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Choe, S., K.A. Hecht, and M. Grabe (2008) A continuum method for determining membrane protein insertion energies and the problem of charged residues. J. Gen. Physiol. 131:563-573 Continuum electrostatic approaches have been extremely successful at describing the charged nature of soluble proteins and how they interact with binding partners. However, it is unclear whether continuum methods can be used to quantitatively understand the energetics of membrane protein insertion and stability. Recent translation experiments suggest that the energy required to insert charged peptides into membranes is much smaller than predicted by present continuum theories. Atomistic simulations have pointed to bilayer inhomogeneity and membrane deformation around buried charged groups as two critical features that are neglected in simpler models. Here, we develop a fully continuum method that circumvents both of these shortcomings by using elasticity theory to determine the shape of the deformed membrane and then subsequently uses this shape to carry out continuum electrostatics calculations. Our method does an excellent job of quantitatively matching results from detailed molecular dynamics simulations at a tiny fraction of the computational cost. We expect that this method will be ideal for studying large membrane protein complexes.
Krzysiak, T.C., M. Grabe, and S.P. Gilbert (2007) Getting in sync with dimeric Eg5: Initiation and regulation of the processive run. J. Biol. Chem. 283:2078-2087 Eg5/KSP is the kinesin-related motor protein that generates the major plus-end directed force for mitotic spindle assembly and dynamics. Recent work using a dimeric form of Eg5 has found it to be a processive motor; however, its mechanochemical cycle is different from that of conventional Kinesin-1. Dimeric Eg5 appears to undergo a conformational change shortly after collision with the microtubule that primes the motor for its characteristically short processive runs. To better understand this conformational change as well as head-head communication during processive stepping, equilibrium and transient kinetic approaches have been used. By contrast to the mechanism of Kinesin-1, microtubule association triggers ADP release from both motor domains of Eg5. One motor domain releases ADP rapidly while ADP release from the other occurs after a slow conformational change at ~1 s(r)-1. Therefore, dimeric Eg5 begins its processive run with both motor domains associated with the microtubule and in the nucleotide-free state. During processive stepping however, ATP binding and potentially ATP hydrolysis signals rearward head advancement 16 nm forward to the next microtubule binding site. This alternating cycle of processive stepping is proposed to terminate after a few steps because the head-head communication does not sufficiently control the timing to prevent both motor domains from entering the ADP-bound state simultaneously.
Grabe, M., H.C. Lai, M. Jain, Y.N. Jan, and L.Y. Jan (2007) Structure prediction for the down state of a potassium channel voltage sensor. Nature 445:550-553 Voltage-gated potassium (Kv) channels, essential for regulating potassium uptake and cell volume in plants and electrical excitability in animals, switch between conducting and non-conducting states as a result of conformational changes in the four voltage-sensing domains (VSDs) that surround the channel pore. This process, known as gating, is initiated by a cluster of positively charged residues on the fourth transmembrane segment (S4) of each VSD, which drives the VSD into a 'down state' at negative voltages and an 'up state' at more positive voltages. The crystal structure of Kv1.2 probably corresponds to the up state, but the local environment of S4 in the down state and its motion in voltage gating remains unresolved. Here we employed several conditional lethal/second-site suppressor yeast screens to determine the transmembrane packing of the VSD in the down state. This screen relies on the ability of KAT1, a eukaryotic Kv channel, to conduct potassium when its VSDs are in the down state, thereby rescuing potassium-transport-deficient yeast. Starting with KAT1 channels bearing conditional lethal mutations, we identified second-site suppressor mutations throughout the VSD that recover yeast growth. We then constructed a down state model of the channel using six pairs of interacting residues as structural constraints and verified this model by engineering suppressor mutations on the basis of spatial considerations. A comparison of this down state model with the up state Kv1.2 structure suggests that the VSDs undergo large rearrangements during gating, whereas the S4 segment remains positioned between the central pore and the remainder of the VSD in both states.
