Entropic Forces Drive Cellular Contact Guidance

Contact guidance—the widely known phenomenon of cell alignment induced by anisotropic environmental features—is an essential step in the organization of adherent cells, but the mechanisms by which cells achieve this orientational ordering remain unclear. Here, we seeded myofibroblasts on substrates micropatterned with stripes of fibronectin and observed that contact guidance emerges at stripe widths much greater than the cell size. To understand the origins of this surprising observation, we combined morphometric analysis of cells and their subcellular components with a, to our knowledge, novel statistical framework for modeling nonthermal fluctuations of living cells. This modeling framework is shown to predict not only the trends but also the statistical variability of a wide range of biological observables, including cell (and nucleus) shapes, sizes, and orientations, as well as stress-fiber arrangements within the cells with remarkable fidelity with a single set of cell parameters. By comparing observations and theory, we identified two regimes of contact guidance: 1) guidance on stripe widths smaller than the cell size (w ≤ 160 μm), which is accompanied by biochemical changes within the cells, including increasing stress-fiber polarization and cell elongation; and 2) entropic guidance on larger stripe widths, which is governed by fluctuations in the cell morphology. Overall, our findings suggest an entropy-mediated mechanism for contact guidance associated with the tendency of cells to maximize their morphological entropy through shape fluctuations.     

Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.     

Force Spectrum Microscopy Using Mitochondrial Fluctuations of Control and ATP-Depleted Cells

A single-cell assay of active and passive intracellular mechanical properties of mammalian cells could give significant insight into cellular processes. Force spectrum microscopy (FSM) is one such technique, which combines the spontaneous motion of probe particles and the mechanical properties of the cytoskeleton measured by active microrheology using optical tweezers to determine the force spectrum of the cytoskeleton. A simpler and noninvasive method to perform FSM would be very useful, enabling its widespread adoption. Here, we develop an alternative method of FSM using measurement of the fluctuating motion of mitochondria. Mitochondria of the C3H-10T1/2 cell line were labeled and tracked using confocal microscopy. Mitochondrial probes were selected based on morphological characteristics, and their mean-square displacement, creep compliance, and distributions of directional change were measured. We found that the creep compliance of mitochondria resembles that of particles in viscoelastic media. However, comparisons of creep compliance between controls and cells treated with pharmacological agents showed that perturbations to the actomysoin network had surprisingly small effects on mitochondrial fluctuations, whereas microtubule disruption and ATP depletion led to a significantly decreased creep compliance. We used properties of the distribution of directional change to identify a regime of thermally dominated fluctuations in ATP-depleted cells, allowing us to estimate the viscoelastic parameters for a range of timescales. We then determined the force spectrum by combining these viscoelastic properties with measurements of spontaneous fluctuations tracked in control cells. Comparisons with previous measurements made using FSM revealed an excellent match.     

Lipid-Protein Interplay in Dimerization of Juxtamembrane Domains of Epidermal Growth Factor Receptor

Transmembrane (TM) helix and juxtamembrane (JM) domains (TM-JM) bridge the extracellular and intracellular domains of single-pass membrane proteins, including epidermal growth factor receptor (EGFR). TM-JM dimerization plays a crucial role in regulation of EGFR kinase activity at the cytoplasmic side. Although the interaction of JM with membrane lipids is thought to be important to turn on EGF signaling, and phosphorylation of Thr654 on JM leads to desensitization, the underlying kinetic mechanisms remain unclear. In particular, how Thr654 phosphorylation regulates EGFR activity is largely unknown. Here, combining single-pair FRET imaging and nanodisc techniques, we showed that phosphatidylinositol 4,5-bis phosphate (PIP₂) facilitated JM dimerization effectively. We also found that Thr654 phosphorylation dissociated JM dimers in the membranes containing acidic lipids, suggesting that Thr654 phosphorylation electrostatically prevented the interaction with basic residues in JM and acidic lipids. Based on the single-molecule experiment, we clarified the kinetic pathways of the monomer (inactive state)-to-dimer (active state) transition of JM domains and alteration in the pathways depending on the membrane lipid species and Thr654 phosphorylation.     

