Comparative Study of High-Resolution LysB29(Nε-myristoyl) des(B30) Insulin Structures Display Novel Dynamic Causal Interrelations in Monomeric-Dimeric Motions

Abstract

The treatment of insulin-dependent diabetes mellitus is characterized by artificial supplementation of pancreatic β-cell ability to regulate sugar levels in the blood. Even though various insulin analogs are crucial for reasonable glycemic control, understanding the dynamic mechanism of the insulin analogs may help to improve the best-protracted insulin analog to assist people with type 1 diabetes (T1D) to live comfortably while maintaining tight glycemic control. Here, we present the high-resolution crystal structure of NN304, known as insulin detemir, to 1.7 Å resolution at cryogenic temperature. We computationally further investigated our crystal structure’s monomeric-dimeric conformation and dynamic profile by comparing it with a previously available detemir structure (PDB ID: 1XDA). Our structure (PDB ID: 8HGZ), obtained at elevated pH, provides electrostatically triggered minor movements in the equilibrium between alternate conformational substates compared to the previous structure, suggesting it might induce an intermediate state in the dissociation pathway of the insulin detemir’s hexamer:dihexamer equilibrium. Supplemented with orientational cross-correlation analysis by a Gaussian network model (GNM), this alternate oligomeric conformation offers the distinct cooperative motions originated by loose coupling of distant conformational substates of a protracted insulin analog that has not been previously observed.

1. Introduction

In recent years, the number of individuals with diabetes has increased at a higher rate in low- and middle-income countries than in high-income countries (WHO). Additionally, in 2019, diabetes was recorded as the ninth leading cause of death, considering a predicted 1.5 million deaths directly caused by diabetes (WHO). Pancreatic insulin delivery can be challenging to reproduce by subcutaneous injection [1]. Among individuals with both type 1 diabetes (T1D) and type 2 diabetes (T2D), the majority of the patients fail to manage glycemic targets, resulting in an increased risk of various complications [2]. The primary purpose of insulin therapy relies on the formulation of both long-acting and rapid-acting insulin analogs. Insulin therapy mimics the function of physiological insulin secretion levels to control endogenous hepatic glucose levels in the blood [3]. Recombinant insulin is a critical peptide hormone for treating insulin-dependent diabetes mellitus (DM) [3,4]. During the last decade, insulin preparations have been significantly modified to reduce the risk of health complications due to breakthroughs in the understanding of insulin structure and its complex aggregation properties [5]. The efficiency, efficacy, and simplicity of insulin analogs can facilitate the patient’s transition to insulin therapy [6,7] (Figure S1). Various insulin analogs provide advantages, consisting of greater convenience (Figure S1), improved physiologic profile, and a reduced risk of hypoglycemia [8]. It is of considerable importance that insulin analogs are long-acting, predictable, and have a flat pharmacodynamic profile to limit the risk of hypoglycemia in diabetic patients [8].

The active form of insulin circulates in the blood as a monomer protein, consisting of two polypeptide chains: an A chain of 21 amino acids and a B chain of 30 amino acids. Insulin is produced by pancreatic β-cells as a monomer and stored in a hexameric form. The hexameric form is generated by three insulin dimers, aggregating around two central zinc cations [7]. Various insulin analogs exist in the market, which have been genetically engineered, and formulations have been characterized by residual substitutions over the recombinant DNA technology [9]. Over the years, the commonly known strategy to produce a long-acting insulin variant is to formulate amorphous suspensions or crystalline insulin that provide a slowly dissolvable depot by subcutaneous injection [10].

The LysB29-tetradecanoyl, des-(B30) human insulin (NN304, insulin detemir), was introduced to the market with the brand name Levemir^® in the mid to late 1990s [11]. Detemir has been created as a neutral, soluble insulin preparation by covalently linking a hydrophobic myristate fatty acid chain to Lys 29 in chain B, which is not strictly essential for the activity of human insulin [11]. The unique mechanism of this covalently modified insulin analog relies on its reversible binding to human albumin through the fatty acid extension [6,11]. This albumin bound form of insulin serves as a reservoir that continually and slowly releases detemir insulin into the bloodstream and delays the hormone’s action [6,11,12] (Figure S2). Detemir has demonstrated greater efficacy and reproducible absorption rate compared to neutral protamine hagedorn (NPH) insulin and insulin glargine [13,14,15]. This is why detemir has had a favorable profile in clinical usage for over a decade.

