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A number of incurable retinal diseases causing vision impairments derive from alterations in visual phototransduction. Unraveling the structural determinants of even monogenic retinal diseases would require network-centered approaches combined with atomistic simulations.
The transducin G38D mutant associated with the Nougaret Congenital Night Blindness (NCNB) was thoroughly investigated by both mathematical modeling of visual phototransduction and atomistic simulations on the major targets of the mutational effect.
Mathematical modeling, in line with electrophysiological recordings, indicates reduction of phosphodiesterase 6 (PDE) recognition and activation as the main determinants of the pathological phenotype. Sub-microsecond molecular dynamics (MD) simulations coupled with Functional Mode Analysis improve the resolution of information, showing that such impairment is likely due to disruption of the PDEγ binding cavity in transducin. Protein Structure Network analyses additionally suggest that the observed slight reduction of theRGS9-catalyzed GTPase activity of transducin depends on perturbed communication between RGS9 and GTP binding site. These findings provide insights into the structural fundamentals of abnormal functioning of visual phototransduction caused by a missense mutation in one component of the signaling network. This combination of network-centered modeling with atomistic simulations represents a paradigm for future studies aimed at thoroughly deciphering the structural determinants of genetic retinal diseases. Analogous approaches are suitable to unveil the mechanism of information transfer in any signaling network either in physiological or pathological conditions.
Author Summary
Incurable retinal diseases causing vision impairments may be due to spontaneous mutations in one component of the visual phototransduction signaling network. Such alterations include the transducin single point mutation G38D associated with the Nougaret Congenital Night Blindness (NCNB). We combined a systems biology approach with atomistic simulations to gain insights into the structural fundamentals of the NCNB disease. Consistent with in vitro evidence, mathematical modeling suggests reduced effector recognition and activation as the main determinants of the pathological phenotype. Sub-microsecond molecular dynamics simulations improve the resolution of information, suggesting that such impairment is likely due to disruption of the effector binding cavity. Atomistic simulations also suggest that the observed slight reduction of the RGS9-catalyzed GTPase activity of transducin depends on perturbed inter-protein communication involving the nucleotide. The study highlighted manifold effects of a single point pathogenic mutation, thus paving the way for analogous studies towards a thorough understanding of the structural determinants of genetic retinal diseases.
Citation: Mariani S, Dell'Orco D, Felline A, Raimondi F, Fanelli F (2013) Network and Atomistic Simulations Unveil the Structural Determinants of Mutations Linked to Retinal Diseases. PLoS Comput Biol 9(8): e1003207. https://doi.org/10.1371/journal.pcbi.1003207
Editor: Roland L. Dunbrack, Fox Chase Cancer Center, United States of America
Received: January 20, 2013; Accepted: July 18, 2013; Published: August 29, 2013
Copyright: © 2013 Mariani et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was supported by a Telethon-Italy grant [GGP11210/S00068TELC]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
A number of incurable diseases in the visual system involve one or more components of the phototransduction signaling network (Figure 1). Visual phototransduction is the G protein-mediated process that generates a neuronal signal following light capture by visual pigments in photoreceptor cells (rods and cones). A unique feature of rod cells, the vertebrate photoreceptors dedicated to dim light vision, is the capability to transduce signals from even single photons due to an extremely efficient amplification not paralleled by other signal transduction pathways [1], [2]. The first event in scotopic vision is the absorption of a photon by rhodopsin (R), the cornerstone of family A of the seven-transmembrane G protein coupled receptors (GPCRs), which leads to the formation of the signaling active state (R*) [3], [4]. The latter, in turn, catalyzes the exchange of bound GDP for GTP on the αβγ heterotrimeric G protein transducin (Gt). The GTP-bound α subunit (GαGTP) dissociates from the βγ dimer thus stimulating the activation of phosphodiesterase 6 (PDE), a tetramer made of two nearly identical α and β catalytic subunits and two identical γ subunits [5]. The binding of GαGTP to the γ subunit of PDE (PDEγ) releases its inhibitory constraint on the catalytic subunits, thus leading to the hydrolysis of guanosine 3′,5′-cyclic monophosphate (cGMP), followed by a rapid closure of the cGMP-gated ionic channels in the outer membrane and a drop in the circulating current. The lowering in intracellular calcium concentration, associated with cell hyperpolarization ultimately signals the presence of light to the secondary neurons of retina. Signaling shutoff includes at least three calcium feedback mechanisms as well as the simultaneous deactivation of GαGTP and PDE. In this respect, the termination of PDE activation by GαGTP is achieved when the GTP-bound to Gα is hydrolyzed to GDP by the intrinsic GTPase activity of the protein. The latter process is significantly accelerated by a multiprotein complex containing the ninth member of the Regulators of G protein Signaling (RGS) family, hereafter indicated as RGS [6]. As a result of the GTPase Activating Protein (GAP) action of RGS, the GαGDP complex re-associates with the βγ dimer restoring the GαGDP-βγ heterotrimer (i.e. Gt).
The different forms depict the molecular species involved in the cascade, whereas lines or arrows indicate reversible or irreversible reactions, respectively. Those reactions whose kinetic parameters were changed in this study are numbered and listed accordingly in Table 1. In this respect, red numbers indicate those reactions that were changed to properly model the NCNB pathological conditions. The molecules involved in these reactions, i.e. GαGTP, PDE, and RGS, are blue, green, and magenta, respectively. Filled red rectangles indicate the stoichiometric quantity of the specific molecule in the heteromeric complex, when higher than one. Yellow stars indicate the number of PDE-activated catalytic subunits. Hexagons indicate the molecular species that were used in atomistic simulations.
Misfunctioning of any component of the phototransduction network causes more or less severe vision impairments. Such an example is the Nougaret form of dominant stationary night blindness (Nougaret Congenital Night Blindness, NCNB) caused by a missense mutation, G38D, found in the rod Gα of affected individuals [7]–[9]. Stationary night blindness is not associated with retinal degeneration and is characterized by the inability to see in the dark, whereas daytime vision is largely unaffected [7]–[9]. In vitro characterization showed that the aspartate substitution for G38 does not alter the interaction between Gα and Gβγ or activation of transducin by R* [9]. Furthermore, the mutant Gα is characterized by modestly reduced kcat value for the intrinsic (∼2.5-fold) and RGS-catalyzed (∼5 fold) GTP hydrolyses. In contrast, biochemical data showed that G38D is totally impaired in its ability to bind and activate PDE [9], whereas suction electrode recordings revealed that homozygous GαGTPG38D−/− rods exhibit residual light responses, indicating that the mutation reduced but did not completely abolish effector function [8]. Functional consequences of substituting the homologous amino acid in other G proteins were found to inhibit GTPase activity and to prevent stimulation by GAP in Ras-p21 [10], Gαi [11], Gαz [12], and Gαs [13].
Thus, a single-point mutation in Gα seems to elicit a multitude of effects not entirely clarified by in vitro and in vivo experiments and likely involving more than one component in the phototransduction signaling network. In this framework, to gain insights into the molecular bases of the NCNB disease, we integrated the information from in vitro/in vivo experiments with systems-based and atomistic modeling. The systems-based approach relied on a comprehensive quantitative model of phototransduction in rod cells that explicitly includes most of the molecular components of the cascade [14] (Figure 1). In this study, that model was extended to the NCNB pathological phenotype, thus highlighting those reactions and intermolecular interactions perturbed by the Gα mutation. The molecular systems involved in those reactions were subjected to atomistic Molecular Dynamics (MD) simulations and included: wild type and mutated GαGTP taken both in their isolated forms (i.e. GαGTPWT and GαGTPG38D) and in the ternary complex with RGS and PDEγ (GαGTP-RGS-PDEγWT and GαGTP-RGS-PDEγG38D) (Figure 2).
