Ring attractor dynamics in the?Drosophila?central brain

???Ring attractors are a class of recurrent networks hypothesized to underlie the representation of heading direction. Such network structures, schematized as a ring of neurons whose connectivity depends on their heading preferences, can sustain a bump-like activity pattern whose location can be updated by continuous shifts along either turn direction. We recently reported that a population of fly neurons represents the animal’s heading via bump-like activity dynamics. We combined two-photon calcium imaging in head-fixed flying flies with optogenetics to overwrite the existing population representation with an artificial one, which was then maintained by the circuit with naturalistic dynamics. A network with local excitation and global inhibition enforces this unique and persistent heading representation. Ring attractor networks have long been invoked in theoretical work; our study provides physiological evidence of their existence and functional architecture.

???studies of neural circuits near the sensory?periphery have produced deep mechanistic insights into circuit functions (1, 2). However, it has been more challenging to understand circuit functions in central brain regions?dominated by recurrent networks,which often produce complex neural activity patterns.These dynamics play a major role in shaping cognitive functions (3–7), such as the maintenance of head- ing information during navigation (8–10). A head- ing representation must be unique (because an animal can face only one direction at a given time) and persistent (to allow an animal to keep its bearings in darkness), yet must allow updating that matches the magnitude and speed of heading changes expected from the animal’s movements. Theoretically, this can be accomplished by ring attractor networks (11–14), wherein the posi- tion of a localized subset of active neurons in a topological ring represents the animal’sheading direction. However, whether the brain uses these hypothesized networks is still unknown (8, 15). A recent study reported that a population of neurons, called E-PG neurons (Fig. 1, C and D; see supplementary materials for nomenclature), in the Drosophila melanogaster ellipsoid body (EB) appears to use bump-like neural activity dy- namics to represent the animal’s heading in visual environments and in darkness (16, 17). Here, we establish essential properties of the network that enables this representation.

We first determined whether the E-PG popu- lation activity bump tracks the fly’s heading direc- tion relative to its visual surroundings during tethered flight (Fig. 1 and fig. S1). We used two- photon imaging with the genetically encoded cal- cium indicator GCaMP6f (18)torecorddendritic calcium activity of the entire E-PG population in the EB while the fly was flying in a virtual-reality LED arena. The azimuthal velocity of the visual scene was proportional to the fly’s yaw velocity (Fig.1,AandB).Aswithwalkingflies(16), E-PG population activity during flight was organized into a single bump, whether the visual scene contained a single bar (fig. S1B) or a more complex pattern(Fig.1G).Theactivitybumpcloselytracked the fly’s heading in flight (Fig. 1K) and persisted in darkness (Fig. 1H). However, unlike in walking, the activity bump seldom tracked the fly’s motor actions in darkness (Fig. 1, H and K, and fig. S1C), potentially because tethering deprives the fly of nor- mal sensory feedback about its rotational move- ments from its halteres (19). Although the location of the activity bump eventually drifted in some flies, the bump’s movement was, on average, uncorrelated to the animal’s turning move- ments in darkness (Fig. 1K). These findings suggest that the representation of heading in the E-PG population has intact, visually driven dynamics as well as persistence, but is largely uncoupled from updating by self-motion cues during tethered flight.

To test whether the fly’s compass network enforces a unique bump within the EB, we took advantage of the relative persistence of the visually evoked activity bump in darkness, and asked wheth- er this bump could coexist with an “artificial” bump of activity. We used localized optogenetic stimula- tion to create artificial activity bumps in different locations within the E-PG population. Using a transgenic fly line in which E-PG neurons co- expressed CsChrimson (20)andGCaMP6f,weused alternating two-photon laser scan lines of excita- tion (higher laser intensity) and imaging (normal laser intensity) to monitor changes in E-PG pop- ulation dynamics in response to an optogeneti- cally created spot of local activity (Fig. 2, A and B, and fig. S2, A and B). By varying the intensity of stimulation light delivered to the target location, we could create bumps of increased calcium ac- tivity(Fig.2,CtoF,andmovieS1).Asthenewbump formed, activity at the previous location began to decline and eventually disappeared (Fig. 2D) without significantly perturbing the fly’sbehavior (but see fig. S2E). When the optogenetic excitation?was terminated, the amplitude of the artificially created bump settled at levels typically evoked by sensory stimuli and did not disappear; it either stayed in the induced location for several sec- onds (fig. S2F) or slowly drifted away (see below) (Fig. 3).

The bump’suniquenessmayarisethroughei- ther recurrent mutual suppression or an indirect mechanism whereby strong bump activity in the EB functionally inhibits feedforward sensory in- puts to other E-PG neurons. To discriminate be- tween these alternatives, we simultaneously excited two locations on the EB ring. A reference location was excited at a fixed laser power, and a second, spatially offset location was excited at increasing levels of laser power (fig. S2G and movies S3 to S5). We could always suppress the reference bump by increasing laser power at the second location above a certain threshold, consistent with mutual suppression.

Recurrent suppression can ensure a unique activity bump through a simple winner-take-all (WTA) circuit (fig. S3A). However, an animal’s representation of its angular orientation should favor more continuous updates based on turning actions. Such gradual, ordered drift to nearby locations would be more consistent with contin- uous, or ring, attractor models (fig. S3, B to D). We therefore examined changes in the location of an artificially created bump after the stabili- zation of its peak activity at the “natural” level. The experiments were performed in darkness to untether the bump from any potentially lingering visual input (Fig. 3). If EB dynamics were driven by a WTA network, bumps would be expected to disappear at times and to jump to random distant locations (fig. S3E). In contrast, the bump drifted gradually around the EB (Fig. 3, B and D, and movie S6); this finding suggests that the fly’s heading representation is updated through functionally excitatory interactions between neigh- boring E-PG neurons, consistent with a ring attractor model. These observations together rule out the possibility that network dynamics in darkness result purely from cell-intrinsic me- chanisms (21, 22) or slowly decaying visual input. Most important, direct manipulation of E-PG neuron activity changed the network state, which implies that E-PG neurons do not merely mirror dynamics occurring in a different circuit, but are themselves an important component of the ring attractor (23).

