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Automated Transformation of Lignin Topologies into Atomic Structures with LigninBuilder Josh V. Vermaas, Lauren Dellon, Linda J. Broadbelt, Gregg T Beckham, and Michael F. Crowley ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.8b05665 • Publication Date (Web): 11 Dec 2018 Downloaded from http://pubs.acs.org on December 18, 2018

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ACS Sustainable Chemistry & Engineering

Automated Transformation of Lignin Topologies into Atomic Structures with LigninBuilder Josh V. Vermaas,† Lauren D. Dellon,‡ Linda J. Broadbelt,‡ Gregg T. Beckham,∗,¶ and Michael F. Crowley∗,† †Biosciences Center, National Renewable Energy Laboratory, Golden, CO 80401 ‡Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208 ¶National Bioenergy Center, National Renewable Energy Laboratory, Golden, CO 80401 E-mail: [email protected]; [email protected]

Abstract Lignin is an abundant aromatic heteropolymer found in secondary plant cell walls, and is a potential feedstock for conversion into bio-derived fuels and chemicals. Lignin chemical diversity complicates traditional structural studies, and so relatively little experimental evidence exists for how lignin structure exists in aqueous solution, or how lignin polymers respond to changes in their chemical environment. Molecular modeling can address these concerns; however, prior computational structural lignin models typically did not capture lignin heterogeneity, as only a few polymers were considered. LigninBuilder creates a framework for building structural libraries for lignin from existing topological libraries, permitting significantly greater diversity of lignin structures to be sampled at atomic detail. As a demonstration of its capabilities, LigninBuilder was applied to three libraries of lignin from hardwood, softwood, and grass, and the resulting polymer structures were simulated in an aqueous environment.

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The lignins adopted compact globular structures, as would be expected for polymers in poor solvents. The differences between the libraries were largest when quantifying the packing of non-adjacent aromatic residues, with greater branching within the polymer resulting in poorer aromatic packing. Individual lignin polymers were also found to undergo rapid conformational changes, with the dwell time within a state growing as the square of the molecular weight. This first application of LigninBuilder demonstrates the potential for atomic-level insight into lignin interactions. LigninBuilder is distributed as a plugin to the visualization software VMD, lowering the barrier for modeling lignin structure in diverse environments.

Keywords: Lignin modeling ; Atomic structure ; Polymer power laws ; Molecular dyanmics

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Introduction Lignin is an abundant biopolymer found in plant secondary cell walls, 1 whose natural function is to provide structural integrity for terrestrial plants responding to mechanical, 2,3 osmotic, 4 and pathogenic 5,6 stressors. Approximately 50 megatons of lignin pass through pulp and paper mills annually, 7 the vast majority of which is burned for power. 8 This represents only a small fraction of the estimated 20 gigatons of lignin produced in the biosphere annually. The aromatic nature of lignin units offers a unique opportunity, since some high value aromatic-derived industrial products, such as muconate or commercial adhesives, have direct biosynthetic routes 9,10 that may be cost-competitive with traditional petrochemical processes. 11 Due to its abundance and synthetic possibilities, lignin has great potential as an industrial feedstock. 8,12,13 For all of its promise, lignin remains a challenge to effectively valorize within industrial processes. 8,12,13 Lignin synthesis is thought to proceed stochastically via radical coupling chemistry. 14–16 Consequently, natural lignin is highly heterogeneous, 17–19 with sample species, 20,21 growth environment, 22,23 and plant tissue type 24,25 all influencing lignin composition and structure. To mitigate the heterogeneity of the feedstock, current valorization approaches fragment native lignin polymers. 26 Compositional heterogeneity frustrates experimental characterization of interactions between both intact and fragmented lignin polymers with other biopolymers. Computational approaches to complement available structural data have yielded insights with respect to lignin interaction with its immediate biological environment, 27,28 its thermal degradation, 29–32 or chemical modification 33–35 and solvation. 36,37 However, these simulations often use a homogeneous lignin polymer, which is not representative of heterogeneous lignin synthesis products that demonstrate wide variation in size and composition. 24,38 To model this morphological diversity, recent work has developed lignin topological libraries that emulate the distributions of sizes and linkages seen in isolated lignin populations. 20,21 With the topological libraries as a foundation, in this study we develop LigninBuilder, a 3



