Membrane potential accelerates sugar uptake by stabilizing the outward facing conformation of the Na/glucose symporter vSGLT.

Sodium-dependent glucose transporters (SGLTs) couple a downhill Na+ ion gradient to actively transport sugars. Here, we investigate the impact of the membrane potential on vSGLT structure and function using sugar uptake assays, double electron-electron resonance (DEER), electrostatic calculations, and kinetic modeling. Negative membrane potentials, as present in all cell types, shift the conformational equilibrium of vSGLT towards an outward-facing conformation, leading to increased sugar transport rates. Electrostatic calculations identify gating charge residues responsible for this conformational shift that when mutated reduce galactose transport and eliminate the response of vSGLT to potential. Based on these findings, we propose a comprehensive framework for sugar transport via vSGLT, where the cellular membrane potential facilitates resetting of the transporter after cargo release. This framework holds significance not only for SGLTs but also for other transporters and channels.

Brominated lipid probes expose structural asymmetries in constricted membranes.

Lipids in biological membranes are thought to be functionally organized, but few experimental tools can probe nanoscale membrane structure. Using brominated lipids as contrast probes for cryo-EM and a model ESCRT-III membrane-remodeling system composed of human CHMP1B and IST1, we observed leaflet-level and protein-localized structural lipid patterns within highly constricted and thinned membrane nanotubes. These nanotubes differed markedly from protein-free, flat bilayers in leaflet thickness, lipid diffusion rates and lipid compositional and conformational asymmetries. Simulations and cryo-EM imaging of brominated stearoyl-docosahexanenoyl-phosphocholine showed how a pair of phenylalanine residues scored the outer leaflet with a helical hydrophobic defect where polyunsaturated docosahexaenoyl tails accumulated at the bilayer surface. Combining cryo-EM of halogenated lipids with molecular dynamics thus enables new characterizations of the composition and structure of membranes on molecular length scales.

Regulation of the mammalian-brain V-ATPase through ultraslow mode-switching.

Vacuolar-type adenosine triphosphatases (V-ATPases)1-3 are electrogenic rotary mechanoenzymes structurally related to F-type ATP synthases4,5. They hydrolyse ATP to establish electrochemical proton gradients for a plethora of cellular processes1,3. In neurons, the loading of all neurotransmitters into synaptic vesicles is energized by about one V-ATPase molecule per synaptic vesicle6,7. To shed light on this bona fide single-molecule biological process, we investigated electrogenic proton-pumping by single mammalian-brain V-ATPases in single synaptic vesicles. Here we show that V-ATPases do not pump continuously in time, as suggested by observing the rotation of bacterial homologues8 and assuming strict ATP-proton coupling. Instead, they stochastically switch between three ultralong-lived modes: proton-pumping, inactive and proton-leaky. Notably, direct observation of pumping revealed that physiologically relevant concentrations of ATP do not regulate the intrinsic pumping rate. ATP regulates V-ATPase activity through the switching probability of the proton-pumping mode. By contrast, electrochemical proton gradients regulate the pumping rate and the switching of the pumping and inactive modes. A direct consequence of mode-switching is all-or-none stochastic fluctuations in the electrochemical gradient of synaptic vesicles that would be expected to introduce stochasticity in proton-driven secondary active loading of neurotransmitters and may thus have important implications for neurotransmission. This work reveals and emphasizes the mechanistic and biological importance of ultraslow mode-switching.

Quaternary structure independent folding of voltage-gated ion channel pore domain subunits.

Every voltage-gated ion channel (VGIC) has a pore domain (PD) made from four subunits, each comprising an antiparallel transmembrane helix pair bridged by a loop. The extent to which PD subunit structure requires quaternary interactions is unclear. Here, we present crystal structures of a set of bacterial voltage-gated sodium channel (BacNaV) 'pore only' proteins that reveal a surprising collection of non-canonical quaternary arrangements in which the PD tertiary structure is maintained. This context-independent structural robustness, supported by molecular dynamics simulations, indicates that VGIC-PD tertiary structure is independent of quaternary interactions. This fold occurs throughout the VGIC superfamily and in diverse transmembrane and soluble proteins. Strikingly, characterization of PD subunit-binding Fabs indicates that non-canonical quaternary PD conformations can occur in full-length VGICs. Together, our data demonstrate that the VGIC-PD is an autonomously folded unit. This property has implications for VGIC biogenesis, understanding functional states, de novo channel design, and VGIC structural origins.