We next aimed to dissect the effective con- nectivity pattern underlying ring attractor dy- namics in the E-PG population. A wide range of network structures can, in principle, implement ring attractors (11, 13, 14, 24, 25). We focused our efforts to a model space between two extreme net- work architectures that are analytically solvable: (i) a“global model” based on global cosine-shaped interactions (fig. S3B) (11, 13, 26) and (ii) a “l(fā)ocal model” based on relatively local excitatory inter- actions (fig. S3D and supplementary text) (24, 27). Under constraints of a fixed bump width of 90° to match physiological observations (Fig. 1J) and an assumption of effectively excitatory visual in- put without any negative bias, both models could?explain the basic properties of bump dynamics, including its uniqueness and its persistence in darkness. We therefore probed the network’sre- sponse to more artificial conditions, such as abrupt visual stimulus shifts.

We first examined experimentally how the E-PG population responded to unnatural, abrupt visual shifts. Depending on the distance of the shift, the E-PG bump either“flowed” continuously (shorter shiftdistances;Fig.4,AandC,andmoviesS7and S8) or “jumped” to the new location (longer shift distances; Fig. 4, B and C, and movie S9) (16). In simulations, both models predicted a mixture of jump and flow responses, depending on the strength and width of the abruptly shifting visual input (Fig. 4D, fig. S4A, and supplementary text). For example, weak wide input induced flows and strong narrow input evoked jumps (Fig. 4D). How- ever, the jump-flow balance predicted by the two?models differed and was more consistent with the local model in several aspects (Fig. 4D and fig. S4A). First, the visual input strength we in- ferred from normal conditions was much weaker than required by the global model for bump jumps (fig. S1D). Second, the global model required a much-wider-than-normal range of visual input strengthstoexplainjumpsatmultipledistances (Fig. 4D, fig. S1D, and fig. S4A). Third, using pa- rameters consistent with the rest of our findings, we could reproduce the jump-flow ratio observed in Fig. 4C with the local model but not with the global model (fig. S4B).

To obtain more concrete evidence, we compared model predictions to experimentally observed bump dynamics, under conditions in which input strength, polarity, and shift distance were control- led through optogenetic stimulation. To simulate moderate and large input shift distances, we sequentially stimulated two small regions in the EB— each with an angular width of 22.5°—separated by either 90° or 180° (Fig. 4, E to G, movie S10, and fig. S4, C to E). We then varied the stimulation laser power to detect the threshold required for the bump to jump (Fig. 4E). The laser power required to elicit a jump was not significantly different be- tween the two different shift distances, favoring the local model (Fig. 4F). We then inferred the strength of input to the network by comparing the amplitude of the optogenetically evoked bump to natural bump amplitudes in darkness. The opto- genetic input strength required to induce jumps was smaller than the global model’s prediction but matched that of the local model (Fig. 4G) and the range of the inferred visual input strength under normal conditions (fig. S1D, fig. S4, D and E, and movie S11). Finally, when we tested inter- mediate?models?that?lie?between?the?extremes?of?the local and global models (fig. S4, H and I, and supplementary text), we found that any model that exhibited the observed jumps in response to a weak 22.5°-wide input had narrow connectivity profiles (fig. S4I). All these observations were once again consistent with the local model.

In mammals, heading representations are thought to be distributed across multiple neural populations and multiple brain areas (8). In Drosophila as well, the compass system likely involves multiple cell types, including neurons in the protocerebral bridge (PB) (17, 23). Further, occasional changes observed in the dynamics suggest network modu- lation by other factors not yet known. For exam- ple, we sometimes observed sudden changes in E-PG dynamics, as when the amplitude of the sensory-evoked activity bump changed depending onwhetherornotthetetheredflywasflying(see supplementary materials) and, occasionally, during flight [population vector average (PVA) amplitude plotsinFig.1,GandH,Fig.4,AandB,andfig. S1B]. Nonetheless, the E-PG population provides a?powerful physiological handle on the internal representation of heading (16): a single activity bump moving through topographically arranged neurons. The experimental approach this enabled provides one avenue for investigating which of multiple populations are key circuit components of a computation and which simply read out the results of that computation. We found that the artificial bump created by directly manipulating E-PG population activity displays natural dynam- ics, which indicates that these neurons are a key component of the heading circuit.

Our finding that the uniqueness of the E-PG activity bump is ensured via global competition strengthens the conclusion that this population encodes an abstract internal representation of the fly’sheadingdirection(16). Such abstract repre- sentations permit an animal to untether its actions from the grasp of its immediate sensory environ- ment and thereby confer flexibility in both time and behavioral use. Combining an analysis of arti- ficially induced bump dynamics with theoretical?modeling allowed us to interrogate this recurrent circuit architecture. We found that the effective network connectivity profile was consistent with ring attractor models characterized by narrow local excitation and flat long-range inhibition. This neural circuit motif of local excitation and long-range inhibition is ubiquitous across many brain areas and across animal taxa (28–31). Such observations support the idea that common circuit motifs might be evolutionarily adapted to serve as crucial building blocks of cognitive function.