framework for transforming these topological libraries into three-dimensional atomic models suitable for use as simulation inputs. LigninBuilder can read the previously developed topological libraries 20,21 and arrange the individual monomers to form an unoptimized lignin scaffold for each polymer present in the library. The library scaffolds are then refined through molecular simulation to eliminate steric clashes or ring piercing artifacts introduced in scaffold construction. LigninBuilder is accessible as a plugin to the widely-used molecular dynamics (MD) visualization software VMD, 39 with the current version of the plugin provided both here as well as maintained on GitHub.∗ As an example of how LigninBuilder may be used, we build lignin models from the spruce, birch, and miscanthus lignin libraries 21 and subsequently perform simulation with these models using the recently updated lignin force field. 40 The simulation of these isolated lignin polymers in aqueous solution yields results consistent with a polymer in a poor solvent, in line with experimental studies. 41 The trend between the radius of gyration (Rgyr ), solvent accessible surface area (SASA), and microkinetic transition measurements follow established polymer physics models 42–44 as well as prior simulation results for lignin. 36,45,46 The advance LigninBuilder provides is the ability to sample population-level differences in structure. One such advance is correlating the differences in branching between lignin polymers and their packing, with greater branching of the polymer leading to poorer packing of aromatic groups. This initial application is only the first example of how LigninBuilder can be used to probe nanoscale lignin structure and dynamics.

Methods The LigninBuilder Process and Algorithm Assembling molecular structures for biopolymers requires defining the connectivity of individual atoms and their position. For other biopolymers, such as proteins or DNA, the ∗

https://github.com/jvermaas/LigninBuilder

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atomic positions can be directly informed by experimental structures, with missing elements (eg., hydrogen atoms or missing loops) filled in via subsequent modeling. For lignin, structural information is very sparse, and so the position of all atoms must be modeled prior to simulation. The basic algorithm for LigninBuilder is to define molecular connectivity based on the input lignin library provided by the user, and then guess a plausible molecular configuration using optimized lignin fragment configurations determined previously. The resulting lignin polymers are then optimized such that ring piercings and atomic clashes are corrected through simulation. Each of these steps will be described in greater detail below to highlight how the LigninBuilder plugin is implemented, along with basic usage instructions. The first step in the process is to obtain or build an input lignin library, named for example purposes here “library.txt”. In this work, input lignin libraries were obtained from Dellon et al. 21 , though users can manufacture any lignin library using the example libraries in the Supporting Information as a guide. Any library file must adhere to this template for LigninBuilder to successfully generate plausible three-dimensional configurations for each lignin molecule. Table 1: Monomer, bond, and position codes that specify lignin topology in a way readable by LigninBuilder. Monomer codes specify the identity of each monomer. Bond codes specify the type of linkage, and the corresponding position code specifies the heavy atom on the first specified monomer the linkage is attached to. For an enumeration of the linkage codes created through this table, see Table S1. Monomer Codes Bond Codes Code # Monomer Code # Bond

Position Codes Code # Position

1 2 3

1 2 3 4 5

S H G

1 2 3 4 5 6 7

β-O-4 β-5 5-5 4-O-5 β-1 α-O-4 β-β

Cβ O4 C5 Cα C1

The process by which LigninBuilder reads and parses “library.txt” is detailed below. 5



Each individual lignin molecule is indicated using several asterisks. LigninBuilder searches for the character sequence “***” to begin the process of reading in a single lignin molecule. Next, three lines, which list the molecular weight, branching coefficient, and distance metric, are skipped, as these are values that are not needed for lignin construction but were provided in existing lignin libraries. Note that these three lines can simply be blank, but can also be used for notes to the user. The next line lists the number of monomers and bonds in the following order: syringyl (S), p-hydroxyphenyl (P), guaiacyl (G), a double dash, β-O-4, β-5, 5-5, 4-O-5, β-1, α-O-4/β-O-4, and β-β. The sum of the monomers and the sum of the bonds are used to notify the LigninBuilder how many monomers and how many bonds will be in the monomer list and the bond list, respectively. Following this step, the monomer list is read by the LigninBuilder, with each line containing an integer residue identifier and the monomer code specifying the identity of the monomer. The monomer codes can be found in Table 1. Similarly, the bond list is parsed to store the linkages between the lignin monomer pairs. The bond and position codes are be found in Table 1, and are used in the specification of linkages. Each linkage is specified by 4 elements, the first two being the residue identifiers used in the linkage, followed by the position code, and finally the bond code for the linkage. The bond and position codes are single values representing each type of bond and position on the first monomer where the patch is applied, respectively. Together, the position and bond codes form a linkage code (see Table S1 for linkage codes used in the demonstration libraries), which encodes both the type and orientation of the linkage between two specified residues. This linkage code arrangement allows the direction of the linkage to be doubly specified; the bond list specification “1 4 1 1”, which applies the β-O-4 from Cβ of monomer 1 to the O4 of monomer 4, is functionally equivalent to “4 1 2 1”, which applies the β-O-4 linkage between the same two atoms. The parsing process described above is repeated for all lignin molecules in the library. It is important to note that the LigninBuilder does not recognize impossible chemistries, and will not warn the user if an incorrect topology is present unless it causes a non-integer

