Transcript Accurate hydrodynamic tensors for biomolecules

Accurate hydrodynamic
transport properties for
biomolecules
Sergio Aragon
San Francisco State University
Dept. of Chemistry and
Biochemistry
CalTech PASI Jan 4-16, 2004
Acknowledgements
Tilman Rosales
Martin Perez
David Hahn, Post-Doctoral Fellow
Funding:
NIH MBRS SCORE Grant SO6 GM52588 (Aragon).
NIH: MBRS-RISE (Rosales & Perez))
I. INTRODUCTION
OUTLINE
How do we find the size and shape of molecules in solution?
Simple expressions everyone knows.
II. HOW DO WE KNOW HYDRODYNAMICS WORKS?
Stick boundary conditions.
Slip boundary conditions.
III. HYDRODYNAMICS WITHOUT BEADS
Focusing on the SURFACE
IV. APPLICATION TO BIOMOLECULES
Proteins
Nucleic Acids
V. SUMMARY & OUTLOOK
MOLECULAR SIZE AND SHAPE IN
SOLUTION?
SOLIDS: x-Ray Diffraction, Microscopy
IN SOLUTION: Diffusion
Tether + atomic force microscope
Optical Tweezers
DIFFUSION SENSITIVE METHODS:
Dynamic Laser Light Scattering
Transient Electric or Magnetic Birefringence
Flow Birefringence
Fluorescence Polarization Anisotropy
Fluorescence photobleaching recovery
Magnetic Resonance
Molecular Sizes: Nano-scale
• Small molecules are less than 2 nm in scale.
• Globular proteins range from 2 to 10 nm in
scale.
• DNA ranges from 3 to 1000 nm in scale.
• Transport properties in the nano-scale can
obtained to high accuracy using classical
hydrodynamics (with appropriate boundary
conditions).
Simple Expressions Everyone Knows
Fick’s First Law
F = -D
 c( x, t )
 x
Fick’s Second Law or, the “Diffusion Equation”
2
D  c ( x2, t )   c ( x, t )
t
 x
Einstein Relation
D = kT f -1
D = kT/f
Stokes-Einstein Relation
D = kT/(6R)
f ~ g/s ; D ~ cm2/s
SOME COARSE GRAINED BEAD MODELS
Rod polymer
Semi-flexible polymer
IgG3
LIMITATIONS OF BEAD MODELS
I. SLIP boundary conditions are not accessible at present.
Small to intermediate sized molecules in non-hydrogen bonding
solvents cannot be accurately treated.
II. Hydrodynamic interaction tensors are approximate
Greatest errors occur for touching and overlapping beads
at the Rotne-Prager level. Use of high order infinite series
instead, runs into matrix inversion problems.
III. No hydrodynamic interaction expressions are available for
unequal sized overlapping beads. This makes atomistic level
modeling difficult and leads to coarse grained models or ad hoc
bead resizing to avoid problems.
HYDRODYNAMICS
WITHOUT BEADS
• Hydrodynamics occurs at the SURFACE
• An Exact solution can be written down for
the Stokes Equations in terms of the Oseen
tensor.
• Both SLIP and STICK boundary conditions
can be exactly formulated.
• Solvent size can be taken into account
BENZENE TUMBLING IN NON-POLAR SOLVENTS
Theory: 3.88 ps/cp
Experiment = 3.53 + 0.07 ps/cp
10% discrepancy!
Alms et al. J. Chem. Phys. 59,5570 (1973).
Slip boundary conditions
Youngren & Acrivos, J. Chem. Phys. 63, 3486 (1975).
BASIC HYDRODYNAMICS
HYDRODYNAMICS
Navier-Stokes Equations -- (complicated!)
Stokes “Creeping Flow Equations”


 2 u = P
 
 u  0
Valid for small Reynolds
number.
HYDRODYNAMIC BOUNDARY CONDITIONS
STICK => Fluid layer sticks to surface
SLIP => Fluid layer slips by surface
Reynolds Number
• Definition of Reynolds Number
d vρ
Re 
η
Flow through tube
• Re >> 2000 turbulent flow
• Re < 2000 laminar flow
• Re << 1 Stokes flow
D ρ
Re 
η
Diffusive flow
kTρ
Re 
6 π η2 a
kT
D
6π η a
Reynold’s Number as a function
of Radius
Reynolds number
0.25
0.2
0.15
0.1
0.05
0.5
1
1.5
Radius a in Angstroms
3
Re  1.1x 10 /a(A)
2
YOUNGREN-ACRIVOS METHOD
J. Fluid Mech.. 69,377(1975)
For Stick Boundary conditions: u(y) = vp + wxrp
 
 
v ( y )  u0 ( y ) 

Sp
   
T( x , y ). f ( x ) dSx
    

 
1
( x  y )( x  y )
T( x , y ) 

  I 


8 x  y 
x  y2

 
f ( x)
is the unknown Surface Stress Force.
HOW DO WE CALCULATE THE TRANSPORT TENSORS?
Discretize the surface:
N
Sp   j
j 1

f j ( y j )  constant on surface element  j
N


v ( y k )   G k j .f j ( y j )
j 1
Gk j
 
  T ( x , y k )dSx 3x3 matrix
j


 f1 
 v ( y1 ) 
 G11 ... G1N 
 




 ... ... ...
 ... 
 ... 


