Supporting Information for Manuscript: Simulation. Analysis of the Temperature Dependence of Lignin. Structure and Dynamics

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1 Supporting Information for Manuscript: Simulation Analysis of the Temperature Dependence of Lignin Structure and Dynamics Loukas Petridis,, Roland Schulz,,, and Jeremy C. Smith,, University of Tennessee/Oak Ridge National Laboratory Center for Molecular Biophysics, P.O.Box 8 Oak Ridge TN , USA., and Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville TN 37996, U.S.A. smithjc@ornl.gov To whom correspondence should be addressed UT/ORNL Center for Molecular Biophysics University of Tennessee These authors contributed equally to this work S

2 Methods Summary The analysis of the collapse transition is based on comparison of the thermodynamic properties of collapsed and extended states as follows. The enthalpy contribution is derived from the interaction energies corresponding to R ext and R col in Figure 6. The translational and rotational entropy contributions of hydration water were derived from ten ps simulations, five starting from extended and the other five from collapsed lignin configurations. The entropy contribution from water density fluctuations was derived from sixty 5ps simulations, 3 from collapsed and 3 from extended states. S

3 Structural Properties of the Collapsed and Extended Lignins 8 collapsed extended 8 collapsed extended W hydr 7 W hydr W hydr (a) 3K collpased extended W hydr (b) 36K collpased extended (c) 4K (d) 48K Figure S: Number of water molecules in the hydration shell as a function of time at (a) 3K, (b) 36K, (c) 4K and (d) 48K. Data from 3 5ps trajectories are appended to yield the.5ns plot. 4 Table S summarizes the structural properties of the 6 simulations that were used to investigate the thermodynamic origin of lignin collapse at 3K. Figure S shows the number of water moelcules in the hydration shell of lignin used to determine water compressibility. S3

4 Temperature Dependence of Lignin Structure P(R g ) K 36K 4K 48K R g [Å] Temperature T [K] (a) (b) Figure S. Temperature dependence of the lignin structural properties. (a) The probability distribution of the radius of gyration,r g. (b) Solvent accessible surface area, see the legend of Figure for error estimates. Surface Area A SAS [Å / 3 ] L a L b L a L b TableS: Comparison of radius of gyration (R), solvent-accessible surface area (A) and number of hydration water molecules of collapsed and extended lignin structures at various temperatures. Values are averages over 3 5ps trajectories. R col A col W col R ext A ext W ext [nm] [nm ] [nm] [nm ] 3K.4±. 7.8±.8 644±4.63±. 8.7±3.9 75±34 36K.4±. 7.4±.4 58±.6±.3 79.±3.4 64±7 4K.4±. 76.±3.3 53±6.6± ±4. 6±3 48K.44±.4 8.5± ±8.64±.4 9.6±4. 54±3 S4

5 Analytic Theory for Effect of Branching on Polymer Size In what follows we modify the Zimm-Stockmayer (ZS) theory 6 8 to render it applicable to polymers in poor solvents, such as lignin in water. The key assumption here is that the distanced ij between monomersiand j is given by D ij =bn /3, (.) where i and j are separated by a linear segment of (N ) monomers and b is the Kuhn length of a monomer, a measure of the monomer average size. By further assuming isotropy in space and long chains (N tot >> ), the R g of a branched chain can be in principle calculated for any degree of branching: R g = Ntot Ntot D ij. (.) i,j= Our discussion is confined to a polymer with one branch point, with its three arms each consisting ofn,n andn 3 monomers, respectively(n tot =N +N +N 3 ). Let the branch point be positioned at the monomer with index k =, the first arm comprising monomers k=[,n ], the second arm k=[n +,N +N ] and the third k=[ni+n +,N tot ]. In the limitn,n,n 3 >>, ther g of a one-branch point polymer in Eq.. is readily decomposed into the following sum: R g, =A +A +A 3 + (A 4 +A 5 +A 6 ), (.3) S5

