In other words, how do the brains of those with BPD differ from those who don't have BPD?
The Wikipedia article doesn't even contain any possible explanations whatsoever.
The Neurobiology and Genetics of Borderline Personality Disorder indicates that a good deal of research has been done but a specific mechanism causing it has not been pinned down. It appears to be largely genetic which would strongly suggest a neurobiological/nature basis as opposed to a "nurture" related cause. (emphasis mine)
In summary, the neurobiological research that has been the most useful in shedding light on the physiology underlying borderline personality disorder has examined this multifaceted disorder by examining simpler dimensions of behavior separately, including impulsive aggression and affective instability. Evidence suggests that impulsive aggression involves a deficit in serotonergic activity. However, the specific mechanism underlying this remains unknown. It is clear that this component of behavior is substantially genetically encoded, and so new research has focused on elucidating the specific receptors underlying impulsive aggression through the examination of genes coding for specific receptors.