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charge on the overall polymer. Thus, it is recommended to follow the template provided to minimize errors, as well as visually inspect the output structures generated when developing new lignin libraries. After input parsing, the lignin topologies are assembled using psfgen to convert the original library into a format suitable for simulation. This is done systematically by first creating the specified monomers, and subsequently linking these monomers together by applying the appropriate patches to the structure. Once all linkages are applied, the structure is checked to identify hydroxyls at the α and β carbon positions. If a monomer has hydroxyl groups at both positions, that monomer is converted to the corresponding monolignol. At this stage, no coordinates have yet been assigned to individual atoms. Initial coordinates for each monomer are drawn randomly from the four possible stereoisomers for each fully hydroxylated monomer from optimized structures originally used for lignin force field parameterization. 40 To determine the correct relative orientation of the monomers, each individual linkage is algorithmically inspected to partition the polymer into “mobile” and “stationary” fragments based on which lignin fragment would be larger if the linkage were not present. The mobile fragment is then moved such that the aromatic rings of the two linked residues superimpose onto optimized dimeric template structures determined during parameterization of the lignin force field. 40 Atoms between the aromatic rings of the linked monomers are then moved to their respective positions in the template structure, which was drawn randomly from applicable stereoisomers. After all linkages are analyzed, remaining residues that are hydroxylated at both the α and β carbons are reduced to a trans alkene, which is thought to be more prevalent in natural lignins. The result of this procedure is a plausible (though likely high energy) configuration for the lignin polymer (Fig. 1), which may also contain structural artifacts that must be remedied. The chief concern is that there may be unphysical ring penetrations within the lignin structure, where a moiety is placed in such a way that a bond crosses an aromatic ring. Unlike many structural artifacts, pierced rings represent a local minimum in a MD potential,

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Figure 1: Example of a lignin structure after initial construction. In this representation, all atoms of the lignin polymer are shown (white for hydrogen, gray for carbon, red for oxygen), with linkages between atoms explicitly drawn. In a compatible pdf viewer, an animation shows the progress of the stepwise linkage placement algorithm. This animation is also included in the Supporting Information.

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and thus are not solved by simple minimization. Instead, we follow an algorithmic way of eliminating pierced rings through simulation through biasing the system away from this pierced state. In the first step, unbiased minimization occurs using NAMD 47 for 500 steps. If no bonds are found to be stretched to a length greater than 1.65 ˚ A, a symptom of a pierced ring, we know we have good starting point for simulation. However, if a bond is stretched, two complementary approaches are used to ameliorate the pierced ring. First, nearby residues are marked to be pushed away from the overlap point, using VMD 39 to generate a volumetric grid and the gridForce feature of NAMD 47 to apply the grid to the polymer, just as in the MD flexible fitting method. 48 Secondly, to reduce the barrier to moving the pierced atoms across the ring, the alchemical module of NAMD 47 is turned on to decouple the atoms with long bonds from the remainder of the system, analogous to procedures used in theromodynamic integration calculations. Minimization is then repeated for 500 steps and the selection for gridForces and alchemy are repeated until no long bonds remain. Unbiased minimization is then performed again for 500 steps. If long bonds persist, the loop starts again; however, within 20 iterations of this cycle all 300 lignin topologies present in the lignin libraries tested were minimized successfully. The implementation details can be found in the code of the plugin distributed via GitHub† , as well as a current version of the code provided as Supporting Information. However, the workflow we envision for a typical user would be to install LigninBuilder as a VMD 39 plugin (instructions provided on GitHub as well as in Supporting Information), and to use LigninBuilder via scripts such as the following: package require l i g n i n b u i l d e r : : l i g n i n b u i l d e r : : b u i l d f r o m l i b r a r y l i b r a r y . t x t Example : : l i g n i n b u i l d e r : : m i n i m i z e s t r u c t u r e s Example namd2 ‘ ‘+ p8 ’ ’ The “buildfromlibrary” command would build all the lignin polymers contained in the library.txt file into a directory called “Example” and generate unoptimized structures. The †

https://github.com/jvermaas/LigninBuilder

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“minimizestructures” command would then take the lignin polymers found in the “Example” directory and run the binary namd2 with the option “+p8” (so that it uses 8 processors rather than 1) to eliminate ring piercings, overwriting the original structures present in the directory. By distributing LigninBuilder as a plugin within widely used software such as VMD, 39 it facilitates integration into existing simulation preparation workflows. In addition to the main LigninBuilder plugin, an additional python tool script is available via GitHub to generate parameters for chemistries that were not explicitly parameterized previously, due to their appearance only when specific linkages appear next to one another (e.g. a 5-5 and β-O-4 linkage on the same residue). The “findmissingterms.py” script within the SMILES string demonstration project analyzes loaded molecules for their required parameters, and fills in missing parameters based on the Hamming distance (also called the edit distance) to existing parameters. The output of this process when applied to the 300 lignins tested here is provided via the “extraterms-par lignin.prm” file. The demonstration also includes a prototype process for converting SMILES strings of arbitrary lignin polymers into structures through a process similar to that described above. We cannot guarantee that this process is error free for any potential lignin inputs due to the limited testing performed on synthetic lignins.

