Limits...
Nasty viruses, costly plasmids, population dynamics, and the conditions for establishing and maintaining CRISPR-mediated adaptive immunity in bacteria.

Levin BR - PLoS Genet. (2010)

Bottom Line: Thus it would seem that protection against infecting phage and plasmids is the selection pressure responsible for establishing and maintaining CRISPR in bacterial populations.But is it?I suggest protocols for estimating these parameters and outline the design of experiments to evaluate the validity of these models and test these hypotheses.

View Article: PubMed Central - PubMed

Affiliation: Department of Biology, Emory University, Atlanta, Georgia, United States of America. blevin@emory.edu

ABSTRACT
Clustered, Regularly Interspaced Short Palindromic Repeats (CRISPR) abound in the genomes of almost all archaebacteria and nearly half the eubacteria sequenced. Through a genetic interference mechanism, bacteria with CRISPR regions carrying copies of the DNA of previously encountered phage and plasmids abort the replication of phage and plasmids with these sequences. Thus it would seem that protection against infecting phage and plasmids is the selection pressure responsible for establishing and maintaining CRISPR in bacterial populations. But is it? To address this question and provide a framework and hypotheses for the experimental study of the ecology and evolution of CRISPR, I use mathematical models of the population dynamics of CRISPR-encoding bacteria with lytic phage and conjugative plasmids. The results of the numerical (computer simulation) analysis of the properties of these models with parameters in the ranges estimated for Escherichia coli and its phage and conjugative plasmids indicate: (1) In the presence of lytic phage there are broad conditions where bacteria with CRISPR-mediated immunity will have an advantage in competition with non-CRISPR bacteria with otherwise higher Malthusian fitness. (2) These conditions for the existence of CRISPR are narrower when there is envelope resistance to the phage. (3) While there are situations where CRISPR-mediated immunity can provide bacteria an advantage in competition with higher Malthusian fitness bacteria bearing deleterious conjugative plasmids, the conditions for this to obtain are relatively narrow and the intensity of selection favoring CRISPR weak. The parameters of these models can be independently estimated, the assumption behind their construction validated, and the hypotheses generated from the analysis of their properties tested in experimental populations of bacteria with lytic phage and conjugative plasmids. I suggest protocols for estimating these parameters and outline the design of experiments to evaluate the validity of these models and test these hypotheses.

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Model of the population dynamics of a conjugative plasmid with CRISPR-mediated adaptive immunity in continuous culture.N - plasmid-free non–CRISPR, NP - plasmid-bearing non–CRISPR, C - plasmid-free CRISPR, CP - plasmid-bearing CRISPR, CX - immune CRISPR. The γs are the rate constants of plasmid transfer, m is the fraction of CP that enter the immune state CX upon receiving the plasmid from an NP or CP, ν is the rate at which immune CRISPR cells lose their immunity and z the rate at which the CRISPR cells lose the CRISPR element and become N or NP. The bacteria reproduce at a rate proportional to the concentration of a limiting resource and their maximum rates of replication. The limiting resource in the reservoir is at concentration A µg/ml and enters the vessel at the rate, w, which is the same as the rate at which the phage and bacterial populations and excess resource, R, are removed from the vessel. For more details see the text.
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pgen-1001171-g003: Model of the population dynamics of a conjugative plasmid with CRISPR-mediated adaptive immunity in continuous culture.N - plasmid-free non–CRISPR, NP - plasmid-bearing non–CRISPR, C - plasmid-free CRISPR, CP - plasmid-bearing CRISPR, CX - immune CRISPR. The γs are the rate constants of plasmid transfer, m is the fraction of CP that enter the immune state CX upon receiving the plasmid from an NP or CP, ν is the rate at which immune CRISPR cells lose their immunity and z the rate at which the CRISPR cells lose the CRISPR element and become N or NP. The bacteria reproduce at a rate proportional to the concentration of a limiting resource and their maximum rates of replication. The limiting resource in the reservoir is at concentration A µg/ml and enters the vessel at the rate, w, which is the same as the rate at which the phage and bacterial populations and excess resource, R, are removed from the vessel. For more details see the text.

Mentions: The model developed here is an extension of that in [29]. There are five bacterial populations. Two populations do not code for CRISPR, N and NP, and three populations code for CRISPR, C and CP and CX. The NP and CP populations bear the conjugative plasmid and CX, carries CRISPR and plasmid sequences that make it completely immune to the receipt of these plasmids. Plasmids are transferred by conjugation at rates proportional to the product of the densities of the plasmid-bearing and plasmid-free populations and rate constants, γNN, γNC, γCN and γCC (ml per cell per hour) respectively for the transfer of the plasmid from NP to N, NP to C, CP to N and CP to C., respectively. Plasmids are lost by vegetative segregation at rates τN and τC per cell per hour, with NP→N and Cp→C. C are converted to CX at a rate proportional to the rate at which C acquires the plasmid and a probability m (0≤m≤1). Cx lose the CRISPR plasmid immunity region and become C at rate ν per cell per hour. Each of the cell lines, have a maximum growth rate, VN, VNP, VC, and VCP, and VX per hour. In Figure 3, I illustrate the interactions between the different cell lines in this model, and, in Table 2, I separately define the parameters and variables. The equations for this model are:


Nasty viruses, costly plasmids, population dynamics, and the conditions for establishing and maintaining CRISPR-mediated adaptive immunity in bacteria.

