Mechanical Principles Governing the Shapes of Dendritic Spines

Comparing Multifunctional Viral and Eukaryotic Proteins for Generating Scission Necks in Membranes

Deterministic formation of membrane scission necks by protein machinery with multiplexed functions is critical in biology. A microbial example is M2 viroporin, a proton pump from the influenza A virus that is multiplexed with membrane remodeling activity to induce budding and scission in the host membrane during viral maturation. In comparison, the dynamin family constitutes a class of eukaryotic proteins implicated in mitochondrial fission, as well as various budding and endocytosis pathways. In the case of Dnm1, the mitochondrial fission protein in yeast, the membrane remodeling activity is multiplexed with mechanoenzyme activity to create fission necks. It is not clear why these functions are combined in these scission processes, which occur in drastically different compositions and solution conditions. In general, direct experimental access to changing neck sizes induced by individual proteins or peptide fragments is challenging due to the nanoscale dimensions and influence of thermal fluctuations. Here, we use a mechanical model to estimate the size of scission necks by leveraging small-angle X-ray scattering structural data of protein-lipid systems under different conditions. The influence of interfacial tension, lipid composition, and membrane budding morphology on the size of the induced scission necks is systematically investigated using our data and molecular dynamic simulations. We find that the M2 budding protein from the influenza A virus has robust pH-dependent membrane activity that induces nanoscopic necks within the range of spontaneous hemifission for a broad range of lipid compositions. In contrast, the sizes of scission necks generated by mitochondrial fission proteins strongly depend on lipid composition, which suggests a role for mechanical constriction.

Making the cut: Multiscale simulation of membrane remodeling

Biological membranes are dynamic heterogeneous materials, and their shape and organization are tightly coupled to the properties of the proteins in and around them. However, the length scales of lipid and protein dynamics are far below the size of membrane-bound organelles, much less an entire cell. Therefore, multiscale modeling approaches are often necessary to build a comprehensive picture of the interplay of these factors, and have provided critical insights into our understanding of membrane dynamics. Here, we review computational methods for studying membrane remodeling, as well as passive and active examples of protein-driven membrane remodeling. As the field advances towards the modeling of key aspects of organelles and whole cells - an increasingly accessible regime of study - we summarize here recent successes and offer comments on future trends.

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.

Sex-specific dendritic morphology of hippocampal pyramidal neurons in the adolescent and young adult rats

CA1 and CA3 pyramidal neurons are the major sources of hippocampal efferents. The structural features of these neurons are presumed to be involved in various normal/abnormal cognitive and emotional outcomes by influencing the pattern of synaptic inputs and neuronal signal processing. Although many studies have described hippocampal structure differences between males and females, these reports mainly focused on gross anatomical features in adult or aged models, and such distinctions on neuronal morphology and dendritic spine density during adolescence, a period of high vulnerability to neurodevelopmental disorders, have received much less attention. In this work, we analyzed dendritic architecture and density of spines in CA1 and CA3 neurons of male and female rats in early adolescence (postnatal day, PND 40) and compared them with those in late adolescence/young adulthood (PND 60). On PND 40, CA1 neurons of male rats showed more Sholl intersections and spine density in apical and basal dendrites compared to those in females. The Sholl intersections in basal dendrites of CA3 neurons were also more in males, whereas the number of apical dendrite intersections was not significantly different between sexes. In male rats, there was a notable decrease in the number of branch and terminal points in the basal dendrite of CA1 neurons of young adults when compared to their sex-matched adolescent rats. On the other hand, CA1 neurons in young adult females also showed more Sholl intersections in apical and basal dendrites compared to adolescent females. Meanwhile, the total cable length, the number of branches, and terminal points of apical dendrites in CA3 neurons also exhibited a significant reduction in young adult male rats compared to their sex-matched adolescents. In young adult rats, both apical and basal dendrites of CA3 neurons in males showed fewer intersections with Sholl circles, but there were no significant differences in dendritic spine density or count estimation between males and females. On the other hand, young adult female rats had more Sholl intersections and dendritic spine count on the basal dendrites of CA3 neurons compared to adolescent females. Although no significant sex- and age-dependent difference in neuronal density was detected in CA1 and CA3 subareas, CA3 pyramidal neurons of both male and female rats showed reduced soma area compared to adolescent rats. Our findings show that the sex differences in the dendritic structure of CA1 and CA3 neurons vary by age and also by the compartments of dendritic arbors. Such variations in the morphology of hippocampal pyramidal neurons may take part as a basis for normal cognitive and affective differences between the sexes, as well as distinct sensitivity to interfering factors and the prevalence of neuropsychological diseases.