6 where, A = A = A 3 = A 4 = = A 5 = = A 6 = = N N di Ntot N +N N +N di Ntot N N +N +N 3 Ntot N +N N N +N N tot 9 8Ntot N N tot 9 8Ntot N +N N tot 9 8N tot dj i j /3 = 9 8N tot N 8/3 (.4) dj i j /3 = 9 N 8Ntot N 8/3 N +N +N 3 di dj i j /3 = 9 N +N 8Ntot N 8/3 3 di dj i+ j N /3 = N [ ] (N +N ) 8/3 N /3 N /3 N +N +N 3 di dj i+ j N N /3 = N +N [ ] (N +N 3 ) 8/3 N /3 N /3 3 N N +N +N 3 di N +N dj i+ j N N 3 /3 = (.5) (.6) [ ] (N 3 +N ) 8/3 N /3 3 N /3. (.7) The squared radius of gyration of an unbranched collapsed polymer isr g, = 9b N /3 tot /8. Hence, by substituting Eqs..4 and.7 into Eq..3 for the R g, of a collapsed polymer with one branch point, we obtain the theoretical prediction of their ratio g= R g, R g, = ( ) N +N 8/3 ( ) N +N 8/3 ( 3 N3 +N + + N tot ( N N tot N tot ) 8/3 ( ) 8/3 ( N N3 N tot N tot N tot ) 8/3 ) 8/3. (.8) Similarly to the ZS theory for polymers in ideal solvents, Eq..8 also predicts g <. However Eq..8 also indicates that branching reduces the size of isotropic collapsed polymers less than isotropic Gaussian chains. For a star polymer, where N = N = N 3 = (N tot /3) Eq..8 gives g=.86, whereas with the ZS theory g ZS =.77. S6

7 Scaling Properties of Branched Lignins [Å] Segment <r g > / 48K 3K 3K including branch ~N /3 N c branch point 6 Segment Length N Figure S3: Root mean square of the radius of gyrationr g (N) of a polymer segment comprising (N+ ) monomers of the ensemble of polymers with one branch point. Also shown, as a green solid line, are data from short ((N 6)) segments that include the branch point. The dashed black line is a N.33 power-law function and all plots are time averages over the last 5ns of the ensemble of MD trajectories. The error bars are the standard deviations of the ensemble distribution. S7

8 Correlationof R g and Asphericity La La Lb Lb L L3 L4 L5 L R g [Å] (a) Asphericity La Lb La Lb R g [Å] (b) Asphericity La Lb La Lb Asphericity La Lb La Lb. 3K R g [Å] R g [Å] (c) (d) Figure S4: (a) Average asphericity and radius of gyration for all nine lignins at T = 3K, values taken from Table ; (b) Same as (a) but from the ensemble of lignins with zero and one branch points. (c) Scatter plot of asphericity againstr g from each frame of the ensemble of lignins with zero and one branch points. at T = 3K. Each point represents a running average over frames and only data with <.6 are shown. (d) Same as (c), but at T = 48K.. Figures S4(a),(b) demonstrates the strong correlation between the R g and the asphericity, δ of a lignin polymer. This correlation is observed for lignins of various degree of branching. Figures Sc,d demonstrate that, in the limit of, the branched lignins have larger R g than the unbranched at 3K, but the opposite trend is observed at 48K. S8

9 Structure of Hydration Water 3.5 g prox g o-o η sh η T=3K 3.5 g prox g o-o η sh η T=36K r [Å] (a) r [Å] (b) 3.5 g prox g o-o η sh η T=4K 3.5 g prox g o-o η sh η T=48K r [Å] (c) r [Å] (d).5 collapsed extended g prox (r) r [Å] (e) Figure S5: Proximal distribution functions of the oxygen atoms of lignin hydration water (g prox ), radial distribution function of bulk water oxygen atoms (g o o ) and the respective cumulative sums, η sh and η. The dashed vertical line,r=4.9å, marks the outer boundary of the hydration shell of lignin. (e) Proximal distribution functions of water oxygen atoms at a distancer from the surface of the collapsed and extended lignins at T = 3K. Structural properties of water close to the surface of the lignin are quantified by the proximal distribution function g prox (r), given by Equation 6. The density of the lignin hydration shell, ρ sh S9