Simulation of Isolated Lignin Polymers in Water Table 2: Reduced table of library properties of the three libraries from Dellon et al. 21 used here to generate lignin structure, indicating the exact number of residues contained within each library, as well as their average sizes and branching propensities. Property

Birch Spruce Miscanthus

Number of G-lignin monomers Number of H-lignin monomers Number of S-lignin monomers Mean mass (number weighted, kDa) Mean mass (mass weighted, kDa) Branching coefficient

471 0 468 1.88 4.45 0.055

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3343 175 36 6.44 23.63 0.301

282 24 306 1.24 2.32 0.000

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1.0

Cumulative Probability

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0.8

0.6

0.4

Spruce Birch Miscanthus

0.2

0.0

100

101 Molecular Weight (kDa)

Figure 2: Size distribution of the lignin polymers found in the disparate libraries. Solid lines indicate the probability when normalized based on the number of molecules (mol percent), and dashed lines indicate the probability when normalized based on polymer mass (weight percent).

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Using LigninBuilder, it is now possible to simulate lignin polymers that represents the structural diversity of native lignins. As an example of this, we used LigninBuilder to construct each of the 100 lignins present in the birch, spruce, and miscanthus topological libraries generated by Dellon et al. 21 Basic properties of these libraries are provided in Table 2, with the size distributions provided in Fig. 2. The generated structures are solvated using the solvate plugin of VMD 39 with 17 ˚ A of padding around the extent of each lignin polymer, which is resized into a cubic box for simulation. Due to the varying sizes of the lignin polymers, ranging from 0.4–40 kDa, the simulation systems themselves ranged from 10,000–200,000 atoms when built. Our simulation process occurs in two steps, both using the newly developed lignin forcefield for CHARMM 40 together with TIP3 water as the system parameters. Each of the 300 lignins was first equilibrated for 20 ns in a constant pressure and temperature ensemble using NAMD 2.12. 47 Pressure was controlled using the Langevin piston method 49,50 to a pressure of 1 atm. Temperature was controlled using a Langevin thermostat with a damping constant of 1 ps−1 and set to 300 K. The SETTLE algorithm 51 was used to fix bond lengths to hydrogen, permitting 2 fs timesteps. Short range nonbonded contributions from the force field used a 12 ˚ A cutoff. Long-range electrostatic interactions were treated using particle mesh Ewald 52,53 (PME) with a 1.2 ˚ A grid. After equilibration, the end state was converted using TopoGromacs 54 for the remaining 200 ns of production simulation using GROMACS 2016 55,56 in a constant volume and temperature ensemble to take advantage of the improved performance on the available computing infrastructure. As above, a 12 ˚ A cutoff was used for short range electrostatics and van der Waals terms, with PME 52,53 setup to use an identical 1.2 ˚ A grid spacing. P-LINCS 57 was used to enable 2 fs timesteps. Temperature was maintained at 300 K using a Nosè-Hoover thermostat 58 during production. The aggregate 60 µs of simulation was analyzed using a python-enabled build of VMD 1.9.3, 39 interfacing with the numpy 59 and scipy libraries where appropriate. Plots were

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generated using Matplotlib. 60 Specifically, we were focused on the relationships between lignin size and structural observables such as the radius of gyration (Rgyr ), solvent accessible surface area, and conformational residence times. Within the (bio)polymer physics literature, these observables are typically related through a power law, first modeled based on polymer viscosity observations from the 1940s. 44,61

O = AM b

(1)

The generic power law described in Eq. 1 is used to fit the relationships between structural observables O, such as Rgyr , internal hydrogen bonds, and SASA, and the molecular weight M for individual lignin polymers. The fitting parameters A and particularly b have meaning when interfaced with polymer theory, and is discussed further within the Results and Discussion section. To cluster lignin conformations along a trajectory into individual states, we used pairwise RMSD as an input metric to a hierarchical clustering algorithm. Specifically, we used the “complete” linkage, as described in M¨ ullner 62 , such that the distance between clusters was the square of the maximum pairwise RMSD between any two members of each cluster. Clusters were then assigned based on the distance metric with a cutoff of half the maximum distance. Since RMSD grows naturally with polymer size, a fixed RMSD cutoff was found to be inappropriate. Once clusters are identified, the mean residence time within a cluster is determined by identifying transitions between clusters. Other distance metrics (such as just the maximum pairwise RMSD rather than the square) and clustering cutoffs were tried, and did not significantly change the “b” parameter when fitting the mean residence times against molecular weight.