Collections of studies have been conducted on detemir to understand its structure, function, and its interaction with serum albumin [12,16]. In this work, we present the high resolution detemir crystal structure determined to 1.7 Å resolution at the cryogenic temperature. Diffraction data were collected at the Turkish Light Source (AKA Turkish DeLight) [17]. Additionally, we employed a computational Gaussian network model (GNM) analysis that we aimed at investigating the differences of monomer:dimer equilibrium dynamics between our high-resolution cryogenic structure with previously published detemir structure (PDB ID: 1XDA). The crystallographic data presented here provide a distinct novel unit cell origin in asymmetric unit compared to the previously published detemir unit cell orientation [11]. GNM analysis performed on the high-resolution structure also displays a previously unobserved pattern of monomeric–dimeric-correlated motion of this long-acting insulin analog. Understanding monomer–dimer correlated motion of the detemir structure still remains to have immense importance in revealing the structural dynamics of the detemir and pharmacokinetics of this important hormone. This will pave the way for improving, modulating, and optimizing the protracted dissociation rate of the hexameric form of detemir into its active monomeric form.

2. Results

Throughout the analysis of the manuscript, the renumbered version of 8HGZ and 1XDA structures were used and uploaded as a Supplementary File (File S1) under the name Renumbered_8HGZ.pdb Renumbered_1XDA.pdb, respectively.

2.1. Crystal Structure of Novel Detemir Crystal Form

Insulin consists of two peptide chains, A and B, which are linked by two disulfide bonds, forming one “monomer.” When two monomers bind together noncovalently, it forms a dimer. Insulin is inactive and released in a hexamer form outside the cells. Once insulin dissociates into its monomer form, it becomes active and can properly bind to its receptor. Detemir insulin is structurally different from other insulin analogs because it contains two hexamers in its unit cell due to the presence of myristic acids [7]. As a result, detemir’s asymmetric unit is also different, and its monomer conformation refers to chains A and B together (or C and D, or E and F, or G and H). Each dimer in detemir refers to the pairs AB-CD and EF-GH.

In this study, the cryogenic detemir structure was determined to 1.7 Å resolution. Based on the RMSD value of each monomer, it contains four nearly identical monomer molecules, with RMSDs, ranging from 0.156 to 0.425 (Figure 1D) in the asymmetric unit cell, as well as four myristic acid residues, four phenol molecules, four zinc cations, four chloride anions, and 157 water molecules (Figure 1, Figures S3 and S4;

Table 1. Data collection and refinement statistics.

Dataset	Insulin Detemir
PDB ID	8HGZ
Data collection
Beamline	Turkish Light Source
Wavelength	1.5
Resolution range	21.64–1.7 (1.761–1.7)
Space group	R 3:H
Unit cell	78.885 78.885 79.272 90 90 120
Total reflections	110,176 (9012)
Unique reflections	20,225 (1834)
Multiplicity	5.4 (4.5)
Completeness (%)	96.94 (90.88)
I/σI	23.33 (3.28)
Wilson B-factor	16.70
Rmerge	0.05 (0.39)
CC1/2	0.99 (0.87)
CC *	1 (0.96)
Refinement
R-work	0.21 (0.26)
R-free	0.24 (0.28)
macromolecules	1601
ligands	103
solvent	188
Protein residues	200
RMS (bonds)	0.003
RMS (angles)	0.37
Ramachandran favored (%)	100.00
Ramachandran allowed (%)	0.00
Ramachandran outliers (%)	0.00
Rotamer outliers (%)	0.55
Average B-factor	25.64

Statistics for the highest-resolution shell are shown in parentheses.

).

Our dimer of dimer crystal structures at cryogenic temperature could not be superimposed with the dimer of dimer 1XDA structure due to the distinct crystal packing of the detemir in the asymmetric unit cells (Figure 2, Figures S5 and S6). Each disulfide bonded monomer chain is labeled as AB, CD, EF, and GH (Figure 1A,B and Figure S3A). Each monomer in dimer form of 8HGZ displays more plasticity/flexibility compared to the body/center of the whole structure in the ellipsoid representation, which is derived from TLS analysis on PyMOL (Figure S3). The 8HGZ structure also displays more negative charge distribution in the structure’s central region compared to its periphery (Figure S3C). Each monomer includes a 14-carbon fatty acid chain (myristic acid) covalently conjugated to the B29 Lys residue. The myristic acids engage in the crystal contacts among the neighboring dimers, radiating out the aliphatic side chains from the crystallographic axis toward the periphery (Figure S4). The crystal structure of 8HGZ and 1XDA exist in a “dimer of dimer” asymmetric form. When complemented and superposed to their hexamer forms, they display minor conformational changes due to their crystal packing difference. Furthermore, cross-correlation analysis, using GNM, supports the observation that the differences in biologically relevant structures between the two forms are significant.

