletion rates, whereas extinction occurs for lower depletion rates. Though prior to extinction at lower depletion rates the population exhibits chaotic dynamics with large amplitudes of variation and very low minima, at higher depletion rates the population persists at chaos but with reduced variation and increased minima. For still higher values, within the band of persistence, the dynamics show period reversal leading to stability. These results illustrate that chaos does not necessarily lead to population extinction. In addition, the persistence of populations at high depletion rates has important implications in the considerations of strategies for the management of biological resources.

The emergence of form by replication

It is shown with a simple mathematical model that if a system exhibits a given form (a spatial structure) and is put in contact with another system of the same type but in a state of spatial disorder, then under certain conditions their mutual interaction as they evolve in time allows replication of form in the disordered system with a controllable degree of faithfulness.

The epidemiology of antibiotic resistance in hospitals: Paradoxes and prescriptions

A simple mathematical model of bacterial transmission within a hospital was used to study the effects of measures to control nosocomial transmission of bacteria and reduce antimicrobial resistance in nosocomial pathogens. The model predicts that: (i) Use of an antibiotic for which resistance is not yet present in a hospital will be positively associated at the individual level (odds ratio) with carriage of bacteria resistant to other antibiotics, but negatively associated at the population level (prevalence). Thus inferences from individual risk factors can yield misleading conclusions about the effect of antibiotic use on resistance to another antibiotic. (ii) Nonspecific interventions that reduce transmission of all bacteria within a hospital will disproportionately reduce the prevalence of colonization with resistant bacteria. (iii) Changes in the prevalence of resistance after a successful intervention will occur on a time scale of weeks to months, considerably faster than in community-acquired infections. Moreover, resistance can decline rapidly in a hospital even if it does not carry a fitness cost. The predictions of the model are compared with those of other models and published data. The implications for resistance control and study design are discussed, along with the limitations and assumptions of the model.

Sensitive detection of DNA polymorphisms by the serial invasive signal amplification reaction

The invasive signal amplification reaction has been previously developed for quantitative detection of nucleic acids and discrimination of single-nucleotide polymorphisms. Here we describe a method that couples two invasive reactions into a serial isothermal homogeneous assay using fluorescence resonance energy transfer detection. The serial version of the assay generates more than 107 reporter molecules for each molecule of target DNA in a 4-h reaction; this sensitivity, coupled with the exquisite specificity of the reaction, is sufficient for direct detection of less than 1,000 target molecules with no prior target amplification. Here we present a kinetic analysis of the parameters affecting signal and background generation in the serial invasive signal amplification reaction and describe a simple kinetic model of the assay. We demonstrate the ability of the assay to detect as few as 600 copies of the methylene tetrahydrofolate reductase gene in samples of human genomic DNA. We also demonstrate the ability of the assay to discriminate single base differences in this gene by using 20 ng of human genomic DNA.

Genetic drift and within-host metapopulation dynamics of HIV-1 infection

Most HIV replication occurs in solid lymphoid tissue, which has prominent architecture at the histological level, which separates groups of productively infected CD4+ cells. Nevertheless, current population models of HIV assume panmixis within lymphoid tissue. We present a simple “metapopulation” model of HIV replication, where the population of infected cells is comprised of a large number of small populations, each of which is established by a few founder viruses and undergoes turnover. To test this model, we analyzed viral genetic variation of infected cell subpopulations within the spleen and demonstrated the action of founder effects as well as significant variation in the extent of genetic differentiation between subpopulations among patients. The combination of founder effects and subpopulation turnover can result in an effective population size much lower than the actual population size and may contribute to the importance of genetic drift in HIV evolution despite a large number of infected cells.

The design of an agent to bend DNA.

