Stochastic models for subpopulation emergence in heterogeneous tumors

A stochastic analog to a deterministic model describing subpopulation emergence in heterogeneous tumors is developed. The resulting system is described by the Fokker-Planck or forward Kolmogorov equation. A finite element approach for the numerical solution to this equation is described. Four biological and clinical scenarios are simulated (emergence of heterogeneity, exclusion of a subpopulation, and induction of drug resistance in both pure and heterogeneous tumors). The results of the simulations show that the stochastic model describes the same basic dynamics as its deterministic counterpart via a convective component, but that for each simulation a distribution of tumor sizes and mixes can also be derived from a diffusive component in the model. These distributions yield estimates for subpopulation extinction probabilities. The biological and clinical relevance of these results are discussed. Research support provided in part by ACS Grant IN45-Z and ACS PDT 243 B. Research support provided in part by the National Science Foundation under NSF Grant MCS-8504316, and by the Air Force Office of Scientific Research under Contract F49620-86-C-0111.     

Adaptation of Spirogyra insignis (Chlorophyta) to an extreme natural environment (sulphureous waters) through preselective mutations

Adaptation of Spirogyra insignis (Chlorophyceae) to growth and survival in an extreme natural environment (sulphureous waters from La Hedionda Spa, S. Spain) was analysed by using an experimental model. Photosynthesis and growth of the alga were inhibited when it was cultured in La Hedionda Spa waters (LHW), but after further incubation for several weeks, the culture survived due to the growth of a variant that was resistant to LHW. A Luria-Delbruck fluctuation analysis was carried out to distinguish between resistant filaments arising from rare spontaneous mutations and resistant filaments arising from other mechanisms of adaptation. It was demonstrated that the resistant filaments arose randomly by rare spontaneous mutations before the addition of LHW (preselective mutations). The rate of spontaneous mutation from sensitivity to resistance was 2.7 x 10(-7) mutants per cell division. Since LHW(resistant) mutants have a diminished growth rate, they are maintained in nonsulphureous natural waters as the result of a balance between new resistants arising from spontaneous mutation and resistants eliminated by natural selection. Thus, recurrence of rare spontaneous preselective mutations ensures the survival of the alga in sulphureous waters.     

Resistance to glyphosate in the cyanobacterium <Emphasis Type="Italic">Microcystis aeruginosa</Emphasis> as result of pre-selective mutations

Adaptation of Microcystis aeruginosa (Cyanobacteria) to resist the herbicide glyphosate was analysed by using an experimental model. Growth of wild-type, glyphosate-sensitive (G^s) cells was inhibited when they were cultured with 120 ppm glyphosate, but after further incubation for several weeks, occasionally the growth of rare cells resistant (G^r) to the herbicide was found. A fluctuation analysis was carried out to distinguish between resistant cells arising from rare spontaneous mutations and resistant cells arising from other mechanisms of adaptation. Resistant cells arose by rare spontaneous mutations prior to the addition of glyphosate, with a rate ranging from 3.1 × 10⁻⁷ to 3.6 × 10⁻⁷ mutants per cell per generation in two strains of M. aeruginosa; the frequency of the G^r allele ranged from 6.14 × 10⁻⁴ to 6.54 × 10⁻⁴. The G^r mutants are slightly elliptical in outline, whereas the G^s cells are spherical. Since G^r mutants have a diminished growth rate, they may be maintained in uncontaminated waters as the result of a balance between new resistants arising from spontaneous mutation and resistants eliminated by natural selection. Thus, rare spontaneous pre-selective mutations may allow the survival of M. aeruginosa in glyphosate-polluted waters via G^r clone selection.     

