Freely-moving mice visually pursue prey using a retinal area with least optic flow

Mice have a large visual field that is constantly stabilized by vestibular ocular reflex driven eye rotations that counter head-rotations. While maintaining their extensive visual coverage is advantageous for predator detection, mice also track and capture prey using vision. However, in the freely moving animal quantifying object location in the field of view is challenging. Here, we developed a method to digitally reconstruct and quantify the visual scene of freely moving mice performing a visually based prey capture task. By isolating the visual sense and combining amouse eye optic model with the head and eye rotations, the detailed reconstruction of the digital environment and retinal features were projected onto the corneal surface for comparison, and updated throughout the behavior. By quantifying the spatial location of objects in the visual scene and their motion throughout the behavior, we show that the image of the prey is maintained within a small area, the functional focus, in the upper-temporal part of the retina. This functional focus coincides with a region of minimal optic flow in the visual field and consequently minimal motion-induced image blur during pursuit, as well as the reported high density-region of Alpha-ON sustained retinal ganglion cells.

to the front of the animal, we next quantified whether this region overlapped with the functional focus 239 observed here ( Figure 3E). 240 The average 50% contour of the functional focus was overlapped by the highest density of On Alpha-ON 241 sustained RGC's by 35 and 67% for left and right eye respectively ( Figure 3E right eye respectively, 168852 frames, N=3 mice). The relatively linear relationships between head and 283 eye rotation around the head pitch and roll axes ( Figure 4B) with a transition through the origin suggests 284 that the horizontal, vertical and torsional eye movements are combined to effectively compensate pitch-285 and roll-related head movements. We next digitally froze each individual eye rotation axis (torsion, 286 vertical and horizontal) and measured the effect on countering the head rotation ( Figure 4C). For rotations 287 around the head x-axis (head pitch changes) the gain of compensation was most affected by freezing torsional rotations ( Figure 4C, gain mean±SD, control: -0.45±0.12and-0.48±0.06; torsion frozen -0.24±0.1 289 and-0.24±0.01, for left and right eyes respectively, N= 168852 frames, N=3 mice), while freezing vertical 290 or horizontal rotations had more minor effects ( Figure 4C, Table 3). The gain of compensation for rotations 291 around the head y-axis (head roll changes) was dramatically affected by freezing vertical rotations ( Figure  292 4C, gain mean±SD, control: -0.51±0.12and -0.62±0.05, vertical frozen -0.16±0.14and -0.17±0.03, for left 293 and right eyes respectively, N= 168852 frames, N=3 mice), with freezing torsion also reducing 294 compensation gain but to a lesser extent ( Figure 4C, Table 3). We next quantified the stability and 295 alignment of the animal's binocular visual field during the pursuit sequences and determined the location 296 of the functional foci within the stabilized region. 297 Functional foci are located in the motion-stabilized binocular visual field 321 Similar to rats, left and right visual fields overlapped extensively (Hughes 1979, Drager andOlsen 1980), 322 with eye movements creating variability in the extent of the overlap at the edges of the two visual fields, 323 the transition from monocular to binocular ( Figure 4D). The functional foci for both eyes were 324 predominately contained within the region of continuous binocular overlap. A horizontal transect through 325 the optical axis for all animals showed a gradual transition from continuous binocular coverage to zero 326 binocular coverage commencing just nasal of the optical axis ( Figure 4D We next quantified the variability of alignment of the left and right visual fields within the binocular 330 region, and specifically in the functional focus location ( Figure 4E) by using the center of mass (50% 331 isodensity contour center) of the left eye functional focus as an initial reference point and projecting this 332 point to the boundary of a hypothetical sphere surrounding the head. This