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Results & Discussion Following the method development required to construct the lignin polymers, we analyze simulation trajectories of isolated lignin polymers within the aqueous environment used as a baseline for comparison with future studies. Largely, the results follow predictions previously established in polymer physics literature, both in population level structural metrics such as Rgyr , as well as microkinetics. These results generally provide confidence in the recently developed lignin force field and the LigninBuilder translation of lignin topologies into real structures.

Practical Equilibration of LigninBuilder Structures The value of constructing these lignin models is their ability to probe their structure and dynamics through simulation at spatial and temporal resolutions that are otherwise difficult to access. These lignin models can be used in variable solvents, temperatures, and other environmental variables to explore lignin. However, during polymer construction using LigninBuilder, none of these variables were considered. This suggests that relatively extended conformations such as those shown in Fig. 1 are unlikely to represent native lignin structure. Thus, simulations are required to equilibrate the systems into native-like configurations in response to their environment. It is unknown a priori how the non-optimized lignin polymers generated by LigninBuilder should be equilibrated prior to extended simulation, and would be expected to depend on solvent, temperature, and the initial configuration of the lignin. One way to assess equilibration is to track observables such as the Rgyr , SASA, and intramolecular hydrogen bonding. When placed in aqueous solution, the Rgyr and SASA of lignin polymers decreases as the lignin compacts, resulting in additional internal hydrogen bonds within the polymer (Fig. 3). The required timescale for these quantities to arrive at an equilibrium value increases with polymer size, as large polymers with molecular weights greater than ∼10 kDa demonstrate

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10.7 kDa Miscanthus lignin

300

30

80

260

60

240 220

40

SASA (nm2)

280

200

90

25

80

20

70

15

60

20 0

50

100 Time (ns)

150

200

SASA (nm2)

45.3 kDa Spruce lignin 100 Rgyr (˚ A) and H-bonds

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Rgyr (˚ A) and H-bonds

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0

50

100 Time (ns)

150

200

Figure 3: Radius of gyration (Rgyr , black), internal hydrogen bonds (blue), and Solvent accessible surface area (SASA, red) for two example lignin polymers. One is the 57th lignin polymer in the spruce library (left), which is 45.3 kDa, representing the largest lignin in any of the libraries. The other is the 29th lignin polymer in the miscanthus library (right), which is 10.7 kDa, representing an intermediate sized lignin that still rapidly equilibrates. The grey background prior to time zero highlights the trend during the first 20 ns of simulation conducted in NAMD, prior to the 200 ns of simulation performed in GROMACS. Rgyr , SASA, and internal hydrogen bonds were all computed using VMD, 39 with the internal hydrogen bond metric using cutoffs of 3.2 ˚ A and 30◦ to define the heavy atom distance and the linearity of the interactions. Similar plots for all 300 lignins are provided in the Supporting Information, sorted by molecular weight, as Figures S1–S300. The example polymers specifically are Figures S1 and S18.

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continued compaction beyond 20 ns (Figs. S1–S17), with eventual equilibration in another 30-40 ns (Fig. 3, left). However, for the great majority of lignin polymers tested (Figs. S18– S300), the polymers collapse quickly, reaching equilibrium within the 20 ns simulation performed to determine the periodic cell size. Thus, for individual small lignin polymers, 20 ns is sufficient equilibration time, and is recommended prior to analysis. For unpolluted statistical averages of the low-energy structural ensembles of larger collapsed lignin polymers, more equilibration time is needed. For this reason, we will only take averages from the last 100 ns of simulation in computing population averages.

Population-Level Lignin Behavior in Extended Simulation Spruce Birch Miscanthus

25 20 Rgyr (˚ A)

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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12

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10 10

8 6

5

4 0

0

10

0 1 20 30 Mass (kDa)

2

3

4

40

Figure 4: Relationship between Rgyr and the molecular weight of the lignin polymer. The mean Rgyr over the last 100 ns of trajectory is marked by circles, while the standard deviation of the Rgyr over the same timeframe is used to convey the range observed in each simulation. Each library is analyzed separately and fit to a power law fitting Eq. 1 reported in Table 3, and is indicated as the colored line. To better discriminate between points at low molecular weights, the subplot in the lower right focuses on this region. The advantage of simulating an ensemble of lignin structures is the ability to develop statistically robust models for structure observables and their scaling with respect to lignin size. A commonly measured observable for lignin polymers is the Rgyr , which describes the extent of the lignin polymer, and can be determined via multi-angle laser light scattering, 63 16


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X-ray 64 or neutron scattering 36 experiments. On its own, a single Rgyr trace is not particularly informative, as there is considerable variation within and across trajectories (Fig. 3). However, when compared with the Rgyr in other polymers (Fig. 4), the results all follow the same trend. Table 3: Power law (Eq. 1) parameters for the relationship between Rgyr and molecular weight, shown as the trendlines in Fig. 4. Parameter A (˚ AkDa−1 ) b

