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, 9 (1), 20050

Mathematical Modeling of Self-Contained CRISPR Gene Drive Reversal Systems


Mathematical Modeling of Self-Contained CRISPR Gene Drive Reversal Systems

Matthew G Heffel et al. Sci Rep.


There is a critical need for further research into methods to control biological populations. Numerous challenges to agriculture, ecological systems, and human health could be mitigated by the targeted reduction and management of key species (e.g. pests, parasites, and vectors for pathogens). The discovery and adaptation of the CRISPR/Cas editing platform co-opted from bacteria has provided a mechanism for a means to alter an entire population. A CRISPR-based gene drive system can allow for the forced propagation of a genetic element that bypasses Mendelian inheritance which can be used to bias sex determination, install exogenous information, or remove endogenous DNA within an entire species. Laboratory studies have demonstrated the potency by which gene drives can operate within insects and other organisms. However, continued research and eventual application face serious opposition regarding issues of policy, biosafety, effectiveness, and reversal. Previous mathematical work has suggested the use of modified gene drive designs that are limited in spread such as daisy chain or underdominance drives. However, no system has yet been proposed that allows for an inducible reversal mechanism without requiring the introduction of additional individuals. Here, we study gene drive effectiveness, fitness, and inducible drive systems that could respond to external stimuli expanding from a previous frequency-based population model. We find that programmed modification during gene drive propagation could serve as a potent safeguard to either slow or completely reverse drive systems and allow for a return to the original wild-type population.

Conflict of interest statement

G.C.F. has applied for CRISPR-related patents: (i) April 20, 2017 by the Univ. of California, Berkeley, “Methods and Compositions for Genomic Editing” International Application No. PCT/US2017/028676 and published as No. WO 2017/189336 A1 on November 2, 2017, (ii) September 29, 2017 (U.S. Provisional Patent Application Serial No. 62/565,651, “Programmed modulation of CRISPR/Cas9 activity”) followed by patent filing on January 31, 2018 and (iii) a PCT application “Multi-Locus Gene Drive System” No. PCT/US2019/041538 on July 12, 2019. M.G.H. has private investments in companies that may utilize various CRISPR-related biotechnologies. Authors declare no non-financial conflict of interest of any kind.


Figure 1
Figure 1
An inducible system to alter gene drive efficiency. (A) A theoretical GD system can translate an external signal into a change in GD effectiveness from initial eW to a desired eW’. The portion of the population that successfully responded to the external cue was designated α; unaffected population was defined by (1 - α). The example illustrated assumed that the initial eW was larger than the final eW’ following the shift (population reversion back to WT) and α was set to one. (B) A reduced eW’ allowed an initially successful GD to be overtaken by the WT population. Graphs plotting GD eW and f (left, no induction) for an inducible system where eW’ was changed to 0.1 (middle) or to 0.01 (right) at generation 10 with an effectiveness of α = 0.9 are illustrated. A sample data point was highlighted with initial conditions of eW = 0.8 and f = 0.7. The coloring scheme was identical to Fig. S2; GD to fixation (red) and WT to fixation (blue). Shading of colors illustrated the length of time required to reach fixation (darker, longer time). (C) Examination of varying initial parameters for a GD with inducible eW. Graphs (i-vi) illustrated GD allele frequencies in red. Population frequency was plotted on the y-axis and generation time was plotted on the x-axis. A single parameter was altered for each graph and the values tested were illustrated with line types (solid, dotted, dashed, and dash/dot). Graph (i) did not include an inducible mechanism. Vertical grey dotted lines indicated the starting point for application of the external signal.
Figure 2
Figure 2
An inducible system to alter gene drive individual fitness. (A) Examination of both GD efficiency (eW) and fitness (f ) was explored for a drive system that included an inducible fitness parameter (f ’). The induction efficiency was denoted as α. Analysis of varying initial parameters for a GD with inducible f; graphs (i-vi) illustrated GD allele frequencies in red. Frequency was plotted on the y-axis and generation time was plotted on the x-axis. Line types corresponded to four tested values within each parameter. Graph (i) did not include an inducible mechanism. Vertical grey dotted lines highlighted the induction times used. (B) Four sets of simulations were performed (i-iv) comparing two parameters for GD systems with inducible f. Graph (i) did not include an inducible GD. The coloring scheme matched the simulations found in Fig. S2.
Figure 3
Figure 3
An inducible self-cleaving gene drive system. (A) Schematic of a GD arrangement that includes an inducible guide RNA cassette—sgRNA(9)—that would activate self-cleavage of the drive itself. (B) Two GD efficiencies were modeled: (i) eW represented the ability to cleave the intended WT target and (ii) eD represented the ability to self-target the drive cassette. Four scenarios were outlined (1–4) between pairing of the GD and WT alleles that resulted in a lethal phenotype, homozygous WT, homozygous GD, and heterozygous GD/WT genotypes. Activation of eD prior to activation of the external cue (e.g. “leaky” activation) was included within the model; eD represented self-cleavage after the induction event. The outcomes of a homozygous GD/GD pairing were also modeled (scenarios 5–6). (C) Graphs (i-vi) illustrated drive allele frequencies in red. The allele frequency was plotted on the y-axis and the generation time was plotted on the x-axis. Line types (solid, dotted, dashed, and dash/dot) corresponded to four values sampled for each simulation. Graph (i) did not include an inducible element; a basal “leaky” value of eD was set to various values at generation 0. Vertical grey dotted lines specified application of the external signal.

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