contact point on the sphere 333 was then re-projected into the right eye to identify the matching location of the left eye ( Figure 4E). We 334 then followed the trajectory of the re-projected point in the right eye to get a measurement of alignment 335 variability ( Figure 4F, for comparison with the locations in the right eye projected into the left eye see 336  Repeating this analysis for all points within the region where the probability of binocular overlap was 341 greater than 5% showed that there was a relatively uniform alignment over the entire region ( Figure 4I), 342 and that the average alignment error in the functional foci was 8-10°. Coordination of eye movements 343 was important for alignment, as freezing the movements of one eye to its mean position resulted in a significant increase in the alignment error when comparing individual cricket tracking sequences (left all 345 rotations vs. left eye frozen P=1.78x -10 , right eye all rotations vs. right eye frozen P=7.12x10 -11 , N=52 346 sequences, unpaired Student's t-test), and a ~54% increase in the mean alignment error over all frames 347 for the reference location ( Figure 4I, left eye projected into right eye (left eye frozen) 13.4±8.3°; Right eye 348 projected into left eye (right eye frozen) 13.4±8.3 o , mean±SD, 159318 frames, N=3 mice), which also 349 resulted in a uniform increase in alignment error over the whole overlap region ( Figure 4J and Figure 4 -350 figure supplement 3J-L). In summary, during pursuit behavior the functional foci are located in a stable 351 binocular region of the mouse's visual field. However, in the absence of a mechanism for voluntarily 352 directing its gaze towards a specific target, such as smooth pursuit, tight coupling of VOR evoked eye 353 movements to head rotations would seem to be restrictive to an animal's ability to move the target into 354 a specific part of their visual field during pursuit. We therefore next measured what mechanisms mice use 355 to bring the prey into their functional focus. 356 357 Behavioral mechanisms for maintaining prey within functional foci 358 At detection, mice orient towards their target, aligning their head with the prey and running towards it 359 ( Figure 2D), keeping the cricket within a narrow window around its forward direction. This provides a 360 direct way for mice to hold their prey within their binocular visual fields ( Figure 4D). We next measured 361 whether additional head or eye movements are used to keep the target within the functional foci. If the 362 mice were actively maintaining the prey within a fixed location of their visual fields the position of the 363 cricket image should not change as the mouse approaches the cricket. The cricket image location could 364 be maintained by either a head or eye rotation. If they were not actively maintaining the prey in a fixed 365 location, the cricket images should shift downwards in the visual fields as the mouse approaches. To 366 distinguish between these two possibilities we plotted the cricket positions in the eye views color-coded by the distance between the mouse and cricket ( Figure 5A). As the mouse approached the cricket during 368 the track behavioral epoch, the projected cricket positions shifted lower in the visual field ( Figure 5A    and right eyes respectively, mean ± SD, N=2 mice, Figure 6C). During free movement both the distance 434 from the eyes to objects in the environment, as well as head and eye-rotations had a strong influence on 435 the optic flow fields. We visualized the average flow fields during free motion by calculating the optic flow 436 on the cornea during multiple pursuit trials (N=20 prey chases containing 52 tracking sequences, initial 437 Euclidean distance mouse-cricket >20 cm). The resulting optic flow density maps were complex with a 438 wide range of average speeds (133.44±221.42 °/s, mean±1SD, median 28.64 °/s, interquartile range 4.57-439 137.18 °/s, N=2 mice, Figure 6D). The area of lowest optic flow extended from nasal field of view to 440 overhead ( Figure 6D) but unlike the simulated case ( Figure 6C Figure 6E). Together this shows that mice preferentially maintain their prey in the region of reduced 458 optic flow during pursuit, where the retinal image of their prey is least distorted due to motion induced 459 image blur. 460