Ultraviolet mutagenesis and genetic analysis of resistance to methylglyoxal-bis (guanylhydrazone) in tobacco

Summary We have isolated cell lines of Nicotiana tabacum resistant to methylglyoxal-bis(guanylhydrazone) (MGBG), a potent inhibitor of S-adenosylmethionine decarboxylase. We obtained 31 resistant lines from ultraviolet light mutagenized cultures, representing at least 13 independent events. No resistant lines were obtained from non-mutagenized control cultures. The increase in mutation rate due to the ultraviolet light treatment was 22 to 62 fold increased over an estimate of the maximum possible spontaneous rate. In reconstruction experiments we reselected resistant cell lines from varying dilutions into a background of a constant concentration of wild type cells; at the minimum ratio of resistant cells to wild type cells, 1:125,000, we recovered resistant colonies at an estimated plating efficiency of 12.5%. A number of resistant lines have been regenerated into plants. All of the ones that flowered are male sterile, sometimes associated with morphological transformations. Some are female sterile as well. Meiotic genetic analysis of one resistant line, Mgr12, suggests that the MGBG resistance is segregating as a nuclear dominant trait. The male sterility and abnormal floral development of Mgr12 cosegregate with the MGBG resistance, suggesting the two phenotypes are coincident.     

On the Origin of Mitochondrial Mutants: Evidence for Intracellular Selection of Mitochondria in the Origin of Antibiotic-Resistant Cells in Yeast

In wild-type Saccharomyces cerevisiae, erythromycin and certain other antibacterial antibiotics inhibit the formation of respiratory enzymes in mitochondria by inhibiting translation on mitochondrial ribosomes. This paper is concerned with the origin of mutant cells, resistant to erythromycin by virtue of having a homogeneous population of mutant mitochondrial DNA molecules. Such mutant cells are obtained by plating wild-type (sensitive) cells on a nonfermentable substrate plus the antibiotic. Colonies of mutant cells appear first about four days after the time of appearance of established mutant cells; new colonies continue to appear, often at a constant rate, for many days. Application of the Newcombe respreading experiment demonstrates that most or all of the mutant cells which form the resistant colonies on selective medium arise only after exposure of the population to erythromycin. It is suggested that this result is most probably due to intracellular selection for mitochondrial genomes. Resistant mitochondria arising from spontaneous mutation are postulated to be at a selective disadvantage in the absence of erythromycin; reproducing more slowly than wild-type sensitive mitochondria, they cannot easily accumulate in sufficient numbers in a cell to render it resistant as a whole. In the presence of erythromycin, resistant mitochondria can continue to reproduce while sensitive mitochondria cannot, until there is a sufficient number to make the cell resistant, i.e. to permit normal cell growth. The same phenomenon is seen with respect to chloramphenicol resistance. Intracellular selection is considered more likely than direct induction of mutation by the antibiotic, since mutant cells do not accumulate in the presence of erythromycin if the mitochondrial genome is rendered non-essential by growth on glucose or nontranslatable by chloramphenicol. Intra-cellular selection provides a mechanism for direct adaptation at the cell level, compatible with currently acceptable ideas of spontaneous mutation and selection at the organelle level.     

Mitogen‐activated protein kinase 3 and 6 regulate Botrytis cinerea‐induced ethylene production in Arabidopsis

Plants challenged by pathogens, especially necrotrophic fungi such as Botrytis cinerea, produce high levels of ethylene. At present, the signaling pathways underlying the induction of ethylene after pathogen infection are largely unknown. MPK6, an Arabidopsis stress‐responsive mitogen‐activated protein kinase (MAPK) was previously shown to regulate the stability of ACS2 and ACS6, two type I ACS isozymes (1‐amino‐cyclopropane‐1‐carboxylic acid synthase). Phosphorylation of ACS2 and ACS6 by MPK6 prevents rapid degradation of ACS2/ACS6 by the 26S proteasome pathway, resulting in an increase in cellular ACS activity and ethylene biosynthesis. Here, we show that MPK3, which shares high homology and common upstream MAPK kinases with MPK6, is also capable of phosphorylating ACS2 and ACS6. In the mpk3 mutant background, ethylene production in gain‐of‐function GVG‐NtMEK2^DD transgenic plants was compromised, suggesting that MPK6 and MPK3 function together to stabilize ACS2 and ACS6. Using a liquid‐cultured seedling system, we found that B. cinerea‐induced ethylene biosynthesis was greatly compromised in mpk3/mpk6 double mutant seedlings. In contrast, ethylene production decreased only slightly in the mpk6 single mutant and not at all in the mpk3 single mutant, demonstrating overlapping roles for these two highly homologous MAPKs in pathogen‐induced ethylene induction. Consistent with the role of MPK3/MPK6 in the process, mutation of ACS2 and ACS6, two genes encoding downstream substrates of MPK3/MPK6, also reduced B. cinerea‐induced ethylene production. The residual levels of ethylene induction in the acs2/acs6 double mutant suggest the involvement of additional ACS isoforms, possibly regulated by MAPK‐independent pathway(s).     

