Difference between revisions of "Team:British Columbia/Modeling"

Imidacloprid is a neurotoxin that acts on the central nervous system of insects by irreversibly blocking acetylcholine receptors. Because of this, it has been suggested that imidacloprid toxicity depends not just on the initial ingestion, but also on secondary biological effects that accumulate over time. Using a cumulative toxicity model proposed by Rondeau et al., our goal was to determine whether our engineered bacteria would be able to improve survival, both at individual and population levels. By incorporating the decay constants of our engineered enzymes, we were able to show that our engineered bacteria is able to slow down the accumulation of toxicity in bees.

Modeling accumulative imidacloprid toxicity in A. mellifera

We are basing our chronic exposure toxicity model on the fact that imidacloprid binds irreversibly to acetylcholine receptors in the nervous system, and as such display patterns of accumulative toxicity over time. As such, the lethal time-to-effect relationship can be expressed as
LT50∝Dt^P
where:

• LT50 = time when half the insects succumb to toxin
• D = dose of toxin per unit time
• P = power law exponent

Our determination of the toxicity threshold is derived from Haber’s rule
C x t = k
where

• C = concentration of gas
• t = time necessary to inhale gas to produce toxic effect
• k = constant, dependent on gas itself and toxic effect

However, one caveat in the use of Haber’s rule is in that it applies to inhalation only, but imidacloprid ingestion in A. mellifera can occur through inhalation (direct dust exposure) or oral ingestion of droplets, nectar, or pollen from treated plants.

As such, we have used the toxicokinetic-toxicodynamic model proposed by Rondeau et al.

where

• D(t) = either a single initial dose or a continuous, lower, chronic dose
• C = change in total-body toxic load
• τ_M = metabolic decay time
• C_B = amount of bound toxin
• τ_D = time constant for dissociation

C_B, the amount of bound toxin, can be determined by

where

• C = change in total-body toxic load
• C_B = amount of bound toxin
• τ_A = time constant for receptor binding
• τ_D = time constant for dissociation

Rondeau et al. also suggest that
E(t)∝∫C_Bdt
where

• E(t) = cumulative damaging biological effect

Using an arbitrary threshold for E(t) (e.g. 1 = LT50), we are able to determine cumulative toxicity both without imidacloprid (thick blue line), with imidacloprid (dashed red line), and with imidacloprid and our genetically engineered Gilliamella (dashed blue line).

For the generation of our cumulative toxicity graphs, we used literature values of 6-CNA decay (time constant = 10 hours), as well as known concentrations of bee gut flora (10⁷ bacteria, of which Gilliamella makes up 12%), bee gut volume (1mm x 1mm x 1cm).

We then conducted sensitivity analysis, determining the range of the concentration of imidacloprid needed to alter bee survival time (as defined by our threshold of 1 = LT50).