Levin BR - PLoS Genet. (2010)

Model of the population dynamics of a conjugative plasmid with CRISPR-mediated adaptive immunity in continuous culture.N - plasmid-free non–CRISPR, NP - plasmid-bearing non–CRISPR, C - plasmid-free CRISPR, CP - plasmid-bearing CRISPR, CX - immune CRISPR. The γs are the rate constants of plasmid transfer, m is the fraction of CP that enter the immune state CX upon receiving the plasmid from an NP or CP, ν is the rate at which immune CRISPR cells lose their immunity and z the rate at which the CRISPR cells lose the CRISPR element and become N or NP. The bacteria reproduce at a rate proportional to the concentration of a limiting resource and their maximum rates of replication. The limiting resource in the reservoir is at concentration A µg/ml and enters the vessel at the rate, w, which is the same as the rate at which the phage and bacterial populations and excess resource, R, are removed from the vessel. For more details see the text.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2965746&req=5

pgen-1001171-g003: Model of the population dynamics of a conjugative plasmid with CRISPR-mediated adaptive immunity in continuous culture.N - plasmid-free non–CRISPR, NP - plasmid-bearing non–CRISPR, C - plasmid-free CRISPR, CP - plasmid-bearing CRISPR, CX - immune CRISPR. The γs are the rate constants of plasmid transfer, m is the fraction of CP that enter the immune state CX upon receiving the plasmid from an NP or CP, ν is the rate at which immune CRISPR cells lose their immunity and z the rate at which the CRISPR cells lose the CRISPR element and become N or NP. The bacteria reproduce at a rate proportional to the concentration of a limiting resource and their maximum rates of replication. The limiting resource in the reservoir is at concentration A µg/ml and enters the vessel at the rate, w, which is the same as the rate at which the phage and bacterial populations and excess resource, R, are removed from the vessel. For more details see the text.
Mentions: The model developed here is an extension of that in [29]. There are five bacterial populations. Two populations do not code for CRISPR, N and NP, and three populations code for CRISPR, C and CP and CX. The NP and CP populations bear the conjugative plasmid and CX, carries CRISPR and plasmid sequences that make it completely immune to the receipt of these plasmids. Plasmids are transferred by conjugation at rates proportional to the product of the densities of the plasmid-bearing and plasmid-free populations and rate constants, γNN, γNC, γCN and γCC (ml per cell per hour) respectively for the transfer of the plasmid from NP to N, NP to C, CP to N and CP to C., respectively. Plasmids are lost by vegetative segregation at rates τN and τC per cell per hour, with NP→N and Cp→C. C are converted to CX at a rate proportional to the rate at which C acquires the plasmid and a probability m (0≤m≤1). Cx lose the CRISPR plasmid immunity region and become C at rate ν per cell per hour. Each of the cell lines, have a maximum growth rate, VN, VNP, VC, and VCP, and VX per hour. In Figure 3, I illustrate the interactions between the different cell lines in this model, and, in Table 2, I separately define the parameters and variables. The equations for this model are:

Bottom Line: Thus it would seem that protection against infecting phage and plasmids is the selection pressure responsible for establishing and maintaining CRISPR in bacterial populations.But is it?I suggest protocols for estimating these parameters and outline the design of experiments to evaluate the validity of these models and test these hypotheses.

View Article: PubMed Central - PubMed

Affiliation: Department of Biology, Emory University, Atlanta, Georgia, United States of America. blevin@emory.edu

ABSTRACT
Clustered, Regularly Interspaced Short Palindromic Repeats (CRISPR) abound in the genomes of almost all archaebacteria and nearly half the eubacteria sequenced. Through a genetic interference mechanism, bacteria with CRISPR regions carrying copies of the DNA of previously encountered phage and plasmids abort the replication of phage and plasmids with these sequences. Thus it would seem that protection against infecting phage and plasmids is the selection pressure responsible for establishing and maintaining CRISPR in bacterial populations. But is it? To address this question and provide a framework and hypotheses for the experimental study of the ecology and evolution of CRISPR, I use mathematical models of the population dynamics of CRISPR-encoding bacteria with lytic phage and conjugative plasmids. The results of the numerical (computer simulation) analysis of the properties of these models with parameters in the ranges estimated for Escherichia coli and its phage and conjugative plasmids indicate: (1) In the presence of lytic phage there are broad conditions where bacteria with CRISPR-mediated immunity will have an advantage in competition with non-CRISPR bacteria with otherwise higher Malthusian fitness. (2) These conditions for the existence of CRISPR are narrower when there is envelope resistance to the phage. (3) While there are situations where CRISPR-mediated immunity can provide bacteria an advantage in competition with higher Malthusian fitness bacteria bearing deleterious conjugative plasmids, the conditions for this to obtain are relatively narrow and the intensity of selection favoring CRISPR weak. The parameters of these models can be independently estimated, the assumption behind their construction validated, and the hypotheses generated from the analysis of their properties tested in experimental populations of bacteria with lytic phage and conjugative plasmids. I suggest protocols for estimating these parameters and outline the design of experiments to evaluate the validity of these models and test these hypotheses.

Show MeSH
Related in: MedlinePlus