Discussion: 461
We developed a technique for reconstructing the visual fields in a freely moving mouse during prey pursuit 462 to quantify the spatial relationship between the environment, cricket and the mouse. Using this approach, 463 we show that mice, while pursuing crickets, preferentially maintain the prey in a localized region of their 464 visual field, termed here the functional focus. The positional maintenance of the cricket was not achieved 465 by active eye movements that followed the prey, but rather by the animal's change in behavior, 466 specifically the head-movement and orientation towards the prey during pursuit. While eye rotations 467 stabilized the visual field via the vestibulo-ocular reflex by countering head rotations, the rotations were 468 not specific to either prey detection or prey tracking. This strongly suggested that eye-rotations in mice, 469 like in rats, primarily stabilize their large field of view and that all three rotational axes, including ocular 470 torsion, combine to counter head rotations. In addition, we also show that eye rotations cannot be 471 In addition, the current study adds to the significance to these previous 509 findings and suggests that the functional focus location is well placed to support stereoscopic depth 510 perception, assuming that this form of visual processing is available to and employed by the mouse ( perhaps not surprisingly, strikingly different from that observed with idealized motion, resulting in large 541 part from the large differences to objects in the environment in which the behaviors were performed. For 542 fast moving, ground dwelling animals like mice, considerable asymmetry in optic flow across the visual 543 field may be the more normal case, considering that objects above the animal are, in general, likely to be 544 more distant. 545 In freely moving rats it has been shown that ocular torsion is correlated with head pitch such that nose-546 up rotation of the head is counteracted by incyclotorsion (rotation towards the nose) of both eyes, with 547 nose-down pitch counteracted by excyclotorsion ( In summary, we show here that during pursuit mice preferentially keep their intended prey in a localized 561 region of their visual fields, referred to here as the functional focus, but do so by orientating their head 562 and body and running directly towards the prey rather than with specific eye movements. The location of 563 the functional focus is within the binocular visual field, but in addition also coincides with the region of 564 minimal optic flow during the pursuit, and presumably also minimally distorted by motion blur. 565 566 567

Methods: 568
Animal details 569 Experiments were carried out in accordance with protocols approved by the local animal welfare 570 authorities (Landesamt für Natur Umwelt und Verbraucherschutz, Nordrhein-Westfalen, Germany). 571 Experiments were carried out using male C57/BL6JCrl mice (acquired from Charles River Laboratories).

572
At the time of the cricket hunting experiments, mice (n=9) were between 2-8 months old, and weighed 573 between 21-29g. Mice were maintained on a 12 hr light/dark cycle. Crickets (Acheta domesticus, Bugs-574 International, Germany) were housed in 480x375x210 cm cages with ad lib water and food (powdered 575 mouse chow). Cricket body sizes ranged from 1 cm to 2 cm (1.8 ± 0.3 cm, mean ± SD, n=25). 576 577 Implant surgery 578 Animals were anaesthetized using fentanyl, medetomidine and midazolam (respectively 50µg/kg, 5mg/kg 579 and 0.5mg/kg, delivered i.p.), and analgesia was provided with carprofen (7mg/kg delivered s.c.). Body 580 temperature was maintained using a thermostatically regulated heating pad. Respiration rate and depth 581 of anesthesia was monitored throughout the procedure. Following opening of the skin and removal of 582 connective tissue overlying the sagittal suture and parietal bones, the skull was cleaned with H2O2 (3%). A 583 custom-made implant, consisting of a flat circular attachment surface for attachment to the skull, and 584 implant body with three anti-rotation pins and a magnet ( Figure 7A-B), was fixed to the dried skull using 585 a UV-curing dental adhesive (Optibond FL, Kerr Corporation, Orange, California, USA) and a UV-curing 586 dental composite (Charisma, Kulzer GmbH, Hanau, Germany). The implant attachment surface and body 587 were made from light-weight, bio-compatible dental resin (Dental SG, Formlabs, Germany). Skin margins 588 were closed with 5/0 Vicryl sutures (Ethicon Inc, Somerville, NJ, USA) and a cyanoacrylate adhesive 589 (Histoacryl, B.Braun, Melsungen, Germany). The injectable anesthetic combination was antagonized with naloxone, atipamezole and flumazenil (respectively 1.2mg/kg, 0.5mg/kg and 0.75mg/kg, delivered i.p.), 591 and the animal was allowed to recover. 592