Fig. 1. E-PG neurons encode body orientation relative to the visual world during tethered closed-loop flight. (A) Setup schematic. (B)Close-upof tethered flying fly. (C)Centralcomplex.(D) Dendrites of each E-PG neuron innervate wedge-shaped segment of EB; axons project to corresponding glomeruli in PB and Gall. (E) Averaged calcium image of dendritic processes of entire E-PG population segmented into 16 regions of interest (ROIs). (F) Position (PVA direction) and strength (PVA amplitude) of bump obtained by summation of 16 vectors whose lengths represent magnitude of fluorescence transients ( DF/F0). (G) GCaMP6f fluorescence transients in E-PG dendrites during tethered flight in complex visual scene. Top: Visual pattern at sample?time points. Second row: Sample frames of calcium imaging.Third row: DF/F0 of 16 ROIs. Grayscale band denotes PVA amplitude; red line is PVA estimate. Fourth row: PVA estimate and heading (blue). Bottom: Same as fourth row, but unwrapped. (H) Fluorescence transients in darkness. (I)Numberofactivity bumpsinE-PGpopulationacrossflies(n = 10) for three visual conditions. Each dot with vertical line indicates mean± SEM for each fly. Population mean ±SEMisshownatleftofeachscatterplot.(J) Bump width measured by full width at half maximum. (K) Correlation between estimated bump position and heading. (L) Angular offset between PVA estimate and scene orientation. Whisker plots, mean ± circular SD.

Fig. 2. E-PG neurons compete by mutually suppressing each other through recurrent connections. (A) Schematic of simultaneous calcium imaging and localized optogenetic stimulation. (B) Analysis procedure for collected images. (C) Top: Temporal profile of two-photon optogenetic stimulation. Bottom: Three sample frames (smoothed with Gaussian filter). Yellow rectangle with arrow, stimulus OFF; red rectangle with arrow, stimulus ON. (D) Time course of calcium dynamics from example fly (left) and population (right). Gray background, optogenetic stimulation period; gray lines, individual trials (left) or flies (right). Top: Mean F of stimulated?ROIs. Bottom: Mean of the four most active ROIs outside optogenetically stimulated area before stimulation. Thick colored lines and colored shaded area denote mean and SEM, respectively. (See fig. S2C for control experiment.) (E) Distribution of fluorescence ratio during and before stimulation. P < 0.001, Wilcoxon rank sum test between stimulated (red) and outside stimulation (blue) areas. (See fig. S2D for control experiment.) (F) Suppression by optogenetic stimulation. The x axis indicates distance from stimulation position to existing bump; P <0.001,t test for each distance. Limited sample size prevented a statistical test for p/8.

Fig. 3. Drift of the ac- tivity bump. (A)Sample frames. Same convention as Fig. 2C. (See movie S6.) (B)Temporalevolution of bump position (PVA) over time. Gray background denotes stimulation period. Top: Original bump positions of individual trials (colored thin lines are PVA estimates). Second row: Distance between bump and stimulation position. Red line and shade denote mean± SEM. Bottom: Population mean ± SEM (red) across flies (gray lines). (C) Same as (B), without CsChrimson. (D) Distribution of bump drift distances after the end of optogenetic stimulation. Colored lines represent different conditions. P = 0.324 between gray and blue, P < 0.0001 between blue and red, P < 0.0001 between gray and red; two-sample Kolmogorov-Smirnov tests without multiple-comparisons correction. Distributions are skewed toward short drift distances. Inset shows fraction of trials with drifting bump in each fly (P = 0.0008, t test compared to 0.5).

Fig. 4. Probing the connectivity profile of the ring attractor network. (A) Example of bump“flow” in response to abrupt shift of vertical bar. Same convention as Fig. 1G. Red dots are bump positions estimated from Bayesian sampling method. (B) Bump “jump.” (C) Jump probability increases with distance of visual input shift. Red line and shading denote mean ± SEM. (D) Input-response phase diagrams. Top: Response of local model (fig. S3D) to various input widths, strengths, and abrupt shift distances. Bottom: Global model (fig. S3B). Note that the y axis increments are different between the two models. Red lines denote input strength for bump jump with narrow input, which is constant for the local model and?increases with shift distances for the global model. (E) Schematics of stimulation protocol to detect the threshold input strength for bump jump in response to narrow (22.5°) input. Two 22.5° areas were sequentially stimulated. (F) Laser power required to make bump jump from the first stimulation position (1 or 2) to a fixed second stimulation position (A or B). P = 0.102, paired t test. (G) Input strength, estimated by normalized bump amplitude, required for bump jump from fixed first stimulation position to second stimulation position. Red dashed line denotes simulated threshold of the local model. Solid dots are trials with first stimulation at position 1; open dots are trials with first stimulation at position 2.

果蠅中央大腦中的環(huán)吸引子動(dòng)力學(xué)茎杂。

???環(huán)形吸引子是一類周期性的網(wǎng)絡(luò)，被假定為頭朝向的代表觅闽。這種網(wǎng)絡(luò)結(jié)構(gòu)被示意為一個(gè)神經(jīng)元環(huán)闸英，其連通性取決于其朝向偏好吹零，可以維持bump-like的活動(dòng)模式，模式位置可以通過(guò)沿任一轉(zhuǎn)彎方向的連續(xù)移動(dòng)來(lái)更新。我們最近發(fā)現(xiàn)一群果蠅神經(jīng)元通過(guò)bump-like的活動(dòng)動(dòng)態(tài)來(lái)代表動(dòng)物的前進(jìn)方向破衔。我們將朝向固定飛行的果蠅中的雙光子鈣成像與光遺傳學(xué)相結(jié)合，以人工的方式覆蓋了現(xiàn)有的種群表征阳惹，然后由具有自然的動(dòng)力學(xué)的回路加以維持谍失。具有局部激勵(lì)和全局抑制的網(wǎng)絡(luò)將強(qiáng)制執(zhí)行這種唯一且持久的朝向代表。環(huán)吸引子網(wǎng)絡(luò)在理論研究中早已被引用莹汤；我們的研究為它們的存在和功能結(jié)構(gòu)提供了生理學(xué)證據(jù)快鱼。

