Mechanics of an atomic crank of 1,6 Linked Polysaccharides by AFM and SMD Calculations
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Mechanics of an atomic crank of 1,6 Linked Polysaccharides by AFM and SMD CalculationsGwangrog Lee
Department of Mechanical Engineering & Materials Science, Duke University, Durham, NC, 27708
Please look at slide notes
Materials and MethodsPolysaccharides: Pustulan (16-linked -D-glucose).
Single Molecule Force Spectroscopy by AFM. 1-5
Steered Molecular Dynamics simulations: NAMD and CHARMM (CSFF).6-7
SMD SimulationPotential being applied to the system:Force Sensor (cantilever)
Demo of SMD simulation using NAMD
Freely jointed chain with segment elasticityx
AFM recordings obtained on individual pustulan molecules of various lengths.
Table 1. Ab initio calculations of the O6-O1 distance in the rotamers of -D-glucose using the B3LYP/6-311++G** method.
Force-spectrograms of 20 different pustulan molecules are normalized at the common force (1400 pN) and superimposed.Definition of rotamergt, gg, and tg rotamer of -D- glucopyranose
5ns water-simulation and normalized force-spectrograms with a scale of monomer.tg +167gt +564.97 6.27 4C1gt4C1tgNormalized Extension per Ring/
A comparison of pulling speeds Normalized Extension per Ring/Green: 5ns SimulationBlue: 200ns SimulationRed: 1micros Simulation
A comparison between force-extension curves of pustulan obtained by AFM and by SMD simulations of 10 rings for 1 micro seconds.Normalized Extension per Ring/Atg +166gt +69tg -174gg -75R5R44.946.066.125.42
Analysis of the one microsecond SMD trajectory of ring #4 reveals thermally driven and force driven conformational transitions between gg, gt, and tg states.
A comparison of the works undergone under stretching condition of each polymer.InsertThe initial and final structures of pyranose ring in pustulan5.7 kcal/mol
ConclusionThe hookean elasticity of pustulan is generated by forced gttg and ggtg rotations about the C5-C6 bond.The work to rotate the atomic crank (O6-C6) about the C6-C5 bond is 5.7 kcal/mol (Wrot= Wpust- Wcell).
ReferenceRief, M., Oesterhelt, F., Heymann, B., and Gaub, H. E. (1997). Science 275, 1295-1297.Marszalek, P. E., Oberhauser, A. F., Pang, Y.-P., and Fernandez, J. M. (1998). Nature 396, 661-664.Marszalek, P. E., Pang, Y. P., Li, H., Yazal, J. E., Oberhauser, A. F., and Fernandez, J. M. (1999). PNAS 96, 7894-7898.Marszalek, P.E., Li, H. & Fernandez, J.M. (2001). Fingerprinting polysaccharides with single molecule AFM. Nat. Biotech. 19, 258-262.Marszalek, P.E., Li, H., Oberhauser, A.F. & Fernandez, J.M. (2002). PNAS 99, 4278-4283Kuttel, M., Brady, J.W. & Naidoo, K.J. (2002) J. Comput. Chem. 23, 1236-1243. Humphrey, W., Dalke, A., & Schulten, K. J. Mol. Graphics, 14, 33-38 (1996). Kirschner, N. Karl & Woods, R.J. (2001) PNAS 98, 10541-10545.
Stretching experiments on single polysaccharide molecules have recently expanded conformational analysis to include force-induced chair-boat and chair-inversion transitions of the pyranose ring.
This study uses a combination of atomic force microscopy (AFM) and steered molecular dynamics (SMD) calculations to investigate in detail the mechanism of the elasticity of 1,6 linked glucose polysaccharides. In contrast to most sugars 1,6 linked polysaccharides have an extra bond in their inter-residue linkage, C5-C6, about which restricted rotations occur increasing the complexity of their mechanics. By comparing our AFM and computational results this work determines that forced rotations about the C5-C6 bond have a significant and different impact on the elasticity of alpha- and beta-linked polysaccharides. Beta linkages of a polysaccharide pustulan force the rotation about the C5-C6 bonds and produce a hookean-like elasticity but do not affect the conformation of the pyranose rings.
