Mechanically induced topological transition of spectrin regulates its distribution in the mammalian cell cortex.

The cell cortex is a dynamic assembly formed by the plasma membrane and underlying cytoskeleton. As the main determinant of cell shape, the cortex ensures its integrity during passive and active deformations by adapting cytoskeleton topologies through yet poorly understood mechanisms. The spectrin meshwork ensures such adaptation in erythrocytes and neurons by adopting different organizations. Erythrocytes rely on triangular-like lattices of spectrin tetramers, whereas in neurons they are organized in parallel, periodic arrays. Since spectrin is ubiquitously expressed, we exploited Expansion Microscopy to discover that, in fibroblasts, distinct meshwork densities co-exist. Through biophysical measurements and computational modeling, we show that the non-polarized spectrin meshwork, with the intervention of actomyosin, can dynamically transition into polarized clusters fenced by actin stress fibers that resemble periodic arrays as found in neurons. Clusters experience lower mechanical stress and turnover, despite displaying an extension close to the tetramer contour length. Our study sheds light on the adaptive properties of spectrin, which participates in the protection of the cell cortex by varying its densities in response to key mechanical features.

Biophysical Modeling of Actin-Mediated Structural Plasticity Reveals Mechanical Adaptation in Dendritic Spines.

Synaptic plasticity is important for learning and memory formation; it describes the strengthening or weakening of connections between synapses. The postsynaptic part of excitatory synapses resides in dendritic spines, which are small protrusions on the dendrites. One of the key features of synaptic plasticity is its correlation with the size of these spines. A long-lasting synaptic strength increase [long-term potentiation (LTP)] is only possible through the reconfiguration of the actin spine cytoskeleton. Here, we develop an experimentally informed three-dimensional computational model in a moving boundary framework to investigate this reconfiguration. Our model describes the reactions between actin and actin-binding proteins leading to the cytoskeleton remodeling and their effect on the spine membrane shape to examine the spine enlargement upon LTP. Moreover, we find that the incorporation of perisynaptic elements enhances spine enlargement upon LTP, exhibiting the importance of accounting for these elements when studying structural LTP. Our model shows adaptation to repeated stimuli resulting from the interactions between spine proteins and mechanical forces.

Biophysical Modeling of Synaptic Plasticity.

Dendritic spines are small, bulbous compartments that function as postsynaptic sites and undergo intense biochemical and biophysical activity. The role of the myriad signaling pathways that are implicated in synaptic plasticity is well studied. A recent abundance of quantitative experimental data has made the events associated with synaptic plasticity amenable to quantitative biophysical modeling. Spines are also fascinating biophysical computational units because spine geometry, signal transduction, and mechanics work in a complex feedback loop to tune synaptic plasticity. In this sense, ideas from modeling cell motility can inspire us to develop multiscale approaches for predictive modeling of synaptic plasticity. In this article, we review the key steps in postsynaptic plasticity with a specific focus on the impact of spine geometry on signaling, cytoskeleton rearrangement, and membrane mechanics. We summarize the main experimental observations and highlight how theory and computation can aid our understanding of these complex processes.Expected final online publication date for the Annual Review of Biophysics, Volume 53 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Membrane mechanics dictate axonal morphology and function.

Axons are thought to be ultrathin membrane cables of a relatively uniform diameter, designed to conduct electrical signals, or action potentials. Here, we demonstrate that unmyelinated axons are not simple cylindrical tubes. Rather, axons have nanoscopic boutons repeatedly along their length interspersed with a thin cable with a diameter of ∼60 nm like pearls-on-a-string. These boutons are only ∼200 nm in diameter and do not have synaptic contacts or a cluster of synaptic vesicles, hence non-synaptic. Our in silico modeling suggests that axon pearling can be explained by the mechanical properties of the membrane including the bending modulus and tension. Consistent with modeling predictions, treatments that disrupt these parameters like hyper- or hypo-tonic solutions, cholesterol removal, and non-muscle myosin II inhibition all alter the degree of axon pearling, suggesting that axon morphology is indeed determined by the membrane mechanics. Intriguingly, neuronal activity modulates the cholesterol level of plasma membrane, leading to shrinkage of axon pearls. Consequently, the conduction velocity of action potentials becomes slower. These data reveal that biophysical forces dictate axon morphology and function and that modulation of membrane mechanics likely underlies plasticity of unmyelinated axons.

Mechanically induced topological transition of spectrin regulates its distribution in the mammalian cortex.

