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Is the golden ratio a universal constant for self-replication?

ABSTRACT: The golden ratio, ? = 1.61803…, has often been found in connection with biological phenomena, ranging from spirals in sunflowers to gene frequency. One example where the golden ratio often arises is in self-replication, having its mathematical origins in Fibonacci's sequence for "rabbit reproduction". Recently, it has been claimed that ? determines the ratio between the number of different nucleobases in human genome. Such empirical examples continue to give credence to the idea that the golden ratio is a universal constant, not only in mathematics but also for biology. In this paper, we employ a general framework for chemically realistic self-replicating reaction systems and investigate whether the ratio of chemical species population follows "universal constants". We find that many self-replicating systems can be characterised by an algebraic number, which, in some cases, is the golden ratio. However, many other algebraic numbers arise from these systems, and some of them-such as [Formula: see text] and 1.22074… which is also known as the 3rd lower golden ratio-arise more frequently in self-replicating systems than the golden ratio. The "universal constants" in these systems arise as roots of a limited number of distinct characteristic equations. In addition, these "universal constants" are transient behaviours of self-replicating systems, corresponding to the scenario that the resource inside the system is infinite, which is not always the case in practice. Therefore, we argue that the golden ratio should not be considered as a special universal constant in self-replicating systems, and that the ratios between different chemical species only go to certain numbers under some idealised scenarios.

SUBMITTER: Liu Y

PROVIDER: S-EPMC6047800 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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Is the golden ratio a universal constant for self-replication?

Liu Yu Y Sumpter David J T DJT

PloS one 20180716 7

The golden ratio, ϕ = 1.61803…, has often been found in connection with biological phenomena, ranging from spirals in sunflowers to gene frequency. One example where the golden ratio often arises is in self-replication, having its mathematical origins in Fibonacci's sequence for "rabbit reproduction". Recently, it has been claimed that ϕ determines the ratio between the number of different nucleobases in human genome. Such empirical examples continue to give credence to the idea that the golden ...[more]

PMID: 30011316

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Project description:BackgroundNumerous self-gated cardiac imaging techniques have been reported in the literature. Most can track either cardiac or respiratory motion, and many incur some overhead to imaging data acquisition. We previously described a Cartesian cine imaging technique, pseudo-projection motion tracking with golden-step phase encoding, capable of tracking both cardiac and respiratory motion at no cost to imaging data acquisition. In this work, we describe improvements to the technique by dramatically reducing its vulnerability to eddy current and flow artifacts and demonstrating its effectiveness in expanded cardiovascular applications.MethodsAs with our previous golden-step technique, the Cartesian phase encodes over time were arranged based on the integer golden step, and readouts near ky?=?0 (pseudo-projections) were used to derive motion. In this work, however, the readouts were divided into equal and consecutive temporal segments, within which the readouts were sorted according to ky. The sorting reduces the phase encode jump between consecutive readouts while maintaining the pseudo-randomness of ky to sample both cardiac and respiratory motion without comprising the ability to retrospectively set the temporal resolution of the original technique. On human volunteers, free-breathing, electrocardiographic (ECG)-free cine scans were acquired for all slices of the short axis stack and the 4-chamber view of the long axis. Retrospectively, cardiac motion and respiratory motion were automatically extracted from the pseudo-projections to guide cine reconstruction. The resultant image quality in terms of sharpness and cardiac functional metrics was compared against breath-hold ECG-gated reference cines.ResultsWith sorting, motion tracking of both cardiac and respiratory motion was effective for all slices orientations imaged, and artifact occurrence due to eddy current and flow was efficiently eliminated. The image sharpness derived from the self-gated cines was found to be comparable to the reference cines (mean difference less than 0.05?mm-?1 for short-axis images and 0.075?mm-?1 for long-axis images), and the functional metrics (mean difference?<?4?ml) were found not to be statistically different from those from the reference.ConclusionsThis technique dramatically reduced the eddy current and flow artifacts while preserving the ability of cost-free motion tracking and the flexibility of choosing arbitrary navigator zone width, number of cardiac phases, and duration of scanning. With the restriction of the artifacts removed, the Cartesian golden-step cine imaging can now be applied to cardiac imaging slices of more diverse orientation and anatomy at greater reliability.

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Is the golden ratio a universal constant for self-replication?

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Is the golden ratio a universal constant for self-replication?

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