Zhuoyi Song

Visual hyperacuity enables animals to resolve spatial details finer than the sampling limits of their eyes. Traditionally, the contribution of eye movements to acuity is characterized by a functional dichotomy: minute fixational eye movements, such as microsaccades, are thought to facilitate this ability, whereas large voluntary saccades are presumed to serve only for gaze redirection. We challenge this view in the context of compound eyes, systems characterized by sparse sampling and broad receptive fields (RFs). We demonstrate that conventional microsaccadic shifts yield negligible acuity gains in these structures. Instead, large saccades actively drive hyperacuity by transiently contracting the RF profile during the shift. We term this saccade-induced dynamic sharpening the `Shift-and-Shrink' mechanism. This mechanism effectively exceeds the resolution limits imposed by optical structures, expanding the retina's spatial bandwidth and enabling the detection of fine details invisible to static sampling. Furthermore, we reveal that this enhancement is ecologically selective, preferentially extracting information from structurally cluttered natural scenes. These findings establish that large saccades are not merely for gaze redirection but are integral to hyperacute visual perception.

In biochemical reaction networks, the first passage time (FPT) of a reaction quantifies the time, from the initial state, that it takes for the reaction to first occur. While the mean FPT historically served as a summary metric, a far more comprehensive characterization of the dynamics of the network is contained within the complete FPT distribution. The relatively uncommon theoretical treatments of the FPT distribution that have been given in the past have been confined to linear systems with zero- and first-order processes. Recently, we presented mathematically exact solutions for the FPT distribution within nonlinear systems involving two-particle collisions, such as A + B → C. Although this research yielded invaluable results, it was based upon the assumption of initial conditions in the form of a Poisson distribution. This somewhat restricts its relevance to real-world biochemical systems, which frequently display intricate behavior and initial conditions that are non-Poisson in nature. Our current study extends prior analyses to accommodate arbitrary initial conditions, thereby expanding the applicability of our theoretical framework and providing a more adaptable tool for capturing the dynamics of biochemical reaction networks.

The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the distribution is challenging because it requires time-dependent solutions of the chemical master equation (CME). Even simple two-particle collisions lead to strong nonlinearities that hinder obtaining such solutions and, hence, the full FPT distribution. Previous research has either focused on analyzing the mean FPT, which provides limited information about a system, or has considered time-consuming stochastic simulations that do not clearly expose causal relationships between parameters and dynamics. This paper presents the first exact solution of the full FPT distribution in a broad class of chemical reaction networks involving A + B → C type of second-order reactions. We obtained this distribution by deriving a closed-form, time-dependent solution of the system’s underlying CME. Approximate analytical solutions are unable to match the exact results of our method. Examples indicate that the approximations can deviate from the exact FPT distribution by more than 100% in both the mean and the variance. Furthermore, our exact method outperforms stochastic simulations in terms of computational efficiency. Given the prevalence of bimolecular reactions in biochemical systems, our approach has the potential to enhance the understanding of real-world biochemical processes.

In biochemical reaction networks, the first passage time (FPT) of a reaction quantifies the time it takes for the reaction to first occur, from the initial state. While the mean FPT historically served as a summary metric, a far more comprehensive characterization of the dynamics of the network is contained within the complete FPT distribution. The relatively uncommon theoretical treatments of the FPT distribution that have been given in the past have been confined to linear systems, with zero and first-order processes. Recently, we presented theoretically exact solutions for the FPT distribution, within nonlinear systems involving two-particle collisions, such as A+B - C. Although this research yielded invaluable results, it was based upon the assumption of initial conditions in the form of a Poisson distribution. This somewhat restricts its relevance to real-world biochemical systems, which frequently display intricate behaviour and initial conditions that are non-Poisson in nature. Our current study extends prior analyses to accommodate arbitrary initial conditions, thereby expanding the applicability of our theoretical framework and providing a more adaptable tool for capturing the dynamics of biochemical reaction networks.

