On an unbiased and consistent estimator for mutation rates

Niccum, Brittany A.; Poteau, Roby; Hamman, Glen E.; Varada, Jan C.; Dshalalow, Jewgeni H.; Sinden, Richard R.

doi:10.1016/j.jtbi.2012.01.029

Cited by 8 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Having identified the number of isolated genetic changes present in each clone, we calculated the mutation rate per base pair per generation based on the number of mutations detected within each clone and the total time in culture for each clone (Figure 1 and Figure 2) [19], [20]. To accurately calculate the mutation rate, we needed to include not only the observed SNVs but also those SNVs that were lethal/deleterious, which were unobserved due to loss of mutants from the population.…”

Section: Resultsmentioning

confidence: 99%

“…The number of dilutions would affect the mutation rate if we were calculating the rate using the fraction of mutants observed after culturing, because population bottlenecks may increase the variance of the fraction of mutants. Calculating the mutation rate from the proportion of mutants versus wild type organisms after parallel culturing is known as the ‘mutation rate problem’ [20] and the experiments used to calculate these rates are called fluctuation tests. However, we avoid these issues by calculating rates from continuous cultures after correcting for selection pressure [61], [62].…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Mitotic Evolution of Plasmodium falciparum Shows a Stable Core Genome but Recombination in Antigen Families

et al. 2013

View full text Add to dashboard Cite

Malaria parasites elude eradication attempts both within the human host and across nations. At the individual level, parasites evade the host immune responses through antigenic variation. At the global level, parasites escape drug pressure through single nucleotide variants and gene copy amplification events conferring drug resistance. Despite their importance to global health, the rates at which these genomic alterations emerge have not been determined. We studied the complete genomes of different Plasmodium falciparum clones that had been propagated asexually over one year in the presence and absence of drug pressure. A combination of whole-genome microarray analysis and next-generation deep resequencing (totaling 14 terabases) revealed a stable core genome with only 38 novel single nucleotide variants appearing in seventeen evolved clones (avg. 5.4 per clone). In clones exposed to atovaquone, we found cytochrome b mutations as well as an amplification event encompassing the P. falciparum multidrug resistance associated protein (mrp1) on chromosome 1. We observed 18 large-scale (>1 kb on average) deletions of telomere-proximal regions encoding multigene families, involved in immune evasion (9.5×10−6 structural variants per base pair per generation). Six of these deletions were associated with chromosomal crossovers generated during mitosis. We found only minor differences in rates between genetically distinct strains and between parasites cultured in the presence or absence of drug. Using these derived mutation rates for P. falciparum (1.0–9.7×10−9 mutations per base pair per generation), we can now model the frequency at which drug or immune resistance alleles will emerge under a well-defined set of assumptions. Further, the detection of mitotic recombination events in var gene families illustrates how multigene families can arise and change over time in P. falciparum. These results will help improve our understanding of how P. falciparum evolves to evade control efforts within both the individual hosts and large populations.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Mitotic Evolution of Plasmodium falciparum Shows a Stable Core Genome but Recombination in Antigen Families

et al. 2013

View full text Add to dashboard Cite

show abstract

“…We note that, different from the LD distribution-based estimation methods which focus on the number of mutants up to a time point t ¼ log ðn=n 0 Þ=β 1 , the sufficient statistic for this estimation is the number of nonmutant cells as well as the number of overall cells. Several recent mutation rate estimators have been developed using these two counts (Xiong et al, 2009;Niccum et al, 2012). However, they are mostly based on the method of moment (MOM) thus cannot incorporate all information from the nonmutant-count distribution.…”

Section: The Birth-death Process Model and Distribution Of Nonmutant mentioning

confidence: 99%

Fast maximum likelihood estimation of mutation rates using a birth–death process

Zhu

2015

Journal of Theoretical Biology

View full text Add to dashboard Cite

“…The answer led to a rich mathematical theory, with important applications in the calculation of mutation rates [2], the emergence of antibiotic-resistant microbes [3], the study of drug therapyresistant cancer cells [4,5] and cancer genetics [6,7]. Theoretical advances includude the analysis of the probability distributions [8,9], asymptotic properties [10], numerical methods for fluctuation analysis [11], and the accuracy of estimates for the mutation rates [12]. Extensions of the theory include different cell cycle distributions and growth laws of wild type cells [13,14].…”