Nayak, S., I. Olkin, H. Liu, M. Grabe, M.K. Gould, I.E. Allen, D.K. Owens, and D.M. Bravata (2006) Accuracy of Calcaneal quantitative ultrasound for identifying patients meeting the world health organizations diagnostic criteria for osteoporosis: A systematic review. Ann. Inter. Med. 144:832-841
Grabe, M., D. Bichet, X. Qian, Y.N. Jan, and L.Y. Jan (2006) K+ channel selectivity depends on kinetic as well as thermodynamic factors. Proc. Natl. Acad. Sci., USA 103:14361-14366 Potassium channels are necessary for a number of essential biological tasks such as the generation of action potentials and setting the resting membrane potential in cells, both of which require that these channels selectively permit the passage of potassium ions while suppressing the flow of other ions. Generally, this selectivity is attributed to a narrow stretch of the channel known as the selectivity filter. Over this stretch ions are dehydrated, and the backbone oxygen atoms of the protein mimic the ion's loss of coordination by water. However, channels are long pores with spatially distinct ion-binding sites that all must be traversed during ion permeation. We have shown that selectivity of mutant Kir3.2 (GIRK2) channels can be substantially amplified by introducing acidic residues into the cavity, a binding site below the selectivity filter. Here, we carry out electrostatic calculations on homology models to quantify the degree of stabilization that these mutations have on ions in the cavity. We then construct a multiion model of ion permeation to calculate the channel's permeability to potassium relative to sodium. This kinetic model uses rates derived from the electrostatic calculations and demonstrates that nonselective electrostatic stabilization of cations in the cavity can amplify channel selectivity independently of the selectivity filter. This nonintuitive result highlights the dependence of channel properties on the entire channel architecture and suggests that selectivity may not be fully understood by focusing solely on thermodynamic considerations of ion dehydration and the energetics of the selectivity filter.
Bichet, D., M. Grabe, Y.N. Jan, and L.Y. Jan (2006) Electrostatic interactions in the channel cavity as an important determinant of potassium channel selectivity. Proc. Natl. Acad. Sci., USA 103:14355-14360 Potassium channels are membrane proteins that allow the passage of potassium ions at near diffusion rates while severely limiting the flux of the slightly smaller sodium ions. Although studies thus far have focused on the narrowest part of the channel, known as the selectivity filter, channels are long pores with multiple ions that traverse the selectivity filter, the water-filled central cavity, and the rest of the pore formed by cytoplasmic domains. Here, we present experimental analyses on Kir3.2 (GIRK2), a G protein-activated inwardly rectifying potassium (Kir) channel, showing that a negative charge introduced at a pore-facing position in the cavity (N184) below the selectivity filter restores both K(+) selectivity and inward rectification properties to the nonselective S177W mutant channel. Molecular modeling demonstrates that the negative residue has no effect on the geometry of the selectivity filter, suggesting that it has a local effect on the cavity ion. Moreover, restoration of selectivity does not depend on the exact location of the charge in the central cavity as long as this residue faces the pore, where it is in close contact with permeant ions. Our results indicate that interactions between permeant ions and the channel cavity can influence ion selectivity and channel block by means of an electrostatic effect.
Lai, H.C., M. Grabe, Y.N. Jan, and L.Y. Jan (2005) The S4 voltage sensor packs against the pore domain in the KAT1 voltage-gated potassium channel. Neuron 47:395-406 In voltage-gated ion channels, the S4 transmembrane segment responds to changes in membrane potential and controls channel opening. The local environment of S4 is still unknown, even regarding the basic question as to whether S4 is close to the pore domain. Relying on the ability of functional KAT1 channels to rescue potassium (K+) transport-deficient yeast, we have performed an unbiased mutagenesis screen aimed at determining whether S4 packs against S5 of the pore domain. Starting with semilethal mutations of surface-exposed S5 residues of the KAT1 pore domain, we have screened randomly mutagenized libraries of S4 or S1-S3 for second-site suppressors. Our study identifies two S4 residues that interact in a highly specific manner with two S5 residues in the middle of the membrane-spanning regions, supporting a model in which the S4 voltage sensor packs against the pore domain in the hyperpolarized, or "down," state of S4.