The cell cortex is a dynamic assembly that ensures cell integrity during passive deformation or active response by adapting cytoskeleton topologies with poorly understood mechanisms. The spectrin meshwork ensures such adaptation in erythrocytes and neurons. Erythrocytes rely on triangular-like lattices of spectrin tetramers, which in neurons are organized in periodic arrays. We exploited Expansion Microscopy to discover that these two distinct topologies can co-exist in other mammalian cells such as fibroblasts. We show through biophysical measurements and computational modeling that spectrin provides coverage of the cortex and, with the intervention of actomyosin, erythroid-like lattices can dynamically transition into condensates resembling neuron-like periodic arrays fenced by actin stress fibers. Spectrin condensates experience lower mechanical stress and turnover despite displaying an extension close to the contour length of the tetramer. Our study sheds light on the adaptive properties of spectrin, which ensures protection of the cortex by undergoing mechanically induced topological transitions.

Can biophysical models of dendritic spines be used to explore synaptic changes associated with addiction?

Effective treatments that prevent or reduce drug relapse vulnerability should be developed to relieve the high burden of drug addiction on society. This will only be possible by enhancing the understanding of the molecular mechanisms underlying the neurobiology of addiction. Recent experimental data have shown that dendritic spines, small protrusions from the dendrites that receive excitatory input, of spiny neurons in the nucleus accumbens exhibit morphological changes during drug exposure and withdrawal. Moreover, these changes relate to the characteristic drug-seeking behavior of addiction. However, due to the complexity of dendritic spines, we do not yet fully understand the processes underlying their structural changes in response to different inputs. We propose that biophysical models can enhance the current understanding of these processes by incorporating different, and sometimes, discrepant experimental data to identify the shared underlying mechanisms and generate experimentally testable hypotheses. This review aims to give an up-to-date report on biophysical models of dendritic spines, focusing on those models that describe their shape changes, which are well-known to relate to learning and memory. Moreover, it examines how these models can enhance our understanding of the effect of the drugs and the synaptic changes during withdrawal, as well as during neurodegenerative disease progression such as Alzheimer's disease.

Exploring new roles for actin upon LTP induction in dendritic spines.

Dendritic spines, small protrusions of the dendrites, enlarge upon LTP induction, linking morphological and functional properties. Although the role of actin in spine enlargement has been well studied, little is known about its relationship with mechanical membrane properties, such as membrane tension, which is involved in many cell processes, like exocytosis. Here, we use a 3D model of the dendritic spine to investigate how polymerization of actin filaments can effectively elevate the membrane tension to trigger exocytosis in a domain close to the tip of the spine. Moreover, we show that the same pool of actin promotes full membrane fusion after exocytosis and spine stabilization.

Reproducing asymmetrical spine shape fluctuations in a model of actin dynamics predicts self-organized criticality.

Dendritic spines change their size and shape spontaneously, but the function of this remains unclear. Here, we address this in a biophysical model of spine fluctuations, which reproduces experimentally measured spine fluctuations. For this, we characterize size- and shape fluctuations from confocal microscopy image sequences using autoregressive models and a new set of shape descriptors derived from circular statistics. Using the biophysical model, we extrapolate into longer temporal intervals and find the presence of 1/f noise. When investigating its origins, the model predicts that the actin dynamics underlying shape fluctuations self-organizes into a critical state, which creates a fine balance between static actin filaments and free monomers. In a comparison against a non-critical model, we show that this state facilitates spine enlargement, which happens after LTP induction. Thus, ongoing spine shape fluctuations might be necessary to react quickly to plasticity events.

Modeling the Shape of Synaptic Spines by Their Actin Dynamics.

Dendritic spines are the morphological basis of excitatory synapses in the cortex and their size and shape correlates with functional synaptic properties. Recent experiments show that spines exhibit large shape fluctuations that are not related to activity-dependent plasticity but nonetheless might influence memory storage at their synapses. To investigate the determinants of such spontaneous fluctuations, we propose a mathematical model for the dynamics of the spine shape and analyze it in 2D-related to experimental microscopic imagery-and in 3D. We show that the spine shape is governed by a local imbalance between membrane tension and the expansive force from actin bundles that originates from discrete actin polymerization foci. Experiments have shown that only few such polymerization foci co-exist at any time in a spine, each having limited life time. The model shows that the momentarily existing set of such foci pushes the membrane along certain directions until foci are replaced and other directions may now be affected. We explore these relations in depth and use our model to predict shape and temporal characteristics of spines from the different biophysical parameters involved in actin polymerization. Approximating the model by a single recursive equation we finally demonstrate that the temporal evolution of the number of active foci is sufficient to predict the size of the model-spines. Thus, our model provides the first platform to study the relation between molecular and morphological properties of the spine with a high degree of biophysical detail.

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex.

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an [Formula: see text] current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the [Formula: see text] current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in [Formula: see text] resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the [Formula: see text] current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.