Section: Introductionmentioning

confidence: 99%

Cellular replication limits in the Luria–Delbrück mutation model

Rodriguez-Brenes

Wodarz

Komarova

2016

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

In this appendix reference to equations that appear in the main text are labeled with arabic numerals, e.g. (1). Equations that appear in this appendix are labelled with the letter "A" followed by an arabic numeral, e.g. (A1). Cellular replication limitsProposition S1. "If the x j (t) are defined by system [1], x k (0) = 1, and x j (0) = 0 for j < k, then ."Proof: From [1] we haveẋ j = 2q x j+1 − x j . Hence, using the initial conditions and integration by parts we find: x j (t) = e −t t 0 2q x j+1 (s) e s ds for 0 < j < k, and x 0 (t) = e (q−1)t t 0 2q x 1 (s)e (1−q)s ds. Given that x k (t) = e −t we can prove by induction that x j (t) = e −t (2qt) k−j (k−j)! for j > 0 and x 0 (t) = 2 k e −t ∞ n=k (qt) n n! . The total cell population X tot (t; q) = k ρ=0 x ρ (t) is then given by:Luria-Delbrück formulation where ψ(z; t, s) = e ize γ(t−s) . Let f (s, z) and g(s) be two functions with continuous second order partial derivates, then:If we make f (s, z) = e ize γ(t−s) −1, we have f (s, 0) = 0 and ∂f (s,0) ∂z = ie γ(t−s) . If we also make g(s) = νX(s), then from the integral expression for Ψ and [A2] we find:Proposition S3. "In the Luria-Delbruck formulation, when the wild type population is modeled with Eq. 3, we have:Proof: Substituting Eq. 3 in the article for X(s) in [A3] we have:For the special case where the growth rate of both populations are equal (γ = 2q − 1), integrating [A6] and simplifying we find [A4]. Expressions of the form e ax Γ(k, bx)dx will show often in our calculations. If a = b, a closed expression for this antiderivative can be found using integration by parts and the fact thatWe can use [A7] to find E[Y (t)] wl when γ = 2q − 1. In this case E(Y (t)) wl is given by Eq. A5.Proposition 4. "In the Luria-Delbruck formulation, when the wild type population is modeled with Eq. 3, we have:(2γ = 2q − 1)Proof: From [5] the characteristic function of the number of mutants Ψ(z; t) = expwhere ψ(z; t, s) = e ize γ(t−s) . Let f (s, z) and g(s) be two functions with continuous second order partial derivates, then:If we make again g(s) = νX(s) and f (s, z) = e ize γ(t−s) − 1, then= −e 2γ(t−s) , and substituting this expression into (A9) we find: Proof: I. From the introduction in the article of the Lea-Coulson formulation, the probability generation function of the number of mutants Y (t) equals:where φ(z; t, s) is given by [19]. ) + E[Y (t)] − E[Y (t)]2 . Again making g(s) = νX(s) and f (s, z) = φ(z; t, s) − 1 and using equations [A2] and [A9], we find:Substituting γ by α−β in Eqs. A3 and A10. It follows that the integrand in [A15] equals E[Y (t)]−V[Y (t)](LD), a n (t, s)z n is the power series representation of φ(z; t, s)−1 centered around z = 0, and X(s) is given by [3], then t 0 νX(s) a n (t, s)z n ds = t 0 νX(s)a n (t, s)z n ds."Proof: The interchange is licit when the growth of the wild type population is exponential, i.e. when X(t) = e δt for any δ > 0 (reference [?]). Hence, since X(t;q) ≤ e (2q−1)t , it follows directly from the dominated convergence theorem that the interchange is also licit when t...

show abstract

On an unbiased and consistent estimator for mutation rates

Cited by 8 publications

References 24 publications

Mitotic Evolution of Plasmodium falciparum Shows a Stable Core Genome but Recombination in Antigen Families

Mitotic Evolution of Plasmodium falciparum Shows a Stable Core Genome but Recombination in Antigen Families

Fast maximum likelihood estimation of mutation rates using a birth–death process

Cellular replication limits in the Luria–Delbrück mutation model

Contact Info

Product

Resources

About