Computational and structural evidence for neurotransmitter-mediated modulation of the oligomeric states of human insulin in storage granules

Human insulin is a pivotal protein hormone controlling metabolism, growth, and aging and whose malfunctioning underlies diabetes, some cancers, and neurodegeneration. Despite its central position in human physiology, the in vivo oligomeric state and conformation of insulin in its storage granules in the pancreas are not known. In contrast, many in vitro structures of hexamers of this hormone are available and fall into three conformational states: T6, T3Rf3, and R6. As there is strong evidence for accumulation of neurotransmitters, such as serotonin and dopamine, in insulin storage granules in pancreatic β-cells, we probed by molecular dynamics (MD) and protein crystallography (PC) if these endogenous ligands affect and stabilize insulin oligomers. Parallel studies independently converged on the observation that serotonin binds well within the insulin hexamer (site I), stabilizing it in the T3R3 conformation. Both methods indicated serotonin binding on the hexamer surface (site III) as well. MD, but not PC, indicated that dopamine was also a good site III ligand. Some of the PC studies also included arginine, which may be abundant in insulin granules upon processing of pro-insulin, and stable T3R3 hexamers loaded with both serotonin and arginine were obtained. The MD and PC results were supported further by in solution spectroscopic studies with R-state-specific chromophore. Our results indicate that the T3R3 oligomer is a plausible insulin pancreatic storage form, resulting from its complex interplay with neurotransmitters, and pro-insulin processing products. These findings may have implications for clinical insulin formulations.

(i) Table S1. X-ray data collection and refinement statistics.

(iii) Partial charges for molecular dynamics simulation
In Table S2 and Figure S5, we provide the list partial atomic charges on the phenolic ligands.

Binding site I -the phenolic pocket
The binding free energy differences ΔΔG between phenol, dopamine, and serotonin were calculated using the thermodynamic integration method, combined with calculation of absolute free energy of binding of the phenol molecule using double annihilation method (1). Composition of the systems was as follows -one insulin R 6 (phenol) 5 hexamer, 9 000 SPC/E water molecules with Na + /Cl − ions added to ensure overall electroneutrality with no excess of salt, and one phenolic ligand (phenol, dopamine, or serotonin) inside the last free phenolic pocket. Differences in free energy of binding ΔΔG 1→2 between phenol (PHN), dopamine (DPN), and serotonin (SEN) were calculated. For these types of calculations, a complete thermodynamic cycle shown in Figure S6 was used (example calculation for ΔΔG PHN→SEN ).
In Figure S6, ΔG b1 represents free energy of binding of a ligand 1 to the insulin while ΔG d2 represents free energy of dissociation of a ligand 2 from the insulin. ΔΔG 1→2 reflects the difference in free energies of binding between these two ligands. As this is a complete thermodynamic cycle, this free energy equals to Each subsequent simulation was performed using linear scaling between the initial and final potentials with lambda windows 0, 0.1, up to 1.0, resulting in 11 windows. The only exception were simulations where the van der Waals parameters were changed with a lambda window of 0.05. All simulations were performed with a simulation step of 2 fs for a total simulation time 5 ns (at first) with preceding 1.2 ns equilibration. Altogether, a single calculation of binding free energy difference ΔΔG 1→2 consisted of 108 subsequent simulations. In order to be able to reasonably estimate an error in these calculations, every calculation was performed in both directions (forward and backwards mutations) and multiple times. This led to 6 separate mutations with the following differences in binding free energies ΔΔG PHN→DPN , ΔΔG DPN→PHN , ΔΔG PHN→SEN , ΔΔG SEN→PHN , ΔΔG DPN→SEN , and ΔΔG SEN→DPN .
