I just know that Acetyl-CoA is a positive allosteric modulator for pyruvate carboxylase, but I cannot find anything else.
Okay so pyruvate carboxylase is a ligase-class enzyme, meaning it forms covalent bonds. What we see is that pyruvate is carboxylated into oxaloacetate by pyruvate carboxylase, here's our proposed reaction,
What this does is replenish mitochondrial oxaloacetate levels, because when we switch into lipogenesis, TCA intermediates must be shuttled into the cytoplasm for forming triglycerides, like so,
Also here, page 2, they go into how the production of NADPH is coupled to acetyl group export and how PC must perform the aforementioned function to keep substantial flow maintained. Block quoted them for ease of access,
As shown in Scheme 1, the generation of NADPH is coupled to the transport of mitochondrial acetyl groups into the cytosol for fatty acid synthesis. Acetyl-CoA is generated in the mitochondria by the oxidative decarboxylation of pyruvate, and, after condensation with oxaloacetate, acetyl groups are transported to the cytoplasm as citrate, which undergoes ATP-dependent cleavage to yield acetyl-CoA and oxaloacetate. This pathway requires a continuous supply of oxaloacetate, which is produced by the activity of PC. AcetylCoA, a building block for the synthesis of long-chain fatty acids, is then converted into malonyl-CoA by acetyl-CoA carboxylase (ACC). Meanwhile, the oxaloacetate generated in the cytosol from citrate is reduced with NADH to malate, which in turn is oxidatively decarboxylated in a reaction catalysed by NADP+- dependent malate dehydrogenase (‘malic enzyme’; EC 18.104.22.168). The pyruvate thereby produced is taken up by the mitochondria and carboxylated to give oxaloacetate, while the NADPH generated is used in the pathway of fatty acid synthesis.