10 was derived using Equation.9: ρ sh = η rmax sh g prox (r)dr =, (.9) r max r max where η sh is the integral of the proximal distribution function and r max the position of the first minimum of g prox (r) that defines the outer boundary of the hydration shell. A similar definition can be obtained for the density of bulk water: ρ = η rmax g o o (r)dr =, (.) r max r max with η the integral of the standard oxygen-oxygen radial distribution function of bulk water. Taking r max = 4.9Å in Equations.9 and. allows comparison of the hydration shell density with that of the bulk: ρ sh = ρ (η sh /η ). Figures a-d show the hydration shell density of lignin to be smaller than the bulk by %, 4%, 7% and % at T = 3K, 36K, 4K and 48K, respectively. This decrease in the hydration shell density is independent of geometric contributions that are also present if the hydration water is unperturbed from the bulk. For the ensemble of nine lignins at T = 3K, with various degrees of branching, the average fraction of the SASA which is hydrophilic is φ pol =.43±., where a hydrophilic atom is crudely defined as having partial charge q >.e. This is higher than the average fraction of the surface area of an isolated monomer that is hydrophilic: φ mon =.37±.. φ pol > φ mon indicates that hydrophilic hydroxyl moieties of lignin are preferentially exposed to the solvent in order to maximize favorable interactions with the water molecules. In a separate 8ns MD simulation of ligninl a in vacuum the behavior was different due to burial of hydrophilic groups, with φ vac pol =.36±. similar to φ mon =.37. S

11 Enthalpy Change at 48K 6 Interaction Energy [kj/mol] Lignin-Lignin Sum Lignin-Water R g [Å] Figure S6: Lignin-lignin and lignin-water interactions energies as a function of the ligninr g at 48K. Data represent ensemble average of the unbranched and one-branch lignins. S

12 Calculation of the Entropy of Water Here, we provide the equations required to calculate the the entropy of water molecules from Eq. of the main text. Full details on how these formulae are derived can be found in Refs [55,56]. The density of states of the gas-like component is assumed to be that of hard spheres g g (ω)= g +(g ω/fw), (.) whereg =g(ω= ),W the number of water molecules, and f is the fluidity factor. f is determined by solving δ 9/ f 5/ 6δ 3 f 5 δ 3/ f 7/ + 6δ 3/ f 5/ + f =, (.) and the normalized diffusivity δ is given by: δ = g ( ) πkb T / ( W 9N wat m V ) /3 ( ) 6 /3, (.3) π wheremis the mass of a water molecule andv the volume of the system. The weighting functions of Eq. are: λ s = βhω exp(βhω) ln[ exp( βhω) ], (.4) where β = /k B T andhis Planck s constant; and λ g = SHS 3k B, (.5) wheres HS is the hard sphere entropy, given by [ S HS = 5 (πmkb ) ] k B + ln T 3/ V h fw z(y) + y(3y 4) ( y), (.6) S

13 wherey= f 5/ /δ 3/ and z(y)= +y+y y 3 ( y) 3. (.7) Substituting Eqs..,.4 and.5 into Eq., permits computation of the entropy of water molecules. Autocorrelation C trn (t)/c trn () time t [ps] Density of States g(ν) [ps] Frequency ν [THz] (a) (b) Figure S7: (a) Rotational velocity autocorrelation functions and the respective (d) density of states of water Figure S7 shows the rotational velocity autocorrelation andg(ω) spectra, indicating almost no variation between the bulk and hydration water S3

14 MSD Figure S8 demonstrates the effect of solvent exposure and chain connectivity on monomer meansquare displacements of the nine lignin molecules of various branching at 3K... (a) La... (g) L4.. (h) L5 Chain ends Small SASA Large SASA Branch point (f) L3.. Chain ends Small SASA Large SASA Branch points... MSD [nm ] MSD [nm ] (c) La Chain ends Small SASA Large SASA Branch points (e) L Chain ends Small SASA Large SASA Branch points (d) Lb (b) Lb Chain ends Small SASA Large SASA Branch point MSD [nm ] MSD [nm ].. Chain ends Small SASA Large SASA Branch point. MSD [nm ]. MSD [nm ].. Chain ends Small SASA Large SASA MSD [nm ] Chain ends Small SASA Large SASA MSD [nm ] MSD [nm ] Chain ends Small SASA Large SASA Branch points... (i) L6 Figure S8: Mean square displacement of lignins with zero (a) and (b), one (c) and (d), two (e), three (f), four (g), five (h), and six (i) branch points. Translation and rotation of the entire molecule have been removed. Highlighted monomers have the largest (red) and smallest (blue) SASA. MSD of monomers at chain ends are shown in orange and of branch points in magenta. S4