2.2. Comparative GNM Analysis of Detemir in Two Different Crystal Forms

The GNM analysis is a minimalist coarse-grained method to reveal a protein’s dynamics [18]. Understanding the equilibrium fluctuations of the proteins is experimentally enabled by measuring the Debye-Waller/B-factor of each atom with X-ray crystallography [18]. Although the interpretation of crystallographic B-factors is complicated, they have represented the total of multiple sources of disorder, as well as various analytical perspectives for decomposing molecular disorder into a hierarchical cluster of contributions, which can also provide an intuitive principle for quantitative structural dynamics analysis [19]. Likewise, expected residue fluctuations can also be obtained by GNM in favorable agreement with experimentally measured fluctuations [18]. Thus, the relation between expected residue fluctuations obtained from GNM and thermal fluctuations/B-factors can be inspected in detail [18]. The fluctuation profile and the orientational cross correlations between pairs of nodes can also be obtained in agreement with experimental or adjustable parameters [18].

To investigate whether there are any differences in dynamics that arise from the differentiation of the unit cell in the asymmetric unit, the dimer of dimer form of the 1XDA and 8HGZ structures was analyzed in detail using GNM (Figure 3 and Figure 4). Orientational cross-correlations between residue motions have been inspected, and flexibility of the residues has been analyzed to describe the mean squared fluctuations. To investigate the communication in the residue networks, a cross-correlation map has been performed. In the cross-correlation heat-maps, blue-colored regions represent the uncorrelated motions, whereas red-colored regions represent the collective residue motions. Accordingly, AB-CD (1st dimer) and EF-GH (2nd dimer) have been observed as dimers with highly correlated motions in the 1XDA structure (Figure 3A). In stark contrast, dimeric positive correlation in the 8HGZ detemir structure cannot be observed thoroughly due to extroverted monomers of the 1st dimer packing in the asymmetric unit cell (Figure 4A). Accordingly, the 1st dimer of the 8HGZ structure (AB-CD) has a weak correlation within each other (Figure 4A, bottom; Figure 4B, top), while the 2nd dimer of the 8HGZ structure (EF-GH) shows relatively higher correlated motions compared to the first dimer (Figure S7A). In the 8HGZ crystal structure, residues between 1–40, 60–62, and 82–90 had at most 25% correlation (Figure 4A bottom; Figure 4B). In addition, interchain residues 60–64 had at most 25% correlation with residues between 100–150, and 150–180. However, the interchain residue cross-correlation map of the 1XDA structure indicated that residue 120 had ~25% correlation with residues 54–58 and residues 68–72, while residue 70 had ~25% correlation with residues 104–108 and residues 118–122 (Figure 3A bottom; Figure 3B).

On the other hand, the first monomer (AB) displays at least 75% intramolecular correlation, followed by the last monomer (GH), which indicates higher (at least 50%) intramolecular correlation compared to monomer CD (~50%) and monomer EF (50%) (Figure 4A). At a cut-off distance of 8 Å, a clear cross-correlation was observed in the GNM analysis of the 1XDA structure, with an overall correlation coefficient of 0.650 (shown in Figure 3C), while, in the GNM analysis of the 8HGZ structure, the correlation coefficient was 0.501 (shown in Figure 4C). Accordingly, contrary to the theoretical B-factor calculation, the experimental B-factor calculation is characterized by the highest fluctuation around 50th, 100th, 150th, and 200th residues in the 8HGZ crystal structure (Figure 4C).