A Population Genetic Model for the Initial Spread of Partially Resistant Malaria Parasites under Anti-Malarial Combination Therapy and Weak Intrahost Competition

To develop public-health policies that extend the lifespan of affordable anti-malarial drugs as effective treatment options, it is necessary to understand the evolutionary processes leading to the origin and spread of mutations conferring drug resistance in malarial parasites. We built a population-genetic model for the emergence of resistance under combination drug therapy. Reproductive cycles of parasites are specified by their absolute fitness determined by clinical parameters, thus coupling the evolutionary-genetic with population-dynamic processes. Initial mutations confer only partial drug-resistance. Therefore, mutant parasites rarely survive combination therapy and within-host competition is very weak among parasites. The model focuses on the early phase of such unsuccessful recurrent mutations. This ends in the rare event of mutants enriching in an infected individual from which the successful spread of resistance over the entire population is initiated. By computer simulations, the waiting time until the establishment of resistant parasites is analysed. Resistance spreads quickly following the first appearance of a host infected predominantly by mutant parasites. This occurs either through a rare transmission of a resistant parasite to an uninfected host or through a rare failure of drugs in removing “transient” mutant alleles. The emergence of resistance is delayed with lower mutation rate, earlier treatment, higher metabolic cost of resistance, longer duration of high drug dose, and higher drug efficacy causing a stronger reduction in the sensitive and resistant parasites’ fitnesses. Overall, contrary to other studies’ proposition, the current model based on absolute fitness suggests that aggressive drug treatment delays the emergence of drug resistance.     

MIRACH: efficient model checker for quantitative biological pathway models

Model checking is playing an increasingly important role in systems biology as larger and more complex biological pathways are being modeled. In this article we report the release of an efficient model checker MIRACH 1.0, which supports any model written in popular formats such as CSML and SBML. MIRACH is integrated with a Petri-net-based simulation engine, enabling efficient online (on-the-fly) checking. In our experiment, by using Levchenko et al. model, we reveal that timesaving gains by using MIRACH easily surpass 400% compared with its offline-based counterpart. AVAILABILITY AND IMPLEMENTATION: MIRACH 1.0 was developed using Java and thus executable on any platform installed with JDK 6.0 (not JRE 6.0) or later. MIRACH 1.0, along with its source codes, documentation and examples are available at http://sourceforge.net/projects/mirach/ under the LGPLv3 license.     

Mutation-selection equilibrium as a possible cause of an interchange chromosome polymorphism in a cultivar of rye,Secale cereale L.

Summary A persistent chromosomal polymorphism exists in a population of cultivated rye, Secale cereale (Candela et al. 1979). In order to ascertain the possible causes that maintain it, we have estimated the fitness values of structurally homozygous and heterozygous plants and the mutation rate of spontaneous interchange. The estimates of the selection coefficient against heterozygotes (s=0.15-0.40) and of the mutation rate u=6.12×10^–2 support a mutation-selection equilibrium as a likely cause of the interchange chromosome polymorphism.     

Fractionation of RNA from tetrahymena by affinity chromatography on poly-u-sepharose

Summary Exponential growing Tetrahymena pyriformis organisms were labelled with (³H) uridine or (³H) adenosine. The labelled RNA was extracted and isolated by affinity chromatography on poly-uridylic-acid Sepharose and further analysed by means of sucrose gradient centrifugation and RNase digestion.Experimental evidence proved the existence of RNase resistant poly adenylic-acid fragments in the RNA of Tetrahymena cells. This poly adenylic-acid segment has a sedimentation rate of 4-5 S and would be localised in the 10-12S region of the RNA which is probably the m-RNA.Supported by Stiftung Volkswagenwerk Research Grant No.112273.     

