What Is The Standard Free Energy Change Per Mol Of Protons Associated With This Gradient At 25 â놫œc?

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ACS Chem Neurosci. 2018 November 21; 9(11): 2815–2823.

Gibbs Free-Energy Gradient along the Path of Glucose Transport through Human Glucose Transporter 3

Huiyun Liang

^†Department of Physics, University of Texas at San Antonio, San Antonio, Texas 78249 Usa

Allen Thousand. Bourdon

^‡Section of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States

Liao Y. Chen

^†Department of Physics, Academy of Texas at San Antonio, San Antonio, Texas 78249 United States

Clyde F. Phelix

^§Department of Biological science, University of Texas at San Antonio, San Antonio, Texas 78249 U.s.a.

George Perry

^∥Department of Biology and Neurosciences Institute, University of Texas at San Antonio, San Antonio, Texas 78249, United States

Received 2018 May iv; Accepted 2018 Jun 4.

Supplementary Materials

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Abstract

Fourteen glucose transporters (GLUTs) play essential roles in human physiology by facilitating glucose diffusion across the jail cell membrane. Due to its central function in the energy metabolism of the central nervous system, GLUT3 has been thoroughly investigated. Still, the Gibbs complimentary-energy gradient (what drives the facilitated diffusion of glucose) has not been mapped out along the transport path. Some fundamental questions remain. Here nosotros present a molecular dynamics study of GLUT3 embedded in a lipid bilayer to quantify the gratis-free energy profile along the unabridged transport path of attracting a β-d-glucose from the interstitium to the within of GLUT3 and, from there, releasing it to the cytoplasm by Arrhenius thermal activation. From the free-energy contour, we elucidate the unique Michaelis–Menten characteristics of GLUT3, depression Thou _M and high 5 _MAX, specifically suitable for neurons' high and constant demand of energy from their low-glucose environments. We compute GLUT3'southward bounden gratis energy for β-d-glucose to exist −iv.6 kcal/mol in agreement with the experimental value of −4.4 kcal/mol (Thousand _Grand = ane.iv mM). We besides compute the hydration energy of β-d-glucose, −18.0 kcal/mol vs the experimental data, −17.8 kcal/mol. In this, we establish a dynamics-based connection from GLUT3'due south crystal construction to its cellular thermodynamics with quantitative accuracy. Nosotros predict equal Arrhenius barriers for glucose uptake and efflux through GLUT3 to be tested in future experiments.

Keywords: Glucose transporter, facilitated diffusion, bounden analogousness, gratuitous free energy, molecular dynamics

Introduction

Glucose is the near of import monosaccharide of the human body. Because of its hydrophilic property, glucose easily circulates in the bloodstream only it needs to be transported across the cell membrane by the glucose transporters (GLUTs), membrane proteins in the family of carbohydrate transporters^ane that belongs to the major facilitator superfamily (MFS).ⁱⁱ Upon its uptake into a prison cell, glucose is either readily consumed (in, e.g., neurons) or converted for storage (in, due east.thousand., hepatocytes). In many physiological processes, the facilitated transmembrane diffusion of glucose is the charge per unit limiting factor for its utilization.^3,4 Therefore, it is fundamentally relevant to know the atomistic structures and the thermodynamic details of GLUTs⁵ in addition to their functional characteristics. Currently, there are 14 GLUTs identified with different substrate specificities and distinct tissue distributions.^ane,6−12 For the central nervous system (CNS), for example, GLUT1 is the main transporter of glucose from the blood into the interstitium^vii while GLUT3 is responsible for the neuron'southward glucose uptake from there.^{8,13,fourteen} In addition to the clear importance of GLUTs in human being physiology, dysregulations or mutations of GLUTs have been correlated to diseases such every bit diabetes, hyper- and hypoglycemia, center disease,^one and Alzheimer's disease.^fifteen Furthermore, overexpressions of GLUTs have been identified in diverse cancer types for the increased glucose uptake necessitated by the uncontrolled cellular proliferation of cancer cells.^sixteen−18

In this newspaper, we focus on GLUT3 that has been investigated very extensively (reviewed in, e.g., refs (v), (6), and (viii)) due to its importance in the energy metabolism of the CNS. In the CNS, GLUT3 is polarly deployed on the dendrites and axons where the synaptic activities are high.¹⁹ Its high analogousness with glucose (Grand _Grand ∼ 1.four mM⁸ in comparing with GLUT1's M _M ∼ 6.five mM²⁰) is critical for the neurons' uptake of glucose from the interstitial fluid where the glucose level is low.²¹⁻²⁸ GLUT3 is as well expressed in lymphocytes, monocytes, macrophages, and platelets where it is stored in the intracellular vesicles and, when needed for an increment in glucose demand, it can be translocated and fused to the plasma membrane upon cellular activation.^vi,29 In the structural studies of GLUTs that are resolved to atomistic resolutions only recently, multiple crystal structures of GLUT3 take been determined,³⁰ all in the outward-open up/occluded (exofacial) conformations but none inwards-open/occluded (endofacial). Interestingly, multiple crystal structures of GLUT1 are currently bachelor in the endofacial conformations^31,32 just none exofacial. On the theoretical–computational front in the recent literature, extensive molecular dynamics (MD) simulations take been performed on how GLUT1^30,33,34 transforms from the exofacial conformation to the endofacial conformation to carry a glucose from the extracellular fluid to the cytoplasm. Similar Doctor studies have been carried out on how E. coli xylose (XYP) transporter (XylE) transforms from the exofacial conformation to the endofacial conformation to bear an XYP from the extracellular space to the intracellular side along with changes in the protonation states of relevant residues.^30,35 Very recently, the gratuitous-free energy profile along the XYP bounden path has been mapped out³⁶ in authentic understanding with the experimentally measured analogousness.