Grabe, M., H. Lecar, Y.N. Jan, and L.Y. Jan (2004) A quantitative assessment of models for voltage-dependent gating of ion channels. Proc. Natl. Acad. Sci., USA 101:17640-17645 Voltage-gated ion channels open and close, or "gate," in response to changes in membrane potential. The electric field across the membrane-protein complex exerts forces on charged residues driving the channel into different functional conformations as the membrane potential changes. To act with the greatest sensitivity, charged residues must be positioned at key locations within or near the transmembrane region, which requires desolvating charged groups, a process that can be energetically prohibitive. Although there is good agreement on which residues are involved in this process for voltage-activated potassium channels, several different models of the sensor geometry and gating motions have been proposed. Here we incorporate low-resolution structural information about the channel into a Poisson-Boltzmann calculation to determine solvation barrier energies and gating charge values associated with each model. The principal voltage-sensing helix, S4, is represented explicitly, whereas all other regions are represented as featureless, dielectric media with complex boundaries. From our calculations, we conclude that a pure rotation of the S4 segment within the voltage sensor is incapable of producing the observed gating charge values, although this shortcoming can be partially remedied by first tipping and then minimally translating the S4 helix. Models in which the S4 segment has substantial interaction with the low-dielectric environment of the membrane incur solvation energies of hundreds of k(B)T, and activation times based on these energies are orders of magnitude slower than experimentally observed.
Grabe, M., J. Neu, G. Oster, and P. Nollert (2003) Protein interactions and membrane geometry. Biophys. J. 84:854-868 The difficulty in growing crystals for x-ray diffraction analysis has hindered the determination of membrane protein structures. However, this is changing with the advent of a new method for growing high quality membrane protein crystals from the lipidic cubic phase. Although successful, the mechanism underlying this method has remained unclear. Here, we present a theoretical analysis of the process. We show that it is energetically favorable for proteins embedded in the highly curved cubic phase to cluster together in flattened regions of the membrane. This stabilizes the lamellar phase, permitting its outgrowth from the cubic phase. A kinetic barrier-crossing model is developed to determine the free energy barrier to crystallization from the time-dependent growth of protein clusters. Determining the values of key parameters provides both a rational basis for optimizing the experimental procedure for membrane proteins that have not yet been crystallized and insight into the analogous cubic to lamellar transitions in cells. We also discuss the implications of this mechanism for protein sorting at the exit sites of the Golgi and endoplasmic reticulum and the general stabilization of membrane structures.
Cohen, B.E., M. Grabe, and L.Y. Jan (2003) Answers and questions from the KvAP structures. Neuron 39:395-400 The recent landmark structures of KvAP, a voltage-gated potassium (Kv) channel, provide the first high-resolution experimental structural models of this class of proteins. Previous extensive studies of Kv channels provide a means to evaluate and interpret the KvAP structures. In this minireview, we survey different experimental approaches to Kv channels and map these findings to KvAP, showing that the relationship between the KvAP structures and other Kv channels is uncertain.
