To my knowledge there is no direct connection between O2 saturation and heart rate..unless I'm forgetting some major contributor, they're controlled separately. Heart rate by regulation that monitors sytemic pressure and O2 sat by factors controlling respiration. There are central and peripheral chemoreceptors that monitor CO2 and O2 in the blood and CSF that are more directly involved in respiration rate. Indirect sensing of O2 in pulmonary capillaries is through local metabolic products that will trigger pulmonary arteriole vasoconstriction in the case of decreased O2 content to divert blood to other areas of the lung that are being better perfused in order to match V to Q as best as possible.
Activation of the sympathetic nervous system will increase CO, and increase RR which will increase pulmonary capillary recruitment (thru increased CO) and O2 ventilation of the alveoli to maintain V/Q.