However, an essential part of the β-d-glucose (BGLC)-GLUT3 thermodynamics remains to be elucidated in the current literature. Some fundamental questions still demand to be addressed. For instance, what characteristics are in the Gibbs complimentary-energy profile along the BGLC-GLUT3 bounden-and-releasing path? How is the Michaelis–Menten constant Chiliad _M (that is direction-dependent) related to the dissociation constant G _D (that is direction-independent)? What is the dynamics-based connection from the crystal structure of GLUT3 to its unique thermodynamic characteristics in low Chiliad ₁₀₀₀ and loftier V _MAX to satisfy the neurons' high need of energy? In this newspaper, nosotros reply these questions with a quantitative written report of the binding affinity (1/K _D), the send path of BGLC from the extracellular fluid through GLUT3 to the intracellular space, and the Michaelis–Menten characteristics of BGLC transport through GLUT3 based on MD simulations of an all-cantlet model system built from the crystal structure (illustrated in Effigy ​ i). We compute the potential of mean force (PMF) along the unabridged send path of the facilitated diffusion, which represents the chemic potential of BGLC, namely, the change in the system'southward Gibbs complimentary free energy as a function of BGLC'southward displacement along the improvidence path. As a further validation of our report, nosotros also compute the hydration energy of BGLC as a problem of binding BGLC from vacuum to inside a bulk of water. The accuracy of our written report is shown in the close agreement between our computed values and the experimental data in GLUT3-BGLC analogousness, BGLC hydration free energy, and so forth. The Michaelis–Menten characteristics drawn from our free-energy profile demonstrate how GLUT3 is specifically suitable for neurons' glucose uptake at maximum velocity from the extracellular interstitium where the glucose concentration is low.

GLUT3-BGLC complex embedded in a lipid bilayer. Top left panel, the protein-sugar complex viewed from the extracellular side. Protein is in ribbons colored by residue types (hydrophobic, white; hydrophilic, light-green; positively charged, blueish; negatively charged, red). Glucose is in large spheres colored by cantlet names (C, cyan; O, red; H, white). Six α-carbons on half-dozen transmembrane helices in the vicinity of BGLC are marked every bit black spheres (Ser21CA on TM1, Ser71CA on TM2, Val163CA on TM5, Val280CA on TM7, Gly312CA on TM8, and Glu378CA on TM10), which are chosen every bit 6 centers for the helices to pivot. Their z-coordinates (six degrees of freedom in total) are fixed during simulations later on long equilibration just their x- and y-degrees of freedom are gratuitous in all simulations. Lesser left, meridian correct, and bottom right panels, respectively, the extracellular, the side, and the intracellular views of the protein–sugar complex embedded in a lipid bilayer. The coordinates were from the last frame of 200 ns MD to fully equilibrate the arrangement. Waters, ions, and some lipids are not shown for clear views of the protein (in cartoons colored past residue types). The lipids are shown in lines colored by atom names (in addition to the afore-listed, P, regal; N, blue). All molecular graphics were rendered with VMD[28].

Results and Discussion

In this section, we showtime present the problem of glucose hydration, which has key relevance to many biological processes and serves to verify the accuracy of the CHARMM36 force field parameters used in this report of the carbohydrate–poly peptide complex and the algorithm of our approach. We so give the detailed, quantitative results on the glucose transport through GLUT3 and elucidate the dynamics-based connection from the atomistic coordinates of the crystal structure to the thermodynamic characteristics fit for satisfying neurons' high need of energy from their low-glucose environments.

Hydration of BGLC

In Figure ​ 2, we plot the PMF along the path of hydrating a glucose molecule from vacuum to within a majority of water by steering two centers (the C2 and C5 atoms of BGLC shown in Figure ​ two insets as big blueish spheres). In the Supporting Information (SI), Flick S1 illustrates such a path of hydrating BGLC. The fluctuations of the two steering centers in vacuum and in water are shown in the bottom console of Figure ​ 2. From the combination of the PMF difference, ΔPMF = −17.9 kcal/mol, and the two partitions of BGLC in water and in vacuum, nosotros obtain the hydration energy of BGLC, ΔG _hydr = −eighteen.0 kcal/mol. From the vapor pressure level (0.813 μPa) and the solubility (909 yard/50) of β-d-glucose,³⁷ 1 can observe the experimental value of BGLC hydration energy, −17.8 kcal/mol, which is in close agreement with our computation. This confirms the accuracy of the parameters and the algorithm employed in this piece of work.

