Biological computations: limitations of attractor-based formalisms and the need for transients

Abstract: Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, e.g., via cell surface receptors or sensory organs. Integrating these time-varying, multi-sensory, and often noisy information with memory using complex molecular or neuronal networks, they generate a variety of responses beyond simple stimulus-response association, including avoidance behavior, life-long-learning or social interactions. In a broad sense, these processes can be understood as a type of biological computation. Taking as a basis generic features of biological computations, such as real-time responsiveness or robustness and flexibility of the computation, we highlight the limitations of the current attractor-based framework for understanding computations in biological systems. We argue that frameworks based on transient dynamics away from attractors are better suited for the description of computations performed by neuronal and signaling networks. In particular, we discuss how quasi-stable transient dynamics from ghost states that emerge at criticality have a promising potential for developing an integrated framework of computations, that can help us understand how living system actively process information and learn from their continuously changing environment.

• The paper demonstrates that attractor-based computation limits adaptability in dynamic, noisy biological environments.
• The paper reveals through EGFR signaling analysis that bistable states hinder rapid response to changing stimuli.
• The paper advocates for transient dynamics, such as chaotic itinerancy and ghost states, to enable robust real-time biological information processing.

Biological Computations: Limitations of Attractor-based Formalisms and the Need for Transients

Introduction

The paper "Biological computations: limitations of attractor-based formalisms and the need for transients" (2404.10369) by Koch et al., explores the intricacies of computational paradigms in biological systems. It scrutinizes the long-standing reliance on attractor-based frameworks and argues for the incorporation of transient dynamics to better represent the computational processes in biological entities ranging from single cells to complex organisms. The study is predicated on understanding real-time information processing within dynamic, noisy environments, which traditional computable frameworks often fail to encapsulate.

Figure 1: Examples of natural and machine computations highlighting the similarities in information processing tasks and illustrating the underlying computational challenges.

Attractor-based Computation and Its Shortcomings

The conventional framework of biological computation has primarily been grounded in attractor-based models, tracing back to Turing-like computational systems and theories posited by Hebb and Hopfield. Such systems describe computations through time evolution from state to state, culminating in stable states or attractors which represent the final output of the computational machinery. This paper contends that while attractor landscapes adequately address robustness, they inherently lack the flexibility to adapt to rapidly changing environmental stimuli—a critical aspect of biological systems.

Figure 2: Attractor-based computations in cell signaling networks, demonstrating how bifurcation leads to bistable states governed by attractor dynamics.

Limitations of Current Frameworks: Single-cell Signaling

The examination of single-cell signaling paths, like the EGFR network, elucidates the limitations inherent in classical attractor frameworks. When cells operate within a bistable regime, state-dependent computation persists but is unresponsive to novel, temporal changes in signal inputs. This inflexibility is particularly exemplified when cells encounter a dynamic chemoattractant environment, leading to locked behavioral responses that defy adaptability unless substantial signal perturbations occur. This underscores the inadequacy of attractor-based formalisms in explaining natural computation dynamics amid non-stationary input signals.

The Potential of Transients: Chaotic Itinerancy and Heteroclinic Networks

The paper advances the argument that transient dynamics, such as chaotic itinerancy and heteroclinic sequences, provide a more compelling framework for modeling biological computations. Transients, manifesting as quasi-attractors or ghost states, can better encapsulate the dynamic and adaptive nature of real-time biological computations. Unlike attractors, these transient states facilitate continuous information processing and responsiveness to fluctuating signals, ensuring adaptability alongside robustness.

Figure 3: Illustration of trajectory-based computations, highlighting chaotic itinerancy and heteroclinic channels as mechanisms for transient-driven computational processes.

Insights into Real-time Computations from Critically Organized Systems

The study presents compelling evidence that systems organized at criticality, particularly within the context of single-cell EGFR signaling networks, not only maintain but require transient states for effective computation. These critical states hover at the intersection of mono- and bistability, transcending traditional steady-state solutions by generating temporal memory traces that allow cells to remain responsive to sequential signals. The ghost states serve as transient memory holders, demonstrating the viability of transient frameworks in replicating and explaining the iterative learning and adaptive responses observed in biological systems.

Figure 4: Diagrammatic representation of cellular responsiveness at criticality, showcasing the emergence of ghost states enabling dynamic signal integration.

Conclusion

The paper advocates for a paradigm shift in the theoretical understanding of biological computation, from attractor-based to transient-oriented models. It postulates that transients—through mechanisms such as ghost states and chaotic itinerancy—can provide a robust framework for capturing the essence of biological responsiveness to dynamic, noisy environments. This perspective not only enhances theoretical models of biological computations but also implicates broader applications in understanding learning and adaptive behavior in both natural and artificial systems. The transition to transient-based frameworks could foster deeper insights into phenomena like memory and learning, both at the cellular and neural network levels, paving the way for new approaches to study information processing in biological systems.