A simple procedure for joint estimation of the long‐term rates of sexuality and mutation in predominantly clonal populations,for use with dominant molecular markers

In highly clonal populations, mutation can contribute to the rate of apparent sexuality. To remove this bias, a method is presented that jointly estimates the rates of sexuality (Ns) and mutation (Nµ) for populations, based upon levels of single‐locus vs. multilocus clonal identity. This effectively haploid model assumes equilibrium, and can be used with dominant molecular data and in conjunction with organisms of various ploidies. Simulations indicate that while equilibrium can take thousands of generations to attain, and afterwards have a large evolutionary variance, the method gives approximate estimates of Ns.     

Short-term adaptation of microalgae in highly stressful environments: an experimental model analysing the resistance of Scenedesmus intermedius (Chlorophyceae) to the heavy metals mixture from the Aznalcóllar mine spill

The toxic spill of acid wastes rich in heavy metals/metalloids (AWHM) from the Aznalcóllar mine in April 1998, threatening the Doñana National Park, is considered to be the worst environmental disaster related to acute pollution in Spanish history. The aim of this work was to study the adaptation of microalgae (which play an important role as primary producers) from AWHM sensitivity to AWHM resistance by using the alga Scenedesmus intermedius as an experimental model. The Malthusian parameter (m) and the carrying capacity (K) were reduced by mud and soil samples collected from the affected area. A dose–effect analysis showed that fitness progressively diminished with increasing sample concentration. A fluctuation analysis demonstrated that AWHM-resistant cells arose by rare spontaneous mutations that occurred randomly prior to the incorporation of the AWHM. The rate of spontaneous mutation from AWHM sensitivity to AWHM resistance was 2·12×10^?5 mutants per cell division. A competition experiment between wild-type AWHM-sensitive cells and AWHM-resistant mutants showed that in small populations the AWHM-resistant mutants are driven to extinction in the absence of selection for AWHM resistance. The resistant phenotypes are maintained in the absence of AWHM as the result of a balance between spontaneous mutation and natural selection, so that about 43 AWHM-resistant mutants per million cells are present in the absence of AWHM. Our experimental model suggests that mutation is essential for adaptation of microalgal populations to environmental changes. Rare spontaneous pre-adaptive mutation is enough to ensure the survival of microalgal populations in contaminated environments when the population size is large enough.     

Adaptive Resistance Mutations at Suprainhibitory Concentrations Independent of SOS Mutagenesis

Emergence of resistant bacteria during antimicrobial treatment is one of the most critical and universal health threats. It is known that several stress-induced mutagenesis and heteroresistance mechanisms can enhance microbial adaptation to antibiotics. Here, we demonstrate that the pathogen Bartonella can undergo stress-induced mutagenesis despite the fact it lacks error-prone polymerases, the rpoS gene and functional UV-induced mutagenesis. We demonstrate that Bartonella acquire de novo single mutations during rifampicin exposure at suprainhibitory concentrations at a much higher rate than expected from spontaneous fluctuations. This is while exhibiting a minimal heteroresistance capacity. The emerged resistant mutants acquired a single rpoB mutation, whereas no other mutations were found in their whole genome. Interestingly, the emergence of resistance in Bartonella occurred only during gradual exposure to the antibiotic, indicating that Bartonella sense and react to the changing environment. Using a mathematical model, we demonstrated that, to reproduce the experimental results, mutation rates should be transiently increased over 1,000-folds, and a larger population size or greater heteroresistance capacity is required. RNA expression analysis suggests that the increased mutation rate is due to downregulation of key DNA repair genes (mutS, mutY, and recA), associated with DNA breaks caused by massive prophage inductions. These results provide new evidence of the hazard of antibiotic overuse in medicine and agriculture.     