Biaxial Structures of Localized Deformations and Line-like Distortions in Effectively 2D Nematic Films

We numerically studied localized elastic distortions in curved, effectively two-dimensional nematic shells. We used a mesoscopic Landau-de Gennes-type approach, in which the orientational order is theoretically considered by introducing the appropriate tensor nematic order parameter, while the three-dimensional shell shape is described by the curvature tensor. We limited our theoretical consideration to axially symmetric shapes of nematic shells. It was shown that in the surface regions of stomatocyte-class nematic shell shapes with large enough magnitudes of extrinsic (deviatoric) curvature, the direction of the in-plane orientational ordering can be mutually perpendicular above and below the narrow neck region. We demonstrate that such line-like nematic distortion configurations may run along the parallels (i.e., along the circular lines of constant latitude) located in the narrow neck regions of stomatocyte-like nematic shells. It was shown that nematic distortions are enabled by the order reconstruction mechanism. We propose that the regions of nematic shells that are strongly elastically deformed, i.e., topological defects and line-like distortions, may attract appropriately surface-decorated nanoparticles (NPs), which could potentially be useful for the controlled assembly of NPs.

Comparing multifunctional viral and eukaryotic proteins for generating scission necks in membranes

Deterministic formation of membrane scission necks by protein machinery with multiplexed functions is critical in biology. A microbial example is the M2 viroporin, a proton pump from the influenza A virus which is multiplexed with membrane remodeling activity to induce budding and scission in the host membrane during viral maturation. In comparison, the dynamin family constitutes a class of eukaryotic proteins implicated in mitochondrial fission, as well as various budding and endocytosis pathways. In the case of Dnm1, the mitochondrial fission protein in yeast, the membrane remodeling activity is multiplexed with mechanoenzyme activity to create fission necks. It is not clear why these functions are combined in these scission processes, which occur in drastically different compositions and solution conditions. In general, direct experimental access to changing neck sizes induced by individual proteins or peptide fragments is challenging due to the nanoscale dimensions and influence of thermal fluctuations. Here, we use a mechanical model to estimate the size of scission necks by leveraging Small-Angle X-ray Scattering (SAXS) structural data of protein-lipid systems under different conditions. The influence of interfacial tension, lipid composition, and membrane budding morphology on the size of the induced scission necks is systematically investigated using our data and molecular dynamic simulations. We find that the M2 budding protein from the influenza A virus has robust pH-dependent membrane activity that induces nanoscopic necks within the range of spontaneous hemi-fission for a broad range of lipid compositions. In contrast, the sizes of scission necks generated by mitochondrial fission proteins strongly depend on lipid composition, which suggests a role for mechanical constriction.

How Cell-Penetrating Peptides Behave Differently from Pore-Forming Peptides: Structure and Stability of Induced Transmembrane Pores

Peptide-induced transmembrane pore formation is commonplace in biology. Examples of transmembrane pores include pores formed by antimicrobial peptides (AMPs) and cell-penetrating peptides (CPPs) in bacterial membranes and eukaryotic membranes, respectively. In general, however, transmembrane pore formation depends on peptide sequences, lipid compositions, and intensive thermodynamic variables and is difficult to observe directly under realistic solution conditions, with structures that are challenging to measure directly. In contrast, the structure and phase behavior of peptide-lipid systems are relatively straightforward to map out experimentally for a broad range of conditions. Cubic phases are often observed in systems involving pore-forming peptides; however, it is not clear how the structural tendency to induce negative Gaussian curvature (NGC) in such phases is quantitatively related to the geometry of biological pores. Here, we leverage the theory of anisotropic inclusions and devise a facile method to estimate transmembrane pore sizes from geometric parameters of cubic phases measured from small-angle X-ray scattering (SAXS) and show that such estimates compare well with known pore sizes. Moreover, our model suggests that although AMPs can induce stable transmembrane pores for membranes with a broad range of conditions, pores formed by CPPs are highly labile, consistent with atomistic simulations.

