Devil Gene

While the exact specifications of this gene are never truly explained, it is generally assumed that the gene allows for a person to have a parasite/host type relationship with a malignant spirit referred to as a "devil" as well as having it (the gene) control the transformations of one to the other. The exact requirements for these transformations are never fully revealed. The spirits can possess the person at any given time during the person's lifespan, even while still in their mother's womb or (apparently) just after death.

The people currently carrying the Devil Gene are, in the order in which it was "revealed": Kazuya Mishima, Jin Kazama, and Azazel. Heihachi Mishima doesn't seem to possess the Devil Gene like the other members of his family.

It was previously believed for a long time that Jinpachi Mishima possessed the Devil Gene due to his appearance, dialogues and his ending in Tekken 5, but it was revealed by Tekken director Katsuhiro Harada's Twitter page that Jinpachi didn't possess the Devil Gene and that a revengeful ghost possessed him. Interesting though, in both console versions of Tekken 5, Jinpachi's ending states that he's possessed by the Devil. Also, in Jinpachi's interlude with Heihachi, the latter theorizes that his father has the Devil's blood and finally, in the character history section of the Tekken 6 CG art book, it states that Jinpachi has the Devil Gene. It says that he is an unique link within the Mishima bloodline, in which the Devil Gene appears after him. When fans mention this on Harada's Twitter page, he reveals that Tekken project team dares to mislead fans (sometimes). He also said that the Tekken stories progress in parallel with each character, and that it only has one true canon (story setting).

The Devil "Possession" Timeline
Kazuya had his encounter with the devil, later to be known as Devil by name, when he was about 5 years old. Heihachi, sickened by his weak and emotionally soft son, threw him off a cliff in order to have him climb back up. Although the injuries nearly killed Kazuya, but because of the devil gene, Kazuya survived the fall and was able to ascend the cliff. This could mean that the Devil Gene may have the skill to heal a Mishima and can keep a person from dying when they are close to death. If one is knocked out, they may possibly be in a coma because of the Devil Gene within his blood.

After the events of Tekken 2, Heihachi threw Kazuya's body into a volcano. This inadvertently caused Devil's soul to be split into two parts; one that stayed with Kazuya and the other that went in search of Kazuya's yet unborn son, Jin Kazama. When it finally found the unborn Jin, it was warded off by his mother, Jun Kazama, and was unsuccessful in taking over Jin. However, 15 years later, it returned, branded Jin's left arm with a mark and (possibly) brainwashed him (as seen in the Tekken 3 opening).

The Common Denominator
Interestingly enough, while Heihachi does not seem to have the powers of the Devil Gene, he has been the catalyst whose actions have resulted in the devil possession of the other Mishimas.

Heihachi staged a coup d'etat against Jinpachi, and locked him away under Hon-Maru, which resulted in Jinpachi being possessed by the "monster" (though this demonic possession is unrelated to the Devil Gene). It was also he, who threw Kazuya off the cliff when Kazuya was a child, almost killing him, causing the Devil gene to surface within Kazuya. Several years later, after the events of the second tournament, Heihachi threw Kazuya into a volcano, thus releasing part of Devil, which then searched for and tried to possess Jin Kazama, though initially unsuccessful. Heihachi and his Tekken Force soldiers fatally shot Jin Kazama near his death after the conclusion of Tekken 3, causing the Devil Gene to awaken within him and partially transform Jin into his Devil self.

Activation of the Devil Gene
It is not explained how the Devil Gene is activated, but evidence within the games seem to suggest that it can be activated consciously, subconsciously, or based on external stimuli. Regardless of which, the effects seem rather clear; the devil side of the person becomes more dominant, to the point of changing the physical appearance of their host, who in turn becomes much stronger.
 * Conscious activation: Kazuya performs a conscious activation of his Devil Gene between the events ofTekken 4 and Tekken 5, during the attack of Hon-Maru by the Jack robots. Jin Kazama seems to have become able to activate his Devil Gene consciously by the time of the events in Tekken 6 without becoming a devil like that of his father.
 * Subconscious activation: Jin's first transformation into Devil Jin at the end of the events of the third tournament was arguably a subconscious activation of his Devil Gene, likely in part of the hatred he felt for Heihachi's betrayal and evil.
 * Activation by external stimuli: Jin partially transforms at the end of the events of the fourth tournament due to Devil's attempts at forcing him to (as seen in Jin's Tekken 4 ending). Perhaps no more than half an hour later, when Jinpachi and his dark energy is freed from under Hon-Maru, Jin completely transforms because of his reaction to Jinpachi's evil energy, meaning that the Devil Gene can come out whenever and wherever there is negative energy around.

Suppression of the Devil Gene
Aside from the suppression of the Devil Gene through sheer force of will, as is implied by the method of conscious, and to some extent subconscious activation, there are also several external factors that can suppress the Devil Gene as well. The exact nature of these things are however not well explained, often not at all. So, it remains unknown how they suppress the Devil Gene; it is only known that they are able to do so.

Kazama Bloodline
Before the concept of a Devil Gene was created, and the concept was instead strictly spiritual, Jun Kazamaseemed able to suppress the Devil inside Kazuya. It was explained as having been because of Jun's serene and pure being. However, when the Devil history was reconnected and the Devil Gene concept created, the influence of the Kazamas became genetic as well; their bloodline, rather than Jun specifically having been a special case.

At the conclusion of Tekken 4 the effect of the bloodline is shown as Devil tries to transform Jin into his devil form by using the anger he has for his Mishima family, but fails and theorizes that it is due to the Kazama blood running in Jin's veins.

Asuka Kazama, in her Tekken 5 ending, was also able to suppress the Devil Gene of Jin, however, the ending was non-canon and it is thus unknown how strong an effect she has on the Devil Gene.

Materials
While it isn't known how, the Mishima Zaibatsu were successfully able to create chains of an unknown material that was able to specifically suppress the Devil Gene.

Angel
Before the concept of the Devil Gene, Angel was able to suppress the devil side of him. However, since the creation of the Devil Gene concept, Angel has all but vanished from the Tekken storyline and it is unknown whether or not she is still able to do suppress Devil or if she even still exists.

GENOCELL
In Tekken 4, when G corporation discovered Kazuya's body, they discovered strange malignant cells in it that they referred to as the "devil cells". With this knowledge, they used Kazuya to further their research and commenced a project known as the (Devil-Human) Integration Program. Using Kazuya's DNA they attempted to combine the devil and human cells, producing a half human half devil organism using human test subjects. But when trying to combine the two, the devil cells destroyed the human cells, making it impossible to create a "devil human", a viable life form similar to Kazuya's genetic make up.

G Corporation used Julia Chang's GENOCELL Program and discovered that the GENOCELL can suppress the devil cell allowing the human cells to combine with the devil cells. In other media such as the Online Tekken Comic, the GENOCELL is also similar or can be referred to as G Corporation's 'Anti Devil Factor'. It is also revealed in the comic that Kazuya and Jin use the 'Anti Devil Factor' to suppress the influence of the 'Devil' (however, in Kazuya's case, it allows him to also control the power of the 'Devil'/Gene without the conscious influence of it consuming his mind).