15 Figure S9 demonstrates the correlation between the monomer mobility and solvent exposure at T=36K and 4K. < r n (t=ns)> [Å ] 5 T=36K chain ends < r n (t=ns)> [Å ] T=4K chain ends Monomer SASA [Å ] Monomer SASA [Å ] (a) 36K (b) 4K Figure S9: Monomer MSD att = ns of the ensemble of polymers with zero and one branch points versus the monomer SASA at T=36K and 4K. Bibliography Complete reference 65: (65) Lieberman-Aiden, E.; van Berkum, N.L.; Williams, L.; Imakaev, M.; Ragoczy, T.; Telling, A.; Amit, I.; Lajoie, B.R.; Sabo, P.J.; Dorschner, M.O.; Sandstrom, R.; Bernstein, B.; Bender, M.A. and Groudine, M.; Gnirke, A.; Stamatoyannopoulos, J.; Mirny, L.A.; Lander, E.S.; Dekker, J. Science9,36, Chain Topology Below are tables describing the linkages connecting the monomers of the nine simulated lignins. Each line contains the type of linkage (capital letters L and R refer to left- and right-handed linkages that contain a chiral center), followed by the numbers of the two monomers that are connected S5

16 Table S: Linkages connecting the monomers of ligninla. 55 b5l 3 bo4l ao4l 5 6 bo4r 6 7 bo4l 7 8 bo4r bo4l 55 bo4r 3 b5l 3 4 b5r 4 5 bo4l 5 6 ao4r 6 7 bo4r bo4l 9 ao4l 55 bo4r 3 bo4l bo4r bo4r 7 8 bo4l 8 9 bo4r bo4l 3 3 bo4r b5r bo4l bo4r bo4l bo4r 39 4 ao4r 4 4 bo4l b5l bo4r bo4l ao4r bo4r bo4l ao4l bo4r b5r bo4l bo4r bo4l S6

17 Table S3: Linkages connecting the monomers of ligninlb. 55 bo4l b5l 4 5 ao4r 5 6 ao4l bo4r bo4l bo4r 55 3 bo4l bo4r bo4l 7 8 b5r 8 9 bo4r 9 55 bo4l bo4r bo4l bo4r 6 7 ao4r 7 8 b5l 8 9 b5r 9 3 bo4l 3 3 bo4r bo4l bo4r bo4l bo4r ao4l 4 4 bo4l 4 4 bo4r 4 43 b5l bo4l bo4r b5r bo4l bo4r bo4l 5 5 bo4r 5 5 bo4l 5 53 bo4r bo4l ao4r bo4r ao4l S7

18 Table S4: Linkages connecting the monomers of ligninla. 55 bo4l 3 bo4r 3 4 bo4l bo4r 6 7 bo4l b5l 9 bo4r 55 bo4l bo4r 4 5 ao4l 5 6 bo4l 6 7 bo4r 7 8 b5r 8 9 ao4r 9 55 bo4l bo4r 3 bo4l bo4r 3 6 b5l 6 7 bo4l bo4r ao4l 3 3 ao4r b5r bo4l bo4r bo4l b5l 39 4 bo4r bo4l bo4r bo4l bo4r bo4l ao4l 49 5 bo4r bo4l b5r ao4r bo4r bo4l bo4r S8

19 Table S5: Linkages connecting the monomers of ligninlb. 55 bo4l 3 bo4r bo4l bo4r 7 8 bo4l bo4r 55 bo4l 3 b5r 3 4 bo4r 4 5 bo4l 5 6 bo4r 6 7 ao4l 7 8 bo4l 8 9 bo4r 9 55 bo4l 55 3 ao4r bo4r 5 6 bo4l 6 7 b5l 7 8 bo4r bo4l 3 3 ao4l bo4r bo4l bo4r bo4l b5r 4 4 b5l 4 43 ao4l bo4r bo4l bo4r bo4l ao4r 5 5 bo4r ao4r bo4l bo4r b5r bo4l b5l 59 6 bo4r 6 6 S9