Hydration of BGLC. Shown in the top console is the 6D PMF along a dehydration path of pulling BGLC out of water by its C2 and C5 atoms. Insets: BGLC is shown as licorices colored by atoms (H, white; C, cyan; O, red) with C2 and C5 shown as blue spheres. Some waters are shown as ball-and-sticks colored by cantlet names. Shown in the bottom console are the fluctuations of the C2 and C5 atoms in water and in vacuum from which the molecule'south partitions in water and in vacuum were computed, respectively.

Comparing the partial partitions of BGLC in h2o and in vacuum, the slightly larger fluctuations in water than in vacuum gives a contribution of −0.1 kcal/mol to the full free energy of hydration (−17.8 kcal/mol). When fully hydrated, BGLC can grade around 12 hydrogen bonds with waters in its hydration beat out. The competition among hydrogen-bonding waters slightly increases the sugar'southward fluctuations, leading a slightly greater partial sectionalisation in water than in vacuum.

The steepest part of the hydration PMF bend is when the sugar is exterior and virtually the water-vacuum interface (z = ten Å, Figure ​ 2). In that range, the van der Waals attractions between the carbohydrate and the waters are the strongest and multiple hydrogen bonds are involved betwixt them as well. When the carbohydrate is deeper inside the water box, information technology breaks more than hydrogen bonds between waters while forming more hydrogen bonds with waters. All these together give rising to the nonmonotonic behavior of the PMF from z = ten Å to z = 0, indicating possibility of higher sugar concentration near the surface than deep inside the bulk of water.

Path of Facilitated BGLC Diffusion

This path is illustrated in Figure ​ 3 and in Movies S2–S4. The first part of the transport path is the bounden path of BGLC from the extracellular space to the inside of GLUT3. It was sampled as the inverse of the "about likely" path of unbinding BGLC from the binding site (z = 4 Å) inside GLUT3 by steering BGLC away from the binding site toward the extracellular fluid at a speed of 0.one Å/ns along the z-axis while the 10- and y-degrees of freedom were gratuitous to fluctuate. The second part of the ship path is the path of releasing BGLC from GLUT3 to the cytoplasm which was sampled by steering BGLC away from the binding site toward the intracellular space at a speed of 0.1 Å/ns forth the negative z-axis while the 10- and y-degrees of liberty were free to fluctuate. Since the steering speed is sufficiently slow, the 10- and y-degrees of freedom tin relax to equilibrium at every step of advancing the z-coordinate by 1.0 × 10^–7 Å. The PMF curve forth the unabridged diffusion path is plotted in Figure ​ 4 which represents 1 or two ns force sampling in each window of 0.i Å in the z-coordinate forth the transport path. The understanding between our computed affinity and the experimental data indeed validates our approach (detailed in the next subsection).

Path of facilitated improvidence of BGLC through GLUT3. Shown in the ii left panels are all the GLUT3 atoms whose y-coordinates y ≥ 4 Å. Shown in the two correct panels are the GLUT3 atoms whose y-coordinates y < 4 Å. The protein is shown in wire-frame surface colored by atom names (H, white; C, cyan; O, red; North, blue; Southward, yellow) so that the cyan-whitish locations are hydrophobic and the cherry-red/blueish locations are hydrophilic. BGLC is shown equally gray spheres in multiple positions along the ship path. The bottom panels are identical to the corresponding top panels except that the BGLC spheres are transparent so that all GLUT3 atoms are visible.

Transporting BGLC through GLUT3. Tiptop panel, PMF forth the glucose transport path (most probable path). Middle panel, fluctuation of BGLC in the bound state (effectually z = four Å). Bottom panel, the van der Waals and hydrogen-bail interactions between BGLC and GLUT3 as well as the dihedral energy of BGLC forth its ship path.

Along the bounden path, the PMF falls well-nigh monotonically from zip (unbound state on the extracellular side) downward to −ix.0 kcal/mol in the spring state (within GLUT3, marked equally binding site in Figure ​ 4). This beginning role of the glucose ship is fast like complimentary diffusion. Forth the releasing path, the PMF rises (from −ix.0 kcal/mol at the binding site) nonmonotonically back to the zero level in unbound state on the intracellular side but, no dips are below −nine.0 kcal/mol and no bumps above zero. This second part, which limits the rate of glucose uptake (the turnover number), gives the highest possible turnover number for a given value of the Michaelis–Menten constant K _Thousand approximately twice the dissociation constant G_D, in contrast to the hypothetical cases (A) and (C) illustrated in Figure ​ 5. Information technology should be noted that glucose is accuse-neutral and, therefore, its PMF (i.eastward., the change of the system's Gibbs free free energy) forth the glucose transport path goes from zero in the extracellular bulk to zero in the intracellular bulk. In other words, the free-energy price of dissociating BGLC from its binding site within GLUT3 (or another protein) to the extracellular fluid is equal to the price of dissociating information technology to the intracellular bulk. This equality is a necessary and strong validation any theoretical–computational research such every bit this work must pass.

