A model of gene-gene and gene-environment interactions and its implications for targeting environmental interventions by genotype

Helen M Wallace

doi:10.1186/1742-4682-3-35

Theoretical Biology and Medical Modelling

Table 3 Further constraints on model parameters

From: A model of gene-gene and gene-environment interactions and its implications for targeting environmental interventions by genotype

Condition	Limits on p^DZ_g	Limits on c_SD
V_e≥ 0	$p g D Z ≤ p g t o p D Z MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCdaqhaaWcbaGaem4zaCgabaGaemiraqKaemOwaOfaaOGaeyizImQaemiCaa3aa0baaSqaaiabdEgaNjabdsha0jabd+gaVjabdchaWbqaaiabdseaejabdQfaAbaaaaa@3D22@$
V_ge≥ 0	$p g D Z ≥ p g min D Z MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCdaqhaaWcbaGaem4zaCgabaGaemiraqKaemOwaOfaaOGaeyyzImRaemiCaa3aa0baaSqaaiabdEgaNjGbc2gaTjabcMgaPjabc6gaUbqaaiabdseaejabdQfaAbaaaaa@3D14@$
V_g≥ 0		C_SD≤ R_SD
γ_max ≥ γ_min		If λ_MD> y_e+ 1 require: c_SD≥ c_SDmwhere $c S D m = 1 − (λ D Z − 1) (1 − R S D) [c M D + f g e 2 (λ D Z − 1) R M D + y e f g e 2 (c M D − 1)] [1 + f g e 2 (λ D Z − 1)] [(λ D Z − 1) R M D − y e] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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T7aSnaaBaaaleaacqWGebarcqWGAbGwaeqaaOGaeyOeI0IaeGymaedacaGLOaGaayzkaaaacaGLBbGaayzxaaWaamWaaeaadaqadaqaaiab=T7aSnaaBaaaleaacqWGebarcqWGAbGwaeqaaOGaeyOeI0IaeGymaedacaGLOaGaayzkaaGaemOuai1aaSbaaSqaaiabd2eanjabdseaebqabaGccqGHsislcqWG5bqEdaWgaaWcbaGaemyzaugabeaaaOGaay5waiaaw2faaaaaaaa@8C1F@$

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