Mutations in artificial self-replicating tiles: A step toward Darwinian evolution

Artificial self-replication and exponential growth holds the promise of gaining a better understanding of fundamental processes in nature but also of evolving new materials and devices with useful properties. A system of DNA origami dimers has been shown to exhibit exponential growth and selection. Here we introduce mutation and growth advantages to study the possibility of Darwinian-like evolution. We seed and grow one dimer species, AB, from A and B monomers that doubles in each cycle. A similar species from C and D monomers can replicate at a controlled growth rate of two or four per cycle but is unseeded. Introducing a small mutation rate so that AB parents infrequently template CD offspring we show experimentally that the CD species can take over the system in approximately six generations in an advantageous environment. This demonstration opens the door to the use of evolution in materials design.

Download Full-text

Litters of self-replicating origami cross-tiles

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1812793116 ◽

2019 ◽

Vol 116 (6) ◽

pp. 1952-1957 ◽

Cited By ~ 2

Author(s):

Rebecca Zhuo ◽

Feng Zhou ◽

Xiaojin He ◽

Ruojie Sha ◽

Nadrian C. Seeman ◽

...

Keyword(s):

Growth Rate ◽

Population Growth ◽

Directed Evolution ◽

Exponential Growth ◽

Growth Conditions ◽

One Dimensional ◽

Replication System ◽

Speed Up ◽

Self Replication ◽

Dimensional Crystal

Self-replication and exponential growth are ubiquitous in nature but until recently there were few examples of artificial self-replication. Often replication is a templated process where a parent produces a single offspring, doubling the population in each generation. Many species however produce more than one offspring at a time, enabling faster population growth and higher probability of species perpetuation. We have made a system of cross-shaped origami tiles that yields a number of offspring, four to eight or more, depending on the concentration of monomer units to be assembled. The parent dimer template serves as a seed to crystallize a one-dimensional crystal, a ladder. The ladder rungs are then UV–cross-linked and the offspring are then released by heating, to yield a litter of autonomous daughters. In the complement study, we also optimize the growth conditions to speed up the process and yield a 103increase in the growth rate for the single-offspring replication system. Self-replication and exponential growth of autonomous motifs is useful for fundamental studies of selection and evolution as well as for materials design, fabrication, and directed evolution. Methods that increase the growth rate, the primary evolutionary drive, not only speed up experiments but provide additional mechanisms for evolving materials toward desired functionalities.

Download Full-text

The minimally displaced set of an irreducible automorphism of $$F_N$$ is co-compact

Archiv der Mathematik ◽

10.1007/s00013-021-01579-z ◽

2021 ◽

Vol 116 (4) ◽

pp. 369-383

Author(s):

Stefano Francaviglia ◽

Armando Martino ◽

Dionysios Syrigos

Keyword(s):

Growth Rate ◽

Free Group ◽

Exponential Growth ◽

Single Point ◽

Irreducible Automorphism

AbstractWe study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth $$\phi $$ ϕ , under the action of the centraliser $$C(\phi )$$ C ( ϕ ) . As a corollary, we get that the same holds for the action of $$ <\phi>$$ < ϕ > on $$Min(\phi )$$ M i n ( ϕ ) . Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.

Download Full-text

Polymer-Controlled Growth Rate of an Amorphous Mineral Film Nucleated at a Fatty Acid Monolayer

Langmuir ◽

10.1021/la0260032 ◽

2002 ◽

Vol 18 (23) ◽

pp. 8902-8909 ◽

Cited By ~ 48

Author(s):

E. DiMasi ◽

V. M. Patel ◽

M. Sivakumar ◽

M. J. Olszta ◽

Y. P. Yang ◽

...

Keyword(s):

Growth Rate ◽

Fatty Acid ◽

Controlled Growth

Download Full-text

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

Journal of Applied Probability ◽

10.1017/s0021900200096224 ◽

1974 ◽

Vol 11 (03) ◽

pp. 437-444 ◽

Cited By ~ 8

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.