A. The cartoon representation of GαGTP structure (PDB code: 1TND) is shown. The G protein holds a Ras-like domain and an α-helical domain. The interface between α-helical and Ras-like domain makes the nucleotide binding cleft. The α-helical domain is an orthogonal bundle of six α-helices. The Ras-like domain holds a Rossmann fold, characterized by a 3-layer(αβα) sandwich architecture due to the inversion in the order of the strands β3 and β1 as well as β1 and β4, which are adjacent to each other. The Ras-like domain is colored according to secondary structure (i.e. helices, strands, and loops are, respectively, violet, yellow and white), whereas the α-helical domain is gray. The mutation site is indicated by a cyan sphere centered on the Cα-atom. The GTP nucleotide is represented by sticks colored by atoms type. The nucleotide docks into a binding site contributed by the β1/α1, α1/β2 (αF/β2 in the Gα proteins), β3/α2, β5/α4 and β6/α5 loops. These are ultraconserved regions also called G boxes 1–5 (G1–G5, colored green). G2 is also called swI (α1/β2 loop (αF/β2 loop in the Gα proteins)), whereas G3 is part of the switch II (swII, or β3/α2 loop, plus the α2-helix). The β2/β3 hairpin in between swI and swII is also called inter-switch. The β4/α3 loop, which is not a G box, is also called swIII [19]. In Gα proteins, the two domains are connected by two loops, linker 1 or α1/αA loop and linker 2 or αF/β2 loop; the latter corresponds to swI. B. According to computational experiments [20], the strands β1 and β4 divide the conserved domain into two dynamically distinct lobes, lobe 1 (i.e. the N-terminal half of the domain, colored magenta) and lobe 2 (i.e. the C-terminal half of the domain, colored blue). C. The cartoon representation of the complex involving GαGTP (gray), RGS (i.e. the RGS domain of RGS9, amino acids 286 to 418, orange), and PDEγ (green) is shown (PDB code: 1FQJ [16]). In deep detail, the RGS domain is a bundle of nine α-helices, configured into two subdomains: an N- and a C-terminal region holding an orthogonal bundle architecture (helices α1, α2, α3, α8 and α9), and a prototypical right-handed, antiparallel four-helix bundle (helices α4, α5, α6 and α7). PDEγ (residues 46–87) comprises three short α-helices and an N-terminal loop region that originates near the C-terminus and winds over helices α1 and α2. D. The primary sequence of Gα is shown. Helices, strands, and loops are, respectively, violet, yellow, and white. The G boxes are delimited by green boxes. Black numbers on the left side of the alignment refer to the sequential numbering, whereas black numbers above the sequences indicate the beginning of a secondary structure/G-box motif. An arbitrary numbering of each residue was set, characterized by the label of the secondary structure segment followed by the amino acid position within the segment. In those cases where the G-boxes overlap with the secondary structure segment, positions refer to the G-boxes. Orange and green stars mark, respectively, RGS and PDEγ recognition sites.
Mathematical modeling of the NCNB phenotype
We presented a dynamical model of the phototransduction signaling network made up of ordinary differential equations, which describe the reactions and their kinetic parameters [14]. The working model used in this study includes also the dynamic scaffolding reactions between dark rhodopsin and Gt [15]. Herein, such model was further extended to describe the heterozygous (GαGTPG38D+/−) and homozygous (GαGTPG38D−/−) mutated conditions of GαGTPG38D. This was accomplished by introducing the mutated G protein as an explicit new molecule and adding all the relative reactions in the phototransduction cascade, which concerned the GαGTPWT+/+ status (Table 1, see Methods). The output of mathematical simulations (i.e. change in photocurrent with respect to dark value, ΔJ) was analyzed and compared with the photoresponses of rods from wild type and transgenic mice (Figure 3A, 3B, and 3C). It is worth noting that, due to the significant difference in the species between in vitro (i.e. mammals, Figure 3A, 3B, and 3C) and in silico (i.e. amphibian rods [14], Figure 3D, 3E, and 3F) experiments, the time scales of the photoresponses is different, thus allowing for semi-quantitative comparisons.
Experimental (A, B, C) versus simulated (D, E, F) responses to flashes of increasing intensities from wild type GαGTPWT+/+ (A, D), heterozygous GαGTPG38D+/− (B, E) and homozygous GαGTPG38D−/− (C, F) rods are shown. Experimental data, i.e. published in Moussaif et al. [8] and provided by Marie E. Burns, refer to mice rods exposed to flashes ranging from 5 to 97000 photons µm−2 (A and B) or from 650 to 94000 photons µm−2 (C). Simulated responses derive from the model of an amphibian rod stimulated with the same light intensities as in vitro recordings. The pathological GαGTPG38D+/− and GαGTPG38D−/− models were generated by changes in the kinetic parameters kP1, kP2 and kRGS1 as described in the text. The dissimilar species justify the time scale difference between in vitro and in silico experiments. The responses were normalized with respect to the maximum photocurrent. G. Normalized simulated light response amplitude is plotted as a function of flash strength. For comparison to in vitro data, see Figure 5B in Moussaif et al. [8]. Flash intensities are the same as in D, E and F.
The results obtained with our GαGTPWT+/+ model were in remarkable agreement with in vitro recordings on wild type cells (Figure 3A and 3D).
In order to fit the models onto the pathological NCNB condition, the rates of a number of reactions involving GαGTPG38D were systematically reduced by tuning the relative kinetic parameters in decreasing steps (Table 1, Figure 1, see Methods). The reductions were combined into specific heterozygous and homozygous models. At the end, the best fit with electrophysiological recordings of the mutant cells was obtained by making changes in the following reactions:
describing, respectively, a) the binding of one molecule of GαGTP to one inactive PDE subunit, b) activation of the GαGTP-PDE complex, and c) binding of the RGS complex to a PDE tetramer with one active subunit. The relative changes in the parameters were 35000-fold reduction in kP1 and kP2 and 2-fold reduction in kRGS1, with respect to the wild type value. Following such changes, heterozygous cells show a similar behavior to wild type cells under dim flash responses but elongated recovery under brighter flashes associated with slight loss in sensitivity (i.e. a 40% brighter flash is required to generate a half-maximal response, Io; Figure 3G and Figure 5B in Moussaif et al. [8] and Table 2). In contrast, homozygous cells show marked decrease in sensitivity to light (50-fold brighter Io, Table 2) and impaired response recoveries for all flash intensities.
The SASA computed on Y254 (in the α3/β5 loop) is shown. Cartoons of the GαGTPWT (A) and GαGTPG38D (B) snapshots halfway through the simulation (frame 50000th) are shown, which are zoomed on the swII/α3 cleft, the primary recognition site for PDEγ. The Gα residues directly involved in PDEγ recognition (i.e. marked by green stars in the primary sequence in Figure 2) are shown in sticks. The atom color code is grey for carbon, blue for nitrogen, and red for oxygen. The residue Y254, on which the SASA index was computed, is green. The cyan ball in B indicates the mutation site. C. The time series of the SASA index calculated on Y254 along the 100 ns trajectories of GαGTPWT (violet) and GαGTPG38D (green) are shown.
Same strengths of flashes delivered to the cells in simulations and electrophysiological recordings [8] result in quantitative differences concerning time scales and sensitivity of the photoresponses, likely due to the different species considered. The higher ΔJ elicited by the dimmest flash in computational experiments compared to electrophysiological recordings is exemplar in this respect (Figure 3A and 3D). Differences between the cellular properties of mammals and amphibian rods include temperature and volume, which likely influence initial conditions and concentrations of the molecular species involved in signal transduction [5].
It is worth noting that, in the actual mathematical model, up to two GαGTP can bind, and in turn activate, either one of the catalytic subunits of PDE, hence leading to a 2∶1 stoichiometry. Nevertheless, as previously discussed [14] (see also Table S4 therein), the 2∶1 GαGTP∶PDE complex is detectable only in the presence of light flashes with intensities in the order of 105 photons/µm2 and, even then, their presence is negligible. As a confirmation of those results, deep reductions of kP3 and kP4 (regulating, respectively, the binding of the second molecule of GαGTP to GαGTP-PDE and the activation of both catalytic subunits of the PDE tetramer), in the background of any of the test models used in this study, did not elicit any change in the photoresponse (Table 1). We cannot, however, exclude that this was due to an inaccurate modeling of this part of the network, whose biochemical detail remains mainly unknown. For example, a finer treatment of the allosteric and regulatory mechanisms may be necessary to recover the role of the second PDE subunit [14]. This might also explain why, with the changes in kP1, kP2, and kRGS1 necessary to reproduce GαGTPG38D−/− photoresponses, loss in sensitivity and delay of the time to peak are more marked in simulated responses compared to in vitro ones (78- vs 47- and 2.4- vs 1.7-fold, respectively, see Table 2).