However, the B-factor analysis of the 1XDA structure around the 100th residue demonstrates higher fluctuation than other regions (Figure 3C). Remarkably, critical residues among the 175–198 and 165–170 are highly correlated with the 130–148 region in dimer EF-GH (Figure S7A). Especially, His 131 and Leu 132 in EF monomer are highly correlated with His 176 and Leu 177 (Figure S7C), supplemented by normalized b-factor fluctuation. Accordingly, when comparing the intra- and inter-monomer residue motions of the 8HGZ structure, the AB monomer displays at least 75% intramolecular correlation, the highest correlated chain among the others (Figure S8A,B). Interestingly, the C-terminal residues between 49–50 in chain B are highly correlated with the critical residues 73, 76–77, 81–82, 85, and 92–98 in chain D (Figure S8C,D). Similarly, the C-terminal residues 99 and 100 in chain D are highly correlated with around critical residues 123, 126–127, 130–131, 134, and 145–148 in chain F (Figure S9A,B). Likewise, the C-terminal residues 149 and 150 in chain F are highly correlated with the critical residues 173, 176–177, 180–181, 184–185, 187–188, and 195–198 in chain H (Figure S9C,D), meaning the intramonomer’s correlation pattern is quite similar in each chain (Figures S8 and S9). Collectively, comparative cross-correlation analysis for intra- and inter-correlation motion in AB, CD, EF, and GH monomers of 1XDA and 8HGZ displays a similar correlated pattern; however, intra- and inter-molecular regions in 1XDA structure are highly and entirely correlated with each other compared to the corresponding regions in 8HGZ structure (Figure S10).

2.3. Radiation Damage Comparison of the 8HGZ Structure and 1XDA Structure

Radiation damage of two structures was calculated using the RABDAM program [20]. B damage values were performed using the total atomic isotropic B-factor values of determined atoms. The results are presented in kernel density plots in Figure S11. The highest B damage value of 2.05 was observed on the Asn 18 C atom (541) in chain C of the 1XDA structure, while, in the 8HGZ structure, the highest B damage value (3.11) was observed on the Glu 154 O atom (1312) (Figure S11).

3. Discussion

The insulin detemir is the first protein structure determined with an engineered fatty acid linkage/conjugation [11]. Even though lipid modification of the proteins occurs routinely in nature, engineering strategies assist in understanding novel possibilities in oligomeric interactions, providing an enabling biotechnological tool for practical applications in drug therapy [11]. While numerous insulin structures are studied in dimer form, the presence of the fatty acid chain in the insulin paves the way to inspect the insulin in two-dimer form [7,9,10]. This provides the understanding of the dynamic profile of the molecule from an oligomeric perspective. Thus, the assembly of subunits interacting through the covalent and noncovalent bonds defines their structure–function correlations [21]. Ideally, phenolic ligands and zinc atoms retain the hexameric form of insulin [22]. The rationale for the long-acting form of the insulin detemir is characterized by keeping the molecule in the dimer form of hexamers compared to other protracted insulins [22]. Thus, after injection of the detemir subcutaneously, phenolic ligands and fatty acid groups attached to insulin rapidly diffuse into the subcutaneous area, establishing the hexamer:dihexamer equilibrium [22]. The accumulated forms slowly dissociate into dimers and monomers, after which the myristic acid groups on insulin permit self-assembly, prolonging its action [11,22] (Figure S2).

The oligomeric state of insulin detemir may further contribute to the understanding of monomeric–dimeric correlated motion by demonstrating comparable properties to 1XDA structure. In this work, we examined the interaction and correlation of each monomer and dimer state of the oligomeric insulin detemir whose crystal structure determined in a novel crystal packing form in asymmetric unit cell (Figure 1, Figures S3 and S4; Table 1). Notice that the presented structure here has a distinct unit cell origin compared to the 1XDA structure (Figure 2 and Figure S5). In our structure, two dimers of the 1XDA indicate that each dimer has an introverted state (Figure 3B), while the 8HGZ have an extroverted dimer form in the unit cell (Figure 4B). Namely, the “dimer of dimer” form of 8HGZ displays minor differences due to the crystal packing form when complemented to its dihexamer form (Figure S6).

Accordingly, in GNM analysis, the second dimer of the presented structure has a higher correlation with each other compared to its first dimer (Figure S7 and Figure 4). Moreover, the C-terminal residues, Pro and Lys, in chains B, D, F, and H, displayed correlated motions with the critical regions in chains D, F, and H, respectively (Figure 5, Figures S8 and S9).