Positioning of the head-mounted cameras 594
The eye cameras for oculo-videography were mounted on mounting arms which were attached to a 595 baseplate with complementary holes to the anti-rotation pins on the implant and fitted with a magnet of 596 complementary polarity. During positioning of the head-camera, mice were anaesthetized with isoflurane 597 (induction: 3-5% isoflurane, maintenance: 2.0% isoflurane in air). Anesthetic depth and body temperature 598 were monitored as above. The cameras were positioned to have a sharp image of the entire eye, with the 599 mounting arms adjusted such that the cameras and mounting system caused minimal disruption to the 600  Figure 7C). Mice were given 2 minutes in which to capture the crickets. 611 Prior to the assessment mice were food deprived overnight before the trial. 612

Placement of torsion tracking marks 613
Crenellations along the iridial-pupil border were less distinct in mice than those previous described in rats 614 To establish the animal's horizontal plane from the head tracking LEDs, a position for the animal's nose 674 was first defined by averaging to 3D positions of the marked nostrils. A pre-forward vector was calculated 675 using the direction between mean of eyes and nose and a pre-up vector as vector orthogonal to the pre-676 forward and vector between the eyes. Next, the left vector was defined as orthogonal to pre-forward and 677 pre-up. Finally, the system was rotated by 40° around the left vector such that forward vector was 678 elevated. This established a head-fixed forward-left-up coordinate system that was based on the bregma-679 lambda sagittal plane by tilting the eyes-nose plane by an angle of 40°. 680 Interpolation 681 Head tracking frame rates were 200Hz, while eye tracking cameras recorded at 60 Hz. Eye positions 682 were consequently interpolated as follows: Let 683 be two rotations that transform the vector (0,0, −1) into the gaze vectors 1 , 2 in head fixed 685 coordinates at times 1 , 2. Then for a time ′ with 686 ′ = 1 + * ( 2 − 1) , 0 < < 1 687 the corresponding rotation ′ is interpolated such that ′ is placed on the geodesic defined by 1 , 2 688 with an angle of * ∠ ( 1 , 2 ) to 1 , and the rotation of a vector perpendicular to (0,0, −1) is 689 continuous and uniform between 1 and 2.

Classification of behavioral periods 762
To decrease the effects of tracking noise and rapid head rotations, mouse velocity, target bearing and 763 inter-animal Euclidean distances were first filtered using a 50ms sliding window Gaussian filter. 764 The criteria used to classify the different hunt phases were based on those described in (Hoy, Yavorska et 765 al. 2016). In an initial step, behavioral end points (tend) for capture periods were identified by manual 766 inspection of the tracking movies. Further identification of the behavioral start points (tstart) and tend points 767 for the different hunt sequence epochs were then identified as described below. 768 The tend points were defined as: 769 A. The tend point for a detect period was defined as the last frame before (1) Mouse head velocity 770 in the direction of the cricket was >= 20 cm/s, (2) The mouse's bearing towards the cricket was constantly 771 below 90° and (3) the Euclidean distance between the mouse and cricket was continuously decreasing. 772 B. The tend point for a tracking period was identified by locating local minima in the mouse-cricket 773 Euclidean distance time plots, where local minima were defined as points at which the mouse came within 774 a contact distance of 6 cm (measured from the tracked point on the mouse's head, giving a > 3 cm 775 separation between the mouse's nose and the cricket). These were followed either by a capture period 776 (see below) or were followed by a ⩾ 5cm increase in inter-animal Euclidean distance, which were defined 777 as cricket escapes. In cases where the absolute value of the target bearing was > 90° before the mouse 778 turned towards the prey, the start of the tracking period was taken as the first frame in which the bearing 779 to the target was <90°. Only tracking periods, in which the initial Euclidean distance between the mouse 780 and cricket was >20 cm were analyzed. 781 C. The tend point for the capture period was taken to be the point 6 cm away from the cricket, 782 following which a cricket captured and consumed.