 


v( y )
 N  3 Nx1 G N 1 ... G NN  3 Nx 3 N  f N  3 Nx1

1 
f  G v 
solve by matrix inversion.

Ellipsoids
Triangulations for an oblate ellipsoid of axial ratio 4 with 528
triangles.
Triangulations for a prolate ellipsoid of axial ratio 1/4
with 504 triangles.
GIVEN THE SURFACE STRESSES, WE HAVE EVERYTHING!
Calculate the Total Force and Torque:

F 
N

j 1

T 



f j  j   K tt .v p  K tr .w p

 

r
x
f



K
.
v

K
.
w
 p j j
rt
p
rr
p
N
j 1
Do 6 BE calculations: Note that G matrix is the same for all!


w p  0, v p  v x ,0,0 , 0, v y ,0 , 0,0, v z 


v p  0, w p  w x ,0,0 , 0, w y ,0 , 0,0, w z 
This makes the K6x6 matrix. Invert it to obtain the D6x6 matrix.
DONE!
Ellipsoid Extrapolations
Data
& Response
Residuals
0.492
1 ´ 10
0.4915
5 ´ 10
0.0006
0.0008
0.0012
-5 ´ 10
0.4905
0.0008
:
-7
x
0.491
0.0006
-6
0.0012
x
-7
-1 ´ 10
-6
-1.5 ´ 10
-6
ParameterTable ®
1
x
x2
Estimate
0.488534
2.70891
- 132.873
SE
0.0000106824
0.0240266
12.3924
>
TStat
45732.5
112.747
- 10.7221
RSquared ® 0.999997, AdjustedRSquared ® 0.999994,
EstimatedVariance ® 3.93299 ´ 10- 12
PValue
0
,
0.0000786579
0.00858652
Ellipsoids: Comparison with Theory
OBLATE
p
Dtta
%
Dtt||
%
Drra
%
Drr||
%
2
0.84104
0.004
0.73655
0.02
0.22105
0.06
0.17728
0.01
4
0.48853
0.004
0.38441
0.02
0.033933
0.07
0.027774
0.03
8
0.26664
0.01
0.19514
0.02
4.5054 10-3
0.07
3.9623 10-3
0.04
30
0.076401
0.02
0.052341
0.02
8.7111 10-5
0.02
8.3765 10-5
0.07
PROLATE
p
Dtta
%
Dtt||
%
Drra
%
Drr||
%
1
1.33356
0.02
1.33356
0.02
1.0003
0.03
1.0003
0.03
1/2
0.96702
0.007
1.10782
0.03
0.3323
0.02
0.61999
0.03
1/4
0.64839
0.006
0.83443
0.003
0.073631
0.01
0.34671
0.003
1/8
0.40954
0.0007
0.57596
0.04
0.013296
0.008
0.18224
0.04
1/30
0.15318
0.01
0.23973
0.06
3.9941 10-5
0.02
0.049895
0.13
Space-filled model of lysozyme (6LYZ), smooth
quartic surface and tesselation of lysozyme.
Table I. Specific volumes of selected proteins.
Protein
Specific Volume
(mL/g)
VDW4
Exp5,6
This work
Lysozyme (6LYZ)
0.526
0.696
0.691
ChymotrypsinogenA (2CGA)
0.527
0.703
0.697
Myoglobin (1MBO)
0.569
0.721
0.720
Ribonuclease (7RSA)
0.539
0.745
0.747
Histogram ofTriangle areas for Ovalbum in
Coalesce Histogram
Number of patches
250
200
150
100
50
0
1.104 1.546 1.988 2.43 2.872 3.313 3.755 4.197 4.639 5.081 5.522 5.964 6.406 6.848 7.289 7.731 8.173 8.615 9.057 9.498 9.94
Patch Area in A^2
Extrapolation for Lysozyme
Estimate
SE
1
1.10262 10-6
2.68559 10-10
x
2.38376 10-5
4.60052 10-5
TStat
4105.68
51.815
RSquared -> 1.
EstimatedVariance -> 1.22447 10-20
Diffusion Coefficients depend on
hydration thickness
1.03 ´ 10
1.02 ´ 10
1.01 ´ 10
0.9
1.7 ´ 10