對(duì)感覺(jué)外圍附近神經(jīng)回路的研究對(duì)回路功能產(chǎn)生了深刻的機(jī)械洞察力（1、2）纲岭。然而抹竹，要了解被周期性網(wǎng)絡(luò)控制的中樞大腦區(qū)域的回路功能卻更具挑戰(zhàn)性，這些網(wǎng)絡(luò)經(jīng)常產(chǎn)生復(fù)雜的神經(jīng)活動(dòng)模式止潮。這些動(dòng)力學(xué)在塑造認(rèn)知功能中起著重要作用（3-7）窃判，例如在導(dǎo)航期間維持朝向信息（8–10）。朝向代表必須是唯一的（因?yàn)閯?dòng)物在給定的時(shí)間只能面對(duì)一個(gè)方向）喇闸，并且必須是持久的（允許動(dòng)物將其方位保持在黑暗中）袄琳，但必須允許更新，以符合從動(dòng)物的運(yùn)動(dòng)預(yù)期朝向變化的規(guī)模和速度燃乍。從理論上講唆樊，這可以通過(guò)環(huán)吸引網(wǎng)絡(luò)（11-14）來(lái)實(shí)現(xiàn)，其中拓?fù)洵h(huán)中活動(dòng)神經(jīng)元的局部子集的位置代表了動(dòng)物的頭朝向刻蟹。但是逗旁，大腦是否使用這些假設(shè)的網(wǎng)絡(luò)仍是未知的（8、15）座咆。最近的一項(xiàng)研究報(bào)告了一種被稱為E-PG神經(jīng)元的一類在黑腹果蠅橢圓體（EB）出現(xiàn)的神經(jīng)元群體（圖1痢艺，C和D；有關(guān)命名法介陶，請(qǐng)參見(jiàn)補(bǔ)充材料）堤舒，這種神經(jīng)元群體使用bump-like神經(jīng)元活動(dòng)動(dòng)力學(xué)來(lái)代表動(dòng)物在視覺(jué)環(huán)境和黑暗環(huán)境中前進(jìn)的朝向（16，17）哺呜。在這里舌缤，我們建立了啟用此表示法的網(wǎng)絡(luò)的基本屬性。

???我們首先確定在束縛飛行期間E-PG的群體活動(dòng)bump是否跟蹤果蠅相對(duì)于其視覺(jué)周圍環(huán)境的頭朝向（圖1和圖S1）某残。我們使用帶有遺傳編碼的鈣指示劑GCaMP6f（18）的雙光子成像技術(shù)來(lái)記錄蒼蠅在虛擬現(xiàn)實(shí)LED舞臺(tái)上飛行時(shí)EB中整個(gè)E-PG種群的樹(shù)突鈣活動(dòng)国撵。視覺(jué)場(chǎng)景的方位角速度與果蠅的偏航速度成正比（圖1，A和B）玻墅。隨著移動(dòng)的果蠅（16）介牙，在飛行過(guò)程中E-PG的種群活動(dòng)被組織為一個(gè)單獨(dú)的bump，無(wú)論視覺(jué)場(chǎng)景中是否包含單個(gè)橫條（圖S1B）或更復(fù)雜的模式（圖1G）澳厢』反。活動(dòng)bump緊密跟蹤飛行中的果蠅朝向（圖1K）囚似，并在黑暗中持續(xù)（圖1H）。但是线得，與步行不同饶唤，活動(dòng)bump很少在黑暗中跟蹤果蠅的運(yùn)動(dòng)行為（圖1，H和K贯钩，以及圖S1C）募狂，這可能是因?yàn)橄道K會(huì)剝奪果蠅從露背上對(duì)其旋轉(zhuǎn)運(yùn)動(dòng)的正常感官反饋（19）。盡管活動(dòng)顛簸的位置最終會(huì)在一些蒼蠅中漂移角雷，但顛簸的運(yùn)動(dòng)平均而言與動(dòng)物在黑暗中的轉(zhuǎn)彎運(yùn)動(dòng)無(wú)關(guān)（圖1K）祸穷。這些發(fā)現(xiàn)表明，在E-PG群體中朝向的表示具有完整的谓罗、視覺(jué)驅(qū)動(dòng)的動(dòng)態(tài)以及持久性粱哼，但是在束縛飛行過(guò)程中，很大程度上不受自運(yùn)動(dòng)提示的更新的影響檩咱。

???為了測(cè)試蒼蠅的羅盤(pán)網(wǎng)絡(luò)是否在EB內(nèi)實(shí)施了獨(dú)特的顛簸揭措，我們利用了在黑暗中視覺(jué)誘發(fā)的顛簸的相對(duì)持久性，并詢問(wèn)該顛簸是否可以與“人造”顛簸共存刻蚯。我們使用局部光遺傳學(xué)刺激在E-PG群中的不同位置創(chuàng)建了人工活動(dòng)bump绊含。使用E-PG神經(jīng)元共表達(dá)CsChrimson（20）和GCaMP6f的轉(zhuǎn)基因蠅，使用交替的激發(fā)（較高激光強(qiáng)度）和成像（正常激光強(qiáng)度）的雙光子激光掃描線監(jiān)測(cè)E-PG群體動(dòng)態(tài)的變化炊汹，E-PG的種群動(dòng)態(tài)響應(yīng)于光遺傳學(xué)造成的局部活動(dòng)點(diǎn)（圖2躬充，A和B，以及圖S2讨便，A和B）充甚。通過(guò)改變傳遞到目標(biāo)位置的刺激光的強(qiáng)度，我們可以創(chuàng)建增加鈣電活性的顛簸（圖2霸褒，CtoF和電影S1）伴找。當(dāng)新的bump形成時(shí)，先前位置的活動(dòng)開(kāi)始下降并最終消失（圖2）废菱。 2D）技矮，而不會(huì)顯著干擾果蠅行為（但請(qǐng)參見(jiàn)圖S2E）。當(dāng)光遺傳學(xué)激發(fā)終止時(shí)殊轴，人工產(chǎn)生的bump的振幅穩(wěn)定在通常由感覺(jué)刺激引起的水平衰倦，并且沒(méi)有消失。它要么在誘導(dǎo)位置停留了幾秒鐘（圖S2F）旁理，要么緩慢地漂移了（見(jiàn)圖3）（圖3）樊零。