In line with the statements above, we relied on the fact that, in the present model, changes in kRGS1 and kRGS2 only affect the formation and activity of the 1∶1∶1 GαGTP-RGS-PDE complex. Noteworthy, as shown in Table 1, kRGS2 is a rather coarse parameter, as it describes the RGS-catalyzed GTPase activity in both GαGTP-RGS-PDE and GαGTP-RGS-PDE-GαGTP complexes as well as disruption of these complexes. For this reason, we couldn't use the mathematical model to properly evaluate mutational effects on the GAP activity of RGS in the GαGTP-RGS-PDE complex.
In summary, consistent with electrophysiological recordings [8] but not with earlier biochemical data [9] mathematical modeling highlights reduction of both PDE binding and activation as the major mutation-induced perturbations in the visual phototransduction signaling network. A marginal reduction in RGS binding helped as well in reproducing the electrophysiological phenotype. On these bases, insights into the structural determinants of such perturbations were searched by atomistic MD simulations targeting both wild type and mutated Gα in its isolated form and in ternary complex with both RGS and PDEγ.
Atomistic simulations on the GαGTP system: The G38D mutant affects the swII/α3 cleft, primary determinant in PDEγ binding
Atomistic simulations were firstly carried out on the isolated GαGTP in its wild type and mutated forms (GαGTPWT and GαGTPG38D, respectively).
The mutation site is the third position of the G box 1 (i.e. G1:3, see Figure 2 and its legend for description and visualization of the G protein regions as well as for explanation of the position-based numbering). Incidentally, the G boxes are five ultra-conserved regions of the Ras-like domain involved in nucleotide binding (Figure 2). Such mutated position is not involved in backbone-mediated H-bonding interactions with the nucleotide neither in the wild type nor in the mutant, (Supplementary Figure 1A (Figure S1A)). The interaction pattern of the nucleotide remains almost unchanged in the two forms following MD simulations, as also indicated by the patterns of interaction energies between GTP and surrounding residues (Figure S2). Collectively, these data are consistent with the results of in vitro evidence that the mutation elicits a marginal effect on the intrinsic GTPase activity of the protein [8], [9].
In contrast to lack of local structural effects, the G38D mutant turned out to affect the intrinsic dynamics of the protein. Indeed, the Cα-atom Root Mean Square Deviation (RMSD) of the mutant is higher than that of the wild type especially over the second half of MD simulation (Figure S3). As expected, Cα-atom fluctuations evaluated in terms of Root Mean Square Fluctuations (RMSFs) show peaks of flexibility in the loops connecting the elements of secondary structure, especially those in the α-helical domain. This effect is greater in the mutant than the wild type (Figure 4). In line with RMSFs, in the mutant form, selected portions of the protein show significant enhancements in their collective motions as inferred from the Principal Component Analysis (PCA) of the trajectories. These portions include linker1, αB/αC loop, αC, αE, αF, inter-switch, and C-term of α3 (Figure 4).
A. The Cα-RMSF profiles from MD trajectories of GαGTPWT (violet) and GαGTPG38D (green) are shown. They refer to the 100000 frames constituting the 100 ns trajectory. The secondary structure elements are shown on the abscissa, following the Noel's nomenclature [19]. B, C, D, E. The Cα-atom projections along the linear combination of the ED analysis-derived principal components, which describe the essential subspace of the trajectories of GαGTPWT (B and C) and GαGTPG38D (D and E) are shown (see text for an explanation of ED). The number of PCs used was 111 for GαGTPWT and 74 for GαGTPG38D. Cα-atom displacements are highlighted by color ranges from violet to blue for GαGTPWT, and from green to blue for GαGTPG38D.
To investigate whether mutation-induced changes in intrinsic dynamics may affect Gα portions deputed to RGS and/or PDEγ recognition, we monitored the solvent accessibility of all the RGS and PDEγ recognition sites on Gα (indicated, respectively, by orange and green stars in Figure 2), finding more marked effects on the PDEγ sites, in particular Y254 (in the α3/β5 loop). The latter is, indeed, exposed to the solvent in the wild type but buried in the mutant form where it is permanently involved in inter-helical interaction with F211(s2:11), another PDEγ recognition site that becomes no longer available to PDEγ as well (Figure 5). In line with these observations, Functional Mode Analysis (FMA, see Methods) found that the Solvent Accessible Surface Area (SASA) of Y254 is correlated with the modes describing the essential subspace of Gα. Incidentally, the essential subspace (ES) is given by a variable number of eigenvectors whose associated eigenvalues account for 90% of the total variance of the Cα-atom displacements in a trajectory. The correlation is already present in the wild type but increases in the mutant form (i.e. the correlation coefficients are 0.73 and 0.86, respectively). Differences in functional modes between wild type and mutant amplify when considering only the first principal component (PC1); in fact, the correlation remains still significant for the mutant (i.e. 0.74) but it drops for the wild type (i.e. 0.39). Collectively, FMA is suggestive of a functional link between protein dynamics and structural environment of Y254. Thus, mutation-induced burying of Y254 results in deformation of the swII/α3 cleft, which is the primary determinant in PDEγ binding.
We also investigated mutational effects on the structural communication features of Gt by the Protein Structure Network (PSN) analysis, a product of graph theory applied to protein structures (see Methods). The analysis searched for mutation-induced changes in network components (e.g. nodes, hubs, links, shortest communication pathways, etc) on the MD trajectories. The comparative analyses of the Protein Structure Graphs (PSGs) of wild type and mutated Gα revealed a slight reduction in number of nodes, hubs, and links in the G38D mutant compared to the wild type (Table 3). In contrast, the number of communication pathways and their average length increases in the mutant compared to the wild type. In line with this trend, the maximal, minimal, and average strengths reached by the totality of links in the paths tend to be higher in the mutant compared to the wild type.
To infer a global and coarse view of mutation-induced changes in the communication pathways of Gα we drew global meta paths, i.e. assemblies of the most recurrent nodes and links in the pool of paths characterized by frequency ≥30% (Figure 6A and 6B, see Methods). In this respect, whereas the wild type is characterized by nucleotide-mediated paths at the interface between Ras-like and α-helical domain, in the mutant form, inter-domain pathways are less frequent as also highlighted by the distribution of linked-node fragments (Figures 6 and S4). This inter-domain uncoupling may be in part related to the fact that, in the mutant, selected portions of the α-helical domain undergo increases in essential dynamics compared to the wild type (Figure 4). Noteworthy, this trend is also evident in the meta paths computed on the sub set of paths made by ≥50% of conserved amino acids (Figure S5A and S5B). Differently from the wild type, in the mutant the most frequent nucleotide-involving pathways transverse essentially β1 and β3 rather than the swII/α3 interface, which is the primary PDEγ binding cleft (Figure 6A and 6B).
The global meta paths regarding GαGTPWT and GαGTPG38D in their free state (A and B panels, respectively) as well as in ternary complex with both RGS and PDEγ (C and D panels, respectively) are represented, colored violet and green, respectively. The width of each link is proportional to r, while the sphere diameter is proportional to the average r of the connecting link (see Methods for r definition). The α-helical and Ras-like domains are dark and light gray, respectively, the PDEγ binding site on Gα is aquamarine, RGS is orange and PDEγ is lemon-green. The mutation site is indicated by the red sphere.
In summary, in spite of the lack of significant differences in the interaction pattern of GTP between wild type and mutated forms, GαGTPG38D is characterized by increased flexibility of the α-helical domain compared to wild type, which reflects on an apparent inter-domain uncoupling in terms of shortest communication pathways. In contrast, in the wild type, inter-domain pathways localized on the nucleotide binding site cover a significant part of the structural communication modes. Above all, the most significant effect of aspartate substitution for G38 is a structural perturbation in the swII/α3 cleft participating in the PDEγ binding site. A marker of such perturbations is the solvent accessibility of Y254, which in the mutant becomes buried and no more available for PDEγ interaction, shielding also F211(s2:11) from effector binding.