Structural Conservation and Effects of Alterations in T Cell Receptor Transmembrane Interfaces

T cell receptors (TCRs) are octameric assemblies of type-I membrane proteins in which a receptor heterodimer (αβ, δγ, or pre-Tαβ) is associated with three dimeric signaling modules (CD3δε, CD3γε, and ζζ) at the T cell or pre-T cell surface. In the human αβTCR, the α and β transmembrane (TM) domains form a specific structure that acts as a hub for assembly with the signaling modules inside the lipid bilayer. Conservation of key polar contacts across the C-terminal half of this TM interface suggests that the structure is a common feature of all TCR types. In this study, using molecular dynamics simulations in explicit lipid bilayers, we show that human δγ and pre-Tαβ TM domains also adopt stable αβ-like interfaces, yet each displays unique features that modulate the stability of the interaction and are related to sequences that are conserved within TCR types, but are distinct from the αβ sequences. We also performed simulations probing effects of previously reported mutations in the human αβ TM interface, and observed that the most disruptive mutations caused substantial departures from the wild-type TM structure and increased dynamics. These simulations show a strong correlation between structural instability, increased conformational variation, and the severity of structural defects in whole-TCR complexes measured in our previous biochemical assays. These results thus support the view that the stability of the core TM structure is a key determinant of TCR structural integrity and suggest that the interface has been evolutionarily optimized for different forms of TCRs.     

Size Matters: Ryanodine Receptor Cluster Size Heterogeneity Potentiates Calcium Waves

Ryanodine receptors (RyRs) mediate calcium (Ca)-induced Ca release and intracellular Ca homeostasis. In a cardiac myocyte, RyRs group into clusters of variable size from a few to several hundred RyRs, creating a spatially nonuniform intracellular distribution. It is unclear how heterogeneity of RyR cluster size alters spontaneous sarcoplasmic reticulum (SR) Ca releases (Ca sparks) and arrhythmogenic Ca waves. Here, we tested the impact of heterogeneous RyR cluster size on the initiation of Ca waves. Experimentally, we measured RyR cluster sizes at Ca spark sites in rat ventricular myocytes and further tested functional impacts using a physiologically detailed computational model with spatial and stochastic intracellular Ca dynamics. We found that the spark frequency and amplitude increase nonlinearly with the size of RyR clusters. Larger RyR clusters have lower SR Ca release threshold for local Ca spark initiation and exhibit steeper SR Ca release versus SR Ca load relationship. However, larger RyR clusters tend to lower SR Ca load because of the higher Ca leak rate. Conversely, smaller clusters have a higher threshold and a lower leak, which tends to increase SR Ca load. At the myocyte level, homogeneously large or small RyR clusters limit Ca waves (because of low load for large clusters but low excitability for small clusters). Mixtures of large and small RyR clusters potentiates Ca waves because the enhanced SR Ca load driven by smaller clusters enables Ca wave initiation and propagation from larger RyR clusters. Our study suggests that a spatially heterogeneous distribution of RyR cluster size under pathological conditions may potentiate Ca waves and thus afterdepolarizations and triggered arrhythmias.     

Simultaneous Determination of Protein Structure and Dynamics Using Cryo-Electron Microscopy

Cryo-electron microscopy is rapidly emerging as a powerful technique to determine the structures of complex macromolecular systems elusive to other techniques. Because many of these systems are highly dynamical, characterizing their movements is also a crucial step to unravel their biological functions. To achieve this goal, we report an integrative modeling approach to simultaneously determine structure and dynamics of macromolecular systems from cryo-electron microscopy density maps. By quantifying the level of noise in the data and dealing with their ensemble-averaged nature, this approach enables the integration of multiple sources of information to model ensembles of structures and infer their populations. We illustrate the method by characterizing structure and dynamics of the integral membrane receptor STRA6, thus providing insights into the mechanisms by which it interacts with retinol binding protein and translocates retinol across the membrane.     

