Saccadic and Postsaccadic Disconjugacy in Zebrafish Larvae Suggests Independent Eye Movement Control

Abstract

Spontaneous eye movements of zebrafish larvae in the dark consist of centrifugal saccades that move the eyes from a central to an eccentric position and postsaccadic centripetal drifts. In a previous study, we showed that the fitted single-exponential time constants of the postsaccadic drifts are longer in the temporal-to-nasal (T->N) direction than in the nasal-to-temporal (N->T) direction. In the present study, we further report that saccadic peak velocities are higher and saccadic amplitudes are larger in the N->T direction than in the T->N direction. We investigated the underlying mechanism of this ocular disconjugacy in the dark with a top-down approach. A mathematic ocular motor model, including an eye plant, a set of burst neurons and a velocity-to-position neural integrator (VPNI), was built to simulate the typical larval eye movements in the dark. The modeling parameters, such as VPNI time constants, neural impulse signals generated by the burst neurons and time constants of the eye plant, were iteratively adjusted to fit the average saccadic eye movement. These simulations suggest that four pools of burst neurons and four pools of VPNIs are needed to explain the disconjugate eye movements in our results. A premotor mechanism controls the synchronous timing of binocular saccades, but the pools of burst and integrator neurons in zebrafish larvae seem to be different (and maybe separate) for both eyes and horizontal directions, which leads to the observed ocular disconjugacies during saccades and postsaccadic drifts in the dark.

Keywords: brainstem; gaze holding; larvae; ocular motor; saccades; zebrafish.

Figure 1

Typical (A) eye position and (B,C) velocity traces of 5–6-day-old zebrafish larva in the dark. The two eyes move together in terms of saccade timing and eye-movement direction. However, the saccades and the postsaccadic eye drifts are not conjugate. The right eye trace is depicted with a thin line, and the left eye with a thick line. Note that for the right eye, a nasal movement is to the left, whereas for the left eye a nasal movement is to the right.

Figure 2

Conceptual model of the larval ocular motor system for spontaneous eye movements in the dark with Laplace notations. (A) Model of larval ocular motor system. Burst neurons generate velocity impulse signals to the velocity-to-position neural integrator (VPNI). The VPNI converts the velocity signals to position commands. The eye plant, then, takes the position commands and generates eye movements. (B) The firing of burst neurons. The firing is described as a gamma function that can be defined by three parameters: gain, skew and duration (as shown in the equation below), where t is time, t_on is the burst onset, σ_DUR is the burst duration, the exponent γ determines the gamma-burst skewness, and Gain determines the amplitude of the gamma function. (C) Schematic plot of the VPNI model. The VPNI model receives velocity signals from burst neurons and integrates these signals to position commands. T_VPNI is the VPNI time constant, V(t) is the velocity signal from burst neurons, x₀ is the initial eye position, offset is the final eye position, and p(t) is the position command. In this study, x₀ and offset are set to zero. (D) The mathematical model of the eye plant, described as a second order system that receives position commands p(t) from the VPNI and generates eye movements. The second order system is determined by the two time constants, T_e1 and T_e2.

Figure 3

Saccades of nine tested larvae. (A) Median saccadic peak velocity, (B) amplitude, and (C) main sequence of nine tested larvae (two eyes and two directions relative to the head. N->T, nasal to temporal direction; T->N temporal to nasal direction.

Figure 4

Simulation saccades of zebrafish larvae in the dark. (A) Eye position and (B) eye velocity of zebrafish larvae in the dark.

Figure 5

Changes in the model simulated outputs corresponding to varying model parameters. The circles depict changes (%) in the saccadic peak velocities, the crosses depict changes (%) in the saccadic amplitudes, the squares depict changes (%) in the ratios of the saccadic peak velocity to the amplitude, and the stars depict changes (%) in the time constants of the postsaccadic eye drifts of the simulated outputs in response to the +50% to −50% changes in (A) gain, (B) duration, (C) skew of the velocity impulse signal generated by the simulated burst neurons, (D) VPNI time constant, (E) ratio of the velocity drag to the elastic stiffness of the simulated orbital tissues and (F) ratio of the mass of the eye ball to the elastic stiffness of the simulated orbital tissues.

Figure 6

Scheme of neuronal populations controlling saccades and gaze holding in the brainstem. (A) Binocular control, where a single command controls the movement of both eyes, similar to Hering’s law in primates. (B) Uniocular control, where each eye receives separate movement commands, similar to Helmholtz’s concept. MN, motor neuron; VPNI, velocity-to-position neural integrator.