Spruce Birch Miscanthus 6.085 0.361

6.226 0.352

6.670 0.311

Rgyr is strongly sensitive to polymer molecular weight, but only weakly sensitive to lignin source, with all three lignin libraries overlaying Rgyr at low molecular weight. When the libraries are treated independently, we see that the fit parameters (Table. 3) are all relatively similar. Of particular note is the scaling parameter “b”, which is ≈ 13 , reflective of a poor solvent in polymer theory, 42 and noted previously for lignin polymers. 36,45,46 Water has long been known to be a poor solvent for lignin, 41 so this is the expected result. As a point of comparison, folded proteins in water have a scaling parameter of approximately 0.4, 65–67 and intrinsically disordered proteins have an even higher scaling parameter of 0.46±0.05 in aqueous solution, 68 implying that lignin is aqueous solution is more globular and solventavoiding than a globular protein. However, the greater the degree of branching within the lignin (spruce > birch > miscanthus, Table 2), the larger the “b” parameter in the fit, indicating somewhat better solvation for these branched polymers. Mechanistically, we hypothesize that the improved aqueous solvation of branched polymers is due to the incomplete collapse near the branch points, as the conformational constraints imposed by neighboring residues frustrates the aromatic packing that is preferred, leading to partial hydration of the polymer interior. In a linear polymer, such as the miscanthus polymers simulated here, the polymer can instead coil freely around neighboring aromatics, maximizing packing. Indirect evidence for this hypothesis is provided by Fig. 5, 17


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Self-Normalized Pair Distance Probability


5-5 4-O-5

Other Linkages Spruce Birch Miscanthus

5 d0 =3.96

4 3

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d0 =4.04

2 1 0

3

4

5 6 Distance (˚ A)

7

8

Figure 5: Normalized pair distance distribution between lignin aromatic rings, determined independently for each of the lignin libraries. The pair distance probability was determined by computing the pair distances between all aromatic ring centers within a polymer, and then normalizing the ensuing histogram by the surface area increment (4πd2 , with d being the distance between aromatic rings) and such that the probability is 1 at 8 ˚ A. The second selfnormalization normalizes the differences between the number of residue pairs considered and trajectory lengths in a relative sense. Specific areas of interest are marked, with probability peaks due to specific linkages marked by colored vertical lines. The first peak positions for miscanthus and birch, corresponding to closely packed aromatics, are denoted d0 and are reported within the figure.

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where the distribution of distances between aromatic rings shifts towards zero as the library of polymers increases in linearity (spruce→birch→miscanthus, Table 2). Indeed, unlike the relatively linear miscanthus and birch lignins (green and orange spots, Fig. 5), local aromatic packing in spruce lignin (interaction distance ∼ 4˚ A) does not have a distance peak before the signal is washed out by linkages directly connecting the aromatic rings. Thus, engineering efforts towards linearizing lignin polymers may result in increased globularity and insolubility of the engineered polymer. 200

Spruce Birch Miscanthus

150 SASA (nm2 )

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


100

30 20

50

10 0

0

0

10

0 1 20 30 Mass (kDa)

2

3

40

Figure 6: Relationship between solvent accessible surface area (SASA) and the molecular weight of the lignin polymer. The mean SASA over the last 100 ns of trajectory is marked by circles, while the standard deviation of the SASA over the same timeframe is used to convey the range observed in each simulation. Each library is analyzed separately and fit to a power law fitting Eq. 1 whose parameters are reported in Table 4, and is indicated as the colored line. To better discriminate between points at low molecular weights, the subplot in the lower right focuses on this region. The companion observable to Rgyr is SASA, measuring the solvent-exposed surface area of the polymer. Just as was the case for the Rgyr , SASA for a given polymer is largely determined by its molecular weight, with the topological differences between plant libraries being a minor contributor (Fig. 6). Variation within SASA values within a trajectory is comparatively smaller than it was for Rgyr , with smaller deviations from the overall power law trend. The SASA trends were tabulated separately for each of the lignin libraries tested (Ta19



Table 4: Power law (Eq. 1) parameters for the relationship between SASA and molecular weight, shown as the trendlines in Fig. 6. Parameter

Spruce

Birch Miscanthus

A (nm2 kDa−1 ) b

11.505 11.741 0.753 0.723

12.222 0.681

ble 4). The scaling parameter “b” is again the more important quantity. For a sphere of 2