An artificial DNA bending agent has been designed to assess helix flexibility over regions as small as a protein binding site. Bending was obtained by linking a pair of 15-base-long triple helix forming oligonucleotides (TFOs) by an adjustable polymeric linker. By design, DNA bending was introduced into the double helix within a 10-bp spacer region positioned between the two sites of 15-base triple helix formation. The existence of this bend has been confirmed by circular permutation and phase-sensitive electrophoresis, and the directionality of the bend has been determined as a compression of the minor helix groove. The magnitude of the resulting duplex bend was found to be dependent on the length of the polymeric linker in a fashion consistent with a simple geometric model. Data suggested that a 50-70 degrees bend was achieved by binding of the TFO chimera with the shortest linker span (18 rotatable bonds). Equilibrium analysis showed that, relative to a chimera which did not bend the duplex, the stability of the triple helix possessing a 50-70 degrees bend was reduced by less than 1 kcal/mol of that of the unbent complex. Based upon this similarity, it is proposed that duplex DNA may be much more flexible with respect to minor groove compression than previously assumed. It is shown that this unusual flexibility is consistent with recent quantitation of protein-induced minor groove bending.

Trypanosome U-deletional RNA editing involves guide RNA-directed endonuclease cleavage, terminal U exonuclease, and RNA ligase activities.

We have studied the mechanism of accurate in vitro RNA editing of Trypanosoma brucei ATPase 6 mRNA, using four mRNA-guide RNA (gRNA) pairs that specify deletion of 2, 3, or 4 U residues at editing site 1 and mitochondrial extract. This extract not only catalyzes deletion of the specified number of U residues but also exhibits a novel endonuclease activity that cleaves the input pre-mRNA in a gRNA-directed manner, precisely at the phosphodiester bond predicted in a simple enzymatic model of RNA editing. This cleavage site is inconsistent with a chimera-based editing mechanism. The U residues to be deleted, present at the 3' end of the upstream cleavage product, are then removed evidently by a 3' U-specific exonuclease and not by a reverse reaction of terminal U transferase. RNA ligase can then join the mRNA halves through their newly formed 5' P and 3' OH termini, generating mRNA faithfully edited at the first editing site. This resultant, partially edited mRNA can then undergo accurate, gRNA-directed cleavage at editing site 2, again precisely as predicted by the enzymatic editing model. All of these enzymatic activities cofractionate with the U-deletion activity and may reside in a single complex. The data imply that each round of editing is a four-step process, involving (i) gRNA-directed cleavage of the pre-mRNA at the bond immediately 5' of the region base paired to the gRNA, (ii) U deletion from or U addition to the 3' OH of the upstream mRNA half, (iii) ligation of the mRNA halves, and (iv) formation of additional base pairing between the correctly edited site and the gRNA that directs subsequent nuclease cleavage at the next editing site.

Evolution as a self-organized critical phenomenon.

We present a simple mathematical model of biological macroevolution. The model describes an ecology of adapting, interacting species. The environment of any given species is affected by other evolving species; hence, it is not constant in time. The ecology as a whole evolves to a "self-organized critical" state where periods of stasis alternate with avalanches of causally connected evolutionary changes. This characteristic behavior of natural history, known as "punctuated equilibrium," thus finds a theoretical explanation as a self-organized critical phenomenon. The evolutionary behavior of single species is intermittent. Also, large bursts of apparently simultaneous evolutionary activity require no external cause. Extinctions of all sizes, including mass extinctions, may be a simple consequence of ecosystem dynamics. Our results are compared with data from the fossil record.

In vivo estimates of division and death rates of human T lymphocytes.

We present data on the decay, after radiotherapy, of naive and memory human T lymphocytes with stable chromosome damage. These data are analyzed in conjunction with existing data on the decay of naive and memory T lymphocytes with unstable chromosome damage and older data on unsorted lymphocytes. The analyses yield in vivo estimates for some life-history parameters of human T lymphocytes. Best estimates of proliferation rates have naive lymphocytes dividing once every 3.5 years and memory lymphocytes dividing once every 22 weeks. It appears that memory lymphocytes can revert to the naive phenotype, but only, on average, after 3.5 years in the memory class. The lymphocytes with stable chromosome damage decay very slowly, yielding surprisingly low estimates of their death rate. The estimated parameters are used in a simple mathematical model of the population dynamics of undamaged naive and memory lymphocytes. We use this model to illustrate that it is possible for the unprimed subset of a constantly stimulated clone to stay small, even when there is a large population of specific primed cells reverting to the unprimed state.