Interestingly, the first monomer of insulin shows at least 75% intramonomer correlation with almost all residues, followed by the last monomer of the insulin, which shows higher intramolecular correlation compared to the other chains (Figure 4A). At neutral pH, the detemir exists as a dimer of dimer form in the asymmetric unit [11]. The best estimated dissociation rate of an insulin dimer into two monomers in water is 0.4 μs⁻¹ [23]. Our best crystallization condition of the insulin detemir has occurred at pH 9. Considering that the dissociation of insulin occurs more effective at higher pH values (pH ≥ 8) and reaches the maximum by pH 10 [24], the minor distinct conformational arrangement of the presented structure’s critical residues compared to 1XDA structure might be related to the slow dissociation of the structure during crystallization. In a study conducted to observe the conformational changes of insulin crystals in the pH range of 7–11, we observed that the conformational changes were closely related to the pH value, which is compatible with our minor conformational changes in symmetry mates’ analysis obtained from 1XDA vs 8HGZ dihexamer form. [25]. Correlated motion of each subunit represented in Figure 5 may confirm the causal interrelationship of the oligomeric insulin’s dissociation (Figures S8 and S9). Additionally, comparative cross-correlation of 1XDA and 8HGZ structures has demonstrated that the 1XDA monomer-dimer correlation is entirely +75–100% rate (Figure S10). However, the corresponding regions in 8HGZ have indicated a weak correlation between monomers and dimers, suggesting a loosely coupled arrangement following the slow dissociation of the crystal structure occurred due to elevated pH value. Moreover, observing increased fluctuations in relevant Pro and Lys residues in normalized B-factors (Figure 4C) might confirm the cooperative motion originated from the alternative conformation of the oligomeric insulin (Figure 5). Ideally, insulin lispro has been introduced as a rapid-acting insulin analog, reversing the proline at position B28 and lysine at position B29 [26]. This substitution causes a conformational shift in the C terminal of the chain, inhibiting the ability of the insulin monomers to form dimers sterically [26]. Therefore, the dissociation constant of the dimer is reduced by 300-fold compared to regular insulin [26]. Previous studies suggest that proline has an inhibitory effect on the protein fibrillation process, promoting the retention of protein conformation [27,28]. Considering the cross-correlation of C-terminal residues with neighboring monomers (Figures S8 and S9), it could be argued that the detemir insulin demonstrates oligomeric cooperativity via the Pro and Lys residues (Pro 49, Lys 50; Pro 99, Lys 100; Pro 149, Lys 150). On the other hand, the C-terminal lysine provides a platform for covalent binding of the structure with the fatty acid, allowing for the long-acting profile of the insulin [11]. Together with the GNM results, these could mean that the dissociation of the oligomeric insulin begins with the Brownian motions and fluctuations of the myristic acid.

To determine and validate the accuracy of the monomeric-dimeric correlated motion of the protracted insulins, coarse-grained normal mode analysis offers a robust dynamic profile for future studies. Furthermore, when exposed to global radiation damage, diffraction patterns can be disrupted, causing an increase in both unit-cell volume and mosaicity. This increase in volume can result in non-isomorphism, which makes determining the structure more challenging. Therefore, considering the radiation damage of the 8HGZ structure compared to the 1XDA structure (Figure S11), the next step is to understand the details of this dynamic profile by a time-resolved ambient temperature radiation-damage free serial femtosecond X-ray (SFX) crystallographic studies supplemented with diffuse X-ray scattering.

4. Materials and Methods

4.1. Sample Preparation and Crystallization

The detemir sold as brand name Levemir^® was crystallized by employing sittingdrop microbatch vapor diffusion screening technique under oil using 72-well Terasaki crystallization plates, as explained by Ertem et al. 2022 [29]. Briefly, the detemir solution was mixed with (1:1 ratio, v/v) ~3500 commercially available sparse matrix crystallization screening conditions at ambient temperature for crystallization. Each well, containing 0.83 µL protein and crystallization condition, was sealed with 16.6 µL of paraffin oil (Cat#ZS.100510.5000, ZAG Kimya, Türkiye) and stored at room temperature until crystal harvesting. Terasaki plates were checked under a compound light microscope for crystal formation and growth. Large crystals were obtained within 48 h. The best crystals were grown in a buffer containing 0.2 M sodium acetate trihydrate, as well as 0.1 M TRIS hydrochloride pH 9.0.

4.2. Crystal Harvesting

The crystals were harvested from the Terasaki crystallization plates using MiTeGen and micro loop sample pins mounted to a magnetic wand under the compound light. microscope. The harvested crystals were immediately flash-frozen by plunging in the liquid nitrogen and placed in a previously cryo-cooled sample puck (Cat#M-CP-111-021, MiTeGen, Ithaca, NY, USA). The filled puck within the liquid nitrogen was transferred to the dewar of the Turkish DeLight for diffraction data collection [17].