????顛簸的獨(dú)特性可能通過(guò)周期性的相互抑制或間接機(jī)制而出現(xiàn)，間接機(jī)制使EB中強(qiáng)烈的顛簸活動(dòng)在功能上抑制了對(duì)其他E-PG神經(jīng)元的前饋感覺(jué)輸入孽文。為了區(qū)分這些替代方案驻襟，我們同時(shí)激發(fā)了EB環(huán)上的兩個(gè)位置十性。以固定的激光功率激發(fā)參考位置，并以增加的激光功率水平激發(fā)第二個(gè)空間偏移位置（圖S2G和電影S3至S5）塑悼。我們總是可以通過(guò)將第二位置的激光功率提高到一定閾值以上來(lái)抑制參考bump，這與相互抑制相一致楷掉。

周期性抑制可以通過(guò)簡(jiǎn)單的贏家通吃（WTA）回路（圖S3A）來(lái)確保獨(dú)特的活動(dòng)bump厢蒜。但是，動(dòng)物的角度方位代表應(yīng)該支持基于轉(zhuǎn)彎動(dòng)作的更連續(xù)的更新烹植。這種漸進(jìn)有序的向附近位置的漂移將與連續(xù)或環(huán)形吸引子模型更加一致（圖S3斑鸦，B至D）。因此草雕，我們檢查了在“自然”水平上其峰值活動(dòng)穩(wěn)定之后巷屿，人工創(chuàng)建的bump位置的變化。實(shí)驗(yàn)是在黑暗中進(jìn)行的墩虹，以消除任何潛在揮之不去的視覺(jué)輸入帶來(lái)的顛簸（圖3）嘱巾。如果EB動(dòng)態(tài)是由WTA網(wǎng)絡(luò)驅(qū)動(dòng)的，則顛簸有時(shí)會(huì)消失诫钓，并會(huì)跳到隨機(jī)的遙遠(yuǎn)位置（圖S3E）旬昭。相反的是，bump在EB周圍逐漸漂移（圖3菌湃，B和D问拘，以及電影S6）。這一發(fā)現(xiàn)表明惧所，果蠅的航向代表是通過(guò)鄰近的E-PG神經(jīng)元之間的功能性興奮性相互作用來(lái)更新的骤坐，這與環(huán)形吸引子模型是一致的。這些觀察結(jié)果共同排除了在黑暗中網(wǎng)絡(luò)動(dòng)態(tài)純粹由細(xì)胞內(nèi)在機(jī)制（21下愈、22）或緩慢衰減的視覺(jué)輸入產(chǎn)生的可能性纽绍。最重要的是，對(duì)E-PG神經(jīng)元活動(dòng)的直接操縱改變了網(wǎng)絡(luò)狀態(tài)驰唬，這意味著E-PG神經(jīng)元不僅反映了在不同回路中發(fā)生的動(dòng)力學(xué)顶岸，而且本身也是環(huán)吸引子的重要組成部分（23）。

???接下來(lái)叫编，我們旨在剖析E-PG群體中環(huán)吸引子動(dòng)力學(xué)的有效連通模式辖佣。原則上，各種各樣的網(wǎng)絡(luò)結(jié)構(gòu)都可以實(shí)現(xiàn)環(huán)形吸引子（11搓逾、13卷谈、14、24霞篡、25）世蔗。我們將工作重點(diǎn)放在了兩個(gè)可以解析解決的極端網(wǎng)絡(luò)體系結(jié)構(gòu)之間的模型空間上：（i）基于全局余弦形相互作用的“全局模型”（圖S3B）（11募闲、13、26）和（ii） 基于相對(duì)局部的刺激相互作用（圖S3D和補(bǔ)充文本）的“局部模型”（24找岖、27）叶洞。在與生理學(xué)觀察相符合的固定bump寬度為90°的規(guī)定下（圖1J），并假設(shè)有效的興奮性視覺(jué)輸入沒(méi)有任何負(fù)偏差寸爆，這兩個(gè)模型都可以解釋bump動(dòng)力學(xué)的基本特性礁鲁，包括其唯一性及其在黑暗中的持續(xù)性。因此赁豆，我們針對(duì)更人工的條件（例如突然的視覺(jué)刺激轉(zhuǎn)移）探究了網(wǎng)絡(luò)的響應(yīng)仅醇。