These results demonstrate the ability of single molecule force spectroscopy, in combination with computational methods, to capture force-induced molecular rearrangements that cannot be measured otherwise. A sugar molecule is one of most important molecule of biological system in terms of a fundamental scaffold of biological structure, a mediator in molecular recognition, and an adhesive interaction under stresses and deformation.
One of examples is a lysozyme, an enzyme that catalyzes the cutting of polysaccharide chains in the cell walls of bacteria. In this situation, the molecule of polysaccharide has to be distorted into a particular shape in which the atoms around the bond have an altered geometry and electron distribution. Because of this distortion, the elasticity of the polysaccharide is important in the cell walls of bacteria and human. Steered molecular dynamics simulations SMD simulations of pustulan were carried out with the programs NAMD2 and XPLOR with the new CHARMM-based Carbohydrate Solution Force Field (CSFF). It is significant that this new force-field was developed to correctly represents the C5-C6 rotamer populations of D glucose within the CHARMM framework. The structures, consisting of 10 glucose rings of pustulan were generated using the program INSIGHT II and the psfgen module of NAMD. The structures were solvated in a box of TIP3P water (pustulan: 38x38x72 , the total of 9309 atoms including 213 atoms of the sugar) with periodic boundary conditions using the program VMD. The structures were equilibrated for 1-5 ns at 300 K. SMD simulations were carried out by fixing the O6 atom of the first sugar and applying a force, through a spring, to the O1 atom of the last sugar using the SMD protocol within NAMD2. The spring constant used in the simulations was similar to the spring constant of AFM cantilevers and ranged between 68 and 680 pN/nm. The SMD stretching proceeded by moving the end of the spring at a constant velocity of 10-4 /fs (simulations in water) and 1x10-7 /fs (in vacuum). The simulations adopted a timestep of 1 fs, a uniform dielectric constant e=1 and a cut-off of Coulomb and vdW interactions with switching function starting at a distance of 8 and reaching zero at 12 . 1 ms simulations in vacuum were carried out with e=80. The temperature was set to 300 K and was controlled by the velocity re-scaling procedure. The simulations were done on a Linux cluster with ten 2GHz AMD CPUs. A: The schematic of home-made AFM for single molecule force spectroscopy.
B: The force applied into a molecule can be calculated by multiplying spring constant (kc) by deflection of cantilever (Zc). The extension of a molecule can be found by the expansion of piezo and deflection of cantilever.
The slope of force-extension curve corresponds to the elasticity of a molecule.The concept of Steered molecular Dynamics simulation:
1) Virtual spring with potential is attached to one end of the molecule. The spring play the exactly same role as cantilever of AFM as a force sensor which allows to measure applied force into the molecule.
2) The potential energy is obtained by the net extension of virtual spring. The force of any direction can be calculated by partial differentiation with respect to that direction. Biopolymers can behave as a freely jointed chain (FJC) with segment elasticity or a worm-like chain (WLC).
A polysaccharide is fitted into FJC which can feely rotate at a jointed position and have freely any angle between two consecutive bonds.
A DNA and protein are fitted into WLC which has a rigidity of persistent length like a tube which has continuous change among chain linkages.Above figure shows a family of force spectrograms obtained from single pustulan molecules with various lengths.
Force spectrograms for single pustulan molecules deviate from the shape expected for a FJC.
AFM recordings was obtained on individual pustulan molecules with various contour lengths. (Inset) Structure of pustulan showing two -D-glucopyranose residues connected by a 16 linkage. Numbers 1-6 mark the carbon atoms of the pyranose structure and the atom position on each ring for the connection of backbone.
The distance between O1 and O6 for gt and gg are almost the same which means both positions are symmetric around virtual line between O1 and O6.
Only way to increase the extension between O1 and O6 is to rotate a rotameric dihedral angle about the C6-C5 bond into the tg state of 180 .
The gain of extension from gg and gt to tg is around 0.92 per ring.
Force-spectrograms of 20 different pustulan molecules are normalized at the common force (1400 pN) and superimposed.
