Transport into the cytosol:

Fatty  acids  are  synthesized  in  the  cytosol,  but  acetyl  CoA  is  generate  from pyruvate in the mitochondria. Thus the acetyl CoA must be transferred  from  the mitochondria  into  the cytosol  to permits  fatty  acid  synthesis  to occur. Moreover, the inner mitochondrial membrane is not readily permeable to this molecule. This problem is overcome through the condensation of acetyl CoA with oxaloacetate to form citrate.  This  is then  transported  into  the  cytosol where  it is cleaved  to regenerate  acetyl  CoA  and  oxaloacetate  through ATP-citrate lyase in an energy-requiring procedure. The oxaloacetate,  that also cannot cross the  inner  mitochondrial   membrane,  is  back  to  the  mitochondrial   matrix through  conversion  first  to malate  (catalyzed  by  malate  dehydrogenase)   and then  to  pyruvate  (catalyzed  through  NADP⁺   -linked  malate  enzyme) shown in the figure.  This latter decarboxylation reaction generates NADPH that can be used in fatty acid synthesis.   The remaining   NADPH needed for fatty acid synthesis   is provided through the pentose phosphate pathway. Once back in the

Figure:   Transport of acetyl CoA from the mitochondrial matrix into the cytosol.

mitochondrial matrix,  pyruvate  is carboxylated  to form  oxaloacetate  through pyruvate carboxylase with the hydrolysis of a although molecule of ATP shown in the figure.