All conjugate eye movements are associated with neural commands which have been characterised by velocity and position information.  
Thus for the VOR, optokinetic eye movement, pursuit, saccades, and vergence, the pool of motoneurons in the 3rd, 4th and 6th nuclei use the same system, that of an initial pulsatile burst of force, and then a long-lasting maintained force, which persists after the movement is complete. This maintained step in force holds the eye stationary by resisting the elastic forces of the muscles and connective tissues surrounding the eye, forces which act passively to restore the eye back towards the straight ahead position of primary gaze1.
The pulsatile burst and maintained force, referred to as the pulse-step of innervation, applies to all types of eye movements: when the discharge occurs for low-velocity eye movements (ie, smooth pursuit, vestibular or optokinetic slow phases, and vergence), the phasic increase is usually smaller than the discharge required for saccades1. Saccades are the most rapid eye movements and serve to bring images of objects onto the fovea in as brief a time as possible, and are particularly illustrative of the pulse and step function: human saccades follow a target jump within ≈250 ms, are fast (up to≈6000/s), brief (typically≈30–100 ms), accurate, and stop abruptly (ie, with little subsequent ocular drift). Saccades are ballistic, ‘preprogrammed’, movements, and are so fast that vision is blurred as the saccade takes place; saccade speed is not under voluntary control, but depends on the size of the movement, with larger saccades having higher velocities2.

Pulse and Step

To make a saccade, the brain must compute two different but related components of innervation: the pulse and step.

For saccades, the velocity command referred to as the pulse generates the initial sequence for movements of the eyes. 

Horizontal Movements:
For generation of a saccade, both FEFs and the contralateral SC project to the PPRF:
The PPRF contains excitatory burst neurons (EBNs) that produce the supranuclear horizontal velocity command sequence (the pulse) for saccadic eye movements.  The pulse is a phasic command which gives the required torque needed to overcome the viscous drag of the orbital tissues, and is due to increased firing of excitatory burst neurons in the brainstem that results in a high-frequency burst of phasic activity in extraocular muscles. 

The number of spikes in the pulse is proportional to saccade amplitude, and hence the step may be calculated from the pulse by a process of integration3: neurons within the neural integrator apparatus (nucleus prepositus hypoglossi (NPH) and medial vestibular nucleus(MVN)) integrate eye velocity signals to produce a position command (the step) for accurate gaze holding.The step function acts to overcome the elastic restoring forces of orbital tissue and thereby assumes steady gaze holding. 

The pulse-step of innervation is sent to the motoneurons to move and maintain the eye in a new position2.

Vertical Movements:
The rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF), lying dorsomedial to the red nucleus in the dorsal midbrain, contains the pre-motor burst neurons for supranuclear vertical saccades.  The third, fourth and sixth cranial nerve nuclei contain the nuclear apparatus in the final common path for eliciting vertical and horizontal eye movements.  Torsional eye movements are also produced by the riMLF and by the cranial nerve nuclei.
For vertical eye movements the integrator apparatus includes the NPH and MVN, in addition to the interstitial nucleus of Cajal.  The generation of position commands to hold the eyes steady also involves the cerebellum.

Abnormalities of neural integration often produce gaze holding deficits such as gaze-evoked and primary position nystagmus. If the pulse and step are not matched correctly, the eye will drift (for about 600 ms) after each saccade from the position reached during the pulse to that corresponding to the step. 

All of the eye movement systems share a final common path, and therefore all share the same neural integrator. The input to the final common path for any type of eye movement (e.g. vestibular, pursuit, saccade) is a desired eye velocity3

 

Figure 1. The brainstem centres for horizontal and vertical generation of saccades:

Figure 2. Disorders of the saccadic pulse and step.  Innervation patterns are shown on the left, eye movements on the right.  Dashed lines indicate the normal response.

A.  Normal

B.  Hypometric saccade: pulse amplitude is too small, but pulse and step are matched appropriately.

C.  Slow saccade: decreased pulse height with normal pulse amplitude and normal pulse-step match.

D.  Gaze-evoked nystagmus: normal pulse, poorly sustained step.

E.  Pulse-step mismatch: step is relatively smaller than pulse

Redrawn from Leigh RJ, Zee DS.The Neurology of Eye Movements. 3rd ed. New York: Oxford University Press; 1999.
 

Figure 3. Pulse-step commands of saccades: pulse height and area under the curve (or “pulse amplitude) are shown.

Pulse height is proportional to the density of the action potentials during saccade generation and to the peak velocity of saccades, i.e. the smaller the pulse, the slower the peak saccadic velocity.
Pulse amplitude, or area under the curve of pulse (pulse height × width), reflects the amplitude of saccades, i.e. abnormally increased area under the curve is related to hypermetric saccades.
The X-axis represents activity of responsible neurons or muscles, and the y-axis represents time.

From: Termsarasab P, Thammongkolchai T, Rucker JC, Frucht SJ. The diagnostic value of saccades in movement disorder patients: a practical guide and review. J Clin Mov Disord. 2015;2:14.

 

References

  1. Glimcher, P. W. (2001). Eye Movement, Control of (Oculomotor Control). In International Encyclopedia of the Social & Behavioral Sciences (pp. 5205–5208). Elsevier. https://doi.org/10.1016/b0-08-043076-7/03542-7
  2. Wong, A. M. (2008). Eye movement disorders. Oxford: Oxford University Press.
  3. 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. doi:10.1093/brain/awl309