Sean Fancher’s research while affiliated with Purdue University and other places

Existing theories of structural adaptation in biological flow networks are largely concerned with steady flows. However, biological networks are composed of elastic vessels, and many are driven by a pulsatile or periodic source, leading to spatiotemporal variations in the pressure and flow fields on short time-scales within each vessel. Here, we investigate the mathematical problem of how long-term adaptation in elastic networks is impacted by short-term pulsatile dynamics at the level of individual vessels. Using a a minimal one-loop network, we show that pulsatility gives rise to resonances that stabilize the loop for a much broader range of metabolic cost functions than predicted by existing theories. Our paper emphasizes the importance of correctly capturing the interplay of the short and long time-scales for a more realistic treatment of adaptation in periodically driven elastic flow networks. Published by the American Physical Society 2024

Truss structures at macro-scale are common in a number of engineering applications and are now being increasingly used at the micro-scale to construct metamaterials. In analyzing the properties of a given truss structure, it is often necessary to understand how stress waves propagate through the system and/or its dynamic modes under time dependent loading so as to allow for maximally efficient use of space and material. This can be a computationally challenging task for particularly large or complex structures, with current methods requiring fine spatial discretization or evaluations of sizable matrices. Here we present a spectral method to compute the dynamics of trusses inspired by results from fluid flow networks. Our model accounts for the full dynamics of linearly elastic truss elements via a network Laplacian; a matrix object which couples the motions of the structure joints. We show that this method is equivalent to the continuum limit of linear finite element methods as well as capable of reproducing natural frequencies and modes determined by more complex and computationally costlier methods.

Existing models of adaptation in biological flow networks consider their constituent vessels (e.g. veins and arteries) to be rigid, thus predicting a non physiological response when the drive (e.g. the heart) is dynamic. Here we show that incorporating pulsatile driving and properties such as fluid inertia and vessel compliance into a general adaptation framework fundamentally changes the expected structure at steady state of a minimal one-loop network. In particular, pulsatility is observed to give rise to resonances which can stabilize loops for a much broader class of metabolic cost functions than predicted by existing theories. Our work points to the need for a more realistic treatment of adaptation in biological flow networks, especially those driven by a pulsatile source, and provides insights into pathologies that emerge when such pulsatility is disrupted in human beings.

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g., the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states. The combination of flow resistance, fluid inertia, and elasticity of the vessel walls causes the flow and pressure of the fluid throughout the network to respond to these transitions and adapt to the new power source operating profiles over a nonzero timescale. We find that this response time can exist in one of two possible regimes; one dominated by the decay rate of traveling wavefronts and independent of system size, and one dominated by the diffusive nature of the fluid mechanical energy over large length scales. These regimes are shown to exist for both single vessels and hierarchically structured networks with systems smaller than a critical size in the former and larger systems in the latter. Applying biologically relevant parameters to the model suggests that animal vascular networks may have evolved to occupy a state within the minimal response time regime but close to this critical system size.

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g. the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states. The combination of flow resistance, fluid inertia, and elasticity of the vessel walls causes the flow and pressure of the fluid throughout the network to respond to these transitions and adapt to the new power source operating profiles over a nonzero time scale. We find that this response time can exist in one of two possible regimes; one dominated by the decay rate of travelling wavefronts and independent of system size, and one dominated by the diffusive nature of the fluid mechanical energy over large length scales. These regimes are shown to exist for both single vessels and hierarchically structured networks with systems smaller than a critical size in the former and larger systems in the later. Applying biologically relevant parameters to the model suggests that animal vascular networks may have evolved to occupy a state within the minimal response time regime but close to this critical system size.

Transport networks are typically optimized, either by evolutionary pressures in biological systems, or by human design, in engineered structures. In the case of systems such as the animal vasculature, the transport of fluids is not only hindered by the inherent resistance to flow but also kept in a dynamic state by the pulsatile nature of the heart and elastic properties of the vessel walls. While this imparted pulsatility necessarily increases the dissipation of energy caused by the resistance, the vessel elasticity helps to reduce overall dissipation by attenuating the amplitude of the pulsatile components of the flow. However, we find that this reduction in energy loss comes at the price of increasing the time required to respond to changes in the flow boundary conditions for vessels longer than a critical size. In this regime, dissipation and response time are found to follow a simple power law scaling relation in single vessels as well as hierarchically structured networks. Applying biologically relevant parameters to the model suggests that animal vascular networks may have evolved to maintain a minimal response time over lesser dissipation.

Morphogen profiles allow cells to determine their position within a developing organism, but not all morphogen profiles form by the same mechanism. Here, we derive fundamental limits to the precision of morphogen concentration sensing for two canonical mechanisms: the diffusion of morphogen through extracellular space and the direct transport of morphogen from source cell to target cell, for example, via cytonemes. We find that direct transport establishes a morphogen profile without adding noise in the process. Despite this advantage, we find that for sufficiently large values of profile length, the diffusion mechanism is many times more precise due to a higher refresh rate of morphogen molecules. We predict a profile lengthscale below which direct transport is more precise, and above which diffusion is more precise. This prediction is supported by data from a wide variety of morphogens in developing Drosophila and zebrafish.

Cellular behaviors such as migration, division, and differentiation rely on precise timing, and yet the molecular events that govern these behaviors are highly stochastic. We investigate regulatory strategies that decrease the timing noise of molecular events. Autoregulatory feedback increases noise. Yet we find that in the presence of regulation by a second species, autoregulatory feedback decreases noise. To explain this finding, we develop a method to calculate the optimal regulation function that minimizes the timing noise. The method reveals that the combination of feedback and regulation minimizes noise by maximizing the number of molecular events that must happen in sequence before a threshold is crossed. We compute the optimal timing precision for all two-node networks with regulation and feedback, derive a generic lower bound on timing noise, and discuss our results in the context of neuroblast migration during Caenorhabditis elegans development.

Metastatic cancer cells detect the direction of lymphatic flow by self-communication: they secrete and detect a chemical which, due to the flow, returns to the cell surface anisotropically. The secretion rate is low, meaning detection noise may play an important role, but the sensory precision of this mechanism has not been explored. Here we derive the precision of flow sensing for two ubiquitous detection methods: absorption vs reversible binding to surface receptors. We find that binding is more precise due to the fact that absorption distorts the signal that the cell aims to detect. Comparing to experiments, our results suggest that the cancer cells operate remarkably close to the physical detection limit. Our prediction that cells should bind the chemical reversibly, not absorb it, is supported by endocytosis data for this ligand-receptor pair.

Metastatic cancer cells detect the direction of lymphatic flow by self-communication: they secrete and detect a chemical which, due to the flow, returns to the cell surface anisotropically. The secretion rate is low, meaning detection noise may play an important role, but the sensory precision of this mechanism has not been explored. Here we derive the precision of flow sensing for two ubiquitous detection methods: absorption vs. reversible binding to surface receptors. We find that binding is more precise due to the fact that absorption distorts the signal that the cell aims to detect. Comparing to experiments, our results suggest that the cancer cells operate remarkably close to the physical detection limit. Our prediction that cells should bind the chemical reversibly, not absorb it, is supported by endocytosis data for this ligand-receptor pair.