To obtain the absolute free energy of a phenol molecule binding to a phenolic pocket ΔG PHN , a thermodynamic cycle shown in Figure S7 was used. The computational protocol was as follows. Each subsequent simulation was performed using linear scaling between the initial and final potentials. The equilibrium values were taken from a non-restrained molecular dynamics simulation. The process of calculating the free energy difference of restraining the phenol (using restraints proposed by Boresch (1))was broken into 12 windows. Each window was equilibrated for 2 ns and then the data were gathered for 5 ns. The second step was turning the electrical charges of the phenol in the binding pocket off (ΔG 8 ), while the restraints are on. This was done in 11 windows, each equilibrated for 2 ns, followed by 30 ns data acquisition. The next step involved full decoupling of the phenol while the proposed restrains stayed on and the electrical charged turned off (ΔG 9 ). This calculation was divided into 33 windows, each equilibrated for 2 ns, followed by 50 ns of data collection. The next step, the transition from the bound to the unbound state (bulk solution) has a zero free energy difference ΔG 10 = 0 as the ligand gets fully decoupled from its environment. The following step is releasing the restraints from the phenol (ΔG 11 ) with correction to a standard concentration of 1 M. After restraints got released, the only remaining steps are to turn on the van der Waals interactions (ΔG 12 ) and electrical charges of the phenol (ΔG 13 ) in the bulk solution. The van der Waals interactions were turned on in 21 windows, each equilibrated for 2 ns, and followed by 10 ns of data collection. The electrostatic interactions were turned on in 11 windows, each equilibrated for 2 ns, and followed by 10 ns of data collection.
Summing all the terms, we obtain the standard free energy difference of decoupling the phenol from the phenolic pocket ΔG PHN ΔG PHN = -(ΔG 7 + ΔG 8 + ΔG 9 + ΔG 11 + ΔG 12 + ΔG 13 ). SI.3 However, due to the symmetry of insulin R 6 hexamer, there is also an additional contribution to the free energy of binding. There are 6 equivalent binding sites for a phenol molecule. To account for this degeneracy entropy effect, the final free energy of binding has to be adjusted by a factor of ΔG symm_i = -RTln(i), SI.4 where the value of i depends on the number of the remaining free binding sites for the phenol molecule. For R 6 insulin hexamer without any phenol bound, i equals 6 hence the contribution is the highest. This number goes to zero as the phenolic pockets get fully occupied by phenol molecules. Table S3 summarizes the values ΔG symm_i . By combining the above two approaches with an average entropy value ‹ΔG symm › one gets the absolute standard free energies of binding of phenol, serotonin, and dopamine to a phenolic pocket of the insulin R 6 hexamer: ΔG°P HN = ΔG PHN + ‹ΔG symm ›, SI.5 ΔG°D PN = ΔG°P HN + ΔΔG PHN→DPN , SI.6 ΔG°S EN = ΔG°P HN + ΔΔG PHN→SEN . SI.7 Binding site III As the three equivalent binding sites III are located on the surface of the insulin hexamer, umbrella sampling turns out to be a suitable method for obtaining binding free energies. As a reaction coordinate, the distance from the center of mass of the insulin hexamer to center of mass of heavy atoms of the phenolic ligand was used. The calculations were performed using 21 evenly spaced windows. This was followed by production runs in each window of 50 ns (phenol), 80ns (dopamine), or 100 ns (serotonin). Free energy profiles were then constructed using the WHAM procedure As our reaction coordinate is expressed in spherical coordinates, one has to correct the results by a Jacobian factor of-RTln(4πr 2 ), where R is a molar gas constant, T stands for the thermodynamic temperature, and r is the distance used in each of the umbrella window. This correction is already accounted for in presented potentials of mean force W(r). Using a square well potential approximation the dissociation constant K d can be expressed as follows SI.8where V b stands for the volume occupied by the ligand when bound to the protein, and W 0 represents the depth of the potential well W 0 = W(r → r flat ) -W(r → r min ), SI.9where r min denotes minimum in the potential of the mean force calculated by the umbrella sampling, and r flat represents the distance where the potential gets flat (bulk solution). The dissociation constant K d in the context of simple protein-ligand binding is then related to the standard free energy of binding ΔG°b by ΔG°b = RTln(C° K d ), SI.10where C° stands here for a standard concentration. The inverse of the standard concentration can be interpreted as the volume V° occupied by a single molecule at standard concentration 1 M. Finally, Table S4 presents entropy corrections to the free energy of binding of phenolic ligand to binding site III because of the symmetry of the insulin hexamer with three equivalent binding sites. The resulting standard free energy of binding ΔG°b,which is calculated by the umbrella sampling method and corrected for symmetry, is then given as ΔG°b = W 0 + RTln(V b /V 0 ) + ‹ΔG symm ›, SI.11 (v) Table S2. List of partial atomic charges of phenolic ligands used in this work. Charges were calculated by a standard HF/6-31G* method in vacuum using RESP method.
