All of the tissues of the "conducting system" demonstrate at least two properties important to their specialized function of regulating and coordinating the contraction of the heart.  All of the tissues in the conducting system demonstrate both...

automaticity:  Automaticity means that the tissues spontaneously depolarize to threshold; the first structure in the conducting system to reach threshold (the fastest to spontaneously depolarize) will typically experience an action potential which will be propagated throughout the conducting system; as the sinoatrial node (SA node) is typically the structure which depolarizes the most rapidly, it typically acts as the key cardiac pacemaker.

rhythmicity:  Rhythmicity refers to an inherent rhythm for "firing frequency" which is specific to each segment of the conducting system; typically, the firing frequency of the SA node is faster than any other segment of the conducting system; the SA node has an inherent rhythm of approximately 100 beats per minute but is tonically slowed by the parasympathetic vagus; the vagus typically slows the heart to approximately 70 beats per minute in adults.

segments of the conducting system:

Sinoatrial node (SA node): The key pacemaker.

Atrioventricular node (AV node): With the next highest rhythmicity in the conducting pathway, the AV node serves as a backup pacemaker; should the SA node fail, the AV node is capable of maintaining heart rates of around 40 beats per minute; ordinarily, however, the AV node simply serves as a conducting element in the pathway, picking up the action potential from the SA node and passing it to the AV bundle.

AV Bundle:  The AV bundle is significant as it is the only major conduction pathway available for electrical activity to pass from the atria to the ventricles; conditions in which AV bundle bundle transmission is delayed or impaired are referred to as AV block (more on this elsewhere!); the AV bundle also serves as a protective device in that, if the sinoatrial rhythm becomes hyper-stimulated (sinus tachycardia, for example), the AV bundle will usually fail to transmit some of the signals, preventing the ventricles from being overtaxed by the SA node; drugs containing adenosine (Adenocard) will slow transmission through the AV bundle; the bundle has the ability to take over pacemaker function but may keep the heart beating at rates as low as 30 beats per minute, not sufficient for very long! (pacemaker)

Left and Right Bundle Branches:  The left and right bundle branches are the major conducting fibers through the inter-ventricular septum; like other tissues in the conducting pathway, the bundle branches can take over pacemaker function in the event of complete failure of the AV bundle; should the AV bundle fail, there is a delay during which the bundle branches spontaneously depolarize before beginning to fire; the term "ventricular escape" refers to the point at which the ventricles begin to beat independently of the atria; once again, the problem with having the bundle branches acting as pacemakers is that they fire too slowly to sustain life (pacemaker)

Purkinje Fibers:  The Purkinjes are the major conducting fibers through the free walls of the ventricles; they must transmit the action potential at phenomenally high speeds in order to allow the heart to beat in a coordinated fashion

Note that the tmp_r of the SA node is higher than for myocardium, making the SA node more irritable than the remainder of the myocardium (ie. the tmp_r of the SA node is pretty close to the tmp_t). The SA node acts as a pacemaker because it demonstrates automaticity and rhythmicity.  These properties are shared by all of the conducting tissues but all other tissues in the conducting pathway normally demonstrate a rhythmicity slower than that of the SA node.  Thus, if the SA node fails to fire or fails to communicate with the ventricles, other tissues in the conducting pathway may take over pacemaker function (ectopic pacemaker) but at a slower rate than the SA node.  Automaticity in the pacemaker (or conducting ) tissues results from a gradual decline in potassium conductance (permeability).  As K⁺ conductance decreases, the tmp becomes more positive, creeps up to threshold and fires!  You should easily be able to determine the effect of decreasing K⁺ permeability on excitable tissue!

The rate of conduction through the conducting fibers increases as the AP moves away from the AV node; this may be of importance in understanding the mechanics of the ECG wave (although it may not be important in clinical interpretation of an ECG wave).  The rate of repolarization of the conducting system is fastest in the Purkinje fibers and gets progressively slower as we move back to the beginning of the conducting system.  The net "electrical" effect is that the AV bundle depolarizes before the Purkinje fibers, but the AV bundle is still depolarized while the Purkinje fibers have already repolarized... in other words, the "depolarization wave" moves out from the AV bundle, but the "repolarization wave" moves from the Purkinje fibers back to the AV bundle!

The speed of repolarization of myocardial muscle is susceptible to parasympathetic (slow down) and sympathetic (speed up) effects.  The major component of any increase or decrease in heart rate reflects an alteration in the rate of repolarization; the rate of depolarization remains relatively constant.  In other words, the parasympathetic system can slow the rate of repolarization of the myocardium!  The Ca²⁺ source for myocardial contraction is of intra- and extra-cellular origin; in order for myocardial tissue to contract, voltage-gated Ca²⁺ channels in the muscle cell membranes must open!  Remember, skeletal muscle required Ca²⁺ for actin and myosin coupling, but in skeletal muscle, the sole source of Ca²⁺ was from the intracellular source (the sarcoplasmic reticulum).

Autonomic Effects on the Heart

The heart is richly innervated by autonomic fibers at the atria, ventricles and the SA and AV nodes.

Sympathetic excitation of the heart (increased Na⁺ and Ca²⁺ permeability):  In general, sympathetic innervation (NE or Epi) of the right heart (& the SA node) increases HR (a positive chronotropic effect) while sympathetic innervation of the left heart (the larger and more powerful left ventricular muscle) increases contractile vigor of the heart (a positive inotropic effect).  Significant sympathetic activity may increase heart rate to 200-250 and increase cardiac output 2 to 3-fold.  You should easily be able to determine the effect of increasing Na⁺ and Ca²⁺ permeability in this "excitable" tissue that requires intra- and extra-cellular Ca²⁺ for contraction!!!

Parasympathetic relaxation (increased K⁺ permeability):  Parasympathetic innervation of the right heart slows the SA node while parasympathetic innervation of the left heart slows the AV node on the septal wall of the right atrium.  Tonic parasympathetic activity slows the heart rate 20-30% below the inherent rhythmicity of the SA node, but strong parasympathetic activity can actually stop the heart for periods of a few seconds.  Thus, parasympathetic activity tends to have a negative chronotropic effect on the heart!  You should easily be able to determine the effect of increased K⁺ permeability on an excitable cell!!!