Mechanism of change in heart rate by autonomic nervous system (chronotropy)

Sympathetic and parasympathetic stimulation affect the nodal action potential to change the heart rate

Sympathetic stimulation increases heart rate

Stimulation of sympathetic system releases noradrenaline which binds with beta 1 receptor. Due to this G alpha S gets activated and it causes activation of adenyl cyclase which in turn leads to formation of cAMP. The HCN channels which are responsible for prepotential.. their opening and closing is affected by the concentration cAMP inside the cells. When cAMP increases, the probability of opening of these channels increases. So, in short sympathetic activation leads to more opening of HCN channels, causing more entry of sodium inside the cells leading to faster change in the potential towards threshold. So there is a change in the slope of the prepotential which becomes steeper and due to this SA node generates more number of impulses in the same time and hence it increases heart rate.

Parasympathetic stimulation decreases heart rate

Acetylcholine released from vagus causes activation of G i type of proteins which inhibits adenyl cyclase leading to decreased production of cAMP. Thus is leads to decreased opening of HCN channels and also T type channels. Hence the slope of pre-potential decreases leading to decrease in the number of impulses generated and hence decreased heart rate. Parasympathetic activation has one more effect. It delays the closure of these potassium channel which are responsible for phase 3. So more potassium moves out which leads to hyperpolarization. that is more negative maximum diastolic potential.