(vi) Table S3. Entropy contribution to the free energy of binding of a phenol to the phenolic pockets according to how many phenolic pockets are unoccupied (ΔG symm_i ). (vii) Table S4. Entropy contribution to the free energy of binding of a phenolic ligand to binding site III according to how many pockets are unoccupied (ΔG symm_i ).
-0.65 -0.41 0.00 -0.36 3 2 1 (viii) Figure S1. Electrostatic surface representation of the main forms of insulin hexamers (top views as in Figure 1). The increasing structural occlusion of the Zn-neighborhood sphere in the TR transition is shown.
(x) Figure S3. An example of the FWPHWT electron density map (blue mesh) for the serotonin in site I, contoured at 1σ level. Labelling as for Figure 8 (top).
(xi) Figure S4. An example of the FWPHWT electron density map (blue mesh) for the arginine binding sites in insulin InsSerArgT 3 R 3 hexamer, contoured at 1σ level. Labelling as for Figure 10. Some interactions showed in Figure 10 are omitted for image clarity.
(xiii) Figure S6. A practical example of a complete thermodynamic cycle used to calculate the differences in the free energies of binding ΔΔG 1→2 between different phenolic ligands to phenolic pocket of insulin R 6 hexamer. A thermodynamic cycle to calculate ΔΔG PHN→SEN is shown here. The restraints are indicated by a red circle; the grey ligand indicates that the electrostatic interactions of a ligand are turned off. ΔG b1 represents free energy of binding of phenol to the phenolic pocket whereas ΔG d2 represents free energy of dissociation of serotonin from the phenolic pocket. ΔG ro represents free energy of restraining phenol to a certain position inside the phenolic pocket. ΔG 1 represents gradual turning off electrical charges of phenol inside the phenolic pocket while keeping proposed restraints on. ΔG 2 represents mutation of a restrained phenol to a restrained serotonin inside the phenolic pocket while all charges are turned off. ΔG 3 represents free energy of turning on the electrical charges of the serotonin while the restrains are on. ΔG roff represents free energy of releasing restraints on the serotonin inside the phenolic pocket. ΔG 4 stands for free energy of turning off electrical charges of the serotonin in the bulk solution. ΔG 5 represents free energy of mutating serotonin to phenol while all electrical charges are off in the bulk solution. ΔG 6 represents free energy of turning on electrical charges of phenol in the bulk solution.
(xiv) Figure S7. A complete thermodynamic cycle used to calculate the absolute free energy of binding of a phenol molecule to a phenolic pocket of insulin R 6 hexamer ΔG PHN . The restraints are depicted by a red circle; grey ligand means that the electrostatic interactions are turned off; fully transparent ligand means that the ligand is fully decoupled from its environment. ΔG 7 represents free energy of restraining phenol to a certain position inside the phenolic pocket. ΔG 8 represents free energy of turning off electrical charges of phenol inside the phenolic pocket while keeping the proposed restraints on. ΔG 9 stands for the free energy of decoupling restrained phenol from the phenolic pocket while all charges stay turned off. ΔG 10 stands for the free energy of transferring decoupled phenol from phenolic pocked to the bulk water environment. As the phenol does not interact with the protein at all, the energy of bound and unbound phenol is the same. Hence the free energy difference between these two states is zero. ΔG 11 represents free energy of releasing the proposed restrains from phenol, which is now situated in the bulk solution. ΔG 12 represents the free energy of turning on the van der Waals interactions of phenol in the bulk solution. ΔG 13 stands for the free energy of turning on electrical charges of phenol in the bulk solution.