The cognitive science of hemispheric asymmetry has long been marred by drastic over-simplification. The left/right distinction has been associated with dichotomies like rational vs. emotional, specific vs. holistic, and analytical vs. synthetic. Such differences are much more graded than dichotomous, to the extent that they exist in the first place. So, before reviewing well-established kinds of hemispheric differences, it might be useful to dispel some "lateralization mythology."
First, although the left hemisphere is generally dominant in linguistic tasks, the right hemisphere also has some ability for language (mostly in terms of comprehending figurative word meanings and pragmatics, but little in the way of a standard lexicon or grammar). Secondly, the relationship between handedness and hemispheric dominance is not absolute: many left-handers will show left-hemisphere dominance, and some right-handers will show right-hemisphere dominance.
Some research shows that functional cerebral asymmetry is larger in the frontal lobes than in posterior regions. In keeping with this week's previous emphasis on functional divisions within the prefrontal cortex (PFC), my review of lateralization models is restricted to those that bear on the frontal lobes.
For the sake of simplicity, I'll just refer to the dominant hemisphere as the "left" hemisphere, and the non-dominant hemisphere as the "right" hemisphere.
Hemispheric Encoding-Retrieval Asymmetry (HERA) Model
Perhaps one of the most well known lateralization theories, the HERA model states that left prefrontal regions are more involved in encoding processes, while right prefrontal regions are more involved in retrieval processes. A 2001 paper using repetitive transcranial magnetic stimulation (rTMS) during encoding and retrieval has provided strong support for this model: temporary disruption of left PFC activity resulted in a larger encoding deficit than disruption of right PFC, and the opposite trend was found for retrieval deficits.
Production-Monitoring and Selection-Monitoring Models
In contrast to the HERA model, this group of theories about prefrontal lateralization suggest that left prefrontal regions are involved in the production or selection of information for memory processes, while right prefrontal regions are involved in monitoring the efficacy of those cues for memory processes. However, as Johnson et al note, "left, as well as right, PFC regions are recruited when monitoring requires more specific source (episodic) information than familiarity." Likewise, Cabeza et al. suggest that the left hemisphere makes more "inferences and generalizations" than the right hemisphere, which is "more veridical." At least one task switching study has also shown striking similarities to this account, in that increased left prefrontal activation is observed during updating (as would be expected of a "production" or "selection" region), and increased right prefrontal activation is observed during negative feedback (as would be expected of a "monitoring" region).
Familiarity-Novelty or Determinant-Indeterminant Models
This class of theories hold that left prefrontal regions are more engaged by "knowledge-intensive" tasks without uncertainty (including familiar tasks), whereas right prefrontal regions are more engaged by tasks involving uncertainty, indeterminacy, or novelty. According to Goel et al., the hemispheres may engage in competition to represent a situation, such that impaired right hemisphere activity may result in "premature interpretation" by the left hemisphere; according to this view, right PFC may effectively "inhibit" processing in the left via competition (which is strikingly reminscent of Chambers et al's finding that rTMS of right vlPFC causes a deficit in stop signal reaction time). Note that the Goel et al. model specifically distinguishes determinacy from amount of conflict.
This class of models suggest that left prefrontal regions are more involved in the processing of positive emotions, whereas right prefrontal regions are more involved in the processing of negative emotions. Although this theory sounds intuitively bizarre, there is nonetheless compelling evidence for this view. For example, verbal memory is improved but spatial memory is impaired by positive emotional states; the opposite trend is true for negative emotional states. Since verbal tasks are generally left-lateralized and spatial tasks are generally right-lateralized, this strongly suggests some degree of hemispheric specialization for emotional processing.
Methodological & Neuroanatomical Considerations
Although a variety of anatomical differences exist between the right and left hemispheres (reviewed in detail here), it is not yet clear exactly how these relate to cognitive processes or to any of the lateralization theories proposed above.
There are two particularly intriguing differences in cellular architecture between the right and left hemispheres. Evidence from diffusion tensor MRI (dt-MRI) suggests that the axonal branching is more densely packed in the left hemisphere than the right. Similarly, the left hemisphere has larger"dendritic branching" than the right, but only at large distances from the main shaft of the dendrite; the opposite trend holds at distances closer to the main dendrite. [Although it's tempting to map these differences onto a left-local/right-global dichotomy, it seems to me that these results actually argue in the opposite direction!]
We can partly blame the lack of strong structure-function relationships on what I see as methodological problems with functional imaging. In fMRI, there are multiple methods for determining lateralization in activation; the commonly used "lateralization index" technique does not actually report whether hemispheric differences are significant (nor do a surprising number of peer-reviewed papers). Secondly, some amount of individual variation in brain topology is normal, but it's unclear how this affects fMRI data analysis, which commonly standardizes activation to an "average" brain before averaging over subjects. All of this activation averaging and structure averaging could obscure important hemispheric differences in the structure/function relationship. Further, left- and right-hemispheric activations are already difficult to distinguish in medial prefrontal cortex because of their proximity (as noted here). Finally, the fMRI signal is affected by "time on task," such that areas engaged in a given activity for longer will be more likely to show significant activations. If activity in the left and right hemispheres differs in terms of their temporal profile, spurious lateralization might appear in fMRI analyses.
Despite these methodological problems, there are several commonalities among the theories reviewed above. For example, right PFC may appear more sensitive to negative feedback or emotions because, in some sense, they signify insufficient or inaccurate monitoring operations. Likewise, left pFC activity may be upregulated in response to positive feedback or emotions because they may suggest that the current cognitive operations are successful.
Monitoring processes may also be particularly important under conditions of novelty or indeterminacy, whereas left-hemispheric production processes can continue without monitoring in determinant or otherwise familiar situations. Finally, left hemispheric production processes may also be important for successful memory encoding; conversely, right hemispheric monitoring will be important for ensuring retrieval of the correct memory, and subsequent regulation of left hemispheric memory "cue" specification.
In conclusion, the production-monitoring model is probably the most parsimonious model of functional asymmetry in left & right PFC. An added benefit is that it falls neatly in line with the local/global processing dichotomy that may describe whole-brain function asymmetry. Production is by it's nature specific and local; monitoring is not likely to be successful unless it's more global.
The production-monitoring model can also be integrated with more recent evidence, reviewed by Ranganath, in which the left PFC is involved in the maintenance of specific information (perhaps for reinstating episodic context, or keeping online specific information for monitoring by right PFC), whereas right PFC is involved in a more global matching procedure (such as might be used in judgments of familiarity or evaluating the appropriateness of memory search results). Finally, it's important to note that the theories reviewed above need not be mutually exclusive.