3 . We see instead that b > 23 , indiuniform density, the SASA should increase with the Msphere

cating that there is excess surface area for real lignin polymers relative to an ideal spherical globule. Indeed, if we naively compute the surface area predicted by the Rgyr , assuming each 2 polymer is perfectly spherical, we find that this predicted SASA (4πRgyr ) underestimates

the SASA observed in simulation by a factor of 2.3-3, depending on the molecular weight. There are two underlying mechanisms that increase the polymer surface area relative to a perfect sphere. The first is that the hydroxyls present on the lignin favorably interact with water. These hydrogen-bonding interactions will protrude from the surface and increase the surface area. Additionally, the frustrated packing that increased the Rgyr of branched polymers also creates additional surface area for the polymer. The significance of the additional surface area may be when lignin interacts with other polymers, such as in prior simulations of cellulose-lignin contact. 27,28 The increased surface area created by the roughness of the lignin surface may be one mechanism to increase the binding affinity between lignin and cellulose, thereby strengthening the “glue” connecting cellulose fibrils. Based on the observables analyzed, the overall behavior of lignin in water is that of a collapsed polymer in a poor solvent for the polymer. Since the polymer theory for these conditions are well developed, there are few surprises at the structural level. Instead, the developed statistical relationships are the valuable result, and may be useful as a reference within experimental studies. For instance, if an observable such as a Rgyr distribution can be tracked in real-time for a lignin population during a pretreatment or degradation process via a non-invasive method like dynamic light scattering, as is done for other biopolymers, 69 the

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power law relationships can directly determine the polymer size distribution during reaction without being coupled to chromatography columns as is done currently for lignin. 63,70,71

Conformational Microkinetics of Lignin Polymers The unique simultaneous spatial and temporal resolution of MD simulation provides a dynamical description of the system that can be used beyond population-level distributions to provide kinetics of lignin polymer conformational change. After collapse of the polymer, individual polymers interconvert between different conformations rapidly (Figs. 7 and S301, Supporting Animations). By inspection of the trajectories, the changes happen faster at the periphery of the polymer, with free ends changing their conformations readily within our simulation timescales. The accelerated motion of peripheral lignin monomers relative to the core has been measured previously. 45 The animations also demonstrate the kinetic traps to conformational changes at the polymer core, as those degrees of freedom are restricted by the outer layers of polymer globule. Thus, the larger the polymer, the longer it visibly takes for conformational change to occur. To quantify the conformational change kinetics, we employed techniques inspired by Markov state models developed to study protein conformational changes. 72–74 However, since the lignin polymer does not have φ or ψ angles defined for all linkages, we adapt current methodology to focus exclusively on pairwise RMSD between configurations observed within a trajectory. The patterns created by the pairwise RMSD matrix along a full trajectory are striking, with structural clusters clearly visible (Fig. 8). Hierarchical clustering techniques were used to algorithmically identify clusters, as described in the Methods, which enables us to assess transition rates between clusters. Due to the length of the simulation trajectories, we typically do not see a round trip between individual lignin microstates for larger lignins, and so cannot populate typical microkinetic models popular for analyzing protein conformation. However, we can determine a dwell time within each cluster of structures from our trajectories, thereby determining a 21



Figure 7: Composite image of three different ≈ 2.5 kDa lignin polymers over the first 20 ns of simulation. In these representations, carbon atoms are gray, oxygen atoms are red, and polar hydrogens are white. For clarity, non-polar hydrogens and surrounding solution are omitted. The full trajectory animation is given as a Supporting Animation. The specific lignin polymers used are the 8th miscanthus, the 94th birch, and 34th spruce polymers, with molecular weights of 2.5, 2.4, and 2.3 kDa, respectively.

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Figure 8: Pairwise RMSD matrices for representative large and small lignins, demonstrating the structural clustering performed. The pairwise heavy atom RMSD for each lignin polymer was compared along its own trajectory and grouped via a hierarchical clustering algorithm into similar states, represented by different colors in the upper cluster identification bar that label the state definitions. Clustering was performed on all 300 trajectories, provided in the Supporting Information as Figures S302–S601 The example clustering for a larger polymer (left) was performed on the 99th lignin polymer in the spruce library (Fig. S314), which is 20.5 kDa. The example clustering for a smaller polymer (right) highlights the trajectory of the 81st lignin polymer in the miscanthus library (Fig. S511), which is 0.9 kDa.

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Mean State Residence Time (ns)


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Spruce Birch Miscanthus 101

100

100

101 Mass (kDa)

Figure 9: Mean state residence time as a function of molecular weight. The state definitions follow the analysis from Fig. 8, with the mean time between state transitions recorded for each trajectory. A power law was fit to residence times within clusters for polymers whose molecular weight was below 10 kDa, and this fit is shown as a line.

