Pseudo-chaotic oscillations in CRISPR-virus coevolution predicted by bifurcation analysis

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Because the DNA segments are cut and reorganized in a direction-specific manner, site-specific recombination has emerged as an efficient genetic engineering technique. Flippase and Cyclization recombinases or Flp and Cre, respectively, are two members of the tyrosine recombinase family derived from bacteriophages, that are used to mediate site-specific DNA insertions, deletions, and targeted expression of proteins in mammalian cell lines.
The recognition sites for Cre recombinase called LoxP...

Bacteria and archaea are susceptible to viral infections just like eukaryotes; therefore, they have developed a unique adaptive immune system to protect themselves. Clustered regularly interspaced short palindromic repeats and CRISPR-associated proteins (CRISPR-Cas) are present in more than 45% of known bacteria and 90% of known archaea.
The CRISPR-Cas system stores a copy of foreign DNA in the host genome and uses it to identify the foreign DNA upon reinfection. CRISPR-Cas has three different...

CRISPR stands for Clustered Regularly Interspaced Short Palindromic Repeats is a adaptive immune system found in bacteria and archaea that protects against viral infections. This system enables prokaryotic cells to identify, remember, and neutralize foreign genetic elements, primarily bacteriophages, by storing fragments of the invader’s DNA as a genetic memory.The CRISPR immune response begins during an initial infection. Cas (CRISPR-associated) proteins play a central role in this...

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...