Lecar, H., H.P. Larsson, and M. Grabe (2003) Electrostatic model of S4 motion in voltage-gated ion channels. Biophys. J. 85:2854-2864 The S4 transmembrane domain of the family of voltage-gated ion channels is generally thought to be the voltage sensor, whose translocation by an applied electric field produces the gating current. Experiments on hSkMI Na(+) channels and both Shaker and EAG K(+) channels indicate which S4 residues cross the membrane-solution interface during activation gating. Using this structural information, we derive the steady-state properties of gating-charge transfer for wild-type and mutant Shaker K(+) channels. Assuming that the energetics of gating is dominated by electrostatic forces between S4 charges and countercharges on neighboring transmembrane domains, we calculate the total energy as a function of transmembrane displacement and twist of the S4 domain. The resulting electrostatic energy surface exhibits a series of deep energy minima, corresponding to the transition states of the gating process. The steady-state gating-charge distribution is then given by a Boltzmann distribution among the transition states. The resulting gating-charge distributions are compared to experimental results on wild-type and charge-neutralized mutants of the Shaker K(+) channel.
Moore, H.P., J.M. Andresen, B.A. Eaton, M. Grabe, M. Haugwitz, M.M. Wu, and T.E. Machen (2002) Biosynthesis and secretion of pituitary hormones: dynamics and regulation. Arch. Physiol. Biochem. 110:16-25
Production and secretion of hormones by the pituitary involve highly orchestrated intracellular transport and sorting steps. Hormone precursors are routed through a series of compartments before being packaged in secretory granules. These highly dynamic carriers play crucial roles in both prohormone processing and peptide exocytosis. We have employed the ACTH-secreting AtT-20 cell line to study the membrane sorting events that confer functionality (prohormone activation and regulated exocytosis) to these secretory carriers. The unique ability of granules to promote prohormone processing is attributed to their acidic interior. Using a novel avidin-targeted fluorescence ratio imaging technique, we have found that the trans-Golgi of live AtT-20 cells maintains a mildly acidic (approximately pH 6.2) interior. Budding of secretory granules causes the lumen to acidify to
Grabe, M., and G. Oster (2001) Regulation of organelle acidity. J. Gen. Physiol. 117:329-344
Intracellular organelles have characteristic pH ranges that are set and maintained by a balance between ion pumps, leaks, and internal ionic equilibria. Previously, a thermodynamic study by Rybak et al. (Rybak, S., F. Lanni, and R. Murphy. 1997. Biophys. J. 73:674-687) identified the key elements involved in pH regulation; however, recent experiments show that cellular compartments are not in thermodynamic equilibrium. We present here a nonequilibrium model of lumenal acidification based on the interplay of ion pumps and channels, the physical properties of the lumenal matrix, and the organelle geometry. The model successfully predicts experimentally measured steady-state and transient pH values and membrane potentials. We conclude that morphological differences among organelles are insufficient to explain the wide range of pHs present in the cell. Using sensitivity analysis, we quantified the influence of pH regulatory elements on the dynamics of acidification. We found that V-ATPase proton pump and proton leak densities are the two parameters that most strongly influence resting pH. Additionally, we modeled the pH response of the Golgi complex to varying external solutions, and our findings suggest that the membrane is permeable to more than one dominant counter ion. From this data, we determined a Golgi complex proton permeability of 8.1 x 10(-6) cm/s. Furthermore, we analyzed the early-to-late transition in the endosomal pathway where Na,K-ATPases have been shown to limit acidification by an entire pH unit. Our model supports the role of the Na,K-ATPase in regulating endosomal pH by affecting the membrane potential. However, experimental data can only be reproduced by (1) positing the existence of a hypothetical voltage-gated chloride channel or (2) that newly formed vesicles have especially high potassium concentrations and small chloride conductance.