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mean residence time (Fig. 9). For lignin polymers of up to approximately 10 kDa in size, there is a linear relationship in logarithmic space between polymer size and mean state residence time within our dataset, which fits the behavior of a power law. For larger lignins, the trendline would predict mean dwell times approximately as long as the total trajectory length. Our simple transition-counting methods for estimating dwell times have large errors under these conditions, which leads to systematic underestimation of the mean state dwell time for larger lignin polymers. Table 5: Power law (Eq. 1) parameters for the relationship between mean state residence time and molecular weight, shown as the trendlines in Fig. 9. Parameter A (ns kDa−1 ) b

Spruce Birch Miscanthus 0.491 1.989

0.463 2.027

0.556 2.033

The power law parameters for small lignin polymer conformational transitions are remarkably simple (Table 5), indicating that the time between conformational transitions scales with the square of the molecular weight. In our testing, this scaling relationship is independent of cutoffs used or the distance metric used in clustering. The theoretical basis for this scaling derives from polymer reptation theory, where polymer relaxation times scale with the square of the molecular weight. 43 Thus, even for the largest individual polymers considered in our system, we would expect conformational sampling to occur on the sub-microsecond timescale. Critically, the scaling only applies to the case where the lignin polymers are isolated from one another. If the lignin polymers were to become entangled, as might occur at high temperature or after exposure to a favorable solvent environment, the disentanglement time is expected to scale as the cube of the molecular weight. 43 Such an entanglement process may be one mechanism by which treated lignins become less amenable to subsequent degradation, although it may be desirable for some applications such as hydrogels 75–77 and other materials. 78–80 25



If lignin aggregates form without entanglement, as may be the case for lignin in a cell wall environment, we hypothesize that the conformational sampling of the aggregate would continue to scale with the square of the molecular weight of the aggregate. In this case, the conformation of the aggregate may be effectively frozen, with sampling timescales that would certainly exceed current computational capabilities. On industrial timescales of minutes to hours, lignin aggregates with a molecular weight on the order of 1000 kDa would exchange conformations within a minute. Thus, lignin aggregates almost certainly change their conformation in solution, and should not be thought of as static and immobile polymers.

Conclusion LigninBuilder provides a robust framework for automatically converting topological representations of lignin linkages from existing lignin libraries into models suitable for simulation, enabling detailed comparisons of lignin interactions with other biopolymers. When simulated in an aqueous environment, the generated lignin polymers from all three libraries tested quickly collapse into a globule, a typical reaction for polymers in a poor solvent. While polymer compaction was a consistent theme across all simulations, the degree of compaction was seen to vary based on the plant species from which the lignin polymer library was derived. For lignins with greater branching, aromatic packing is impeded, which increases their solvation relative to linear lignin polymers. The molecular simulations also highlight the conformational heterogeneity of individual lignin polymers. Rapid conformational changes between states typify this heterogeneity, with a characteristic time proportional to the square of the molecular weight. Thus, lignin is not a static and immobile material, and this conformational plasticity should be considered in lignin interaction with other biopolymers. LigninBuilder is a necessary tool to enable fundamental research into lignin structure and interactions, allowing computational models to be created of experimental systems that

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are otherwise difficult to probe. By incorporating LigninBuilder as a plugin within VMD, we lower the barrier to entry for lignin simulation, and foresee LigninBuilder being utilized in conjunction with experiment to address engineering and scientific questions surrounding lignin valorization. Future example applications may be altering simulation temperature or solvent to study lignin polymers themselves, or probe interactions between lignin and other biopolymers, such as cellulose surfaces or ligninolytic enzymes.

Acknowledgement The authors thank Noah Trebesch for a fruitful discussion that guided the design of the algorithm for automated ring piercing amelioration, as well as Loukas Petridis and Nicholas Rorrer for discussions relating to polymer theory. This work was authored in part by Alliance for Sustainable Energy, LLC, the manager and operator of the National Renewable Energy Laboratory for the U.S. Department of Energy (DOE) under Contract No. DEAC36-08GO28308. JVV was supported by the NREL Director’s Fellowship funded by the Laboratory Directed Research and Development (LDRD) program. LDD and LJB received financial support from the National Science Foundation (CBET-1435228). JVV, MFC, and GTB acknowledge funding from the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Bioenergy Technology Office. GTB acknowledges funding from the Center for Bioenergy Innovation, which is a U.S. DOE Bioenergy Research Center supported by the Office of Biological and Environmental Research in the DOE Office of Science. The research was performed using computational resources sponsored by the Department of Energy’s Office of Energy Efficiency and Renewable Energy and located at the National Renewable Energy Laboratory.

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Supporting Information Available The Supporting Information contains a pdf file with ancillary figures, as well as a user guide for the LigninBuilder in its current form. For updates and enhancements, we encourage the reader to check the current github repository, https://github.com/jvermaas/ LigninBuilder.

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For Table of Contents Only. The LigninBuilder modeling workflow transforms two dimensional lignin topologies into three dimensional structures suitable for simulation and lignin material property exploration.

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Automated Transformation of Lignin Topologies ... - ACS Publications

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