???我們首先通過(guò)實(shí)驗(yàn)檢查了E-PG群體如何應(yīng)對(duì)不自然的、突然的視覺(jué)轉(zhuǎn)變魔种。根據(jù)變化的距離析二，E-PGbump要么連續(xù)地“流動(dòng)”（較短的移動(dòng)距離；圖4节预，A和C叶摄，以及電影S7和S8），要么“跳到”新位置（較長(zhǎng)的移動(dòng)距離心铃；圖4准谚，B和B）C和電影S9）（16）。在模擬中去扣，兩個(gè)模型都根據(jù)移動(dòng)的視覺(jué)輸入的強(qiáng)度和寬度預(yù)測(cè)了跳躍和流動(dòng)響應(yīng)的混合（圖4D柱衔，圖S4A和補(bǔ)充文字）。例如愉棱，較弱的寬輸入引起的流動(dòng)和較強(qiáng)的窄輸入引起的跳躍（圖4D）唆铐。但是，兩個(gè)模型所預(yù)測(cè)的跳躍流平衡有所不同奔滑，并且在幾個(gè)方面與局部模型更加一致（圖4D和圖S4A）艾岂。首先，我們從正常條件下推斷得出的視覺(jué)輸入強(qiáng)度要比全局模型對(duì)顛簸跳躍所要求的弱得多（圖S1D）朋其。其次王浴，全局模型要求視覺(jué)輸入強(qiáng)度的范圍要比正常范圍大得多，以便解釋在多種距離的跳躍（圖4D梅猿，圖S1D和圖S4A）氓辣。第三，使用與我們的其他發(fā)現(xiàn)一致的參數(shù)袱蚓，我們可以使用局部模型而不是整體模型來(lái)再現(xiàn)圖4C中觀察到的跳流比（圖S4B）钞啸。

????為了獲得更多具體證據(jù)，我們?cè)谕ㄟ^(guò)光遺傳學(xué)刺激控制輸入強(qiáng)度、極性和移動(dòng)距離的條件下体斩，將模型預(yù)測(cè)與實(shí)驗(yàn)觀察到的碰撞動(dòng)力學(xué)進(jìn)行了比較梭稚。為了模擬中等和較大的輸入移位距離，我們依次刺激了EB中的兩個(gè)小區(qū)域絮吵，每個(gè)小區(qū)域的角度寬度為22.5°弧烤，分開(kāi)了90°或180°（圖4，E至G蹬敲，電影S10和圖S4扼褪，C至E）。然后粱栖，我們改變刺激激光的功率，以檢測(cè)bump跳躍所需的閾值（圖4E）脏毯。引起跳躍所需的激光功率在兩個(gè)不同的移位距離之間沒(méi)有顯著差異闹究，這支持局部模型（圖4F）。然后食店，我們通過(guò)比較光遺傳學(xué)引起的顛簸的振幅與黑暗中自然顛簸的振幅來(lái)推斷網(wǎng)絡(luò)輸入的強(qiáng)度渣淤。誘發(fā)跳躍所需的光遺傳輸入強(qiáng)度小于全局模型的預(yù)測(cè)，但與局部模型（圖4G）和正常條件下推斷的視覺(jué)輸入強(qiáng)度的范圍相匹配（圖S1D吉嫩，圖S4价认， D和E，以及電影S11）自娩。最后用踩，當(dāng)我們測(cè)試介于極端的局部模型和全局模型（圖S4，H和I忙迁，以及補(bǔ)充文本）之間的中間模型時(shí)脐彩，我們發(fā)現(xiàn)，任何顯示出觀察到的對(duì)弱22.5°寬輸入響應(yīng)的跳躍具有較窄的連接配置文件（圖S4I）姊扔。所有這些觀察結(jié)果再次與局部模型一致惠奸。

????在哺乳動(dòng)物中，朝向代表被認(rèn)為分布在多個(gè)神經(jīng)種群和多個(gè)腦區(qū)中（8）恰梢。同樣在果蠅中佛南，指南針系統(tǒng)可能涉及多種細(xì)胞類型，包括前腦橋（PB）中的神經(jīng)元（17嵌言，23）嗅回。此外，在動(dòng)力學(xué)中偶爾觀察到的變化表明呀页，網(wǎng)絡(luò)調(diào)制是由其他未知因素引起的妈拌。例如，有時(shí)我們會(huì)觀察到E-PG動(dòng)力學(xué)的突然變化，因?yàn)楦杏X(jué)誘發(fā)的活動(dòng)顛簸的幅度取決于系繩的果蠅是否飛動(dòng)（參見(jiàn)補(bǔ)充材料）以及偶爾在飛行過(guò)程中發(fā)生變化[圖中的種群矢量平均值（PVA）幅度圖.1尘分，GandH猜惋，圖4，AandB和圖培愁。 S1B]著摔。盡管如此，E-PG群體在航向的內(nèi)部表示上提供了強(qiáng)大的生理處理（16）：?jiǎn)蝹€(gè)活動(dòng)顛簸穿過(guò)拓?fù)渑帕械纳窠?jīng)元定续。這種啟用的實(shí)驗(yàn)方法為研究多個(gè)群體中的哪些是計(jì)算的關(guān)鍵回路元件以及簡(jiǎn)單地讀出該計(jì)算的結(jié)果提供了一種途徑谍咆。我們發(fā)現(xiàn)，通過(guò)直接操縱E-PG種群活動(dòng)而產(chǎn)生的人工碰撞顯示出自然的動(dòng)力私股，這表明這些神經(jīng)元是航向回路的關(guān)鍵組成部分摹察。

????我們的發(fā)現(xiàn)通過(guò)全局競(jìng)爭(zhēng)確保了E-PG活動(dòng)顛簸的唯一性，這一發(fā)現(xiàn)進(jìn)一步證實(shí)了這一種群編碼果蠅頭朝向的抽象內(nèi)部代表的結(jié)論（16）倡鲸。這種抽象代表使動(dòng)物可以從其直接的感覺(jué)環(huán)境的控制中解脫出來(lái)供嚎，從而在時(shí)間和行為使用上都具有靈活性。將人為引起的沖擊動(dòng)力學(xué)分析與理論建模相結(jié)合峭状，使我們可以研究這種周期回路結(jié)構(gòu)克滴。我們發(fā)現(xiàn)有效的網(wǎng)絡(luò)連接配置與環(huán)吸引子模型一致，該模型以狹窄的局部刺激和平坦的長(zhǎng)范圍抑制為特征优床。這種局部刺激和長(zhǎng)范圍抑制的神經(jīng)回路膜體在許多腦區(qū)和動(dòng)物類群中普遍存在（28-31）劝赔。這樣的觀察結(jié)果支持了這樣一種觀點(diǎn)，即常見(jiàn)的回路motifs可能在進(jìn)化上被用作認(rèn)知功能的重要組成部分胆敞。