Spine apparatus modulates Ca 2+ in spines through spatial localization of sources and sinks

Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work, we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, spine membrane geometry, and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on where it is localized in the SER and on the SER geometry. In order to maximize Ca 2+ in the dendrites (for activating clusters of spines and spine-spine communication), a laminar SA was favorable with RyRs localized in the neck region, closer to the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization.

Highlights

1RyR opening in dendritic spine ER is location dependent and spine geometry dependent. Ca 2+ buffers and SERCA can buffer against runaway potentiation of spines even when CICR is activated. RyRs located towards the ER neck allow for more Ca 2+ to reach the dendrites. RyRs located towards the spine head are favorable for increased Ca 2+ in spines.

Cristae formation is a mechanical buckling event controlled by the inner membrane lipidome

Cristae are high curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous mechanisms for lipids have yet to be elucidated. Here we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the IMM against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. The model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that CL is essential in low oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of CL is dependent on the surrounding lipid and protein components of the IMM.

Transport and localization on dendrite-inspired flat band linear photonic lattices

The capacity of a physical system to transport and localize energy or information is usually linked to its spatial configuration. This is relevant for integration and transmission of signals as performed, for example, by the dendrites of neuronal cells. Inspired by recent works on the organization of spines on the surface of dendrites and how they promote localization or propagation of electrical impulses in neurons, here we propose a linear photonic lattice configuration to study how the geometric features of a dendrite-inspired lattice allows for the localization or propagation of light on a completely linear structure. We show that by increasing the compression of the photonic analogue of spines and thus, by increasing the coupling strength of the spines with the main chain (the "photonic dendrite"), flat band modes become prevalent in the system, allowing spatial localization in the linear - low energy - regime. Furthermore, we study the inclusion of disorder in the distribution of spines and show that the main features of ordered systems persist due to the robustness of the flat band states. Finally, we discuss if the photonic analog, having evanescent interactions, may provide insight into linear morphological mechanisms at work occurring in some biological systems, where interactions are of electric and biochemical origin.

Spatiotemporal modelling reveals geometric dependence of AMPAR dynamics on dendritic spine morphology

The modification of neural circuits depends on the strengthening and weakening of synaptic connections. Synaptic strength is often correlated to the density of the ionotropic, glutamatergic receptors, AMPARs, (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors) at the postsynaptic density (PSD). While AMPAR density is known to change based on complex biological signalling cascades, the effect of geometric factors such as dendritic spine shape, size and curvature remain poorly understood. In this work, we developed a deterministic, spatiotemporal model to study the dynamics of AMPARs during long-term potentiation (LTP). This model includes a minimal set of biochemical events that represent the upstream signalling events, trafficking of AMPARs to and from the PSD, lateral diffusion in the plane of the spine membrane, and the presence of an extrasynaptic AMPAR pool. Using idealized and realistic spine geometries, we show that the dynamics and increase of bound AMPARs at the PSD depends on a combination of endo- and exocytosis, membrane diffusion, the availability of free AMPARs and intracellular signalling interactions. We also found non-monotonic relationships between spine volume and the change in AMPARs at the PSD, suggesting that spines restrict changes in AMPARs to optimize resources and prevent runaway potentiation. KEY POINTS: Synaptic plasticity involves dynamic biochemical and physical remodelling of small protrusions called dendritic spines along the dendrites of neurons. Proper synaptic functionality within these spines requires changes in receptor number at the synapse, which has implications for downstream neural functions, such as learning and memory formation. In addition to being signalling subcompartments, spines also have unique morphological features that can play a role in regulating receptor dynamics on the synaptic surface. We have developed a spatiotemporal model that couples biochemical signalling and receptor trafficking modalities in idealized and realistic spine geometries to investigate the role of biochemical and biophysical factors in synaptic plasticity. Using this model, we highlight the importance of spine size and shape in regulating bound AMPA receptor dynamics that govern synaptic plasticity, and predict how spine shape might act to reset synaptic plasticity as a built-in resource optimization and regulation tool.

