The same motor neurons and extraocular muscles are active for all types of eye movements (eg, saccades, pursuit and vergence), indicating that the systems generating these different movement types share a final common path1. Three major regions are important: midbrain, pon-medulla, and cerebellum.

1. Midbrain centers for Saccades and Gaze Holding:

The center for vertical saccades is the rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF), and the center for vertical gaze-holding function is the interstitial nucleus of Cajal (INC).
Clinically, this means that an isolated vertical saccadic paresis or isolated vertical gaze evoked nystagmus would suggest a midbrain lesion. 
The INC projects to the ocular motoneurons, mainly via the posterior commissure2.

2. Pontine and pontomedullary centers for Saccades and Gaze Holding:

The connections of the horizontal semicircular canal to the medial vestibular nucleus in the medulla activate second order neurons in the vestibular nucleus, which project to the contralateral abducens nucleus.
The abducens nucleus projects to:
  -Ipsilateral lateral rectus (the 3rd neuron in the three neuron arc of the vestibulo-ocular reflex)
  -Contralateral medial rectus via the medial longitudinal fasciculus.

Pons
The center for horizontal saccades is the paramedian pontine reticular formation (PPRF). 
Clinically, this means that isolated horizontal saccadic palsy indicates a pontine lesion, and a unilateral PPRF lesion will result in saccadic disturbances on the side of the lesion. 

Medulla

The medulla contains most of the vestibular nuclei. Other major medullary structures involved in the control of eye movements include the perihypoglossal nuclei, including the nucleus prepositus hypoglossi (NPH), the paramedian nuclei and tracts, the inferior olivary nuclei, and the inferior cerebellar peduncles.

Components of the neural integrator in the medulla

The center for horizontal gaze-holding function is the NPH, which acts in concert with the vestibular nuclei of the medulla, and the vestibulocerebellum, together forming the “neural integrator.”

Disturbances of the medulla are best described in relation to a stroke of the dorsolateral medulla, a Wallenberg syndrome.

   

 
Vestibular nuclei
The vestibular nuclei receive information about the vestibular function of the opposite ear through the vestibular commissure which carries excitatory and inhibitory
signals from the vestibular systems, left and right. Multimodal integration of information at the level of the vestibular nuclei takes place allowing vision and proprioception
to guide vestibular responses.

Multimodal input to Vestibular Nuclei

   

Input to the vestibular nuclei comes from the three paired semicircular canals, the otolith organs, and from the cerebellum.  There is also vestibular nerve input directly to the cerebellum (flocculo-nodular lobe)(the vestibular nuclei can be viewed as ectopic cerebellar nuclei).
  Projections to the vestibular nuclei from the vestibular apparatus derive from:
  -The semicircular canals predominantly to the rostral portions of the vestibular nuclei complex (medial and superior vestibular nuclei).
  -The otolith organs extend predominantly to the caudal portions of the vestibular nuclei complex (lateral and inferior vestibular nuclei).  

    Output from the vestibular nuclei (superior) runs in the medial longitudinal fasciculus, connecting the oculomotor nuclei together (3rd, 4th and 6th).
Similarly, output from the vestibular nuclei in the form of the vestibulospinal tracts passes to the brain stem and spinal cord, and brings information about the body's position in space to the antigravity muscles.

See: Vestibular Neuron & Vestibular Nuclei

 

3. Cerebellar centers:

Cerebellar lesions are often accompanied by clinically easily identifiable oculomotor disturbances.
For example, defects of the flocculus/paraflocculus are characterized by saccadic pursuit, downbeat nystagmus, and impairment of the visual fixation suppression of the VOR.
Paraneoplastic cerebellar disorders often lead to opsoclonus, in addition to a range of oculomotor disturbances. 

Figure 1. Brainstem centres for gaze holding and saccade generation

Figure redrawn from Clinical Examination of the Ocular Motor and Cerebellar Ocular Motor System. Strupp, M. https://www.youtube.com/watch?v=meXAjVoQdCI

 

 

References

  1. Ramat S, Leigh RJ, Zee DS, Optican LM. What clinical disorders tell us about the neural control of saccadic eye movements. Brain. 2007;130(Pt 1):10-35.
  2. Kheradmand A, Colpak AI, Zee DS. Eye movements in vestibular disorders. Handb Clin Neurol. 2016;137:103-17.