Elasticities

In some cases we might be interested in testing certain intervention strategies on our models. In general we will be most intested in what is the consequence for the environment, meaning what happens with the exchange reactions in the model. Here, micom allows you to respond two kind of questions:

1. What impact does changing a bacterial abundance have on the exchanges?

2. What impact does changing the exchnage bounds (ergo diet) have on the exchanges?

For that we use the concept of elasticity coefficients which are a dimensionless normalized measure of how much the parameter \(p\) affects the flux \(v\):

\[\varepsilon_p^v = \frac{\partial v}{\partial p}\frac{p}{v} = \frac{\partial\ln v}{\partial\ln p}\]

micom can calculate the elasticities for abundances and diet in one go.

This again uses cooperative tradeoff to limit the solution space.

from micom import Community, data
from micom.elasticity import elasticities

tax = data.test_taxonomy()
com = Community(tax)

eps = elasticities(com, fraction=1.0, reactions=com.exchanges)
eps.head()

100%|██████████| 5/5 [00:02<00:00,  2.39models/s]
100%|██████████| 4/4 [00:00<00:00, 16.06optimizations/s]
100%|██████████| 5/5 [00:00<00:00,  7.38optimizations/s]

	reaction	taxon	effector	direction	elasticity	type
0	EX_ac_m	medium	EX_glc__D_m	zero	0.000014	exchanges
1	EX_acald_m	medium	EX_glc__D_m	zero	0.000012	exchanges
2	EX_akg_m	medium	EX_glc__D_m	zero	0.000017	exchanges
3	EX_co2_m	medium	EX_glc__D_m	forward	0.923854	exchanges
4	EX_etoh_m	medium	EX_glc__D_m	zero	0.000009	exchanges

Here reaction refers to the target flux and effector to the changed parameter. The direction indicates the flux direction and the type whether we changed an exchange bound or a taxa abundance. So for instance the 4th row would tell us that raising glucose import by one unit (one unit of additional glucose in the diet) would increase the carbon dioxide production by 0.92 units. The other rows do not impose a significant change, are not sensitive to glucose availability.