Temperature-Dependent Estimation of Gibbs Energies Using an Updated Group-Contribution Method

Reaction-equilibrium constants determine the metabolite concentrations necessary to drive flux through metabolic pathways. Group-contribution methods offer a way to estimate reaction-equilibrium constants at wide coverage across the metabolic network. Here, we present an updated group-contribution method with 1) additional curated thermodynamic data used in fitting and 2) capabilities to calculate equilibrium constants as a function of temperature. We first collected and curated aqueous thermodynamic data, including reaction-equilibrium constants, enthalpies of reaction, Gibbs free energies of formation, enthalpies of formation, entropy changes of formation of compounds, and proton- and metal-ion-binding constants. Next, we formulated the calculation of equilibrium constants as a function of temperature and calculated the standard entropy change of formation $\left({\mathit{\Delta }}_{\text{f}}{S}^{°}\right)$ using a model based on molecular properties. The median absolute error in estimating ${\mathit{\Delta }}_{\text{f}}{S}^{°}$ was 0.013 kJ/K/mol. We also estimated magnesium binding constants for 618 compounds using a linear regression model validated against measured data. We demonstrate the improved performance of the current method (8.17 kJ/mol in median absolute residual) over the current state-of-the-art method (11.47 kJ/mol) in estimating the 185 new reactions added in this work. The efforts here fill in gaps for thermodynamic calculations under various conditions, specifically different temperatures and metal-ion concentrations. These, to our knowledge, new capabilities empower the study of thermodynamic driving forces underlying the metabolic function of organisms living under diverse conditions.     

Extended-Depth 3D Super-Resolution Imaging Using Probe-Refresh STORM

Single-molecule localization microscopy methods for super-resolution fluorescence microscopy such as STORM (stochastic optical reconstruction microscopy) are generally limited to thin three-dimensional (3D) sections (≤600 nm) because of photobleaching of molecules outside the focal plane. Although multiple focal planes may be imaged before photobleaching by focusing progressively deeper within the sample, image quality is compromised in this approach because the total number of measurable localizations is divided between detection planes. Here, we solve this problem on fixed samples by developing an imaging method that we call probe-refresh STORM (prSTORM), which allows bleached fluorophores to be straightforwardly replaced with nonbleached fluorophores. We accomplish this by immunostaining the sample with DNA-conjugated antibodies and then reading out their distribution using fluorescently-labeled DNA-reporter oligonucleotides that can be fully replaced in successive rounds of imaging. We demonstrate that prSTORM can acquire 3D images over extended depths without sacrificing the density of localizations at any given plane. We also show that prSTORM can be adapted to obtain high-quality, 3D multichannel images with extended depth that would be challenging or impossible to achieve using established probe methods.     

Revealing Nanoscale Morphology of the Primary Cilium Using Super-Resolution Fluorescence Microscopy

Super-resolution (SR) microscopy has been used to observe structural details beyond the diffraction limit of ～250 nm in a variety of biological and materials systems. By combining this imaging technique with both computer-vision algorithms and topological methods, we reveal and quantify the nanoscale morphology of the primary cilium, a tiny tubular cellular structure (～2–6 μm long and 200–300 nm in diameter). The cilium in mammalian cells protrudes out of the plasma membrane and is important in many signaling processes related to cellular differentiation and disease. After tagging individual ciliary transmembrane proteins, specifically Smoothened, with single fluorescent labels in fixed cells, we use three-dimensional (3D) single-molecule SR microscopy to determine their positions with a precision of 10–25 nm. We gain a dense, pointillistic reconstruction of the surfaces of many cilia, revealing large heterogeneity in membrane shape. A Poisson surface reconstruction algorithm generates a fine surface mesh, allowing us to characterize the presence of deformations by quantifying the surface curvature. Upon impairment of intracellular cargo transport machinery by genetic knockout or small-molecule treatment of cells, our quantitative curvature analysis shows significant morphological differences not visible by conventional fluorescence microscopy techniques. Furthermore, using a complementary SR technique, two-color, two-dimensional stimulated emission depletion microscopy, we find that the cytoskeleton in the cilium, the axoneme, also exhibits abnormal morphology in the mutant cells, similar to our 3D results on the Smoothened-measured ciliary surface. Our work combines 3D SR microscopy and computational tools to quantitatively characterize morphological changes of the primary cilium under different treatments and uses stimulated emission depletion to discover correlated changes in the underlying structure. This approach can be useful for studying other biological or nanoscale structures of interest.     