Atomistic simulations on the GαGTP-RGS-PDEγ ternary complex: The G38D mutant affects the communication between nucleotide binding site and RGS
Atomistic MD simulations on monomeric GαGTP highlighted long-distance mutational effects on the Gα regions deputed to PDEγ recognition likely related to the reduced PDE binding and consequently activation inferred from both mathematical simulations and in vitro experiments [8].
In order to clarify ambiguities by in vitro experiments on the GAP activity of RGS towards the G38D mutant [8], [9], which couldn't be properly addressed by mathematical simulations, wild type and mutated Gα were simulated also in the context of the ternary complex with PDEγ and RGS. In this respect, MD simulations on the GαGTP-RGS-PDEγG38D ternary complex are justified by the fact that the mutated Gα holds a residual binding to PDEγ [8].
Comparing the dynamics and structural communication features of all the components of the ternary complex in the presence of either wild type or mutated Gα served to infer the effects of the G38D mutation on different structural aspects such as: a) communication and interaction features of the nucleotide, b) intrinsic dynamics of each component of the complex, and c) inter-protein communication.
In line with simulations on monomeric GαGTP, simulations on the ternary complex show that the interaction pattern of the nucleotide is substantially similar in wild type and mutated Gα (Figure S1 and S2), thus not providing any clue on mutational effects on the GAP activity of RGS.
As for the intrinsic dynamics of the three proteins in the complex, differently from PDEγ, GαGTP and RGS are characterized by low mobility in terms of RMSDs, (Figure S3). The higher mobility of PDEγ is likely due to the poor intramolecular and intermolecular tertiary contacts made by such protein, which is a 42-amino acid fragment of a small subunit. In deep detail, as for GαGTP, the wild type and mutated forms do not differ significantly in terms of RMSDs or RMSFs; major differences concern only the swIII region, which fluctuates less in the mutant than in the wild type (Figures S3 and S6). In line with such behavior, the overlap between the ES of the two Gα forms in the context of the heterotrimer is quite high (0.90), the essential motions of β2/β3 loop and swIII contributing to such differences (Figure S6). RGS shows low mobility as well, its intrinsic flexibility being comparable in the complexes with wild type and mutated Gα (Figure S3). In contrast, the intrinsic flexibility of PDEγ is higher in the complex with mutated GαGTP than in the complex with wild type GαGTP (Figures S3 and S7). This suggests that the pathogenic Gα mutation increases the intrinsic flexibility of PDEγ, which would imply increased instability of the PDEγ-GαGTP interface.
According to the crystal structure of the heterotrimeric complex, RGS does not contribute directly to the active site by donating residues or through water-mediated interactions [16]. It is rather thought that RGS would increase the GTP hydrolysis rate by stabilization of the Gα switch regions in their transition state conformation and orientation of the critical Gα carbonyls used to position the nucleophilic water [16], [17]. Thus, RGS action is likely due to inter-protein structural communication. On these bases, possible structural relations with the postulated mutation-induced reduction of the GAP activity of RGS were searched by the PSN analysis. Significant differences between the two simulated ternary complexes could be inferred from the analysis of the shortest communication pathways, which were almost halved in the mutated complex compared to the wild type (Table 3). Remarkably, more than 60% of the communication paths that characterize the wild type form hold the GTP-Q200(G3:5)-R:N364 fragment of linked nodes, which is completely absent in the mutant (Figure S4). The global meta path representation clearly shows that the most significant communication in the GαGTP-RGS-PDEγWT involves GTP, Q200(G3:5), R:N364, and E203(s2:3) (i.e. the GTP-Q200(G3:5)-R:N364-E203(G3:8) meta fragment of linked nodes; Figure 6C and 6D). Remarkably, the GTP-Q200(G3:5)-R:N364 connection found in the wild type form is essential for the GAP activity of RGS [16]. Such connection is no longer present in the mutant. In line with path fragment distribution, the most representative nucleotide-mediated paths in the GαGTP-RGS-PDEγG38D complex are intra-Gα located (Figure 6C, 6D, and S4). These differences between wild type and mutant forms are strengthened by the meta paths computed on the sub set of paths made by ≥50% of conserved amino acids (Figure S5). Thus, nucleotide-mediated paths involving the RGS-Gα interface are few and characterized by the D38(G1:3)-Q200(G3:5)-R:N364 fragment of linked nodes (Figure S4). Another difference concerning the structural communication of wild type and mutated Gt is that, whereas for the wild type some (4%) of the shortest pathways describe a communication between Gα and PDEγ, in the mutant form such communication could not be found, likely due to the increased flexibility of the effector subunit.
In summary, atomistic simulations on the ternary complexes highlight a possible disturbing effect of the pathogenic mutation on the GAP activity of RGS. This would act, at least in part, by destabilizing the Q200(G3:5)-mediated communication between GTP and R:N364. Finally, they strengthen the influence of the mutation on the G protein-effector interface, in line with electrophysiological recordings and mathematical simulations.
Mutations in any components of the visual phototransduction signaling network may cause more or less severe impairments in vision. Because of the complexity of such network, any alteration of one of the cascade components would lead to unpredictable and not easily determinable results. Thus, a monogenic disease such as NCNB, considered in this study, can result from perturbations not circumscribed to the mutated protein but involving also other members of the network. In this framework, modeling the effects of mutation by systems-based approaches serves to infer how the pathogenic signal propagates through the network and which molecular species are involved. When possible, the latter information is passed to atomistic simulations to gain insights into the structural determinants of the disease.
In this study, we combined visual phototransduction modeling with atomistic simulations to thoroughly investigate the defect associated with the NCNB-causing G38D mutation of Gα. The mathematical model of visual phototransduction was able to reproduce the key features of the behaviors of heterozygous and homozygous rods typical of the NCNB disease. This could be possible upon reducing the constants governing: a) the binding of GαGTP to PDE, b) the activation of the catalytic activity of PDE, and c) the binding of the RGS complex to a PDE tetramer with one active subunit. In fact, a strong reduction in PDE recognition and activation by GαGTP coupled to a two-fold reduction in the RGS binding constant was essential to reproduce the visual responses in Nougaret patients, while decreasing the intrinsic or RGS-catalyzed GTPase activities did not seem to have a significant effect. Thus, mathematical modeling emphasized the formation and activation of the GαGTP-PDE complex as the processes more significantly affected by the aspartate substitution for G38 in Gα, in line with electrophysiological recordings [8]. MD simulations on monomeric GαGTP suggest that such reduction in the PDEγ binding ability of mutated Gα is likely due to altered dynamics of the protein associated with changes in the architecture of the swII/α3 cavity, essential recognition point for PDEγ. A detrimental effect of the mutation on such cavity had been also postulated based upon crystallographic analyses [16]. We ended up independently with this conclusion by individuating also the main actors of this structural effect. In this framework, the Y254 position seems to be particularly sensible to the concerted motions of the protein triggered by the mutation. Indeed, deformation of the swII/α3 cavity results in the burying of Y254 in the α3/β5 loop, preventing both the Y254 itself and F211(s2:11) from being available to PDEγ. We also speculated that mutation-induced reductions of the catalytic activity of PDE may derive from the formation of an improperly assembled GαGTP-PDEγ complex. Along this line, also in the ternary complex with RGS and PDEγ the mutation exerts a long distance effect on the effector binding site resulting in increase in the intrinsic flexibility of PDEγ and lack of communication pathways at the Gα-PDEγ interface. Another clear effect of the Gα mutation is the incapacity to form a stable Q200(G3:5)-mediated communication between the nucleotide and N364 of RGS. Such communication is instead present in the wild type and is necessary for the GAP action of RGS [16].
In conclusion, the main structural effects of the G38D mutation turned out to be deformation of the primary effector binding site in monomeric Gα and enhanced flexibility of PDEγ in the ternary complex, which would destabilize the Gα-effector interface. Collectively these effects are connectable with the impaired effector recognition and activation shown by in vitro experiments. Finally, the pathogenic mutation of Gα seems to affect the communication between RGS and nucleotide essential for the GAP activity, thus suggesting that the observed slight reduction of the RGS-catalyzed GTPase activity is a matter of perturbed inter-protein communication.
