Lets compare the normal and diabetic scenario of how adipose tissue controls blood glucose release from the liver.
In the normal scenario, appropriate insulin signaling restrains lipolysis (release of fatty acids from the tissue into the bloodstream). With restricted fat release from adipose tissue, the liver sees a limited amount of acetyl-Coa (that results from the break down of those fatty acids). If the liver sees limited amounts of acetyl-CoA then there are fewer intermediates feeding into the TCA cycle. With fewer intermediates available in the TCA cycle, there’s no need to handle ‘excess substrate’ by turning that into glucose (or glycogen or fat via DNL eventually). This is why we see pyruvate carboxylase (PC), the enzyme turning pyruvate into oxaloacetate (OAA), downregulated when there’s less acetyl-CoA. Recall that sufficient oxaloacetate is what’s required to create new glucose (aka gluconeogenesis aka GNG). Less oxaloacetate, less chance of creating new glucose. Downregulated PC also means less glyceraldehyde 3-phosphate activity (G3P), is a crucial step in the gluconeogenic pathway. So appropriate lipolysis limits FFA release from adipose tissue into the blood, limiting acetyl-CoA for TCA cycle replenishment in the liver, limiting the relevant intermediates necessary for pyruvate that the PC enzyme turns into OAA, and limited OAA means less substrate for GNG and G3P activity = less hepatic blood glucose release.
In the abnormal/diabetic scenario lipolysis is poorly restrained ===>INappropriate lipolysis increases FFA release from adipose tissue into the blood, increasing acetyl-CoA availability for TCA cycle replenishment in the liver, creating ‘excesses’ of the relevant intermediates necessary to make pyruvate that the PC enzyme turns upregulates to turn into OAA, and abundant OAA means more substrate for GNG and concomitant increased G3P activity = more hepatic blood glucose release.