First, the normalized pustulan recordings overlap well, proving that the measurements were obtained on individual molecules and not on their bundles. Next, in the force range100-800 pN, the pustulan length increases almost linearly with the force (pustulan behaves as a hookean spring) and its elasticity strongly deviates from that of a FJC (methylcellulose). This is an interesting observation indicating that the mechanical properties rendered by -16 linkages are significantly different from those rendered by the freely rotating -14 linkages.
From this it is concluded that the segments in pustulan experience rotational restrictions and an additional work, equal to the area between the blue and black curves, needs to be done to fully extend the pustulan chain.
This is an interesting feature of pustulan in terms of the similarity with a elasticity of bulk material.
A comparison between force-extension curves for pustulan obtained by AFM (black curves) and by SMD simulations of 10 rings in water (green traces, 5 ns calculations).
The AFM extensions for the pustulan traces were normalized at a force of 3500 pN to be equal to 1/10th of the chain extension obtained by SMD (6.3 ). (Inset) Structures of ring #4 at the beginning and at the end of the SMD stretching process reveal a gttg transition with no significant change to the conformation of the ring.
The difference between green and black is due to the fast pulling speed with 5 nano-seconds (5ns), which was not enough time for each ring of the sugar molecule to find a equilibrium in the water and 5ns simulation does not represent well the behavior of pustulan of experimental results. The pulling speed of real experiment is about several hundred micro-seconds.
Therefore, A long simulation with a slow pulling speed is required for a good agreement between theoretic and experimental result.In order to carry out a long simulation, the decrease of the number of atoms in simulation-system is required because it take long time to finish the simulation with water of many atoms. For example, 5ns water simulation took 3 weeks on linux cluster with 8 CPU.
Implicit solvent was used instead of explicit water molecule which allow the dramatic decrease of atoms. Implicit solvent means that the parameter for dielectric constant was 80, the dielectric constant of water.
The simulation of several different speeds was performed: 5ns water simulation (Green) ; 200ns implicit solvent simulation (Blue); 1 micros implicit solvent simulation (Red).
It is clear that the slower pulling simulation become close to experimental records. A one-microsecond SMD simulation of pustulan reproduces well the AFM stretching data.
A comparison between the normalized force-extension curves for pustulan obtained by AFM (black traces) and by SMD ( red trace, 1 ms simulation).
The conformational dynamics of ring #5 during the 1 ms simulation as revealed by the three torsions: w (black trace), t1 (red trace) and t2 (blue trace).
The conformational dynamics of ring #4 during the 1 ms simulation. w=O6-C6-C5-O5 reports the rotameric status about the C6-C5 bond, t1=O1-C1-C2-O2 and t2=O5-C5-C4-C3 report the conformational status of the pyranose ring, e.g. chair-boat transitions.
Time trajectory evolution of the three torsions. The initial gggt transitions occur at a minimal stretching force and therefore are driven thermally. The gg tg transition at 368.52 ns is driven by the external force. Time evolution of the O1-O6 distance reveals a step-wise increase at 368.52 ns due to the gg tg transition.
Two structures of ring #4, separated by 10 ps, immediately before and after the gg tg transition. A comparison of normalized force-extension relationships for methylcellulose, (blue trace), pustulan (red trace) measured by AFM. The normalization procedure assumed that the extension of the three polysaccharides at the maximum force for the cellulose trace (1538 pN) was equal to 1.
This comparison of pustulan (red line) permits to evaluate the work necessary to rotate the atomic crank: O6-C6 in pustulan (hatched area). (Inset) The initial and final structures of the pyranose ring in pustulan subjected to large stretching forces (2900 pN). The dotted lines on ring show the residue vector O6-O1. In conclusion, these results have determined the nanomechanical fingerprint of the rotation of the O6-C6 bond around the C5-C6 bond on the glucopyranose ring.
The stretching (or relaxing) of 16-linked polysaccharides provides a unique means to control the distribution of their gt, gg and tg rotamers.
These manipulations of single 16-linked polysaccharides increase the understanding of the conformational mechanics of the pyranose ring and expand single molecule mechanical_chemistry.