Hypothetical free-energy profiles (A) and (C) in comparison with contour (B) for the glucose transport through GLUT3. The uptake management is along the negative z-axis. The binding site is effectually z = 4 Å. The extra- and intracellular sides are so marked. The rate constants from the extracellular side to the binding site and its reverse are noted as one thousand _i and k _–1, respectively. The rate constants from the binding site to the intracellular side and its reverse are noted as thou _cat and k _–2, respectively. BGLC-GLUT3 and these two hypothetical cases have identical M _D's but very different M _G'due south because an extra 5 kcal/mol barrier is on the extracellular side (in case (A)) or the intracellular side (in example (C)).

Standard Bounden Gratis Energy of BGLC-GLUT3

To compute the standard bounden gratuitous energy, we sampled the fluctuations of BGLC in the bound state inside GLUT3 (around z = 4 Å) (shown in Figure ​ iv, key panel) for the spring-state division. From the PMF difference, ΔPMF = −9.0 kcal/mol, the partial division in the bound state (Z ₀ = 1.02 Åⁱⁱⁱ), and the partial partition in the unbound state (Z _∞ = 1), nosotros computed the Gibbs free energy of binding, using eq 4, Δ1000 _demark = −4.half-dozen kcal/mol. From the experimental data of the dissociation constant, K _D = 0.7 mM (K _K = one.four mM),⁸ nosotros obtain the free energy of binding to exist ΔG _demark ^exp = one thousand _B T ln(Chiliad _D/c ₀) = −4.iv kcal/mol. The difference between the experimental data and our computed binding gratis energy is less than yard _B T, indicating that chemic accuracy can exist achieved in all-atom simulations when the statistical mechanics is adequately implemented. The current force field parameters (in this study, CHARMM 36) are sufficiently optimized for quantifying protein–sugar interactions with chemical accuracy.

In the lesser panel of Figure ​ four, we prove how BGLC interacts with GLUT3 forth the transport path. The small fluctuations in BGLC dihedral energy and the all-negative van der Waals (vdW) interaction between BGLC and GLUT3 testify that there are no steric clashes between them when the center of mass of BGLC is steered/pulled from the extracellular fluid to the binding site and to the intracellular space at the pulling speed of 0.i Å/ns. The extracellular side of GLUT3 has sufficient room to conform a glucose along with multiple waters (shown in Moving picture S5) dragged forth with BGLC. The intracellular side of GLUT3 does non take sufficient room or hydrophilicity to allow as many waters post-obit BGLC (Movie S5) but it does have sufficient flexibility for BGLC traversing through without steric clashes, which are also illustrated in Figures ​ 6 and ​ vii. In Figures ​ 6 and ​ 7, we chose nine representative frames along the glucose diffusion path from the extracellular to the intracellular side. In frame 1, the BGLC center-of-mass z-coordinate z = 27.7 Å, GLUT3 side chains that come to within five Å from BGLC are THR 60, HIS 425. Frame 2: z = 22.6, GLU 35, LYS 39, THR sixty, TRP 63, TYR 290, PRO 421, HIS 425. Frame 3: z = xvi.3, ASN 32, ILE 285, ASN 286, ALA 287, PHE 289, TYR 290, THR 293, PHE 420. Frame 4: z = 10.3, PHE 24, THR 28, ASN 32, VAL 67, PHE 70, SER 71, ILE 285, ASN 286, PHE 289, TYR 290, ASN 413, GLY 417. Frame five: z = 4.1, PHE 24, THR 28, GLN 159, ILE 162, VAL 163, ILE 166, GLN 280, GLN 281, ILE 285, ASN 286, PHE 289, ASN 315, PHE 377, GLU 378, GLY 382, PRO 383, TRP 386, ASN 409, ASN 413. Frame 6: z = −1.eight, PHE 24, THR 28, PRO 139, GLY 155, ASN 158, GLN 159, ILE 162, ILE 166, GLN 280, PHE 377, PRO 381, GLY 382, PRO 383, ILE 384, PRO 385, TRP 386, PHE 387, ILE 388, ASN 409. Frame vii: z = −7.3, THR 135, PRO 139, ILE 142, GLY 143, ARG 151, GLY 152, ALA 153, GLY 155, THR 156, ASN 158, GLN 159, VAL 326, PRO 383, ILE 384, PRO 385, TRP 386, PHE 387, ILE 388, MET 402. Frame 8: z = −thirteen.0, PRO 139, MET 140, ILE 142, GLY 143, GLU 144, SER 146, ARG 151, GLY 152, GLY 155, ARG 331, PHE 387, ALA 390, GLU 391, PHE 393, ARG 398, MET 402, PHE 458. Frame nine: z = −19.2, GLY 143, SER 146, THR 148, ARG 151, ARG 210, GLU 241, GLU 245, TRP 386, ALA 390, GLU 391, ARG 398, MET 402, PHE 458.