This study extends the dynamic model of visual phototransduction to the pathological NCNB phenotype and provides insights at the atomic level into the structural bases of the disease. This is an example of a thorough computational investigation employing different scales of description, an approach which should be pursued to unveil the structural determinants of genetic retinal diseases. Analogous approaches are suitable to infer the mechanisms of information transfer in any signaling network either in physiological or pathological conditions.
Mathematical modeling
The mathematical model of rod phototransduction (BioModels ID: BIOMD0000000326), employed in the present work for numerical simulations of the phototransduction cascade includes 91 reactions, 71 molecular species, and 63 parameters and was previously developed and validated over a wide range of experimental data on normal and genetically modified rods [14]. The rate of change of the molecular species are monitored by calculating, at given time steps, their rates of production and consumption [14]. The original model was recently modified to account for the postulated R-Gt precoupling in the dark [15], leading to the inclusion of the following reactions, which describe: a) the dynamic formation and b) dissociation of dark R-Gt complexes:
- a) and its reverse
- b)
The parameters were calculated as relative kinetic constants, following the relationships and taken from Surface Plasmon Resonance (SPR) experiments [15]. This led to a ≈20% of Gt to be dynamically precoupled to Rin the dark, consistent with published data [15].
In this study, we built a dynamic model able to describe the GαGTPG38D+/− and GαGTPG38D−/− mutated conditions of GαGTPG38D by introducing the mutated G protein as an explicit new molecule and adding all the relative reactions in the phototransduction cascade, which concerned the GαGTPWT+/+ status (Table 1). The concentration of the new species (GαGTPG38D) was obtained by using its ratio to the normal concentration of Gα in wild type cells taken from expression levels in transgenic mice for the mutation [8]. Therefore, the total level of Gα (25% of which is GαGTPG38D) in heterozygous cells is the same as in wild type rods, while only 35% of the native levels are found in homozygous cells for the mutation. The levels of all the other proteins were kept unchanged and the mutation was assumed to have no effect on rhodopsin-GαGTPG38D binding [8], [9].
In order to fit the models onto the pathological NCNB condition, the rates of a number of reactions involving GαGTPG38D were systematically reduced by tuning the relative kinetic parameters in decreasing steps (Table 1, Figure 1). The reductions were combined into specific heterozygous and homozygous models. In detail, these reactions refer to: a) intrinsic GTPase activity of GαGTP, b) binding of GαGTP to PDE and resulting PDE activation, and c) shut-off of the photoresponse by RGS binding and RGS-catalyzed GTP hydrolysis. These reactions are highlighted in Figure 1 and listed in Table 1. In line with in vitro electrophysiological recordings on rods from transgenic mice, we monitored the following features of the photocurrent elicited by increasingly stronger flashes of light (Figure 3): a) rate of the activation phase, b) light sensitivity, and c) speed of the recovery phase. In detail, a) the rate of the activation phase was evaluated as the time needed to reach the maximum value of ΔJ after the delivery of the flash; b) light sensitivity was taken as the normalized response amplitude as a function of flash strength (Figure 3G and Figure 5B in Moussaif et al. [8]); and c) the speed of the recovery phase was evaluated as the time needed for the photocurrent to reestablish its dark value (ΔJ = 0) after a flash. In some cases, the parameters had to be eventually set equal to 0, while in other cases also more limited reductions led to modification of the output (Table 1). All the numerical simulations were carried out by means of Matlab, within the SBTOOLBOX2 framework [18] (http://www.sbtoolbox2.org/main.php) as already described [14].
MD simulations: The structural models
The following PDB structures were selected as inputs of MD simulations: GαGTPWT (PDB code: 1TND [19], residue range 27–342), which is the GTP-bound form of Gα, and the GαGTP-RGS-PDEγWT ternary complex (PDB code: 1FQJ [16]) involving GαGTP (amino acids from 28 to 344), RGS (i.e. the RGS domain of RGS9, amino acids 286 to 418) and the 42-amino acid C-terminal fragment of PDEγ (residues 46–87). Input structure setup required a number of modifications in the original crystal structures. As for 1TND, the original GTPγS analogue was replaced by GTP, as recently reported [20]. As for 1FQJ, the original Gα was indeed a chimera identical to Gαt except for residues 216–294 which were replaced with the corresponding homologous region of Gαi1 (residues 220–298). The Gαi1 sequence was therefore mutated into the corresponding one in bovine Gαt. Moreover, the original GDP-AlF4− was replaced by GTP.
All the simulated systems hold the Mg2+ ion together with the coordinating water molecules.
The native G protein in the GαGTPWT and GαGTP-RGS-PDEγWT complexes was finally subjected to the substitution of aspartate for G38, in order to produce the pathogenic mutant (i.e. GαGTPG38D and GαGTP-RGS-PDEγG38D). In silico mutagenesis was performed by means of the Quanta software (www.accelrys.com).
MD simulation: Set-up
MD simulations on the four systems, GαGTPWT, GαGTP-RGS-PDEγWT, GαGTPG38D and GαGTP-RGS-PDEγG38D, were carried out by using the GROMACS4 simulation package [21] with the AMBER03 all atoms force field [22], [23]. The TIP3P water model was employed to describe the solvent. AMBER parameters to describe the GDP and GTP molecules were taken from the literature [24]. Depending on the dimensions of the systems, a variable number of Na+ and Cl− ions were placed at optimum electrostatic positions in order to neutralize the system. In detail, the systems included: 63740 total atoms for GαGTPWT (19512 water molecules, 48 Na+ and 38 Cl− ions); 63743 total atoms for GαGTPG38D (19511 water molecules, 49 Na+ and 38 Cl− ions); 81906 total atoms for GαGTP-RGS-PDEγWT (24609 water molecules, 60 Na+ and 50 Cl− ions); 81882 total atoms for GαGTP-RGS-PDEγG38D (24599 water molecules, 61 Na+ and 50 Cl− ions).
Periodic Boundary Conditions (PBC) were applied by using an octahedric box as a unit cell, imposing a minimum distance of 12 Å between the solute and the box boundaries.
MD simulation setup is the same as the one recently employed to simulate a number of Ras GTPases [20]. All the input crystallographic structures were subjected to energy minimization keeping restricted the positions of the main chain atoms, the nucleotide, the Mg2+ cation and the coordinating water molecules. The systems were then equilibrated at 300 K for 4 ns of backbone restricted MD simulations. The Particle Mesh Ewald (PME) method was employed to compute the electrostatic interactions. Short range repulsive and attractive interactions were computed by using a Lennard-Jones potential with a cutoff of 10 Å. The LINCS algorithm [25] was used to constrain all bond lengths except those in water molecules, allowing for an integration time step of 2 fs through the leap-frog algorithm. The v-rescale thermostat [26] was employed to keep the system at a constant temperature of 300 K, by using a coupling constant (τt) of 0.1 ps. The pressure of the system was kept fixed at 1 atm, using the Berendsen weak coupling algorithm [27] with a coupling constant (τp) of 1 ps. The pre-equilibrated systems were then subjected to 100 ns of unrestrained isothermal-isobaric (T = 300K, P = 1 atm) MD simulations.
MD analyses of the intrinsic flexibility
MD trajectories were subjected to a variety of analyses aimed at inferring a) the time series of a number of structural descriptors such as the SASA, b) the intrinsic flexibility of the systems (e.g. RMSD, RMSF, and Essential Dynamics (ED) or PCA), and c) potential correlations between structural descriptors and essential motions (i.e. FMA).
As for ED, resting on the assumption that the major collective modes of fluctuation dominate the functional dynamics of a system, information on such global motions can be inferred from the atomic fluctuations by means of the PCA. The latter allows the decomposition of the atomic fluctuations into a set of principal components (eigenvectors of the covariance matrix of positional fluctuations) that describe the concerted motions of these atoms (e.g. the Cα-atoms). The technique is based on the diagonalization of such covariance matrix producing a set of eigenvector and eigenvalue pairs in which the eigenvector and the eigenvalue describe, respectively, direction and amplitude of the concerted atomic motion (a mode). The atomic components of an eigenvector provide a quantitative measure of the participation of each Cα-atom to the collective motion described by the corresponding eigenvector. The subspace spanned by the major modes of collective fluctuations is accordingly often referred to as "essential subspace (ES)". In the same framework, FMA is a technique to identify collective atomic motions related to a specific protein function. Given a large set of structures of one protein, for example from an MD trajectory, the method detects a mode that is maximally correlated to an arbitrary quantity of interest.