How cell penetrating peptides behave differently from pore forming peptides: structure and stability of induced transmembrane pores

Peptide induced trans-membrane pore formation is commonplace in biology. Examples of transmembrane pores include pores formed by antimicrobial peptides (AMPs) and cell penetrating peptides (CPPs) in bacterial membranes and eukaryotic membranes, respectively. In general, however, transmembrane pore formation depends on peptide sequences, lipid compositions and intensive thermodynamic variables and is difficult to observe directly under realistic solution conditions, with structures that are challenging to measure directly. In contrast, the structure and phase behavior of peptide-lipid systems are relatively straightforward to map out experimentally for a broad range of conditions. Cubic phases are often observed in systems involving pore forming peptides; however, it is not clear how the structural tendency to induce negative Gaussian curvature (NGC) in such phases is quantitatively related to the geometry of biological pores. Here, we leverage the theory of anisotropic inclusions and devise a facile method to estimate transmembrane pore sizes from geometric parameters of cubic phases measured from small angle X-ray scattering (SAXS) and show that such estimates compare well with known pore sizes. Moreover, our model suggests that whereas AMPs can induce stable transmembrane pores for membranes with a broad range of conditions, pores formed by CPPs are highly labile, consistent with atomistic simulations.

Crosstalk between biochemical signalling network architecture and trafficking governs AMPAR dynamics in synaptic plasticity

Synaptic plasticity involves modification of both biochemical and structural components of neurons. Many studies have revealed that the change in the number density of the glutamatergic receptor AMPAR at the synapse is proportional to synaptic weight update; an increase in AMPAR corresponds to strengthening of synapses while a decrease in AMPAR density weakens synaptic connections. The dynamics of AMPAR are thought to be regulated by upstream signalling, primarily the calcium-CaMKII pathway, trafficking to and from the synapse, and influx from extrasynaptic sources. Previous work in the field of deterministic modelling of CaMKII dynamics has assumed bistable kinetics, while experiments and rule-based modelling have revealed that CaMKII dynamics can be either monostable or ultrasensitive. This raises the following question: how does the choice of model assumptions involving CaMKII dynamics influence AMPAR dynamics at the synapse? To answer this question, we have developed a set of models using compartmental ordinary differential equations to systematically investigate contributions of different signalling and trafficking variations, along with their coupled effects, on AMPAR dynamics at the synaptic site. We find that the properties of the model including network architecture describing different stability features of CaMKII and parameters that capture the endocytosis and exocytosis of AMPAR significantly affect the integration of fast upstream species by slower downstream species. Furthermore, we predict that the model outcome, as determined by bound AMPAR at the synaptic site, depends on (1) the choice of signalling model (bistable CaMKII or monostable CaMKII dynamics), (2) trafficking versus influx contributions and (3) frequency of stimulus. KEY POINTS: The density of AMPA receptors (AMPARs) at the postsynaptic density of the synapse provides a readout of synaptic plasticity, which involves crosstalk between complex biochemical signalling networks including CaMKII dynamics and trafficking pathways including exocytosis and endocytosis. Here we build a model that integrates CaMKII dynamics and AMPAR trafficking to explore this crosstalk. We compare different models of CaMKII that result in monostable or bistable kinetics and their impact on AMPAR dynamics. Our results show that AMPAR density depends on the coupling between aspects of biochemical signalling and trafficking. Specifically, assumptions regarding CaMKII dynamics and its stability features can alter AMPAR density at the synapse. Our model also predicts that the kinetics of trafficking versus influx of AMPAR from the extrasynaptic space can further impact AMPAR density. Thus, the contributions of both signalling and trafficking should be considered in computational models.