GLUT3 and BGLC shown in nine representative frames forth the glucose diffusion path. BGLC is shown as large spheres, protein equally cartoons, and the protein side chains within 5 Å of BGLC equally licorices, all colored past frame numbers.

BGLC (spheres colored past frame numbers) and nearby GLUT3 side chains (licorices colored by residue types: white, hydrophobic; green, hydrophilic; red, negatively charged; blueish, positively charged). The choice of frames and remainder selections are identical to those in Figure ​ 6.

Interestingly, there is a deep dip at z = 4 Å in both the vdW and the hydrogen-bonding interactions between BGLC and GLUT3. (Here the supposition of −four kcal/mol per hydrogen bond is only for the illustration purpose. Using some other number, east.g., −2 kcal/mol, would lead to the same conclusion considering the PMF was computed from direct force samplings without a presumed value for hydrogen bonds.) Therefore, nosotros observe that the BGLC-GLUT3 bounden is due to the vdW attractions and the hydrogen bonds betwixt BGLC and the GLUT3 residues³⁰ forming the binding site. Going from the binding site to the intracellular side, waters hydrogen-bonded to BGLC are forced by GLUT3 to pause away from BGLC, which contributes partly to the barrier in PMF on the intracellular side of the binding site (z = −10 to −5 Å). The other contributors to this barrier are the lower hydrophilicity of GLUT3 (fewer hydrogen bonds between GLUT3 and BGLC) and the less negative vdW indicating closer contacts between BGLC and GLUT3 on the repulsive side of the vdW wells (Figure ​ 4, bottom console). All these dynamic, atomistic interactions, based on the crystal structure,^xxx parametrized by CHARMM 36 strength field parameters,^38,39 tin can give an accurate account of the thermodynamic characteristics of BGLC transport through GLUT3 when the statistical mechanics is implemented correctly with sufficient sampling in theoretical–computational investigations such as this current work.

Additionally, nosotros also conducted two independent studies of GLUT3 transport of α-d-glucose and β-d-glucose, which involve big-scale conformational changes illustrated in Figure S1. The PMF curves for the two anomers, shown in Figures S2 and S3, are similar to 1 another. They both confirm the Michaelis–Menten characteristics of low Thou _{One thousand} and high V _MAX of GLUT3, in back up of the chief study.

Michaelis–Menten Characteristics

The Michaelis–Menten characteristics of glucose transport facilitated by GLUT3 tin be better understood when contrasting it with the simple cases of hypothetical free-energy profiles shown in Effigy ​ 5. All three cases have identical binding affinity and thus identical K _D considering they take identical PMF at the bound land −ix kcal/mol at z = four Å and identical fluctuation characteristics indicated past the local curvatures of the PMF curve around z = iv Å. Yet, the three cases have very unlike Michaelis–Menten characteristics for the uptake transport (facilitated improvidence from the actress- to the intracellular side, forth the negative z-axis). In case (A), we accept K _M ^(A) ≫ 2G _D. In case (B), K _K ^(B) = 2K _D. In instance (C), K _M ^(C) = K _D.

In terms of the on and off rates illustrated in Figure ​ five, the dissociation abiding (changed affinity),

1

Hither, k ₁ is the charge per unit constant for a substrate to demark onto the poly peptide from extracellular side and k _–one is the rate constant for the substrate to revert back to the extracellular side. k _cat is the rate of catalysis, namely, the rate constant for the product (which is identical to the substrate in this written report of transport rather than the general case of reaction) to come off the poly peptide into the intracellular side. m _–2 is the rate abiding for the product to bind back to the poly peptide from the intracellular side. Within the context of our send study, the substrate concentration on the intracellular side is zero. Therefore, we take the following Michaelis–Menten equation for the transport velocity

2

for the full poly peptide concentration [E ₀] and the substrate concentration on the extracellular side [S]. The Michaelis constant

iii

Because the numeric factors, yard _B T ∼ 0.6 kcal/mol, the well depth 9 = kcal/mol, and the barriers in cases (A) and (C) = 5 kcal/mol. We take these results: (A) ; (B) ; and (C) . The send of a substrate molecule from the extra- to the intracellular side involves the Arrhenius thermal activation over (A) an extra bulwark on the extracellular side, (B) no extra bulwark, and (C) an extra barrier on the intracellular side. These three cases take very different Michaelis constants even though they accept identical affinity for the substrate.