Download Full-text

Bounds on the Nonlinear Diffusion Controlled Growth Rate of Spherical Precipitates

Journal of Applied Physics ◽

10.1063/1.1735904 ◽

1960 ◽

Vol 31 (9) ◽

pp. 1621-1627 ◽

Cited By ~ 4

Author(s):

J. A. Morrison ◽

H. L. Frisch

Keyword(s):

Growth Rate ◽

Nonlinear Diffusion ◽

Controlled Growth ◽

Diffusion Controlled

Download Full-text

SETI, Evolution and Human History Merged into a Mathematical Model

International Journal of Astrobiology ◽

10.1017/s1473550413000086 ◽

2013 ◽

Vol 12 (3) ◽

pp. 218-245 ◽

Cited By ~ 17

Author(s):

Claudio Maccone

Keyword(s):

Mathematical Model ◽

Exponential Growth ◽

Numerical Estimate ◽

Mean Value ◽

Darwinian Evolution ◽

Human History ◽

The Galaxy ◽

Positive Time ◽

A Cell ◽

Geometric Locus

AbstractIn this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.

Download Full-text

Optimal Strategies for Prudent Investors

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024998000254 ◽

1998 ◽

Vol 01 (04) ◽

pp. 473-486 ◽

Cited By ~ 10

Author(s):

Roberto Baviera ◽

Michele Pasquini ◽

Maurizio Serva ◽

Angelo Vulpiani

Keyword(s):

Growth Rate ◽

Random Walk ◽

Exponential Growth ◽

Optimal Strategies ◽

Maximum Amount ◽

Exponential Growth Rate ◽

One Dimensional ◽

Economic Level ◽

Random Walk With Drift ◽

Analytical Expressions

We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

Download Full-text

LANGUAGES WITH A FINITE ANTIDICTIONARY: SOME GROWTH QUESTIONS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054114400164 ◽

2014 ◽

Vol 25 (08) ◽

pp. 937-953

Author(s):

ARSENY M. SHUR

Keyword(s):

Growth Rate ◽

Structural Properties ◽

Exponential Growth ◽

Regular Languages ◽

The Other ◽

Exponential Growth Rate ◽

Strong Component ◽

Order Of Growth ◽

Finite Sets ◽

Complex Order

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.

Download Full-text

Validation and Analysis of Modeled Predictions of Growth of Bacillus cereus Spores in Boiled Rice

Journal of Food Protection ◽

10.4315/0362-028x-63.2.268 ◽

2000 ◽

Vol 63 (2) ◽

pp. 268-272 ◽

Cited By ~ 27

Author(s):

DANA M. McELROY ◽

LEE-ANN JAYKUS ◽

PEGGY M. FOEGEDING

Keyword(s):

Growth Rate ◽

Bacillus Cereus ◽

Exponential Growth ◽

Generation Time ◽

Time Lag ◽

Lag Phase ◽

Exponential Growth Rate ◽

Phase Duration ◽

Margin Of Safety ◽

Fail Safe

The growth of psychrotrophic Bacillus cereus 404 from spores in boiled rice was examined experimentally at 15, 20, and 30°C. Using the Gompertz function, observed growth was modeled, and these kinetic values were compared with kinetic values for the growth of mesophilic vegetative cells as predicted by the U.S. Department of Agriculture's Pathogen Modeling Program, version 5.1. An analysis of variance indicated no statistically significant difference between observed and predicted values. A graphical comparison of kinetic values demonstrated that modeled predictions were “fail safe” for generation time and exponential growth rate at all temperatures. The model also was fail safe for lag-phase duration at 20 and 30°C but not at l5°C. Bias factors of 0.55, 0.82, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, indicated that the model generally was fail safe and hence provided a margin of safety in its growth predictions. Accuracy factors of 1.82, 1.60, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, quantitatively demonstrated the degree of difference between predicted and observed values. Although the Pathogen Modeling Program produced reasonably accurate predictions of the growth of psychrotrophic B. cereus from spores in boiled rice, the margin of safety provided by the model may be more conservative than desired for some applications. It is recommended that if microbial growth modeling is to be applied to any food safety or processing situation, it is best to validate the model before use. Once experimental data are gathered, graphical and quantitative methods of analysis can be useful tools for evaluating specific trends in model prediction and identifying important deviations between predicted and observed data.

Download Full-text