Except for FMA, which was carried out by using the GROMACS package, all these MD analyses were performed by means of the Wordom software [28]. As for PCA, the covariance matrices were built on the Cα-atoms of the isolated MD trajectories.
FMA [29] was carried out by using the Linear Mutual Information (LMI) estimator [30]. The structural descriptor correlated with the Principal Components (PCs) was the SASA calculated on selected Gα amino acids involved in Gα-PDEγ and Gα-RGS interactions. A number of PCs were probed.
Non bonded interaction energies for the nucleotide were monitored every 20 ps along the trajectory with GROMACS4.
MD analyses of the structural communication
The structural communication (i.e. PSGs and shortest communication paths) in the four simulated systems was inferred by means of the graph-based approach proposed by Vishveshwara and coworkers [31] and defined as Protein Structure Network (PSN), that was recently implemented in the Wordom software [28]. With this approach, the dynamics of the system is taken into account in terms of occurrence of network components along the trajectory and of correlated motions [32]–[34].
A graph is defined by a set of points (nodes) and connections (edges) between them. In a PSG, each amino acid is represented as a node and these nodes are connected by edges based on the strength of non-covalent interactions between nodes [31]. The strength of interaction between residues i and j (Iij) is evaluated as a percentage given by the following equation:where Iij is the percentage interaction between residues i and j; nij is the number of atom-atom pairs between the side chains of residues i and j within a distance cutoff (4.5 Å); Ni and Nj are normalization factors for residue types i and j, which take into account the differences in size of the side chains of the residue types and their propensity to make the maximum number of contacts with other amino acid residues in protein structures. The normalization factors for the 20 amino acids were taken from the work by Kannan and Vishveshwara [35]; the normalization values for GTP (derived from 3 heterotrimeric G proteins), Mg2+ (based on 4 heterotrimeric G proteins to properly describe the coordination of such ion in the system under study) and water (based on 5 structures, comprising G proteins and rhodopsin) were 361.3, 23.8 and 27.0, respectively. Thus, Iij are calculated for all nodes, excluding i ± n, where n is a given neighbor cutoff of 3. An interaction strength cutoff Imin is then chosen and any residue pair ij for which Iij≥Imin is considered to be interacting and hence is connected in the PSG.
As previously demonstrated [31], the optimal Imin is the one at which the size of the largest cluster of nodes at Imin 0% halves. Incidentally a node cluster is a set of connected nodes in a graph. We approximated the Imin value to the second decimal place. The final Imin cutoffs were: 3.24% for GαGTPWT, 3.23% for GαGTPG38D, 3.52% for GαGTP-RGS-PDEγWT, and 3.58% for GαGTP-RGS-PDEγG38D. To build the PSG, only the edges present in at least 30% of the trajectory frames were used. Those nodes involved in at least four links are named as hubs.
Possible shortest communication paths or optimal paths (OPs) in the different GαGTP binary complexes as well as between wild type and mutated GαGTP and the other two proteins in the GαGTP-RGS-PDEγ ternary complex were searched. All residue pairs except those at sequence distance ±5 were considered as path extremities (i.e. the first and last amino acids in the path). In detail, the number of intra-Gα amino acid pairs was 49770 for the wild type and mutated forms of isolated GαGTP and 50090 for the wild type and mutated forms of GαGTP in the ternary complex with RGS and PDEγ. Finally, 56350 amino acid pairs were considered to search all possible communication paths between wild type and mutated GαGTP and the two proteins in the ternary complex. Vishveshwara and co-workers implemented also the search for suboptimal paths (SOPs), alternate routes of communication, which can be computed by systematically removing all interactions of an OP node(s), thus forcing the traversal of a less than optimal path [36]. Since our path searches, different from those by Vishveshwara and co-workers [36]–[38], are not limited to a few selected node pairs but systematically consider almost all node pairs in a system, the additional search for SOPs would have been too costly in terms of computer time with the high risk to produce more noise than relevant information. For this reason our approach is dedicated exclusively to OPs.
The search for the shortest path(s) between pairs of nodes as implemented in the PSN-path module of Wordom relies on the Dijkstra's algorithm [39]. They were searched by combining PSN data with cross-correlation of atomic motions calculated by using the LMI method.
Following calculation of the PSG and of correlated motions (by means of the LMI method [30]), for each frame, the procedure to search for the shortest path(s) between each residue pair consists of a) searching for the shortest path(s) between each selected amino acid pair based upon the stable PSN connectivities, and b) selecting the shortest path(s) that contains at least one residue correlated (i.e., with a LMI cross-correlation ≥0.3) with either one of the two extremities. All the shortest paths that pass the filter of correlated motions are subjected to a further filter based upon path frequency, i.e. number of frames containing the selected path divided by the total number of frames in the trajectory. The relative number of amino acids holding correlated motions with either one of the two extremities is quantified by the correlation score, i.e. the ratio between the number of correlated amino acids and the path length; the latter excludes the two extremities.
Outcome of this stage is the total pool of paths for the system under study. Meta paths made of the most recurrent nodes and links in the path pool (i.e. global meta paths) are worth computing to infer a coarse/global picture of the structural communication in the considered system. In this study, meta paths were computed on the ensemble of paths with frequency ≥30%. For each link a recurrence score r is calculated using the following equation:where l is a given link present in the considered set of shortest paths, pij is the total number of shortest paths from node i to node j and pij(l) is the total number of shortest paths from node i to node j that include link l. Finally, only those links with a recurrence score ≥30% of the highest score are used in the meta path representation.
Supporting Information
Figure S1.
Details of GTP binding modes in GαGTP (top) and GαGTP-RGS-PDEγ (bottom). In both panels, the superimposed structures of wild type (violet) and mutated (green) forms are shown. The nucleotide is always colored by atom type. Only the amino acids that contribute the most to interactions with the nucleotide are shown in sticks. For those amino acids, which contribute through the backbone NH group, only the latter is shown. The mutated side chain is cyan. See the legend to Figure 2 for the labeling scheme.
Figure S2.
Nucleotide-protein non bonded interaction energies averaged along the trajectories for GαGTP (A) and GαGTP-RGS-PDEγ (B). In both panels, violet bars refer to the wild type form and green bars to the mutated form. Vertical black bars indicate standard errors. Only the non bonded interactions whose average values along the simulations were smaller than −20 kJ mol−1 were plotted.
Figure S3.
Cα-RMSD plots. The time series of the Cα-RMSD with respect to the input structures concerning isolated GαGTP from 1TND, complexed GαGTP from 1FQJ, PDEγ from 1FQJ, and RGS from 1FQJ are shown. Violet refers to the wild type whereas green refers to the mutant.
Figure S4.
Fragment analysis on the pool of paths generated by GαGTP (top) and GαGTP-RGS-PDEγ (bottom) structures. In both panels, violet bars refer to the wild type form and green bars to the mutated form. Fragment recurrence is the number of paths containing the given fragment divided by the total number of paths. On the abscissa, the nodes constituting the fragment are numbered according to the secondary structure nomenclature explained in the legend to Figure 2 and used throughout the text. Only fragments of length 3 were taken into account.
Figure S5.
Global and coarse view of the communication pathways with high content of conserved amino acids. The meta paths computed over those paths holding ≥50% of conserved amino acids are shown. They concern GαGTPWT and GαGTPG38D in their free state (A and B panels, respectively) as well as in ternary complex with both RGS and PDEγ (C and D panels, respectively), colored violet and green respectively. The width of each link is proportional to r, while the sphere diameter is proportional to the average r of the connecting link (see Methods for r definition). The α-helical and Ras-like domains are dark and light gray, respectively, the PDEγ binding site on Gα is aquamarine, RGS is orange and PDEγ is lemon-green. The mutation site is indicated by the red sphere.
Figure S6.