Role of ribosomes in cycloheximide resistance of Neurospora mutants

Summary In Neurospora crassa, mutants resistant against cycloheximide appear with a marked time lag after mutation induction. We have suggested (Neuhäuser et al., 1970) that this lag indicates the time needed for the synthesis of altered ribosomes (phenotypic lag), that the drug in the wildtype acts upon the ribosomes, and that resistance is due to alterations in them.By measurements of poly-U directed poly-Phe synthesis on ribosomes of the wildtype and two different cycloheximide resistant mutants in a cell free system it is shown here that mutant ribosomes indeed differ from those of the wildtype. Poly-Phe synthesis on mutant ribosomes proceeds in the presence of the drug, whereas that on wildtype ribosomes is inhibited. This means that the earlier suggestions are correct.Abbreviation CHX cycloheximide     

Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models.

The emergence of antibiotic resistance in a wide variety of important pathogens of humans presents a worldwide threat to public health. This paper describes recent work on the use of mathematical models of the emergence and spread of resistance bacteria, on scales ranging from within the patient, in hospitals and within communities of people. Model development starts within the treated patient, and pharmacokinetic and pharmacodynamic principles are melded within a framework that mirrors the interaction between bacterial population growth, drug treatment and the immunological responses targeted at the pathogen. The model helps identify areas in which more precise information is needed, particularly in the context of how drugs influence pathogen birth and death rates (pharmacodynamics). The next area addressed is the spread of multiply drug-resistant bacteria in hospital settings. Models of the transmission dynamics of the pathogen provide a framework for assessing the relative merits of different forms of intervention, and provide criteria for control or eradication. The model is applied to the spread of vancomycin-resistant enterococci in an intensive care setting. This model framework is generalized to consider the spread of resistant organisms between hospitals. The model framework allows for heterogeneity in hospital size and highlights the importance of large hospitals in the maintenance of resistant organisms within a defined country. The spread of methicillin resistant Staphylococcus aureus (MRSA) in England and Wales provides a template for model construction and analysis. The final section addresses the emergence and spread of resistant organisms in communities of people and the dependence on the intensity of selection as measured by the volume or rate of drug use. Model output is fitted to data for Finland and Iceland and conclusions drawn concerning the key factors determining the rate of spread and decay once drug pressure is relaxed.     

On visual adaptation: II. The electroretinogram and the bipolar cells

First a model for theb-wave of the electroretinogram is given. The essential part of the model is the diffusion into the rod-bipolar synapse of a transmitter substance, followed by the induction of an inhibitor. Making use of this model, adaptation to an illumination too weak to cause of significant decrease in the concentration of visual pigment is interpreted as due to a decreased effectiveness of the rod impulse in exciting the bipolar cell. The disparity between threshold changes for very small test spots and for relatively large spots is explained simply, without invoking any additional physiological mechanisms. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF(638)-414 and in part by the United States Public Health Service Training Grant 2G-833.     

Convergence of one-dimensional diffusion processes to a jump process related to population genetics

A conjecture on the convergence of diffusion models in population genetics to a simple Markov chain model is proved. The notion of bi-generalized diffusion processes and their limit theorems are used systematically to prove the conjecture. Three limits; strong selection-weak mutation limit, moderate selection-weak mutation limit, weak selection-weak mutation limit are considered for typical diffusion models in population genetics.Supported in part by Research Grant from the Ministry of Education, Science and Culture of JapanSupported by the Air Force Office of Scientific Research Contract No. F49620 85C 0144     

The mutagenic effect of gamma rays on leaf protoplasts of haploid and dihaploid Nicotiana plumbaginifolia,estimated by valine resistance mutation frequencies

Summary Leaf protoplasts isolated from haploid and dihaploid Nicotiana plumbaginifolia plantlets were treated with different doses of gamma-rays and their survival was determined by scoring for plating efficiency at each irradiation dose. A fixed number of surviving protoplast-derived colonies was then plated in the presence of inhibitory concentrations of L-valine and incubated until growing resistant calli could be scored and mutation rates calculated. Though haploid protoplasts were found to be a little more sensitive than dihaploids to the lethal effect of radiation, the two dose-response curves of gamma-rays that induced mutagenesis were very similar. The irradiation dose capable of causing a ten-fold increase of spontaneous mutation frequencies was about 500 rads with both haploid and dihaploid protoplasts.Contribution No. 2173 of the Biology Radiation Protection and Medical Research Programme, Directorate General XII of the Commission of the European Communities