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

Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, for e.g. via cell surface receptors or sensory organs. By 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.

Non-asymptotic transients away from steady states determine cellular responsiveness to dynamic spatial-temporal signals.

Majority of the theory on cell polarization and the understanding of cellular sensing and responsiveness to localized chemical cues has been based on the idea that non-polarized and polarized cell states can be represented by stable asymptotic switching between them. The existing model classes that describe the dynamics of signaling networks underlying polarization are formulated within the framework of autonomous systems. However these models do not simultaneously capture both, robust maintenance of polarized state longer than the signal duration, and retained responsiveness to signals with complex spatial-temporal distribution. Based on recent experimental evidence for criticality organization of biochemical networks, we challenge the current concepts and demonstrate that non-asymptotic signaling dynamics arising at criticality uniquely ensures optimal responsiveness to changing chemoattractant fields. We provide a framework to characterize non-asymptotic dynamics of system's state trajectories through a non-autonomous treatment of the system, further emphasizing the importance of (long) transient dynamics, as well as the necessity to change the mathematical formalism when describing biological systems that operate in changing environments.

Cells use molecular working memory to navigate in changing chemoattractant fields.

In order to migrate over large distances, cells within tissues and organisms rely on sensing local gradient cues which are irregular, conflicting, and changing over time and space. The mechanism how they generate persistent directional migration when signals are disrupted, while still remaining adaptive to signal's localization changes remain unknown. Here, we find that single cells utilize a molecular mechanism akin to a working memory to satisfy these two opposing demands. We derive theoretically that this is characteristic for receptor networks maintained away from steady states. Time-resolved live-cell imaging of Epidermal growth factor receptor (EGFR) phosphorylation dynamics shows that cells transiently memorize position of encountered signals via slow-escaping remnant of the polarized signaling state, a dynamical 'ghost', driving memory-guided persistent directional migration. The metastability of this state further enables migrational adaptation when encountering new signals. We thus identify basic mechanism of real-time computations underlying cellular navigation in changing chemoattractant fields.

If we are injured, or fighting an infection, cells in our body migrate over large distances to the site of the wound or infection to act against any invading microbes or repair the damage. Cells navigate to the damaged site by sensing local chemical cues, which are irregular, conflicting and change over time and space. This implies that cells can choose which direction to travel, and stick to it even if the signals around them are disrupted, while still retaining the ability to alter their direction if the location of the signal changes. However, how cells are able to effectively navigate their way through this field of complex chemical cues is poorly understood. To help resolve this mystery, Nandan, Das et al. studied the epidermal growth factor receptor (EGFR) signaling network which controls how some cells in the body change shape and migrate. The network is activated by specific chemical cues, or ligands, binding to EGFR proteins on the cell surface. The receptors then join together to form pairs, and several tags known as phosphate groups are added to each molecule. This process (known as phosphorylation) switches the receptor pair to an active state, allowing EGFR to relay signals to other proteins in the cell and promote the activity of receptors not bound to a ligand. The phosphorylation state of EGFRs is then modulated over time and across the cell by a network of enzymes called phosphatases which can remove the phosphate groups and switch off the receptor. To study EGFR phosphorylation dynamics in human cells, Nandan, Das et al. imaged individual cells over time using a microscope. This data was then combined with a mathematical model describing the EGFR signaling network and how cells change their shape over time. The experiment revealed that the phosphate groups attached to EGFR are not removed immediately when the chemical cue is gone. Instead, the active state is transiently maintained before complete inactivation. This had the effect of encoding a short-lived memory in the signaling network that allowed the cells to continue to migrate in a certain direction even when chemical cues were disrupted. This memory state is dynamic, enabling cells to adapt direction when the cue changes location. The findings of Nandan, Das et al. reveal the underlying mechanism for how cells decipher complex chemical cues to migrate to where they are needed most. The next steps to follow on from this work will be to understand if other receptors involved in migration work in a similar way.

A self-organized synthetic morphogenic liposome responds with shape changes to local light cues.

Reconstituting artificial proto-cells capable of transducing extracellular signals into cytoskeletal changes can reveal fundamental principles of how non-equilibrium phenomena in cellular signal transduction affect morphogenesis. Here, we generated a Synthetic Morphogenic Membrane System (SynMMS) by encapsulating a dynamic microtubule (MT) aster and a light-inducible signaling system driven by GTP/ATP chemical potential into cell-sized liposomes. Responding to light cues in analogy to morphogens, this biomimetic design embodies basic principles of localized Rho-GTPase signal transduction that generate an intracellular MT-regulator signaling gradient. Light-induced signaling promotes membrane-deforming growth of MT-filaments by dynamically elevating the membrane-proximal tubulin concentration. The resulting membrane deformations enable recursive coupling of the MT-aster with the signaling system, which generates global self-organized morphologies that reorganize towards local external cues in dependence on prior shape. SynMMS thereby signifies a step towards bio-inspired engineering of self-organized cellular morphogenesis.

Organization at criticality enables processing of time-varying signals by receptor networks.

How cells utilize surface receptors for chemoreception is a recurrent question spanning between physics and biology over the past few decades. However, the dynamical mechanism for processing time-varying signals is still unclear. Using dynamical systems formalism to describe criticality in non-equilibrium systems, we propose generic principle for temporal information processing through phase space trajectories using dynamic transient memory. In contrast to short-term memory, dynamic memory generated via "ghost" attractor enables signal integration depending on stimulus history and thereby uniquely promotes integrating and interpreting complex temporal growth factor signals. We argue that this is a generic feature of receptor networks, the first layer of the cell that senses the changing environment. Using the experimentally established epidermal growth factor sensing system, we propose how recycling could provide self-organized maintenance of the critical receptor concentration at the plasma membrane through a simple, fluctuation-sensing mechanism. Processing of non-stationary signals, a feature previously attributed only to neural networks, thus uniquely emerges for receptor networks organized at criticality.