The maximum velocity V _MAX = grand _{true cat} [E ₀], the saturated rate of transport when the substrate concentration is far greater than the Michaelis abiding, [S] ≫ M _M. Fifty-fifty though case (A) and example (B) have equal maximum rate which is greater than the maximum rate of case (C), V _MAX ^(A) = V _MAX ^(B) ≫ V _MAX ^(C), it takes a much higher substrate concentration in example (A) than in example (B) to achieve the maximum charge per unit because K _Grand ^(A) ≫ Chiliad _M ^(B).

In light of the differing transport characteristics of the two hypothetical profiles, nosotros note that case (B) has the highest maximum rate possible for a given protein–substrate affinity (dissociation constant K _D) and the maximum rate is attainable at relatively depression substrate concentrations Yard _K ∼ twoK _D. Therefore, the free-energy profile of glucose transport through GLUT3 in case (B) is an optimal scenario for a near-maximum uptake of substrate from an surroundings where the substrate concentration is depression.

Limitations

At this point, it is appropriate to discuss the applicability and limitations of this theoretical–computational piece of work.

First, GLUT3 facilitates diffusion of glucose down the concentration gradient. It is non an active transporter but a passive facilitator. Information technology is a uniporter which may or may not deed in ways identical to many other members of MFS, peculiarly symporters/antiporters that rely on the proton/ion gradients to drive the transport of a substrate across the cell membrane. Therefore, applicability of this report is not expected for MFS in general even if it is applicable to other passive uniporters.

2nd, the aim of this piece of work is limited. Information technology is not to validate or invalidate the long-held hypothesis that the big-scale conformational modify of GLUT3 is required for glucose transport but, instead, to elucidate the free-energy profile of GLUT3 that agrees with the existing experimental facts on this one uniporter. Our free-energy contour of glucose send through GLUT3 is validated by the experimental evidence of GLUT3's loftier Five _MAX and low Grand _Yard (high affinity) in the Michaelis–Menten characteristics. Interestingly, our simulations without invoking large-scale conformational changes produced results in total agreement with the experimental facts. Furthermore, our simulations of GLUT3 invoking large-scale conformational changes produced similar gratuitous-energy profiles that are also in full agreement with the experimental facts, which are detailed in Figures S1–S3. In the latter ready of simulations, the transmembrane helices were steered so that GLUT3 transforms from the exofacial conformation (Effigy S1, left column) to the endofacial conformation (Effigy S1, right column) while glucose was held in identify at the binding site. The free-free energy profiles in the endofacial conformation (red curves in Figures S2 and S3) differ from the curve obtained without invoking the conformational change (Figure ​ 4). The barrier betwixt z = −ten Å and z = ii Å disappears because glucose does not take to clasp through the poly peptide side chains equally allowed by their thermal fluctuations (Figures ​ half dozen and ​ 7). However, these two PMF curves in the endofacial conformation do not differ significantly from the 1 shown in Effigy ​ 4 in that they all produce similar the Michaelis–Menten characteristics of high 5 _MAX and low 1000 _M in glucose transport.

Third, from the all-encompassing experimental studies of GLUTs, the crystal structures of GLUT3 take only been found in the exofacial conformation. (Interestingly, GLUT1 has only been crystallized in the endofacial conformation.) The exofacial-to-endofacial conformational changes of GLUTs have but been in the Medico simulations where the transmembrane helices were biased (forced) to rotate. Unforced rotations of transmembrane helices take not observed in unbiased Physician simulations or in experiments. However, the Michaelis–Menten characteristics for glucose transport through GLUT3 are unambiguous: high V _MAX and low K _M. And in that location is no doubt that GLUT3 is not an active transporter but a uniporter facilitator, which dictates that the right gratuitous-free energy profile levels off to the same level on the intra- and the extra-cellular sides away from the membrane. Our study produced costless-energy profiles satisfying all these requirements with/without the hypothesized exofacial-endofacial conformational changes. The free-energy profile does level off to the same level on both sides away from the protein. And it does not have an extra bulwark above the bulk level on either the extracellular or the intracellular side. Otherwise, we would not have both loftier V _MAX and low K _M. Even though this work is in full agreement with existent experimental facts, it is incapable of validating or invalidating the alternating-access theory of the current literature of GLUTs. More experiments are needed to reply the question whether glucose transport through GLUTs requires big-calibration conformational changes of a uniporter poly peptide.

Conclusions

Based on the quantitative agreements between the computed hydration energy and the experimental data and between the computed GLUT3 affinity for glucose and the experimental values of the Michaelis constant, information technology is fair to country that our all-atom MD study is accurate for glucose transport across the prison cell membrane facilitated by GLUT3. The free-free energy profile along the glucose transport path shows that GLUT3 is ideal for glucose uptake from the extracellular fluid of low glucose concentration with the highest possible maximum velocity. The protein structure of GLUT3 presents no major barriers for glucose to overcome either on the extracellular side or on the intracellular side. The bottleneck of the facilitated improvidence is largely the Arrhenius thermal activation over a nine kcal/mol climb from the biding site to the intracellular side. This free-energy profile corroborates the functional experiments in that GLUT3 has loftier analogousness for glucose and that GLUT3 has high maximum velocity of glucose ship. In this, we now have a dynamics-based connection from the atomistic coordinates of the crystal structure to the thermodynamic characteristics in the transporter protein's functional roles in human physiology.

