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Bacteria and archaea have evolved an adaptive, heritable immune system that recognizes and protects against viruses or plasmids. This system, known as the CRISPR-Cas system, allows the host to recognize and incorporate short foreign DNA or…
The CRISPR (clustered regularly interspaced short palindromic repeats) mechanism allows bacteria to adaptively defend against phages by acquiring short genomic sequences (spacers) that target specific sequences in the viral genome. We…
Clustered regularly interspaced short palindromic repeats (CRISPR) in bacterial and archaeal DNA have recently been shown to be a new type of anti-viral immune system in these organisms. We here study the diversity of spacers in CRISPR…
Features of the CRISPR-Cas system, in which bacteria integrate small segments of phage genome (spacers) into their DNA to neutralize future attacks, suggest that its effect is not limited to individual bacteria but may control the fate and…
CRISPR-Cas is a genetic adaptive immune system unique to prokaryotic cells used to combat phage and plasmid threats. The host cell adapts by incorporating DNA sequences from invading phages or plasmids into its CRISPR locus as spacers.…
CRISPR-Cas mediated immunity in bacteria allows bacterial populations to protect themselves against pathogens. However, it also exposes them to the dangers of auto-immunity by developing protection that targets its own genome. Using a…
CRISPR-Cas systems are an adaptive immunity that protects prokaryotes against foreign genetic elements. Genetic templates acquired during past infection events enable DNA-interacting enzymes to recognize foreign DNA for destruction. Due to…
Bacteria and their bacteriophages are the most abundant, widespread and diverse groups of biological entities on the planet. In an attempt to understand how the interactions between bacteria, virulent phages and temperate phages might…
The problem of evolutionary complexification of life is considered one of the fundamental aspects in contemporary evolutionary theory. Parasitism is ubiquitous, inevitable, and arises as soon as the first replicators appear, even during the…
Viruses utilize various means to circumvent the immune detection in the biological systems. Several mathematical models have been investigated for the description of viral dynamics in the biological system of human and various other…
This paper analyzes a simplified model of viral infection and evolution using the 'grand canonical ensemble' and formalisms from statistical mechanics and thermodynamics to enumerate all possible viruses and to derive thermodynamic…
We consider a non-attractive three state contact process on $\mathbb Z$ and prove that there exists a regime of survival as well as a regime of extinction. In more detail, the process can be regarded as an infection process in a dynamic…
Some prokaryotes possess CRISPR-Cas systems that provide adaptive immunity to viruses guided by DNA segments called spacers acquired from invading phage. However, the patchy incidence and limited memory breadth of CRISPR-Cas systems suggest…
Clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated proteins (Cas) constitute a multi-functional, constantly evolving immune system in bacteria and archaea cells. A heritable, molecular memory is…
We estimate the number of spacers in a CRISPR array of a bacterium which maximizes its protection against a viral attack. The optimality follows from a competition between two trends: too few distinct spacers make the bacteria vulnerable to…
Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), linked with CRISPR associated (CAS) genes, play a profound role in the interactions between phage and their bacterial hosts. It is now well understood that CRISPR-CAS…
Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best adapted genotype, leading to a population…
The coexistence between different informational molecules has been the preferred mode to circumvent the limitation posed by imperfect replication on the amount of information stored by each of these molecules. Here we reexamine a classic…
Viruses like influenza have long coevolved with host immune systems, gradually shaping the evolutionary trajectory of these pathogens. Host immune systems develop immunity against circulating strains, which in turn avoid extinction by…
The evolution of many microbes and pathogens, including circulating viruses such as seasonal influenza, is driven by immune pressure from the host population. In turn, the immune systems of infected populations get updated, chasing viruses…