Detecting looming signals for collision avoidance encounters challenges in real‐world scenarios, where moving backgrounds can interfere as an agent navigates through complex natural environments. Remarkably, even insects with limited neural systems adeptly respond to looming stimuli while in motion at high speeds. Existing insect‐inspired looming detection models typically rely on either motion‐pathway or feature‐pathway signals, yet both are susceptible to dynamic visual scene interference. Coordinating interneuron signals from both pathways can enhance the looming detection performance under dynamic conditions. An artificial neural network is employed to construct a combined‐pathway model based on Drosophila anatomy. The model outperforms state‐of‐the‐art bio‐inspired looming‐detection models in tasks involving dynamic backgrounds, simulated by animated 2D‐moving natural scenes or recorded in reality when an unmanned aerial vehicle performs obstacle collision avoidance tasks. Notably, by combining neural anatomy architecture and appropriate multiobjective tasks, the model exhibits convergent neural dynamics with biological counterparts post‐training, offering network explanations and mechanistic insights. Specifically, a multiplicative interneuron operation enhances looming signal patterns and reduces background interferences, generalizing to more complex scenarios, such as AirSim 3D environments and real‐world situations. The work introduces testable biological hypotheses and a promising bioinspired solution for looming detection in dynamic visual environments.

Refractory period (RP), the waiting time between signals, can induce complex signaling dynamics, such as acceleration, adaptation, and oscillation, within many cellular biochemical networks. However, its underlying molecular mechanisms are still unclear. Rigorously estimating the RP distribution may be essential to identify its causal regulatory mechanisms. Traditional methods of estimating the RP distribution depend on solving the underlying Chemical Master Equations (CMEs), the dominant modeling formalism of biochemical systems. However, exact solutions of the CME are only known for simple reaction systems with zero- and first-order reactions or specific systems with second-order reactions. General solutions still need to be derived for systems with bimolecular reactions. It is even more challenging if large state-space and nonconstant reaction rates are involved. Here, we developed a direct method to gain the analytical RP distribution for a class of second-order reaction systems with nonconstant reaction rates and large state space. Instead of using the CME, we used an equivalent path-wise representation, which is the solution to a transformed martingale problem of the CME. This allowed us to bypass solving a CME. We then applied the method to derive the analytical RP distribution of a real complex biochemical network with second-order reactions, the Drosophila phototransduction cascade. Our approach provides an alternative to the CMEs in deriving the analytical RP distributions of a class of second-order reaction systems. Since the bimolecular reactions are common in biological systems, our approach could enhance understanding real-world biochemical processes.

Detecting looming signals for collision avoidance faces challenges in real-world scenarios due to interference from moving backgrounds. Astonishingly, animals, like insects with limited neural systems, adeptly respond to looming stimuli while moving at high speeds. Existing insect-inspired looming detection models integrate either motion-pathway or feature-pathway signals, remaining susceptible to dynamic visual scene interference. We propose that coordinating interneuron signals from the two pathways could elevate looming detection performance in dynamic conditions. We used artificial neural network (ANN) to build a combined-pathway model based on Drosophila anatomy. The model exhibits convergent neural dynamics with biological counterparts after training. In particular, a multiplicative interneuron operation enhances looming signal patterns. It reduces background interferences, boosting looming detection accuracy and enabling earlier warnings across various scenarios, such as 2D animated scenes, AirSim 3D environments, and real-world situations. Our work presents testable biological hypotheses and a promising bio-inspired solution for looming detection in dynamic visual environments.

Significance: To move efficiently, animals must continuously work out their x,y,z positions with respect to real-world objects, and many animals have a pair of eyes to achieve this. How photoreceptors actively sample the eyes’ optical image disparity is not understood because this fundamental information-limiting step has not been investigated in vivo over the eyes’ whole sampling matrix. This integrative multiscale study will advance our current understanding of stereopsis from static image disparity comparison to a morphodynamic active sampling theory. It shows how photomechanical photoreceptor microsaccades enable Drosophila superresolution three-dimensional vision and proposes neural computations for accurately predicting these flies’ depth-perception dynamics, limits, and visual behaviors.