scholarly journals THE PROPORTION OF MUTANTS IN BACTERIAL CULTURES

1957 ◽  
Vol 41 (1) ◽  
pp. 119-129 ◽  
Author(s):  
John H. Northrop ◽  
M. Kunitz
Keyword(s):  
Growth Rate ◽  
Mutation Rate ◽  
Rate Constant ◽  
Growth Rates ◽  
Mutation Frequency ◽  
Growth Rate Constant ◽  
Bacterial Cultures ◽  
Frequency Rate ◽  
Back Mutation ◽  
Mutant Cells

The proportion of mutants in a growing culture of organisms will depend upon (a) the rate at which the wild cells produce them (with or without growth), (b) the back mutation rate, and (c) the growth rates of the wild and mutant cells. If the mutation rate without growth and the back mutation rate are neglected, the growth of a mutant is expressed by See PDF for Equation and the ratio of the mutant to wild by See PDF for Equation in which λ = mutation frequency rate constant, "mutation rate," A = growth rate constant of wild cells W, B = growth rate constant of mutant cells M. If the term [B – (1 – 2λ)A] is positive, the proportion of mutants increases continuously. If it is negative, the proportion of mutants reaches a constant value See PDF for Equation If mutation is assumed to occur without growth at the rate C, then the corresponding equations are (11), (12), and (14). See PDF for Equation If (B + C – A) is negative and t = ∞, See PDF for Equation If C << A, See PDF for Equation

scholarly journals THE PROPORTION OF TERRAMYCIN-RESISTANT MUTANTS IN B. MEGATHERIUM CULTURES

1957 ◽  
Vol 41 (1) ◽  
pp. 131-141 ◽  
Author(s):  
John H. Northrop ◽  
Keyword(s):  
Growth Rate ◽  
Mutation Rate ◽  
Rate Constant ◽  
Growth Rate Constant ◽  
Resistant Mutants ◽  
Mutant Cells ◽  
Fraction Method

The number of terramycin-resistant mutants in Bacillus megatherium cultures, their mutation rate, and the growth rate of the wild and mutant cells have been determined under various conditions. These values are in agreement with the following equations (Northrop and Kunitz, 1957):— See PDF for Equation λ = mutation rate, A = growth rate constant of wild cells, B = growth rate constant of mutants, See PDF for Equation equilibrium. The value of the mutation rate as determined from equation (6) agrees with that found by the null fraction method.

scholarly journals STUDIES ON THE ORIGIN OF BACTERIAL VIRUSES

1958 ◽  
Vol 42 (2) ◽  
pp. 329-334 ◽  
Author(s):  
John H. Northrop ◽  
Keyword(s):  
Growth Rate ◽  
Temperature Coefficient ◽  
Rate Constant ◽  
Growth Rates ◽  
Rate Constants ◽  
Mutation Frequency ◽  
Burst Size ◽  
Time Rate ◽  
Frequency Rate ◽  
Bacterial Viruses

The growth rates, the mutation frequency rate constants of the terramycin-resistant cells, the burst size of the phage-producing cells, and the ratio of phage to cells all have a temperature coefficient of about 2 from 20 to 35° (µ = 9 x 103 calories), with a maximum at 40°. The mutation frequency rate constant (or time rate constant) of the phage-producing cells increases from 20 to 45° with a temperature coefficient of about 3 (µ = 2 to 3 x 104 cal.). The change in the values for the growth rate, mutation rate, and cell volume occurs in less than 1 hour, after the temperature is changed. The value for the burst size of phage-producing cells changes for 3 to 4 hours. Prolonged growth of megatherium 899 at 48 to 50° results in the production of C + S phage, in place of T. Returning the culture to 25° results in the production of small T phage.

A population birth-and-mutation process, I: explicit distributions for the number of mutants in an old culture of bacteria

1974 ◽  
Vol 11 (03) ◽  
pp. 437-444 ◽  
Author(s):  
Benoit Mandelbrot
Keyword(s):  
Growth Rate ◽  
Mutation Rate ◽  
Growth Rates ◽  
Random Variable ◽  
Mutation Process ◽  
Limit Condition ◽  
Rate Of Growth ◽  
Mathematical Techniques ◽  
First Time