Mitochondrial uncouplers induce proton leak by activating AAC and UCP1.

Mitochondria generate heat due to H+ leak (IH) across their inner membrane1. IH results from the action of long-chain fatty acids on uncoupling protein 1 (UCP1) in brown fat2-6 and ADP/ATP carrier (AAC) in other tissues1,7-9, but the underlying mechanism is poorly understood. As evidence of pharmacological activators of IH through UCP1 and AAC is lacking, IH is induced by protonophores such as 2,4-dinitrophenol (DNP) and cyanide-4-(trifluoromethoxy) phenylhydrazone (FCCP)10,11. Although protonophores show potential in combating obesity, diabetes and fatty liver in animal models12-14, their clinical potential for treating human disease is limited due to indiscriminately increasing H+ conductance across all biological membranes10,11 and adverse side effects15. Here we report the direct measurement of IH induced by DNP, FCCP and other common protonophores and find that it is dependent on AAC and UCP1. Using molecular structures of AAC, we perform a computational analysis to determine the binding sites for protonophores and long-chain fatty acids, and find that they overlap with the putative ADP/ATP-binding site. We also develop a mathematical model that proposes a mechanism of uncoupler-dependent IH through AAC. Thus, common protonophoric uncouplers are synthetic activators of IH through AAC and UCP1, paving the way for the development of new and more specific activators of these two central mediators of mitochondrial bioenergetics.

Berkeley Madonna Version 10-A simulation package for solving mathematical models.

Berkeley Madonna is a software program that provides an easy and intuitive environment for graphically building and numerically solving mathematical equations. Our users range from college undergraduates with little or no mathematical experience to academic researchers and professionals building and simulating sophisticated mathematical models that represent complex systems in the biological, chemical, and engineering fields. Here we briefly describe our recent advances including a new Java-based user interface introduced in Version 9 and our transition from a 32- to 64-bit architecture with the release of Version 10. We take the reader through an example tutorial that illustrates how to construct a mathematical model in Berkeley Madonna while highlighting some of the recent changes to the software. Specifically, we construct a standard pharmacokinetic model of the antifungal medication amphotericin B taken from the literature and discuss aspects related to model building, key numerical considerations, data fitting, and graphical visualization. We end by discussing planned functionality and features intended for future releases.

Taking the Monte-Carlo gamble: How not to buckle under the pressure!

Consistent buckling distortions of a large membrane patch (200 × 200 Å) are observed during molecular dynamics (MD) simulations using the Monte-Carlo (MC) barostat in combination with a hard Lennard-Jones (LJ) cutoff. The buckling behavior is independent of both the simulation engine and the force field but requires the MC barostat-hard LJ cutoff combination. Similar simulations of a smaller patch (90 × 90 Å) do not show buckling, but do show a small, systematic reduction in the surface area accompanied by ~1 Å thickening suggestive of compression. We show that a mismatch in the way potentials and forces are handled in the dynamical equations versus the MC barostat results in a compressive load on the membrane. Moreover, a straightforward application of elasticity theory reveals that a minimal compression of the linear dimensions of the membrane, inversely proportional to the edge length, is required for buckling, explaining this differential behavior. We recommend always using LJ force or potential-switching when the MC barostat is employed to avoid undesirable membrane deformations.

Elucidation of the molecular interactions that enable stable assembly and structural diversity in multicomponent immune receptors.

Multicomponent immune receptors are essential complexes in which distinct ligand-recognition and signaling subunits are held together by interactions between acidic and basic residues of their transmembrane helices. A 2:1 acidic-to-basic motif in the transmembrane domains of the subunits is necessary and sufficient to assemble these receptor complexes. Here, we study a prototype for these receptors, a DAP12-NKG2C 2:1 heterotrimeric complex, in which the two DAP12 subunits each contribute a single transmembrane Asp residue, and the NKG2C subunit contributes a Lys to form the complex. DAP12 can also associate with 20 other subunits using a similar motif. Here, we use molecular-dynamics simulations to understand the basis for the high affinity and diversity of interactions in this group of receptors. Simulations of the transmembrane helices with differing protonation states of the Asp-Asp-Lys triad identified a structurally stable interaction in which a singly-protonated Asp-Asp pair forms a hydrogen-bonded carboxyl-carboxylate clamp that clasps onto a charged Lys side chain. This polar motif was also supported by density functional theory and a Protein Data Bank-wide search. In contrast, the helices are dynamic at sites distal to the stable carboxyl-carboxylate clamp motif. Such a locally stable but globally dynamic structure is well suited to accommodate the sequence and structural variations in the transmembrane helices of multicomponent receptors, which mix and match subunits to create combinatorial functional diversity from a limited number of subunits. It also supports a signaling mechanism based on multisubunit clustering rather than propagation of rigid conformational changes through the membrane.