Methods

All-Atom Model Systems

For the glucose hydration problem, a BGLC is placed inside a 60 Å × 60 Å × 60 Å cubic box of water. The sugar is centered at the origin of the Cartesian coordinates which is 10 Å below the top side of the water box (the plane of z = 10 Å in parallel to the xy-plane). Reflective purlieus weather are implemented for water molecules (but not for BGLC) on the planes of z = ten Å and z = −50 Å, which proceed the water molecules inside the system box when BGLC moves out of the water box into the vacuum above the plane of z = 10 Å. This all-atom model organization consists of xx 502 atoms. Periodic boundary atmospheric condition are enforced on the x- and y-dimensions.

For the glucose transport problem, nosotros take the coordinates of the GLUT3 and BGLC from the high-resolution crystal construction of Deng et al.³⁰ (PDB lawmaking: 4ZW9), interpret and rotate the BGLC-GLUT3 complex then that its middle is located at the origin of the Cartesian coordinates and its orientation is such that the protein opens toward the z-centrality for computational convenience, embed the circuitous in a patch of Phosphatidylethanolamine (POPE) lipid bilayer, solvate the saccharide-protein–membrane circuitous with a cubic box of water whose dimensions are 100 Å × 100 Å × 120 Å, and so add sodium and chloride ions to neutralize the net charges of the protein and to salinate the system to the physiological concentration of 150 mM NaCl. The all-atom model system and then constructed is illustrated in Figure ​ one. It consists of 107 970 atoms.

Simulation Parameters

In all the MD runs, CHARMM36 force field parameters^38,39 were used for all the intra- and intermolecular interactions. The Langevin stochastic dynamics was implemented with NAMD⁴⁰ to simulate the systems at the constant temperature of 298 K and the constant force per unit area of i bar using the Langevin pistons. The damping constant was 5.0/ps. The fourth dimension step was 1.0 fs. The bonded interactions were updated every time-step while the long-range forces every two fourth dimension-steps. The covalent bonds of hydrogens were not fixed. The van der Waals interactions were smoothly switched off at 10 Å (starting at 9.0 Å). Explicit solvent (water) was represented with the TIP3P model. Full electrostatics was implemented via particle mesh Ewald at the level of 128 × 128 × 128 for the BGLC transport problem.

Nosotros followed the standard protocol of the literature⁴¹⁻⁴³ to embed a membrane protein in a lipid bilayer, to cook lipid tails, and to equilibrate the system. In detail, we conducted 0.25 ns Physician run (afterward initial energy minimization) to cook the lipid tails during which the protein and the lipid heads were fixed. And then we ran 6.0 ns equilibration with protein constrained only. During these two equilibration runs, the water molecules (if they fall inside the membrane nigh the lipid tails) were pushed constantly into the aqueous spaces on the two sides of the membrane. Then we conducted 25 ns Dr. run with the α-carbons on the transmembrane helices constrained to fully equilibrate the system. Afterwards all these, we conducted 200 ns Md run without any constraints. All the afore-stated MD runs were nether constant temperature and constant pressure.

Steered Dr. Runs for PMF

We followed the multisectional protocol detailed in ref (44). Briefly, we divided the entire range of the membrane region from z = −28 Å to z = 32 Å into 60 evenly divided sections. We steered (pulled) the center-of-mass z-coordinate of BGLC for 10 ns at a speed of 0.one Å/ns beyond each of the sixty sections. Pulling BGLC from the bounden site (z = four Å) to the extracellular side (z ≥ 32 Å) with its x- and y-degrees of liberty being free (unconstrained), the path so sampled is nigh reversible and thus taken every bit the dissociation path because the protein remains in the exofacial open conformation during the entire procedure. (Reversibility was tested and confirmed over five sections from z = 4 Å to z = ix Å. From z = ix Å to the extracellular side, there is no hindrance in the way of BGLC being dissociated that may give rise to an irreversible contribution to the pulling path.) The total force on the BGLC center-of-mass past all other degrees of freedom of the entire system was recorded for computing the work needed to dissociate BGLC forth the dissociation path, which will be shown equally the PMF curve on the extracellular side.