Cα-RMSF profiles and Cα-atom projections. A. The Cα-RMSF profiles from MD trajectories of Gα from GαGTP-RGS-PDEγWT (violet) and Gα from GαGTP-RGS-PDEγG38D (green) are shown. They refer to the 100000 frames constituting the 100 ns trajectory. The secondary structure elements are shown on the abscissa, following the Noel's nomenclature (see [19] in the text). B, C, D, E. The Cα-atom projections along the linear combination of the PCA-derived principal components, which describe the ES of the trajectories of Gα from GαGTP-RGS-PDEγWT (B and C) and of Gα from GαGTP-RGS-PDEγG38D (D and E) are shown. The ES is given by a variable number of eigenvectors that describe 90% of the total variance (sum of eigenvalues). The number of PCs used was 108 for B and C, and 103 for D and E. Cα-atom displacements are highlighted by color ranges from violet to blue or and from green to blue, respectively.
Figure S7.
Cα-RMSF profiles. The Cα-RMSF profiles from MD trajectories of PDEγ (top) and RGS (bottom) from GαGTP-RGS-PDEγWT (violet) and Gα from GαGTP-RGS-PDEγG38D (green) are shown. The secondary structure elements are shown on the abscissa.
We'd like to thank Marie E. Burns for kindly sending us data from electrophysiological recordings that allowed us to compare the outcome of computational and in vitro experiments. We also thank Nikolai O. Artemyev for providing clarifications on the results of in vitro experiments.
Author Contributions
Conceived and designed the experiments: SM FF. Performed the experiments: SM. Analyzed the data: SM FF. Wrote the paper: FF. Contributed to network simulation setup and analysis: DD. Contributed to Protein Structure Network analysis: AF. Contributed to Molecular Dynamics simulation setup and analysis: FR.
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text:
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text:
- Beklager. Denne hendelse har allerede funnet sted.
Artist Kaarina Kaikkonen (f. 1952) has transformed sites in large scale internationally with personal garments since 1987. Hand in hand, 1200 shirts from people in Finland and Oslo are connected in the installation 'We are still the same' on the Arctic Pyramide Structure. Her work is presented in collaboration with The Finnish-Norwegian Cultural Institute.
Foto: Endre Lohne
"In every shirt there is a story, because someone with a warm heart has been wearing it. All kind of people are together here, but we are still the same, we are no wiser than fish. We still act like fish, always going in a group, following each other in the same direction, like a shoal of fish. We are a part of nature, and nature is within us." Artist Kaarina Kaikkonen
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In some cases, even make a transition to actually become a 'producer' rather than hired labor.
What does HL stand for?
HL stands for Hired Labor (USACE)
This definition appears somewhat frequently and is found in the following Acronym Finder categories:
- Military and Government
See other definitions of HL
Other Resources:
We have 67 other meanings of HL in our Acronym Attic
- Abbreviation Database Surfer
- « Previous
- Next »
- Hierarchical Leader-based (routing scheme)
- High Land
- High Level
- High Limit
- High Temperature Limit
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Samples in periodicals archive:
Cerda works with agricultural employers to assist with hiring workers and provides education and counseling about the Department of Labor rules and regulations governing the guest worker and other hired labor in agriculture.
For this text and the issue of hired labor in the Neo-Assyrian Empire see now Radner 2007: 207-8.
With the help of locally hired labor, he supervised preparation of 2 hot meals, which were usually the pinnacle of our day.
As for hired labor, the cooperative and the producers are fully entitled to hire additional people when it is harvest time; there is no limitation on that, as long as it is occasional.
cheese and wheat) to a capitalized country economy where connections between farm and community, between family and farming, among family, community and hired labor, and, in McMurry's case, the ecological connection among crops, animals and farm products, all decreased or dissolved.
In effect, dependence on hired labor suspends Say's Law by making labor costs downwardly rigid.


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Solar Panel Glass – Tempered Vs Plate
When shopping for a solar panel brand, the issues at the forefront of people's minds are typically topics such as efficiency and wattage. An often overlooked issue is glass – and the type of glass used on a solar panel really does matter. When you buy a solar panel, it's a long term investment –…Details


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Intikana Tantra
Return To Ecstasy
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In our Leichhardt training we give meticulous directions for lingam worship ritual by employing sydney sacred sexuality activities.
The fundamental contrast between Tantric way of life and other mystical teachings is that it has an optional avenue to personal fulfilment. Tantra takes a holistic procedure to the real human state as when compared to other belief systems who strive to split up the man from the central being.
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Recent Posts
October 2019 S M T W T F S « Apr 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Finally we got some snow to build a snowman this year. It hasn't even felt like winter here in Canada. All the kids were excited to get started after we red this story. Then we got all dressed up and … Continue reading
What a beautiful morning to take the kids to the park. It was sunny and the temperature was above zero which is not a typical February day here in Canada. I buckled the little ones in the wagon while the … Continue reading
I received some laminated pictures of winter clothing from one of my networking members along with a song to sing with the kids when we are getting dressed to play outside. It has helped to show the kids the order … Continue reading
It's the middle of January and all the kids have been waiting for the snow. The snow came this morning but with the windchill it was too cold for the little ones to go outside, so we brought the snow … Continue reading
Today it was all about apples. We read stories about apple picking, the kids painted an apple tree using their thumbs for leaves and apples, we watched a Max and Ruby show about apples and we even made applesauce from … Continue reading
It's a beautiful time of year when all the leaves change to pretty colours, it's Thanksgiving, it's Halloween and we eat warm comforting fall food. We created our Fall banner with leaf sponges and glued on apple and leaf shapes. … Continue reading
I borrowed some trucks from the ASCY Caregiver library and thought the kids would like to play with it at the park today and boy was I right. They started playing with them right away, filling the trucks with the … Continue reading


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Use the Courses submenus on the right side of the screen for recent or upcoming Fall, Spring, and Summer listings.
For all Russian courses, search the CU Boulder Course Catalog. Not every course listed is offered each semester.
Use the CU Class Search to search by core, gen ed, specific subjects, keywords, instructors, etc. for the current and upcoming semesters.
Russian Major Requirements and Russian Minor Requirements are also available in the CU Catalog online.
A&S Policy on Enrollment in Undergraduate Language Courses
Special Topics for Spring 2019
RUSS 4210-3. Open Topics in Russian Culture: Vladmir Nabokov
Studies the major novels and short stories of Vladimir Nabokov, one of the 20th-century's most celebrated and controversial literary figures. Nabokov's works examine the relationship between memory and lived experience, fiction and reality, and nature and art, often blurring these categories. Readings include Pale Fire, Lolita, Invitation to a Beheading, Despair, Pnin, and The Real Life of Sebastian Knight, among others. Taught in English. Equivalent - Duplicate Degree Credit Not Granted: RUSS 5210 Repeatable: Repeatable for up to 6.00 total credit hours. Arts Sci Gen Ed: Distribution-Arts Humanities
New Courses for Spring 2019
RUSS 2271 (3) Space, Invention, and Wonder in Fairy Tales, Literature and Film
Explores the themes of space, invention, technology and wonder in fairy tales from Italian, Russian, French, German, and Spanish traditions in order to compare their transformation in different national and historical settings. Students analyze the intersection of fairy tales and science in literature and film. Counts for the Space Minor. Taught in English. Equivalent - Duplicate Degree Credit Not Granted: ITAL 2271 Arts Sci Gen Ed: Distribution-Arts Humanities


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Charlotte must not go backward on recycling at apartments
Charlotte's City Council and Solid Waste Services are discussing whether to eliminate municipal trash and recycling service to apartment complexes. This is a step in the wrong direction because it would result in fewer Charlotteans being able to recycle at home and would move the city further from its own stated goal of diverting waste from the landfill. The ability to recycle at home should be a right, not a privilege.
The 2013 Multi-family, Small Business, and Rate Structure Review report commissioned by the city shows that it's not the norm for cities across the nation to provide recycling service to apartment complexes. But Charlotte lacks the incentives or, in some cases, requirements to recycle that some of the peer cities evaluated in the consultant's report have. For example, the Maryland Recycling Act requires Baltimore City to recycle at least 20 percent of waste generated. Greensboro residents are required to recycle many materials by county ordinance. Austin, Texas, offers residents a choice of trash can sizes at different prices so they can control costs by reducing waste, recycling and composting.