Genetically Encoded, pH-Sensitive mTFP1 Biosensor for Probing Lysosomal pH.

Lysosomes are important sites for macromolecular degradation, defined by an acidic lumenal pH of ∼4.5. To better understand lysosomal pH, we designed a novel, genetically encoded, fluorescent protein (FP)-based pH biosensor called Fluorescence Indicator REporting pH in Lysosomes (FIRE-pHLy). This biosensor was targeted to lysosomes with lysosomal-associated membrane protein 1 (LAMP1) and reported lumenal pH between 3.5 and 6.0 with monomeric teal fluorescent protein 1 (mTFP1), a bright cyan pH-sensitive FP variant with a pKa of 4.3. Ratiometric quantification was enabled with cytosolically oriented mCherry using high-content quantitative imaging. We expressed FIRE-pHLy in several cellular models and quantified the alkalinizing response to bafilomycin A1, a specific V-ATPase inhibitor. In summary, we have engineered FIRE-pHLy, a specific, robust, and versatile lysosomal pH biosensor, that has broad applications for investigating pH dynamics in aging- and lysosome-related diseases, as well as in lysosome-based drug discovery.

Allosteric cooperation in a de novo-designed two-domain protein.

We describe the de novo design of an allosterically regulated protein, which comprises two tightly coupled domains. One domain is based on the DF (Due Ferri in Italian or two-iron in English) family of de novo proteins, which have a diiron cofactor that catalyzes a phenol oxidase reaction, while the second domain is based on PS1 (Porphyrin-binding Sequence), which binds a synthetic Zn-porphyrin (ZnP). The binding of ZnP to the original PS1 protein induces changes in structure and dynamics, which we expected to influence the catalytic rate of a fused DF domain when appropriately coupled. Both DF and PS1 are four-helix bundles, but they have distinct bundle architectures. To achieve tight coupling between the domains, they were connected by four helical linkers using a computational method to discover the most designable connections capable of spanning the two architectures. The resulting protein, DFP1 (Due Ferri Porphyrin), bound the two cofactors in the expected manner. The crystal structure of fully reconstituted DFP1 was also in excellent agreement with the design, and it showed the ZnP cofactor bound over 12 Å from the dimetal center. Next, a substrate-binding cleft leading to the diiron center was introduced into DFP1. The resulting protein acts as an allosterically modulated phenol oxidase. Its Michaelis-Menten parameters were strongly affected by the binding of ZnP, resulting in a fourfold tighter Km and a 7-fold decrease in kcat These studies establish the feasibility of designing allosterically regulated catalytic proteins, entirely from scratch.

K2P channel C-type gating involves asymmetric selectivity filter order-disorder transitions.

K2P potassium channels regulate cellular excitability using their selectivity filter (C-type) gate. C-type gating mechanisms, best characterized in homotetrameric potassium channels, remain controversial and are attributed to selectivity filter pinching, dilation, or subtle structural changes. The extent to which such mechanisms control C-type gating of innately heterodimeric K2Ps is unknown. Here, combining K2P2.1 (TREK-1) x-ray crystallography in different potassium concentrations, potassium anomalous scattering, molecular dynamics, and electrophysiology, we uncover unprecedented, asymmetric, potassium-dependent conformational changes that underlie K2P C-type gating. These asymmetric order-disorder transitions, enabled by the K2P heterodimeric architecture, encompass pinching and dilation, disrupt the S1 and S2 ion binding sites, require the uniquely long K2P SF2-M4 loop and conserved "M3 glutamate network," and are suppressed by the K2P C-type gate activator ML335. These findings demonstrate that two distinct C-type gating mechanisms can operate in one channel and underscore the SF2-M4 loop as a target for K2P channel modulator development.

