How are personality traits "encoded" in the brain? How are personality traits – such as optimism, sensation seeking or need for cognition – "encoded" in the brain?

Do people with different levels of, say, extraversion have different neuronal structures? Or do they have different amounts of certain neurochemicals, different numbers of receptors, or other kinds of functional differences?

So if you want to change a trait, can you simply stimulate or supplement neuronal functionality, e.g. by administering the lacking neurochemicals, or do you have to "destroy" and "rebuild" the neuronal structure, e.g. through learning?
Cool question...really huge though. I'll have to revisit this as I find time to add more. For starters, I just saw an interesting link in @ForbiddenOverseer's question, "Are there any personality theories that use the scientific method?" For some info on cerebral blood flow and extraversion, check out Johnson and colleagues (1999). Here's an excerpt of the abstract:


  RESULTS: Overall, introversion was associated with increased blood flow in the frontal lobes and in the anterior thalamus. Regions in the anterior cingulate gyrus, the temporal lobes, and the posterior thalamus were found to be correlated with extraversion. CONCLUSIONS: The findings of the study lend support to the notion that introversion is associated with increased activity in frontal lobe regions. Moreover, the study suggests that individual differences in introversion and extraversion are related to differences in a fronto-striato-thalamic circuit.


In an earlier answer today (to What makes a sight or an image mesmerizing and irresistible?), I implied that sensation-seeking relates to the behavioral activation system, the nucleus accumbens and VTA, and dopamine. Support for those relationships ought to be available through Wikipedia.

Here's a summary of other info from my lecture on biopsych for my class on personality a few years ago:


Frontal lobe


Activity has been correlated to negative emotionality via fMRI.
Cooperative people show more activity during social interaction, implicating reward sensitivity.
Aversive attention and motivation is right lateralized; approach motivation and aversion inhibition is left lateralized.
Transcranial magnetic stimulation (TMS) knocks out self-enhancement bias temporarily.
Damage reduces emotional experience, regulation, and inhibition – cf. Phineas Gage, Capgras syndrome, and the history of frontal lobotomies.

Amygdala


Implicated in identification of rewards &amp; threats


Activates in extraverts receiving pleasant stimuli (e.g., happy faces, scenes, &amp; emotion words; pleasant tastes)
Activates during social attraction; generates sexual responsiveness
Activates in shy people viewing unfamiliar faces
Also in pessimists when shown a picture of a snake
Overactive in people with anxiety disorders such as PTSD

Activated by unexpected emotional conflict – stronger in neurotics viewing conflicting cues.
Inhibited by anterior cingulate – cf. brain tumor in Charles Whitman, UT tower sniper ’66


“I have been a victim of many unusual and irrational thoughts.  These thoughts constantly recur, and it requires a tremendous mental effort to concentrate on useful and productive tasks.”


Ascending reticular activating system – acts like a valve on incoming stimulation


More “wide open” (active) in introverts


Stronger reaction to lemon juice stimulus
Faster responses to noises in brainstem via EEG

Reaction to erotica, violence, mutilation, insects, etc.:


High sensation-seeking: arousal and reward area activation
Low sensation-seeking: emotional self-control area activation

Electrode stimulation of substantia nigra $\rightarrow$ depression!
Governs reactivity, not baseline arousal


Optimal arousal threshold is the same distance from rest regardless of extraversion
ARAS affects acceleration from stimulation toward the threshold. See simplistic figure:





I've got a few answers here on neurotransmitters and hormones already:


Testosterone affects aggression, competitiveness, sexual motivation, sensation-seeking, risk aversion, empathy, and abstract reasoning. See "Are there recent theories on physiognomy?" and "What are the cognitive effects of increasing testosterone levels in men?"
Monoamine oxidase A affects maladaptive vulnerability to stress resulting in antisocial behavior. Mu-opioid receptors relate to collectivism and pain sensitivity. Serotonin also relates to collectivism and anxiety. See "Innate personality tests: do they exist? If not, why?"


Judging from effects of TMS (and tDCS), intelligence may relate to cortical excitability and myelination – see "Can learning be facilitated by transcranial magnetic stimulation?" As for changing personality in general, neuroplasticity may be important to consider, but biofeedback may be able to take advantage of it to alter neuroticism – see "Neuroplasticity and Treatment of Depression". Chronic malnutrition might even affect neuroticism by deeper mechanisms than subjective stress resulting directly from deprivation – see "The effect of proper food intake on emotions and brain function". Other links seem to exist between physical and mental well-being – see "Does mental satisfaction lead to physical satisfaction?" – but I'm probably getting further afield here than you intended answers to go.

Reference
- Johnson, D. L., Wiebe, J. S., Gold, S. M., Andreasen, N. C., Hichwa, R. D., Watkins, G. L., &amp; Ponto, L. L. B. (1999). Cerebral blood flow and personality: A positron emission tomography study. American Journal of Psychiatry, 156(2), 252–257. Retrieved from http://journals.psychiatryonline.org/article.aspx?articleid=173270.