Luria and Delbrück (1943) have observed that, in old cultures of bacteria that have mutated at random, the distribution of the number of mutants is extremely long-tailed. In this note, this distribution will be derived (for the first time) exactly and explicitly. The rates of mutation will be allowed to be either positive or infinitesimal, and the rate of growth for mutants will be allowed to be either equal, greater or smaller than for non-mutants. Under the realistic limit condition of a very low mutation rate, the number of mutants is shown to be a stable-Lévy (sometimes called “Pareto Lévy”) random variable, of maximum skewness ß, whose exponent α is essentially the ratio of the growth rates of non-mutants and of mutants. Thus, the probability of the number of mutants exceeding the very large value m is proportional to m –α–1 (a behavior sometimes referred to as “asymptotically Paretian” or “hyperbolic”). The unequal growth rate cases α ≠ 1 are solved for the first time. In the α = 1 case, a result of Lea and Coulson is rederived, interpreted, and generalized. Various paradoxes involving divergent moments that were encountered in earlier approaches are either absent or fully explainable. The mathematical techniques used being standard, they will not be described in detail, so this note will be primarily a collection of results. However, the justification for deriving them lies in their use in biology, and the mathematically unexperienced biologists may be unfamiliar with the tools used. They may wish for more details of calculations, more explanations and Figures. To satisfy their needs, a report available from the author upon request has been prepared. It will be referred to as Part II.

Growth Rates of Cranes Reared in Captivity

The Auk ◽  
1986 ◽  
Vol 103 (1) ◽  
pp. 125-134 ◽  
Author(s):  
Robert E. Ricklefs ◽  
Donald F. Bruning ◽  
George W. Archibald
Keyword(s):  
Growth Rate ◽  
Incubation Period ◽  
Rate Constant ◽  
Bird Species ◽  
Growth Rate Constant ◽  
Egg Mass ◽  
In Captivity ◽  
Altricial Birds ◽  
Adult Mass ◽  
Rates Of Growth

Abstract We measured eggs, incubation periods, growth of chicks, and masses of adults of 10 species of cranes at the Bronx Zoo and the International Crane Foundation. Growth rate constants of Gompertz equations fitted to the data varied between 0.034 and 0.057/day. These values were 50-90% of those for altricial birds of comparable adult mass, and were considerably greater than those of other precocial species, such as galliforms. Rates of growth intermediate between altricial and precocial species are consistent with the fact that crane chicks, although precocial, are brooded and fed by their parents during much of the early development period. Within species, asymptote (A) and growth-rate constant (K) of the Gompertz equations were negatively correlated, owing to their inherent relationship in the curve-fitting process. Masses of chicks during the first month after hatch were unrelated to the mass asymptote, but correlated strongly with the estimated growth-rate constant. The mass of the neonate was about 60% of the fresh mass of the egg. Egg mass was unrelated to subsequent chick mass during the first month, but correlated with the mass asymptote in two species when the relationship between A and K was accounted for statistically. Egg mass also was correlated with incubation period, fledging period, and the growthrate constant in isolated instances. Growth rate and asymptote among species were inversely related, as found among large samples of diverse bird species. The size of the egg relative to the mass of the adult was related inversely to adult mass, again consistent with patterns in other groups of birds. Fledging period was related strongly to the length of the incubation period and weakly to the asymptote to the growth curve, and it was unrelated to growth-rate constant of the Gompertz equation.

Tumor regression and growth rates determined in two intramural NCI prostate cancer trials: The growth rate constant as an indicator of therapeutic efficacy.

2012 ◽  
Vol 30 (5_suppl) ◽  
pp. 133-133
Author(s):  
Bamidele Adesunloye ◽  
Wilfred Donald Stein ◽  
Julia Wilkerson ◽  
Xuan Huang ◽  
Fatima H Karzai ◽  
...  
Keyword(s):  
Growth Rate ◽  
Rate Constant ◽  
Tumor Regression ◽  
Acquired Resistance ◽  
Assessment Method ◽  
Prolonged Treatment ◽  
Growth Rate Constant ◽  
Two Phase ◽  
Phase Equation ◽  
D Values

