Fig 1.
Main enzyme reactions involved in the synthesis and breakdown of glycogen.
In vivo, the GS and GBE enzymes synthesise glycogen, while the GP and GDE degrade it. Besides, GN is the initial precursor of the granule and stands in its core. Enzymes are noted in orange, glucose residues are in blue, and GN is highlighted with a yellow sphere.
Fig 2.
Geometrical description of glucose chains.
Left: Coarse-grained linear chain. Assuming helical chains, glucose units are described as interpenetrated spheres with radius ρ = 0.65 nm. Two consecutive glucoses are distant by l = 0.24 nm, which is the radial contribution to the chain length of one glucose in a helical structure. Right: Description of a branching point. We generate the direction of the new branch by randomly picking two angles φ and ψ. The first monomer of the new branch will be located at a distance greater than 2ρ to insure no overlapping between the mother and the daughter branches.
Fig 3.
Glycogen Synthase (GS) catalyses the elongation reaction. It needs a branch with a minimal DP as a substrate and a glucose unit to react. Glycogen Branching Enzyme (GBE) catalyses the branching reaction if the substrate’s DP is greater than the sum of 3 different minimal lengths.
Fig 4.
Illustration of the potential outcomes by GBE branching with .
With these minimal lengths, the minimal DP required for a branching to occur is DP = 7. If the chain length is longer, the number of possible outcomes increases. Left: With a substrate of DP = 7, only one outcome is possible. Right: With a substrate of DP = 9, up to 6 distinct outcomes are possible. Light grey represents the structure as it would be in case only one outcome would be possible, from a chain of DP equal 7.
Fig 5.
Simulated glycogen granule structures for different elongation to branching ratios (Γ).
50,000 glucose units are incorporated. Top: 3D structures of glycogen granules. Blue spheres represent the glucose units, green spheres the non-reducing ends. When Γ = 0.2, the structure of the granule is tightly packed. For Γ = 10.0, the structure of the granule is sparsely packed. Bottom: Associated chain length distributions. The light grey histogram shows the CLD for the tightly packed granule, while the black one shows that of the sparsely packed granule. The inset shows the full range of DP for Γ = 10.0. The longest chain is found to have a DP of 226.
Fig 6.
Dynamics of the occupancy profiles for a tightly (Γ = 0.2, Left) and sparsely (Γ = 10.0, Right) packed granule.
Occupancy as a function of the radius at different simulation times. Each line corresponds to an incorporation of N = 5,000 glucose units. The simulation stops at N = 50,000. The grey arrow highlights the two phases of the granule synthesis dynamics. In phase 1, steric hindrance constrains are low, allowing occupancy to increase. In phase 2, i.e. after incorporation of ca. N = 10,000 glucose units, the occupancy reaches a plateau and the granule expands.
Fig 7.
Effect of the minimal lengths of the branching mechanism on the CLD.
Top-left: CLD for , 4, and 6, respectively. When
increases, a multi-modal distribution emerges. Top-right: CLD for
, 4, and 6, respectively. When
increases, the peak is reduced and the overall distribution spreads towards higher DPs. Bottom-left: CLD for
, 4, and 6, respectively. When
increases, the distribution shifts towards higher DPs. Bottom-right: CLD for
, 4, and 6, respectively. Varying these distinct minimal lengths concomitantly, combines the individual effects described above, when a single length is varied. Each CLD is the result of averaging 200 simulations of granules with 5,000 glucose units each.
Fig 8.
Heat-maps showing fitting scores for various sets of parameter values.
The Y-axis shows ranging from 1 to 6. The X-axis shows the elongation to branching ratio Γ ranging from 0.1 to 5.0. A given cell corresponds to a set of parameter values {Γ,
,
,
, ρ}. Additional sets of parameter values are tested around good scores, i.e. the resolution on the elongation to branching ratio is increased, as well as the number of runs averaged. This area is surrounded by a red rectangle in which the average score is 12.26. Fitting scores are ranging from 8.6 to 249.1. The best score is 8.6 (red square in the inset heat-map) which corresponds to {Γ = 0.6,
,
, ρ = 0.65 nm}.
Fig 9.
Comparison of simulated versus experimental CLDs.
Experimental data are from Sullivan and coworkers [25] (black squares). In each simulation run 50,000 glucose units are incorporated in the growing granule (grey line). The average over 200 runs is represented as a red dotted line. Left: The CLD for the best fitting score () is obtained with {Γ = 0.6,
,
,
, ρ = 0.65 nm}. Our best fit almost perfectly captures the experimental CLD. Right: CLD using parameter values typically assumed in the literature {Γ = 0.6,
,
,
, ρ = 0.65 nm} [49, 50]. The simulated CLD differs a lot from the experimental one, with under-representation of small DPs, and over-representation of high ones.
Table 1.
Summary of the granule structural features and macroscopic characteristics.
Fig 10.
Two schematic branched structures with different A:B ratios.
For a “Haworth”-like structure, branching reactions tend to occur on A chains, leading to a low A:B ratio, while for a “Staudinger”-like structure, branching on B chains is favoured, leading to a high A:B ratio.