Adrenergic receptоrs аre а clаss оf G prоtein-coupled receptors (GPCRs) that respond to catecholamines like epinephrine and norepinephrine. In adipose tissue, adrenergic receptors play a key role in regulating lipolysis, the breakdown of stored triglycerides into free fatty acids and glycerol, which can be used as energy. The primary adrenergic receptors in adipose tissue include β₁, β₂, β₃, α₂, and α₁ receptors, each coupled to different G proteins that mediate distinct signaling pathways and physiological responses. β₁, β₂, and β₃ adrenergic receptors are coupled to Gs proteins, which activate adenylyl cyclase. The activation of adenylyl cyclase leads to an increase in cyclic AMP (cAMP) levels, which then activates protein kinase A (PKA). PKA phosphorylates hormone-sensitive lipase (HSL), an enzyme that catalyzes the breakdown of triglycerides in adipose cells. Among these receptors, β₃ is predominantly expressed in adipose tissue and plays a crucial role in thermogenesis and lipolysis in response to cold exposure and stress. In contrast, α₂ adrenergic receptors are coupled to Gi proteins, which inhibit adenylyl cyclase, leading to a reduction in cAMP levels. This inhibitory pathway decreases PKA activity, thereby inhibiting lipolysis. The α₁ adrenergic receptors, however, are coupled to Gq proteins, which activate phospholipase C (PLC). PLC catalyzes the production of inositol triphosphate (IP₃) and diacylglycerol (DAG), which promote calcium release from the endoplasmic reticulum and activate protein kinase C (PKC), respectively. The activation of PKC by α₁ receptors in adipose tissue is less directly involved in lipolysis but may play a modulatory role. The balance of activation between these adrenergic receptors determines the rate of lipolysis and, consequently, the availability of free fatty acids for energy production. Under conditions of stress or cold exposure, β₃ receptor activation predominates, promoting lipolysis and heat generation, while α₂ receptor activation can dampen this response by inhibiting adenylyl cyclase. Which of the following best describes the signaling pathway activated by β₃ adrenergic receptors in adipose tissue?