46
The start points of the hunt epochs were defined as follows: 784 A. The tstart for the detect period was the frame 500 ms prior to the detect tend point. 785 B. The tstart for the tracking period was the first frame after the tend detect frame. be the idealized environment. For a given direction ∈ 2 we calculate the projection into the right eye 845 ∈ ℝ 3 by: 846 The average alignment is then calculated using the formula: where ∑ ̅ denotes mean and 〈 〉 denotes normalization. 850 851 Visual field overlap 852 Visual field overlap was analyzed in the idealized finite-distant spherical environment described above for 853 ocular alignment. Visual overlap was calculated from the frame-wise maps of 3D object intersection points 854 in the contralateral eye (see above section "Generation of animal's eye view") generated for the ocular 855 alignment analysis: pixels whose 3D object intersection points had an angle of less than 90° to the optical 856 axis were considered part of the overlapping field of view. Probability maps of overlap were calculated by 857 averaging. 858 To calculate the optic flow in a given pixel for a given eye, we consider the difference vector between the 863 3D positions in the static eye coordinate system of the object intersection point for this pixel one frame 864 before and after the frame of interest, divided by 2 • and mapped to unit distance by dividing by the 865 distance between eye and interception point. This yields a 3D motion vector which is independent of 866 influences of the frame rate. The spherical projection used in the rendering process described above is a 867 non-conformal, locally non-isometric map, meaning that angles between lines and distances between 868 points are not preserved. This makes it necessary to evaluate the flow in each point in a local, orthonormal 869  Table 1). While we recognize that this study employed a different strain of mice to the one 901 used here, the methodology used provides estimates of physical and optical parameters measured under 902 conditions closest to those relevant for the current study. Further, variation of these parameters was not 903 found to change the model to an extent that would influence the conclusions drawn from analyses 904 involving the eye model (see below). These values distinctly define the spatial shapes and positions of the 905 refractive components of the model eye ( Figure 3A), as well as refractive indices for all but the lens, . 906 We further assume a pupil radius of 594 µm, which is the mean of constricted and dilated mouse pupil 907 sizes from (Pennesi, Lyubarsky et al. 1998). We define the focal point of a bundle of rays as the point with 908 minimal least squares distance to the rays. To optimize the missing refractive index ∶ Ω → + 909 inside the lens body Ω ⊂ ℝ 3 , we first calculated two lens models and optimized them such that the focal 910 point of 10000 rays emitted from an object at 10 cm distance on the optical axis lay on the retina. The 911 first model, for optimization of the lens surface, was derived with optimal constant refractive index ∈ 912 + over the volume. The second model, for lens gradient optimization, was derived with a smooth 913 transition of refractive index to the anterior and posterior lens boundary, ie. = 1.333 on Ω. We then 914 used Poisson's equation ∆ = , and optimized the strength of the gradient ∈ + . We assumed the 915 final lens model as a linear combination of these two models: 916 with ∈ [0,1], where we optimized as described for the above models, but from a point 10 cm away 918 and 45° off optical axis. The derived refractive indices (Table 2) were within the range measured in (Cheng,919 Parreno et al. 2019). 920 To test the sensitivity of the model to changes in assumed physical parameters, we systematically changed 921 the radius of curvatures listed in Table 1, and the thickness listed in Table 2  To quantify the effect of head rotations on VOR evoked eye movements in a common coordinate system, 971 head rotations were normalized such that the average pitch and roll were 0. Axes were labeled X and Y 972 respectively and eye rotations were represented using this horizon-aligned X-Y coordinate system.    Figure 3A). (E) Regions within the isodensity contours from A and the 50% isodensity contour from the track epochs from Figure 2H projected through the mouse eye model into the corneal view from the left eye (from Figure 3B). (F) Top-down view of the coverage region for the left eye of the 50% isodensity contour (blue) and second highest RGC region (brown). Bars represent the probability density function for the respective regions at that azimuth angle. Mouse's forward direction directed to 0o, and mouse's right directed to 90 o. (G) Top-down view of the coverage region for the right eye of the 50% isodensity contour (green) and second highest RGC region