Membrane curvature governs the distribution of Piezo1 in live cells

Piezo1 is a bona fide mechanosensitive ion channel ubiquitously expressed in mammalian cells. The distribution of Piezo1 within a cell is essential for various biological processes including cytokinesis, cell migration, and wound healing. However, the underlying principles that guide the subcellular distribution of Piezo1 remain largely unexplored. Here, we demonstrate that membrane curvature serves as a key regulator of the spatial distribution of Piezo1 in the plasma membrane of living cells. Piezo1 depletes from highly curved membrane protrusions such as filopodia and enriches to nanoscale membrane invaginations. Quantification of the curvature-dependent sorting of Piezo1 directly reveals the in situ nano-geometry of the Piezo1-membrane complex. Piezo1 density on filopodia increases upon activation, independent of calcium, suggesting flattening of the channel upon opening. Consequently, the expression of Piezo1 inhibits filopodia formation, an effect that diminishes with channel activation.

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations and analyses, we found that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries, suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

Tuning brain networks: The emerging role of transcranial direct current stimulation on structural plasticity

Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique (NIBS) that has been proven to promote beneficial effects in a range of neurological and psychiatric disorders. Unfortunately, although has been widely investigated, the mechanism comprehension around tDCS effects presents still some gaps. Therefore, scientists are still trying to uncover the cellular and molecular mechanisms behind its positive effects to permit a more suitable application. Experimental models have provided converging evidence that tDCS elicits improvements in learning and memory by modulating both excitability and synaptic plasticity in neurons. Recently, among tDCS neurobiological effects, neural synchronization and dendritic structural changes have been reported in physiological and pathological conditions, suggesting possible effects at the neuronal circuit level. In this review, we bring in to focus the emerging effects of tDCS on the structural plasticity changes and neuronal rewiring, with the intent to match these two aspects with the underpinning molecular mechanisms identified so far, providing a new perspective to work on to unveil novel tDCS therapeutic use to treat brain dysfunctions.

The many faces of membrane tension: Challenges across systems and scales

Our understanding of the role of membrane tension in the field of membrane biophysics is rapidly evolving from a passive construct to an active player in a variety of cellular phenomena. Membrane tension has been shown to be a key regulator of many cellular processes ranging including trafficking, ion channel activation, and the invasion of red blood cells by malaria parasites. Recent experimental advances in cells, including the development of a fluorescent tension reporter, have shown that membrane tension is heterogeneous. In this mini-review, I summarize the recent advances in membrane tension measurements and discuss the contributions from different cellular constituents such as the cortical cytoskeleton. Then, I will explore how these different complexities can be considered in biophysical models of different scales. Finally, I will elaborate on the need for iterations between models and experiments as technologies in both fields advance to enable us to obtain critical insights into the physiological role of membrane tension as a critical component of mechanotransduction.

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 the 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.

Revisiting I-BAR Proteins at Central Synapses

Dendritic spines, the distinctive postsynaptic feature of central nervous system (CNS) excitatory synapses, have been studied extensively as electrical and chemical compartments, as well as scaffolds for receptor cycling and positioning of signaling molecules. The dynamics of the shape, number, and molecular composition of spines, and how they are regulated by neural activity, are critically important in synaptic efficacy, synaptic plasticity, and ultimately learning and memory. Dendritic spines originate as outward protrusions of the cell membrane, but this aspect of spine formation and stabilization has not been a major focus of investigation compared to studies of membrane protrusions in non-neuronal cells. We review here one family of proteins involved in membrane curvature at synapses, the BAR (Bin-Amphiphysin-Rvs) domain proteins. The subfamily of inverse BAR (I-BAR) proteins sense and introduce outward membrane curvature, and serve as bridges between the cell membrane and the cytoskeleton. We focus on three I-BAR domain proteins that are expressed in the central nervous system: Mtss2, MIM, and IRSp53 that promote negative, concave curvature based on their ability to self-associate. Recent studies suggest that each has distinct functions in synapse formation and synaptic plasticity. The action of I-BARs is also shaped by crosstalk with other signaling components, forming signaling platforms that can function in a circuit-dependent manner. We discuss another potentially important feature-the ability of some BAR domain proteins to impact the function of other family members by heterooligomerization. Understanding the spatiotemporal resolution of synaptic I-BAR protein expression and their interactions should provide insights into the interplay between activity-dependent neural plasticity and network rewiring in the CNS.