圖1. E-PG神經(jīng)元在系繩閉環(huán)飛行過(guò)程中編碼相對(duì)于視覺(jué)世界的身體朝向着帽。 （A）設(shè)置原理圖。 （B）系繩飛蠅的特寫(xiě)鏡頭移层。（C）中央復(fù)合體启摄。（D）每個(gè)E-PG神經(jīng)元的樹(shù)突神經(jīng)支配EB的楔形節(jié)段；軸突投射到PB和Gall的相應(yīng)腎小球幽钢。 （E）將整個(gè)E-PG群的樹(shù)突狀過(guò)程的平均鈣圖像分為16個(gè)感興趣區(qū)域（ROIs）歉备。 （F）通過(guò)對(duì)長(zhǎng)度為熒光瞬變幅度（??F / F0）的16個(gè)矢量求和而獲得的bump位置（PVA方向）和強(qiáng)度（PVA振幅）。 （G）在復(fù)雜的視覺(jué)場(chǎng)景中匪燕，系留飛行中E-PG樹(shù)突中的GCaMP6f熒光瞬變蕾羊。頂部：采樣時(shí)間點(diǎn)的視覺(jué)模式。第二行：鈣成像的樣本框架帽驯。第三行：16個(gè)ROI的DF / F0龟再。灰階表示PVA振幅尼变；紅線是PVA估算值利凑。第四行：PVA估算和朝向（藍(lán)色）浆劲。底部：與第四行相同，但解開(kāi)了哀澈。（H）在黑暗中的熒光瞬變牌借。 （I）在三種視覺(jué)條件下，跨蠅（n=10）的E-PG種群中的活性突觸數(shù)量割按。每個(gè)帶有垂直線的點(diǎn)表示每個(gè)蠅的平均值±SEM膨报。總體平均值±SEM顯示在每個(gè)散點(diǎn)圖的最左邊适荣。（J）bump寬度通過(guò)半高全寬測(cè)量（K）估計(jì)的顛簸位置與航向之間的相關(guān)性现柠。 （L）PVA估計(jì)值與場(chǎng)景方向之間的角度偏移。晶須圖弛矛，平均值±圓形SD够吩。

圖2. E-PG神經(jīng)元通過(guò)周期性連接相互抑制而競(jìng)爭(zhēng)。（A）同時(shí)進(jìn)行鈣成像和局部光遺傳學(xué)刺激的示意圖丈氓。 （B）收集圖像的分析程序废恋。 （C）上圖：雙光子光遺傳學(xué)刺激的時(shí)間分布。底部：三個(gè)樣本框（使用高斯濾鏡平滑）扒寄。帶箭頭的黃色矩形，關(guān)閉刺激拟烫；帶有箭頭的紅色矩形该编，啟用刺激。 （D）實(shí)例蠅（左）和種群（右）的鈣動(dòng)力學(xué)時(shí)程硕淑】慰ⅲ灰色背景，光遺傳刺激期置媳；灰線于樟，個(gè)別試驗(yàn)（左）或果蠅群體（右）。上圖：受刺激的ROI的平均值F拇囊。底部：刺激前迂曲，在光遺傳學(xué)刺激區(qū)域之外的四個(gè)最活躍的ROI的平均值。粗線和彩色陰影區(qū)域分別表示平均值和SEM寥袭。 （對(duì)照實(shí)驗(yàn)見(jiàn)圖S2C路捧。）（E）刺激期間和刺激之前的熒光比分布。 P <0.001传黄，在受激區(qū)域（紅色）和外部刺激區(qū)域（藍(lán)色）之間進(jìn)行Wilcoxon秩和檢驗(yàn)杰扫。 （對(duì)照實(shí)驗(yàn)見(jiàn)圖S2D。）（F）通過(guò)光遺傳學(xué)刺激進(jìn)行抑制膘掰。 x軸表示從刺激位置到現(xiàn)有bump的距離章姓；P <0.001，對(duì)每個(gè)距離進(jìn)行t檢驗(yàn)。樣本量有限凡伊，無(wú)法進(jìn)行派/ 8的統(tǒng)計(jì)檢驗(yàn)零渐。

圖3.活動(dòng)bump·的漂移。（A）樣品架窗声。與圖2C相同相恃。 （請(qǐng)參見(jiàn)電影S6。）（B）碰撞位置（PVA）隨時(shí)間的瞬時(shí)旋轉(zhuǎn)笨觅±鼓停灰色背景表示刺激期。頂部：各個(gè)試驗(yàn)的原始凹凸位置（彩色細(xì)線為PVA估算值）见剩。第二行：bump與刺激位置之間的距離杀糯。紅線和陰影表示平均值±SEM。下圖：果蠅（灰線）的種群平均數(shù)±SEM（紅色）苍苞。 （C）與（B）相同固翰，但沒(méi)有CsChrimson。 （D）在光遺傳學(xué)刺激結(jié)束后羹呵，bump漂移距離的分布骂际。彩色線代表不同的條件「曰叮灰色和藍(lán)色之間P = 0.324歉铝，藍(lán)色和紅色之間P <0.0001，灰色和紅色之間P <0.0001凑耻；兩樣本Kolmogorov-Smirnov測(cè)試太示，無(wú)需進(jìn)行多重比較校正。分布偏向較短的漂移距離香浩。插圖顯示了每只果蠅中移動(dòng)bump的試驗(yàn)分?jǐn)?shù)（P = 0.0008类缤，t檢驗(yàn)為0.5）。