Charlotteans pay the same solid waste fee regardless of how much they throw away. Recycling isn't mandated for residential customers, and there's no financial incentive to recycle. Plastic bottles have been banned from landfills by state law since 2009. But how are we going to keep recyclables out of the landfill if we don't provide a practical way for apartment residents to recycle?
Then there's the question of how we can protect the environment and offer municipal services equitably as we grow. Charlotte is facing the second-fastest population growth rate among large U.S. cities. We the nation's 21st most-expensive rental market. The housing choices that current and future residents make will largely determine whether Charlotte continues to sprawl or whether we manage our growth sustainably.
If apartment complexes are required to independently contract with and pay for their own solid waste haulers, the additional cost will inevitably be passed on to residents. This will hurt some of our lowest-income citizens who can least afford it. And after paying for trash pickup, how many apartment complex owners will also take on the additional, optional expense of contracting with recycling haulers so their residents have the ability to recycle at home?
There has been vigorous debate about which option is best, but largely missing from the discussion has been the question of how the final decision will move the city closer to its 2016 Environment Focus Area Plan goal of developing "a baseline toward 100 percent achievement of waste diversion from landfill."
It's time for a new solid waste ordinance that will move Charlotte toward a way of managing waste that is sustainable in every possible way: environmentally responsible, fiscally sound, and socially equitable.
Meg Fencil is education and outreach director at Sustain Charlotte.


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New York - Bowmansville
Sales Tax Calculator of Bowmansville for 2019
Calculation of the general sales taxes of the city Bowmansville, New York for 2019
How 2019 Sales taxes are calculated in Bowmansville
The Bowmansville, New York, general sales tax rate is 4%. The sales tax rate is always 8.75%
Every 2019 combined rates mentioned above are the results of New York state rate (4%), the county rate (4.75%). There is no city sale tax for Bowmansville. There is no special rate for Bowmansville.
The Bowmansville's tax rate may change depending of the type of purchase.
Please refer to the New York website for more sales taxes information.
Bowmansville city rate(s)
8.75% is the smallest possible tax rate (14026, Bowmansville, New York)
The average combined rate of every zip code in Bowmansville, New York is 8.75%
Last sales taxes rates update
The last rates update has been made on July 2019.


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How To Organize and Promote An Open Mic Bandzoogle
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How To Set Up Open Mic Overwatch
30/05/2014 · Phones How to set up and start using Cortana. These tips will help you get started with Microsoft's brand new voice assistant in Windows Phone 8.1.
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- Set your tanks up in the larger of the two buildings adjacent the point and keep your healers with them. You can run dive or a shield composition here – it doesn't really matter.
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OK, here's what I do: I meet someone who wants to change their body, either functionally or aesthetically (actually most often it's actually a complex, opaque amalgamation of the two). After determining where they are, physically-speaking, I decide how I can help them go where they want to go, and try to communicate that to them.
As such, I spend about half my time understanding where someone is currently--the industry term is "assessment"--and the other half thinking about what they can do to change (fit-biz term: "intervention").
And then we get to work.
We talk, we laugh, we move, we cry, we sweat, we think, we make plans, and we abandon them. We shed the parts that don't serve us, and we hone in on the stuff that works. Together we are actively creating change, as specific as possible to that person.
That's all.
Over the years, it slowly dawned on me that perhaps the most challenging part of this process is a simple misconception: people don't know where they're starting from. In fact, most of the time they don't care.
Sometimes, I'd even guess that they actively would like to ignore that starting point. It's too scary to see themselves with that sort of accuracy/reality.
But this lack of clarity makes the process of Change feel--to them--completely disjointed and complex, because they don't have their bearings.
On top of that, it also fundamentally changes how I must interact with the person. Of course, to coach them I need to clearly see both sides of the "Change Equation" (assessment, intervention); but at the same time I must consider how much the person sees, or wants to see, of themselves.
Too much realness, too soon, can make us fold. 🤷
So how quickly and effectively they shift really comes down one question: Do they care enough to face up to what their body can do, right now?
Yikes--that looks so dramatic when I write it like that. I love me some good drama, but it's not very useful for instigating action. Drama isn't very practical.
Enter CARs. Controlled Articular Rotations. CARs are as practical as it gets in the fitness world.
One of the first things I learned about CARs was that it was, while being a way of "training" your joints, it effectively had a self-assessment system built right in. In fact, this was one of the main qualities that differentiates Functional Range Conditioning (FRC, the system from which CARs originate) from most other movement systems.
This changed everything for me (and my students).
Because if you can assess yourself well--truly know your starting point--your whole attitude toward Change as a possibility shifts.
It shifts to be more true, more effective, but simpler to conceptualize, too. If you really know where you are (point A), and you can clearly understand where you want to go (point B), to improve you just need to draw straighter and stronger lines from A toward B.
But the biggest benefit? Change shifts into being a journey that you control, not one that controls you.
These days, when I first work with that new someone, and we're discussing how the exercises I just taught them--CARs--can change the whole game, I mention this assessment benefit.
I mention how, by going slow and controlled, right at the outskirts of their range of motion, they can deftly side-step painful areas and make sure that their CARs are safe. And in doing so they can effectively "see" what's really going on in their body.
Almost no one believes me that first day about the power of CARs. But the ones who do--who go home and practice their CARs--come back with a familiar look: relief.
Because while going slow, avoiding their painful areas, they actually saw themselves. For many, this is a sobering moment, a harsh reminder of the realities of their body. But it's also inherently hopeful.
Because it's a starting point.
Go find your gold,
Coach Will


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Send Someone Away EP by Embee on Spotify
The playlist still looks the same, but now, if you share the link to the playlist with another person (using the HTTP Link or Spotify URI, also pictured), they can add, delete, and reorder songs — and those changes will be reflected for everyone with access to the playlist.... I use spotify all of the time (love it) but a preset playlist can't anticipate the flow of the evening involving hundreds of people, and you'll need someone to keep things on schedule and MC your event. I think this would be far too risky on your wedding day.
Want to Suggest a Song for a Playlist? How To Message a
Send it to the person with whom you want to share this playlist. The recipient can then open iTunes and choose File > Import Playlist, then select the XML file....Each member of a Premium for Family plan has their own personal account - so you can use your existing account. All of your account details will remain the same, including any saved music, playlists…
Send Someone Away EP by Embee on Spotify
What happens if you've clicked someone's link to a playlist, it launches within Spotify, and you feel like subscribing to it? All you have to do is click Subscribe next to the playlist. (You also see a similar Subscribe link next to a playlist when it's listed in a public profile.) After you click Subscribe, the playlist appears at the bottom of your left sidebar, along with all the how to train for university soccer try outs Click Follow beside someone's name to follow their activity on Spotify. The Radio feature lets you pick a song, artist, playlist, or album and have Spotify play a random mix of …. How to send imovie to email pc
How To Send Someone Spotify Playlist
Asking Crush Out Via Spotify How to Tell Your Crush You
- Asking Crush Out Via Spotify How to Tell Your Crush You
- Spotify's Collaborative Playlists Let Friends Listen
- How to Create a Spotify Playlist PCMag.com
- Send Someone Away EP by Embee on Spotify
How To Send Someone Spotify Playlist
Created in 2011, the playlist has a collection of tracks that will send you into a pleasant trance. Best listened to on shuffle in order to mix up all the gems from the past six years. —
- 2018-10-12 · This wikiHow teaches you how to convert one of your Spotify playlists into a collaborative playlist, which you can share with a contact and edit together, using an iPhone or iPad. Once you share your collaborative playlist with someone else, you can both add, remove, and arrange all …
- Created in 2011, the playlist has a collection of tracks that will send you into a pleasant trance. Best listened to on shuffle in order to mix up all the gems from the past six years. —
- Creating and sharing playlists on Spotify is pretty cool, but Spotify has taken this far beyond by giving you the power to work together with your friends to manage your playlists. It means that
- People Are Asking Out Their Crushes Via Spotify Playlist Now and the Results Are Hilarious. But does it work? By Carina Hsieh. Apr 19, 2017 Hannah Woodley. Ah, young love. Gone are the days of
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