A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface.

Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces.

A systems-biology approach to molecular machines: Exploration of alternative transporter mechanisms.

Motivated by growing evidence for pathway heterogeneity and alternative functions of molecular machines, we demonstrate a computational approach for investigating two questions: (1) Are there multiple mechanisms (state-space pathways) by which a machine can perform a given function, such as cotransport across a membrane? (2) How can additional functionality, such as proofreading/error-correction, be built into machine function using standard biochemical processes? Answers to these questions will aid both the understanding of molecular-scale cell biology and the design of synthetic machines. Focusing on transport in this initial study, we sample a variety of mechanisms by employing Metropolis Markov chain Monte Carlo. Trial moves adjust transition rates among an automatically generated set of conformational and binding states while maintaining fidelity to thermodynamic principles and a user-supplied fitness/functionality goal. Each accepted move generates a new model. The simulations yield both single and mixed reaction pathways for cotransport in a simple environment with a single substrate along with a driving ion. In a "competitive" environment including an additional decoy substrate, several qualitatively distinct reaction pathways are found which are capable of extremely high discrimination coupled to a leak of the driving ion, akin to proofreading. The array of functional models would be difficult to find by intuition alone in the complex state-spaces of interest.

A kinetic mechanism for enhanced selectivity of membrane transport.

Membrane transport is generally thought to occur via an alternating access mechanism in which the transporter adopts at least two states, accessible from two different sides of the membrane to exchange substrates from the extracellular environment and the cytoplasm or from the cytoplasm and the intracellular matrix of the organelles (only in eukaryotes). In recent years, a number of high resolution structures have supported this general framework for a wide class of transport molecules, although additional states along the transport pathway are emerging as critically important. Given that substrate binding is often weak in order to enhance overall transport rates, there exists the distinct possibility that transporters may transport the incorrect substrate. This is certainly the case for many pharmaceutical compounds that are absorbed in the gut or cross the blood brain barrier through endogenous transporters. Docking studies on the bacterial sugar transporter vSGLT reveal that many highly toxic compounds are compatible with binding to the orthosteric site, further motivating the selective pressure for additional modes of selectivity. Motivated by recent work in which we observed failed substrate delivery in a molecular dynamics simulation where the energized ion still goes down its concentration gradient, we hypothesize that some transporters evolved to harness this 'slip' mechanism to increase substrate selectivity and reduce the uptake of toxic molecules. Here, we test this idea by constructing and exploring a kinetic transport model that includes a slip pathway. While slip reduces the overall productive flux, when coupled with a second toxic molecule that is more prone to slippage, the overall substrate selectivity dramatically increases, suppressing the accumulation of the incorrect compound. We show that the mathematical framework for increased substrate selectivity in our model is analogous to the classic proofreading mechanism originally proposed for tRNA synthase; however, because the transport cycle is reversible we identified conditions in which the selectivity is essentially infinite and incorrect substrates are exported from the cell in a 'detoxification' mode. The cellular consequences of proofreading and membrane slippage are discussed as well as the impact on future drug development.

Protons in small spaces: Discrete simulations of vesicle acidification.

The lumenal pH of an organelle is one of its defining characteristics and central to its biological function. Experiments have elucidated many of the key pH regulatory elements and how they vary from compartment-to-compartment, and continuum mathematical models have played an important role in understanding how these elements (proton pumps, counter-ion fluxes, membrane potential, buffering capacity, etc.) work together to achieve specific pH setpoints. While continuum models have proven successful in describing ion regulation at the cellular length scale, it is unknown if they are valid at the subcellular level where volumes are small, ion numbers may fluctuate wildly, and biochemical heterogeneity is large. Here, we create a discrete, stochastic (DS) model of vesicular acidification to answer this question. We used this simplified model to analyze pH measurements of isolated vesicles containing single proton pumps and compared these results to solutions from a continuum, ordinary differential equations (ODE)-based model. Both models predict similar parameter estimates for the mean proton pumping rate, membrane permeability, etc., but, as expected, the ODE model fails to report on the fluctuations in the system. The stochastic model predicts that pH fluctuations decrease during acidification, but noise analysis of single-vesicle data confirms our finding that the experimental noise is dominated by the fluorescent dye, and it reveals no insight into the true noise in the proton fluctuations. Finally, we again use the reduced DS model explore the acidification of large, lysosome-like vesicles to determine how stochastic elements, such as variations in proton-pump copy number and cycling between on and off states, impact the pH setpoint and fluctuations around this setpoint.