133 Background: Like ATTP [bevacizumab + thalidomide + docetaxel + prednisone], ARTP [bevacizumab + lenalidomide + docetaxel + prednisone] is active in CRPC and in both the data suggest acquired resistance does not develop, supporting a strategy that continues therapy if tolerable. Discerning amongst new therapies in CRPC would be helped by novel assessment strategies that yield answers from smaller trials and allow comparisons across trials. We have validated a novel assessment method that quantifies tumor regression (d) and growth (g) rate constants using data obtained while pts are treated in a trial. We utilized this method to evaluate a phase II trial of ARTP in CRPC contrasting this with a previous study using thalidomide instead of lenalidomide (ATTP). Methods: Using PSA values and a two-phase mathematical equation we determined d and g. A three-phase equation was used to determine resistant fractions. Results: The median log g value with ARTP (-2.84) was statistically similar (p=0.204) to that observed with ATTP (-3.16). Both therapies had similar effects on log d (ARTP=-2.18; ATTP=-2.64; p=0.404). In a subset of pts with robust data both regimen are highly effective with only 3.01% and 5.46% of tumor resistant to ATTP and ARTP, respectively. In individual pt, statistically valid g and d values could be estimated after the fourth PSA value had been obtained, long before PSA increased - providing an early indicator of treatment failure. In most pts receiving prolonged treatment – as long as 700 d – the growth rate constant did not change, despite rising PSA values, indicating acquired resistance did not develop, and that if tolerable, therapy can be continued for longer periods of time. Conclusions: The substitution of daily thalidomide with lenalidomide 14/21 days in ARTP resulted in a combination statistically as effective as ATTP. As with ATTP majority of pts experienced marked reductions in the tumor’s g, and surprisingly in most, there was no evidence of acquired resistance, g remaining unchanged over prolonged time periods. Given the tolerability of this combination, pts with marked reductions in g may benefit from prolonged ARTP therapy.

Effect of Ag Addition on Growth of the Interfacial Intermetallic Compounds between Sn-0.7Cu Solder and Cu Substrate

2015 ◽  
Vol 815 ◽  
pp. 129-134 ◽  
Author(s):  
Xiao Chen Xie ◽  
Xiu Chen Zhao ◽  
Ying Liu ◽  
Jing Wei Cheng ◽  
Bing Zheng ◽  
...  
Keyword(s):  
Growth Rate ◽  
Intermetallic Compound ◽  
Rate Constant ◽  
Growth Rate Constant ◽  
Solder Joint Reliability ◽  
Ag Addition ◽  
Cu Substrate ◽  
Joint Reliability ◽  
Aging Properties ◽  
Interfacial Intermetallic Compounds

The effect of Ag content on the morphology of the intermetallic compound (IMC) layer at the interface between Sn-xAg-0.7Cu (x=0.0 wt.%, 0.3 wt.%, 0.8 wt.%, 3.0 wt.%) and Cu substrate has been investigated. After reflow, the slight addition of Ag element can suppress the growth of IMC. However, as the Ag content increases, the thickness of IMC is enhanced. After aging at 150°C, the IMC growth rate constant decreases with the addition of Ag. The IMC growth rate constant of Sn-3.0Ag-0.7Cu is 0.94864×10-5μm2/s, which is the lowest among these solders. As the Ag addition is 0.8wt% and 3.0wt%, the Cu3Sn growth rate constant is 0.16641×10-5μm2/s and 0.18496×10-5μm2/s, compared to the Sn-0.7Cu solder decreased 54% and 49%, respectively. As a result, the addition of Ag element improves the anti-aging properties and suppresses the growth of Cu3Sn layer, which leads to the improvement of solder joint reliability.

Modeling cement hydration by connecting a nucleation and growth mechanism with a diffusion mechanism. Part I: C3S hydration in dilute suspensions

2016 ◽  
Vol 23 (3) ◽  
pp. 345-356 ◽  
Author(s):  
Xueyu Pang ◽  
Christian Meyer
Keyword(s):  
Growth Rate ◽  
Rate Constant ◽  
Diffusion Mechanism ◽  
Diffusion Constant ◽  
Nucleation And Growth ◽  
Growth Rate Constant ◽  
Particle Interactions ◽  
Diffusion Controlled ◽  
Dilute Suspensions ◽  
Hydration Model

AbstractA particle-based C3S hydration model, which mathematically connects a nucleation and growth controlled mechanism with a diffusion controlled mechanism, is developed in this study. The model is first formulated and fitted with C3S hydration in stirred dilute suspensions in Part I where interactions between different particles can be ignored, and further developed and fitted with Portland cement paste hydration in Part II to account for inter-particle interactions. Excellent agreement was observed between experimental and modeled results. Three critical rate-controlling parameters, including a parallel growth rate constant, a perpendicular growth rate constant and a diffusion constant, were identified from the proposed model. The dependencies of these parameters on particle size and initial quantity of nuclei are investigated in Part I while their dependencies on cement composition, water-cement ratio, and curing condition are studied in Part II.

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