20 Table S6: Linkages connecting the monomers of ligninl. 55 bo4l 3 bo4r bo4l 5 6 b5r 6 7 bo4r bo4l 9 55 bo4r bo4l 3 bo4r 3 4 b5l 4 5 ao4l bo4r 7 8 bo4l 8 9 bo4r 9 ao4r bo4l 55 3 bo4r bo4l ao4l 7 8 ao4r 8 9 bo4r 9 3 bo4l b5r 3 33 bo4r bo4l b5l bo4r bo4l 39 4 bo4r 4 4 ao4l bo4l bo4r bo4l bo4r bo4l 49 5 ao4r bo4r bo4l bo4r b5r b5l 59 6 bo4l 6 6 S

21 Table S7: Linkages connecting the monomers of ligninl3. 55 bo4l 3 bo4r ao4l 5 6 bo4l 6 7 bo4r 7 8 ao4r 8 9 ao4l 9 bo4l 55 bo4r 3 b5l 3 4 b5r 4 5 bo4l bo4r bo4r 9 bo4l bo4r 55 3 ao4r bo4l 5 6 bo4r bo4l 8 9 ao4l bo4r bo4l bo4r b5l bo4l bo4r b5r 4 4 bo4l bo4r ao4r bo4l bo4r bo4l 49 5 bo4r b5l 5 53 b5r bo4l bo4r bo4l bo4r 59 6 bo4l 6 6 S

22 Table S8: Linkages connecting the monomers of ligninl4. 55 bo4l 3 bo4r 3 4 bo4l 4 5 bo4r 5 6 b5l 6 7 bo4l bo4r 9 55 b5r bo4l 3 bo4r bo4l b5l 7 8 bo4r ao4l 55 bo4l ao4r 8 5 ao4l 5 6 bo4r 6 7 bo4l bo4r ao4r 3 3 bo4l bo4r bo4l 4 36 bo4r bo4l bo4r 39 4 b5r 4 4 ao4l bo4l bo4r bo4l bo4r ao4r bo4l 5 5 bo4r 5 5 b5r 5 53 b5l bo4l bo4r bo4l bo4r 6 6 S

23 Table S9: Linkages connecting the monomers of ligninl5. 55 bo4l bo4r 4 5 bo4l 5 6 b5r 6 7 bo4r bo4r 9 bo4l ao4l bo4r bo4l 4 5 b5l 5 6 ao4r bo4r 8 9 bo4l 9 ao4l bo4r 55 3 ao4r b5r 5 6 b5l 6 7 bo4l 7 8 bo4r bo4l 3 3 bo4r 3 3 bo4l 3 33 b5r bo4r bo4l bo4r bo4l 39 4 bo4r 4 4 ao4l bo4l bo4r b5l bo4l bo4r bo4l bo4r 5 5 bo4l bo4l bo4r ao4r S3

24 Table S: Linkages connecting the monomers of ligninl6. bo4l bo4r bo4l 4 5 bo4r bo4l b5r 9 b5l b5r bo4r 3 bo4l 3 4 bo4r 4 5 bo4l 5 6 bo4r ao4l 9 ao4r 9 55 ao4l 55 3 bo4l bo4r 5 6 b5l 6 7 bo4l 7 8 bo4r 8 9 bo4l bo4r bo4l bo4r bo4l bo4r bo4l bo4r bo4l ao4r bo4r bo4l bo4r 49 5 ao4l bo4l bo4r bo4l 3 56 ao4r b5r b5l 53 6 bo4r 6 6 S4

Supporting information for: Mechanism of lignin inhibition of enzymatic. biomass deconstruction

Supporting information for: Mechanism of lignin inhibition of enzymatic biomass deconstruction Josh V. Vermaas,, Loukas Petridis, Xianghong Qi,, Roland Schulz,, Benjamin Lindner, and Jeremy C. Smith,,