Wu, M.M., M. Grabe, S. Adams, R.Y. Tsien, H.P. Moore, and T.E. Machen (2001) Mechanisms of pH regulation in the regulated secretory pathway. J. Biol. Chem. 276:33027-33035
A precise pH gradient between organelles of the regulated secretory pathway is required for sorting and processing of prohormones. We studied pH regulation in live endocrine cells by targeting biotin-based pH indicators to cellular organelles expressing avidin-chimera proteins. In AtT-20 cells, we found that steady-state pH decreased from the endoplasmic reticulum (ER) (pH(ER) = 7.4 +/- 0.2, mean +/- S.D.) to Golgi (pH(G) = 6.2 +/- 0.4) to mature secretory granules (MSGs) (pH(MSG) = 5.5 +/- 0.4). Golgi and MSGs required active H(+) v-ATPases for acidification. ER, Golgi, and MSG steady-state pH values were also dependent upon the different H(+) leak rates across each membrane. However, neither steady-state pH(MSG) nor rates of passive H(+) leak were affected by Cl(-)-free solutions or valinomycin, indicating that MSG membrane potential was small and not a determinant of pH(MSG). Therefore, our data do not support earlier suggestions that organelle acidification is primarily regulated by Cl(-) conductances. Measurements of H(+) leak rates, buffer capacities, and estimates of surface areas and volumes of these organelles were applied to a mathematical model to determine the H(+) permeability (P(H+)) of each organelle membrane. We found that P(H+) decreased progressively from ER to Golgi to MSGs, and proper acidification of Golgi and MSGs required gradual decreases in P(H+) and successive increases in the active H(+) pump density.
Chandy, G., M. Grabe, H.P. Moore, and T.E. Machen (2001) Regulation of intra-Golgi pH in respirotary epithelial cells: Does CFTR regulate Golgi pH? Am. J. Physiol. Cell Ph. 281:C908-C921
Work addressing whether cystic fibrosis transmembrane conductance regulator (CFTR) plays a role in regulating organelle pH has remained inconclusive. We engineered a pH-sensitive excitation ratiometric green fluorescent protein (pHERP) and targeted it to the Golgi with sialyltransferase (ST). As determined by ratiometric imaging of cells expressing ST-pHERP, Golgi pH (pH(G)) of HeLa cells was 6.4, while pH(G) of mutant (DeltaF508) and wild-type CFTR-expressing (WT-CFTR) respiratory epithelia were 6.7-7.0. Comparison of genetically matched DeltaF508 and WT-CFTR cells showed that the absence of CFTR statistically increased Golgi acidity by 0.2 pH units, though this small difference was unlikely to be physiologically important. Golgi pH was maintained by a H(+) vacuolar (V)-ATPase countered by a H(+) leak, which was unaffected by CFTR. To estimate Golgi proton permeability (P(H(+))), we modeled transient changes in pH(G) induced by inhibiting the V-ATPase and by acidifying the cytosol. This analysis required knowing Golgi buffer capacity, which was pH dependent. Our in vivo estimate is that Golgi P(H(+)) = 7.5 x 10(-4) cm/s when pH(G) = 6.5, and surprisingly, P(H(+)) decreased as pH(G) decreased.
Machen, T.E., G. Chandy, M. Wu, M. Grabe, and H.P. Moore (2001) Cystic fibrosis transmembrane conductance regulator and H+ permeability in regulation of Golgi pH. JOP 2:229-236
This paper reviews experiments from this lab that have tested the hypothesis that pH of the Golgi (pH(G)) of cystic fibrosis (CF) airway epithelial cells is alkaline compared to normal, that this altered pH affects sialyltransferase and other Golgi enzymes controlling biochemical composition of the plasma membrane and that altered surface biochemistry increases bacterial binding. We generated a plasmid encoding a modified green fluorescence protein-sialyltransferase (GFP-ST) chimera protein that was pH-sensitive and localized to the Golgi when transfected into HeLa cells and also CF and normal or cystic fibrosis transmembrane conductance regulator- (CFTR)-corrected airway epithelial cells. Digital imaging microscopy of these Golgi-localized probes showed that there was no correlation between pH(G) (6.4-7.0) and the presence of CFTR, whether cells were in HCO(3)(-)/CO(2)-containing or in HCO(3)(-)/CO(2)-free solutions. Activation of CFTR by raising cell [cAMP] had no effect on pH(G). Thus, CFTR seemed not to be involved in controlling pH(G). Experiments on HeLa cells using an avidin-sialyltransferase chimera in combination with a pH-sensitive fluorescent biotin indicated that even in cells that do not express CFTR, Cl(-) and K(+) conductances of the Golgi and other organelle membranes were large and that pH(G) was controlled solely by the H(+) v-ATPase countered by a H(+) leak. A mathematical model was applied to these and other published data to calculate passive H(+) permeability (P(H+)) of the Golgi, endoplasmic reticulum, trans-Golgi network, recycling endosomes and secrety granules from a variety of cells. An organelle's acidity was inversely correlated to its calculated P(H+). We conclude that the CFTR plays a minor role in organelle pH regulation because other (Cl(-) and K(+)) channels are present in sufficient numbers to shunt voltages generated during H(+) pumping. Acidity of the Golgi (and perhaps other organelles) appears to be determined by the activity of H(+) pumps countered by H(+) leaks.