Theory of orientation tuning in visual cortex.

The role of intrinsic cortical connections in processing sensory input and in generating behavioral output is poorly understood. We have examined this issue in the context of the tuning of neuronal responses in cortex to the orientation of a visual stimulus. We analytically study a simple network model that incorporates both orientation-selective input from the lateral geniculate nucleus and orientation-specific cortical interactions. Depending on the model parameters, the network exhibits orientation selectivity that originates from within the cortex, by a symmetry-breaking mechanism. In this case, the width of the orientation tuning can be sharp even if the lateral geniculate nucleus inputs are only weakly anisotropic. By using our model, several experimental consequences of this cortical mechanism of orientation tuning are derived. The tuning width is relatively independent of the contrast and angular anisotropy of the visual stimulus. The transient population response to changing of the stimulus orientation exhibits a slow "virtual rotation." Neuronal cross-correlations exhibit long time tails, the sign of which depends on the preferred orientations of the cells and the stimulus orientation.

Water Deficit and Spatial Pattern of Leaf Development. Variability in Responses Can Be Simulated Using a Simple Model of Leaf Development1

We analyzed the effect of short-term water deficits at different periods of sunflower (Helianthus annuus L.) leaf development on the spatial and temporal patterns of tissue expansion and epidermal cell division. Six water-deficit periods were imposed with similar and constant values of soil water content, predawn leaf water potential and [ABA] in the xylem sap, and with negligible reduction of the rate of photosynthesis. Water deficit did not affect the duration of expansion and division. Regardless of their timing, deficits reduced relative expansion rate by 36% and relative cell division rate by 39% (cells blocked at the G0-G1 phase) in all positions within the leaf. However, reductions in final leaf area and cell number in a given zone of the leaf largely differed with the timing of deficit, with a maximum effect for earliest deficits. Individual cell area was only affected during the periods when division slowed down. These behaviors could be simulated in all leaf zones and for all timings by assuming that water deficit affects relative cell division rate and relative expansion rate independently, and that leaf development in each zone follows a stable three-phase pattern in which duration of each phase is stable if expressed in thermal time (C. Granier and F. Tardieu [1998b] Plant Cell Environ 21: 695–703).

Simple model of protein folding kinetics.

A simple model of the kinetics of protein folding is presented. The reaction coordinate is the "correctness" of a configuration compared with the native state. The model has a gap in the energy spectrum, a large configurational entropy, a free energy barrier between folded and partially folded states, and a good thermodynamic folding transition. Folding kinetics is described by a master equation. The folding time is estimated by means of a local thermodynamic equilibrium assumption and then is calculated both numerically and analytically by solving the master equation. The folding time has a maximum near the folding transition temperature and can have a minimum at a lower temperature.

Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

The present study explores a “hydrophobic” energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its “hydrophobicity” and the number of contacts it makes, i.e., E(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.

A simple explanation for taxon abundance patterns

For taxonomic levels higher than species, the abundance distributions of the number of subtaxa per taxon tend to approximate power laws but often show strong deviations from such laws. Previously, these deviations were attributed to finite-time effects in a continuous-time branching process at the generic level. Instead, we describe herein a simple discrete branching process that generates the observed distributions and find that the distribution's deviation from power law form is not caused by disequilibration, but rather that it is time independent and determined by the evolutionary properties of the taxa of interest. Our model predicts—with no free parameters—the rank-frequency distribution of the number of families in fossil marine animal orders obtained from the fossil record. We find that near power law distributions are statistically almost inevitable for taxa higher than species. The branching model also sheds light on species-abundance patterns, as well as on links between evolutionary processes, self-organized criticality, and fractals.