圖4.探測(cè)環(huán)形吸引器網(wǎng)絡(luò)的連接配置文件邻吭。 （A）響應(yīng)垂直條的突然偏移而引起的bump“流動(dòng)”的示例餐弱。與圖1G相同。紅點(diǎn)是根據(jù)貝葉斯采樣方法估算的bump位置囱晴。（B）bump跳”岸裙。 （C）跳躍概率隨視覺(jué)輸入移位距離的增加而增加。紅線和陰影表示平均值±SEM速缆。 （D）輸入-響應(yīng)相位圖降允。頂部：局部模型（圖S3D）對(duì)各種輸入寬度，強(qiáng)度和突變距離的響應(yīng)艺糜。下：全局模型（圖S3B）剧董。請(qǐng)注意幢尚，兩個(gè)模型之間的y軸增量不同。紅線表示窄輸入時(shí)bump跳躍的輸入強(qiáng)度翅楼，這對(duì)于局部模型是恒定的尉剩，而對(duì)于整體模型，其隨移位距離而增加毅臊。（E）刺激協(xié)議的示意圖理茎，用于檢測(cè)響應(yīng)于狹窄（22.5°）輸入的bump跳躍的輸入強(qiáng)度閾值。依次刺激兩個(gè)22.5°區(qū)域管嬉。 （F）使bump從第一刺激位置（1或2）跳到固定的第二刺激位置（A或B）所需的激光功率皂林。 P = 0.102，配對(duì)t檢驗(yàn)蚯撩。 （G）輸入強(qiáng)度础倍，由歸一化的碰撞幅度估計(jì)，從固定的第一刺激位置到第二刺激位置的bump跳躍所需的輸入強(qiáng)度胎挎。紅色虛線表示局部模型的模擬閾值沟启。實(shí)心點(diǎn)是在位置1進(jìn)行第一次刺激的試驗(yàn)；空心點(diǎn)是在位置2處首次刺激的試驗(yàn)犹菇。

#脈絡(luò)

在一項(xiàng)新的研究中德迹，來(lái)自美國(guó)霍華德-休斯醫(yī)學(xué)研究所的研究人員發(fā)現(xiàn)存在于果蠅大腦中間的一個(gè)神經(jīng)元環(huán)路（a ring of neurons）起著指南針（compass）的作用，有助這種昆蟲(chóng)知道它在何處揭芍，它去過(guò)哪里和它將去往哪里胳搞。他們解釋了他們?nèi)绾螖U(kuò)展他們?cè)趦赡昵伴_(kāi)始的研究，以及他們的發(fā)現(xiàn)可能對(duì)哺乳動(dòng)物的內(nèi)部導(dǎo)航意味著什么沼沈。相關(guān)研究結(jié)果于2017年5月4日在線發(fā)表在Science期刊上，論文標(biāo)題為“Ring attractor dynamics in the Drosophila central brain”币厕。

正如這些研究人員注意到的那樣列另，他們?cè)趦赡昵耙寻l(fā)現(xiàn)大約50個(gè)神經(jīng)元在果蠅大腦中間形成一個(gè)環(huán)路，并且這個(gè)神經(jīng)元環(huán)路似乎起著導(dǎo)航的作用旦装。從那之后页衙，他們研究了這個(gè)神經(jīng)元環(huán)路如何可能有助這種昆蟲(chóng)在環(huán)境中追蹤其行蹤。

為此阴绢，這些研究人員將果蠅固定在一根金屬棒上店乐，這根金屬棒讓它們呆在原處。他們隨后在它們周圍播放虛擬現(xiàn)實(shí)場(chǎng)景呻袭，模擬在它們的自然環(huán)境中的運(yùn)動(dòng)眨八。當(dāng)果蠅扇動(dòng)翅膀試圖在這種模擬的場(chǎng)景中飛行時(shí)，他們記錄了這個(gè)神經(jīng)元環(huán)路中的神經(jīng)活性左电。他們發(fā)現(xiàn)在這個(gè)神經(jīng)元環(huán)路中廉侧，單個(gè)神經(jīng)元簇集會(huì)依據(jù)果蠅試圖飛行的方向放電页响。

這些研究人員隨后對(duì)這個(gè)神經(jīng)元環(huán)路中的一些神經(jīng)元進(jìn)行基因修飾，從而使得當(dāng)接受光線照射時(shí)段誊，這些神經(jīng)元會(huì)被激活闰蚕。這允許他們操縱這些果蠅接受到的關(guān)于它們的飛行路線的信息。給這些神經(jīng)元照射光線導(dǎo)致這些果蠅不能夠在它們的環(huán)境中進(jìn)行自我追蹤连舍，這強(qiáng)烈地提示著他們的觀點(diǎn)是對(duì)的没陡，即這個(gè)神經(jīng)元環(huán)路類似于指南針。他們也開(kāi)展了類似的實(shí)驗(yàn)：讓這些果蠅在黑暗中飛行索赏，結(jié)果發(fā)現(xiàn)盡管它們似乎分不清方向盼玄，但是并不清楚的是，這是由于他們的干擾参滴，或者僅是因?yàn)樗鼈冊(cè)诤诎抵芯哂休^差的導(dǎo)航技巧强岸。

正如這些研究人員指出的那樣，他們的研究提供證據(jù)證實(shí)了這個(gè)神經(jīng)元環(huán)路的用途砾赔，但是并沒(méi)有解釋它的神經(jīng)元是如何被激活的蝌箍，或者果蠅如何接受來(lái)自這個(gè)神經(jīng)元環(huán)路的信息和利用它輔助導(dǎo)航。他們計(jì)劃繼續(xù)開(kāi)展他們的研究以便觀察他們是否能夠找到這些問(wèn)題的答案暴心。