From the binding site (z = iv Å) to the intracellular side (z ≤ −28 Å), the middle-of-mass z-caste of freedom of BGLC was steered for ten ns over i section for a z-deportation of −1.0 Å to sample a forward path over that section. At the end of each department, the z-coordinate of the BGLC middle-of-mass was fixed (or, technically, pulled at a speed of 0.0 Å/ns) while the system was equilibrated for 12 ns. From the end of the 12 ns equilibration, the z-coordinate of BGLC center-of-mass was pulled for 10 ns for a z-displacement of +1.0 Å to sample a reverse path. The total force on the z-caste of liberty of BGLC middle-of-mass was recorded along the forward and the reverse pulling paths for computing the PMF along the dissociation path from the binding site to the intracellular side. The PMF was approximated every bit the simple average betwixt the forward and the reverse paths. This part of the PMF computation is more hard than the extracellular side because BGLC has to move through the protein side chains as they thermally fluctuate.

Absolute Binding Free Free energy from PMF in 3nD

Following the standard literature (e.thou. ref (45)), one can chronicle the standard (accented) free energy of bounden to the PMF departure in threenorth dimensions (threenD) and the two partial partitions every bit follows:

4

Here c ₀ is the standard concentration of 1 M, g _B is the Boltzmann constant, T is the accented temperature, Z ₀ is the partial partition of the carbohydrate in the bound state which can be computed by sampling the fluctuations in 3n degrees of freedom of the sugar and invoking the Gaussian approximation for the fluctuations in the bound land,^46,47 and Z _∞ is the partial partitioning of the sugar in the unbound country for the iii(n – 1) degrees of freedom of the saccharide when 3 degrees of freedom are fixed so that the saccharide rotates and fluctuates in the aqueous bulk far away from the poly peptide. In this study, we cull north = 1 and use the center-of-mass coordinates of glucose to represent its position. The partial sectionalisation of the unbound state Z _∞ = i. The PMF is 3D, and Z ₀ contains the 3D fluctuations of glucose in the bound state. We fix the z-coordinate of six Cα atoms of GLUT3 near BGLC, each on a transmembrane helix, Ser21CA on TM1, Ser71CA on TM2, Val163CA on TM5, Val280CA on TM7, Gly312CA on TM8, and Glu378CA on TM10 (Figure ​ 1). The x- and y-coordinates of these vi Cα atoms are freely subject to the stochastic dynamics of the organization without any constraints. Therefore, the six transmembrane helices tin freely move in the lateral dimensions (in parallel to the prison cell membrane) and they can pivot around their centers.

It should be emphasized that eq 4 tin be applied from either the extracellular or the intracellular side to produce a unique value for the Gibbs free free energy of binding. It definitely indicates inaccuracy of a theoretical–computational study if the two sides give differing values for this equilibrium part of the state.

Hydration Energy from PMF in iiinorthwardD

The problem of hydrating glucose is just a trouble of bounden a glucose molecule to a large bulk of water. The bound state is when glucose is completely inside the water bulk and the unbound state is when it is in the vacuum far abroad from the water-vacuum interface. eq four can be easily adjusted into the following grade for the hydration energy:

5

Here Z ^aq and Z ^vac are the partial sectionalisation of glucose in the hydrated and in the dehydrated states, respectively. In this study, nosotros use due north = two for the hydration problem for computing efficiency. The C2 and C5 atoms are chosen every bit the 2 centers to stand for glucose'southward position and orientation. The PMF is in 6D and the partial sectionalisation of glucose is 3D involving rotation of one centre around the other center (two degrees of freedom) and the vibration between the 2 centers (one degree of freedom).⁴⁸

Acknowledgments

The authors thank Roberto Rodriguez for helpful discussions. The authors admit the calculating resources provided by the Texas Advanced Computing Center at Academy of Texas at Austin.

Glossary

Abbreviations

GLC	d-glucose, glucopyranose
CNS	central nervous system
Glut	human glucose transporter
MD	molecular dynamics
MFS	major facilitator superfamily
nD	n dimensions, n-dimensional
PMF	potential of mean forcefulness, chemical potential
XylE	E. coli xylose permease
XYP	xylose, xylopyranose

Supporting Information Bachelor

Five movies that are discussed but not included in the master context. . The Supporting Data is available free of charge on the ACS Publications website at DOI: 10.1021/acschemneuro.8b00223.

• Hydration of BGLC (AVI)

• Facilitated diffusion of BGLC through GLUT3 viewed from the extracellular side (AVI)

• Facilitated diffusion of BGLC through GLUT3 viewed from the intracellular side (AVI)

• Facilitated diffusion of BGLC through GLUT3 viewed from the membrane (AVI)

• Waters following BGLC forth its send path through GLUT3 (AVI)

• Two additional studies of d-glucose transport through GLUT3: one on α-d-glucose and one on β-d-glucose (PDF)

Writer Contributions

H.L. and A.Thousand.B. contributed as. G.P. initiated the research. L.Y.C. conducted the simulations and drafted the manuscript. All authors contributed to analyses and manuscript edits.

Notes

The authors acknowledge support from the NIH (Grant GM121275), San Antonio Life Sciences Establish (SALSI) Encephalon Wellness-Clusters in Inquiry Excellence, Semmes Foundation.

Notes

The authors declare no competing financial interest.

Supplementary Material

References

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Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6256350/

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