Grabe, M., H. Wang, and G. Oster (2000) The mechanochemistry of V-ATPase proton pumps. Biophys. J. 78:2798-2813
The vacuolar H(+)-ATPases (V-ATPases) are a universal class of proton pumps that are structurally similar to the F-ATPases. Both protein families are characterized by a membrane-bound segment (V(o), F(o)) responsible for the translocation of protons, and a soluble portion, (V(1), F(1)), which supplies the energy for translocation by hydrolyzing ATP. Here we present a mechanochemical model for the functioning of the V(o) ion pump that is consistent with the known structural features and biochemistry. The model reproduces a variety of experimental measurements of performance and provides a unified view of the many mechanisms of intracellular pH regulation.
Oster, G., H. Wang, and M. Grabe (2000) How Fo-ATPase generates rotary torque. Philos T Roy Soc B 355:523-528
The F-ATPases synthesize ATP using a transmembrane ionmotive force (IMF) established by the electron transport chain. This transduction involves first converting the IMF to a rotary torque in the transmembrane Fo portion. This torque is communicated from Fo to the F1 portion where the energy is used to release the newly synthesized ATP from the catalytic sites according to Boyer's binding change mechanism. Here we explain the principle by which an IMF generates this rotary torque in the Fo ion engine.
Dimroth, P., H. Wang, M. Grabe, and G. Oster (1999) Energy transduction in the sodium F-ATPase of Propionigenium modestum. Proc. Natl. Acad. Sci., USA 96:4924-4929
The F-ATPase of the bacterium Propionigenium modestum is driven by an electrochemical sodium gradient between the cell interior and its environment. Here we present a mechanochemical model for the transduction of transmembrane sodium-motive force into rotary torque. The same mechanism is likely to operate in other F-ATPases, including the proton-driven F-ATPases of Escherichia coli.
Curry, W.B., M.D. Grabe, I.V. Kurnikov, S.S. Skourtis, D.N. Beratan, J.J. Regan, A.J. Aquino, P. Beroza, and J.N. Onuchic (1995) Pathways, pathway tubes, pathway docking, and propagators in electron transfer proteins. J. Bioenerg. Biomembr. 27:285-293
The simplest views of long-range electron transfer utilize flat one-dimensional barrier tunneling models, neglecting structural details of the protein medium. The pathway model of protein electron transfer reintroduces structure by distinguishing between covalent bonds, hydrogen bonds, and van der Waals contacts. These three kinds of interactions in a tunneling pathway each have distinctive decay factors associated with them. The distribution and arrangement of these bonded and nonbonded contacts in a folded protein varies tremendously between structures, adding a richness to the tunneling problem that is absent in simpler views. We review the pathway model and the predictions that it makes for protein electron transfer rates in small proteins, docked proteins, and the photosynthetic reactions center. We also review the formulation of the protein electron transfer problem as an effective two-level system. New multi-pathway approaches and improved electronic Hamiltonians are described briefly as well.
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