Mechanosensitivity of Cancer Cells in Contact with Soft Substrates Using AFM

Cancer cells are usually found to be softer than normal cells, but their stiffness changes when they are in contact with different environments because of mechanosensitivity. For example, they adhere to a given substrate by tuning their cytoskeleton, thus affecting their rheological properties. This mechanism could become efficient when cancer cells invade the surrounding tissues, and they have to remodel their cytoskeleton in order to achieve particular deformations. Here we use an atomic force microscope in force modulation mode to study how local rheological properties of cancer cells are affected by a change of the environment. Cancer cells were plated on functionalized polyacrylamide substrates of different stiffnesses as well as on an endothelium substrate. A new correction of the Hertz model was developed because measurements require one to account for the precise properties of the thin, layered viscoelastic substrates. The main results show the influence of local cell rheology (the nucleus, perinuclear region, and edge locations) and the role of invasiveness. A general mechanosensitive trend is found by which the cell elastic modulus and transition frequency increase with substrate elasticity, but this tendency breaks down with a real endothelium substrate. These effects are investigated further during cell transmigration, when the actin cytoskeleton undergoes a rapid reorganization process necessary to push through the endothelial gap, in agreement with the local viscoelastic changes measured by atomic force microscopy. Taken together, these results introduce a paradigm for a new—to our knowledge—possible extravasation mechanism.     

Control of Transmembrane Helix Dynamics by Interfacial Tryptophan Residues

Transmembrane protein domains often contain interfacial aromatic residues, which may play a role in the insertion and stability of membrane helices. Residues such as Trp or Tyr, therefore, are often found situated at the lipid-water interface. We have examined the extent to which the precise radial locations of interfacial Trp residues may influence peptide helix orientation and dynamics. To address these questions, we have modified the GW^5,19ALP23 (acetyl-GGALW⁵(LA)₆LW¹⁹LAGA-[ethanol]amide) model peptide framework to relocate the Trp residues. Peptide orientation and dynamics were analyzed by means of solid-state nuclear magnetic resonance (NMR) spectroscopy to monitor specific ²H- and ¹⁵N-labeled residues. GW^5,19ALP23 adopts a defined, tilted orientation within lipid bilayer membranes with minimal evidence of motional averaging of NMR observables, such as ²H quadrupolar or ¹⁵N-¹H dipolar splittings. Here, we examine how peptide dynamics are impacted by relocating the interfacial Trp (W) residues on both ends and opposing faces of the helix, for example by a 100° rotation on the helical wheel for positions 4 and 20. In contrast to GW^5,19ALP23, the modified GW^4,20ALP23 helix experiences more extensive motional averaging of the NMR observables in several lipid bilayers of different thickness. Individual and combined Gaussian analyses of the ²H and ¹⁵N NMR signals confirm that the extent of dynamic averaging, particularly rotational “slippage” about the helix axis, is strongly coupled to the radial distribution of the interfacial Trp residues as well as the bilayer thickness. Additional ²H labels on alanines A3 and A21 reveal partial fraying of the helix ends. Even within the context of partial unwinding, the locations of particular Trp residues around the helix axis are prominent factors for determining transmembrane helix orientation and dynamics within the lipid membrane environment.