4.3. Data collection and Processing

Diffraction data were collected by using Rigaku’s XtaLAB Synergy Flow XRD equipped with CrysAlisPro software (Agilent, 2014), as described by Atalay et al. 2022 [17]. Before the data collection, the system was cooled to 100 K by adjusting Oxford Cryosystems’s Cryostream 800 Plus. After that, the dewar was filled with liquid nitrogen, and a loaded sample puck was placed into the cryo sample storage dewar installed at the Turkish DeLight. The robotic auto sample changer (UR3) mounted the MiTeGen sample pin inside the sample storage dewar to the Intelligent Goniometer Head (IGH) by the six- axis robotic arm. The crystal was centered using the automatic centering feature of the CrysAlisPro software to the X-ray interaction position. For the data collection, the PhotonJet-R X-ray generator with Cu X-ray source was operated at full-power of 40 kV and 30 mA, and the beam intensity was set to 10% by using the piezo slit system to minimize the cross-fire and overlap of the Bragg’s reflections. The diffraction data, which contain 1800 frames in total, is collected to 1.7 Å resolution at a 45 mm detector distance, 0.2-degree scan width, and 1 s exposure time. The data were processed by the automatic data reduction feature of CrysAlisPro. When data reduction is completed, the output files, which contain both unmerged and unscaled files (*.rrpprof format), were converted to the structure factor file (*.mtz format) through the *.hkl file. This step is performed by integrating CCP4 crystallography suite [30] into CrysAlisPro software.

4.4. Structure Determination and Refinement

The high-resolution crystal structure of detemir is determined to 1.7 Å resolution at cryogenic temperature in space group R3:H. Molecular replacement is performed by using the automated molecular replacement program PHASER [31], implemented in PHENIX software package [32] by using the previous detemir X-ray crystal structure at cryogenic temperature as a search model [11] (PDB ID: 1XDA). Coordinates of the 1XDA were used for the initial rigid-body refinement with the PHENIX software package. After simulated-annealing refinement, individual coordinates and translation/libration/screw (TLS) parameters were refined. The potential positions of altered side chains and water molecules were checked in COOT [33], and positions with strong difference densities were retained. Missing water molecules were manually added, or water molecules located outside of significant electron density were removed. The Ramachandran statistics for detemir structure (most favored/additionally allowed/disallowed) are 100%/0.0%/0.0%, respectively. The structure refinement statistics are summarized in Table 1. All X-ray crystal structure figures were generated with PyMOL [34].

4.5. GNM Analysis

The 1XDA and 8HGZ structures were analyzed by normal mode analysis using ProDy [18]. Orientational cross-correlation map was defined with all Cα atoms of the proteins (residues 0–200). Myristic acids, phenols, zinc, and chloride atoms were excluded from the analysis. The cut-off distance of 8 Å was preferred in both structures to assume pairwise interactions, and the default spring constant was defined as 1.0 for both models. 1883 and 1673 atoms were parsed, and 198 non-zero modes were calculated with GNM for 8HGZ and 1XDA structures, respectively. The experimental B-factors were compared with the theoretical fluctuations calculated, as well as orientational cross-correlations between residue fluctuations, which were calculated over all GNM modes. The differences in cross-correlations between 8HGZ and 1XDA structures were calculated at determined sections. Accordingly, intra-chain cross-correlations of each monomer in 8HGZ were compared to the intra-chain cross-correlations of each chain in the 1XDA reference model; and the interchain cross-correlations between all chains were calculated similarly, presenting as heat-maps.

4.6. Normalization of B-Factor

B-factor normalization involves transforming experimental B-factors to define their distribution in terms of expected value and variance. This allows for comparing B-factors across different datasets while eliminating prominent influences that may skew the data. To carry out this normalization, the pdb library transfers the normalized data into a temporary record set, containing B’-factors per residue. The first algorithm for B-factor normalization was proposed by Karplus and Schulz, which related the experimental B-factor of a given residue to the arithmetic mean of all B-factors in a structure [35].

B’i = B_i − <B> + <B_all>

where B’i is the normalized B-factor of residue i, B_i is the experimental B-factor of residue i, <B> is the average B-factor for all residues in the structure, and <B_all> is the average B-factor for all atoms in the structure.

5. Conclusions

Here, we present the detemir insulin structure at 1.7 Å resolution, displaying distinct unit cell origin in the asymmetric unit. Considering comparative structural and computational analysis with 8HGZ and 1XDA structures, this study suggests that elevated pH can induce an intermediate state in the dissociation pathway of a protracted insulin analog. The distinct correlations, especially induced at Lys and Pro residues in the C-terminus of the B, D, F, and H chains, can offer a clue about the insulin detemir’s hexamer:dihexamer equilibrium. Coarse-grained normal-mode analysis to determine the accuracy of monomeric-dimeric correlated motion of long-acting insulins provides a robust dynamic profile for future studies.