Harmonizing Experimental Data with Modeling to Predict Membrane Protein Insertion in Yeast.

Membrane proteins must adopt their proper topologies within biological membranes, but achieving the correct topology is compromised by the presence of marginally hydrophobic transmembrane helices (TMHs). In this study, we report on a new model membrane protein in yeast that harbors two TMHs fused to an unstable nucleotide-binding domain. Because the second helix (TMH2) in this reporter has an unfavorable predicted free energy of insertion, we employed established methods to generate variants that alter TMH2 insertion free energy. We first found that altering TMH2 did not significantly affect the extent of protein degradation by the cellular quality control machinery. Next, we correlated predicted insertion free energies from a knowledge-based energy scale with the measured apparent free energies of TMH2 insertion. Although the predicted and apparent insertion energies showed a similar trend, the predicted free-energy changes spanned an unanticipated narrow range. By instead using a physics-based model, we obtained a broader range of free energies that agreed considerably better with the magnitude of the experimentally derived values. Nevertheless, some variants still inserted better in yeast than predicted from energy-based scales. Therefore, molecular dynamics simulations were performed and indicated that the corresponding mutations induced conformational changes within TMH2, which altered the number of stabilizing hydrogen bonds. Together, our results offer insight into the ability of the cellular quality control machinery to recognize conformationally distinct misfolded topomers, provide a model to assess TMH insertion in vivo, and indicate that TMH insertion energy scales may be limited depending on the specific protein and the mutation present.

Biophysics at the coffee shop: lessons learned working with George Oster.

Over the past 50 years, the use of mathematical models, derived from physical reasoning, to describe molecular and cellular systems has evolved from an art of the few to a cornerstone of biological inquiry. George Oster stood out as a pioneer of this paradigm shift from descriptive to quantitative biology not only through his numerous research accomplishments, but also through the many students and postdocs he mentored over his long career. Those of us fortunate enough to have worked with George agree that his sharp intellect, physical intuition, and passion for scientific inquiry not only inspired us as scientists but also greatly influenced the way we conduct research. We would like to share a few important lessons we learned from George in honor of his memory and with the hope that they may inspire future generations of scientists.

A multiscale model of mechanotransduction by the ankyrin chains of the NOMPC channel.

Our senses of touch and hearing are dependent on the conversion of external mechanical forces into electrical impulses by the opening of mechanosensitive channels in sensory cells. This remarkable feat involves the conversion of a macroscopic mechanical displacement into a subnanoscopic conformational change within the ion channel. The mechanosensitive channel NOMPC, responsible for hearing and touch in flies, is a homotetramer composed of four pore-forming transmembrane domains and four helical chains of 29 ankyrin repeats that extend 150 Å into the cytoplasm. Previous work has shown that the ankyrin chains behave as biological springs under extension and that tethering them to microtubules could be involved in the transmission of external forces to the NOMPC gate. Here we combine normal mode analysis (NMA), full-atom molecular dynamics simulations, and continuum mechanics to characterize the material properties of the chains under extreme compression and extension. NMA reveals that the lowest-frequency modes of motion correspond to fourfold symmetric compression/extension along the channel, and the lowest-frequency symmetric mode for the isolated channel domain involves rotations of the TRP domain, a putative gating element. Finite element modeling reveals that the ankyrin chains behave as a soft spring with a linear, effective spring constantof 22 pN/nm for deflections ≤15 Å. Force-balance analysis shows that the entire channel undergoes rigid body rotation during compression, and more importantly, each chain exerts a positive twisting moment on its respective linker helices and TRP domain. This torque is a model-independent consequence of the bundle geometry and would cause a clockwise rotation of the TRP domain when viewed from the cytoplasm. Force transmission to the channel for compressions >15 Å depends on the nature of helix-helix contact. Our work reveals that compression of the ankyrin chains imparts a rotational torque on the TRP domain, which potentially results in channel opening.