7
1.675 ´ 10
7
1.65 ´ 10
7
1.625 ´ 10
7
-6
-6
0.8
0.8
7
-6
Drr
Dtt
1.725 ´ 10
1.1
1.2
d A
1.3
1.4
1.5
0.9
7
1.575 ´ 10
1.55 ´ 10
7
1.1
1.2
1.3
d A
1.4
1.5
Table II. Comparison of transport properties and
hydration content d= 1.1 +- 0.1
Exp.
Protein
Lysozyme (6LYZ)
Chymotrypsinogen
(2CGA)
Myoglobin
(1MBO)
RibonucleaseA
(7RSA)
Data2
Computed
Hydration
(NMR freeze3)
Calc. Data
Dt
Dr
Dt
Dr||
Dr trace
107cm2/s
105 s-1
107cm2/s
105 s-1
105 s-1
11.2(.2)
2.0(.1)
11.0
1.9
9.2(.2)
1.28(.01)
9.24
10.4(.8)
1.67(.05)
10.68(.1)
2.2(.1)
Computed
Hydration
VDW4
(gH2O/gprotein)
(gH2O/gprotein)
2.16
0.325
(0.34)
0.386
1.22
1.26
0.303
(0.34)
0.401
10.2
1.62
1.74
0.314
(0.42)
0.399
10.2*
1.87
2.11
0.388*
(0.34)
0.381
V(cm3/g)
subunits
Mass
(kDa)
Calc.
Exp.
Ref.
% Err.
Calc.
BPTI (5PTI)
1
6.5
0.699
0.718
1
-3
0.414
Cytochrome c (1HRC)
1
12.4
0.706
0.715
1
-1
0.336
Ribonuclease (7RSA)
1
13.7
0.687
0.703
1
-2
0.360
Lysozyme (6LYZ)
1
14.3
0.699
0.703
1
-1
a-Lactalbumin (1HFX)
1
14.4
0.692
0.704
2
Myoglobin (1MBO)
1
17.2
0.726
0.745
Trypsin (1TPO)
1
23.2
0.728
Trypsinogen (1TGN)
1
24.0
Chymotrypsinogen A (2CGA)
1
Elastase (1EST)
Protein Volume/Hyd
h(g/g)
Exp.
Ref.
% Err.
0.35
5
-4
0.325
0.34
5
-4
-1
0.329
0.362
9
-9
1
-3
0.348
0.42
5
-17
0.727
1
0
0.286
0.702
0.73
3
-4
0.290
25.7
0.728
0.721
1
1
0.304
0.34
5
-11
1
25.9
0.732
0.73
1
0
0.294
Subtilysin (1SUP)
1
27.5
0.722
0.731
1
-1
0.260
Carbonic Anhydrase B (2CAB)
1
28.7
0.703
0.731
1
-4
0.283
Taka - Amylase A (6TAA)
1
54.0
0.733
0.700
4
2
0.223
Apo Ovotransferrin (1AIV)
1
75.4
0.722
0.732
11
-1
0.328
0.28
12
18
Transferrin (1H76)
1
76.0
0.711
0.725
5
-2
0.289
-Lactoglobulin (1BEB)
2
36.7
0.705
0.751
5
-6
0.294
0.29
5
0
Oxyhemoglobin (1HHO)
4
64.6
0.727
0.749
6
-3
0.295
0.42
5
-29
Alkaline Phosphatase (1ALK)
2
94.7
0.740
0.725
7
2
0.219
Citrate Synthase (1CTS)
2
97.9
0.711
0.733
8
-3
0.245
0.339
10
-28
Lactate Dehydrogenase (6LDH)
4
146.2
0.772
0.741
2
4
0.231
0.362
9
-36
Aldolase (1ADO)
4
156.0
0.754
0.743
5
1
0.258
Catalase (4BLC)
4
232.0
0.746
0.73
5
2
0.205
0.290
9
-29
subunit
s
Mass
(kDa)
Calc.
Exp.
Ref.
%
Err.
Calc.(1)
Calc.(2)
Calc.
Exp.
Ref
.
%
Err.
BPTI (5PTI)
1
6.5
13.66
14.4
1
-5
4.96
3.48
3.98
4.25
33
-6
Cytochrome c (1HRC)
1
12.4
11.63
11.1 - 11.6
2-4
3
2.59
2.36
2.46
Ribonuclease (7RSA)
1
13.7
10.84
10.68
5
2
2.34
1.73
1.93
2.01
48
-4
Lysozyme (2CDS)
1
14.3
10.99
10.9
6, 39 41
1
2.62
1.82
2.09
2.04
42
2
a-Lactalbumin (1HFX)
1
14.4
10.84
10.57
7
2
2.48
1.73
1.98
Profilin (1PNE)
1
14.8
10.74
10.6
8
1
2.15
1.84
1.95
1.57
8
24
Myoglobin (1MBO)
1
17.2
10.24
10.4
9
-2
1.88
1.56
1.67
1.46
56
13
Leghemoglobin (1LH1)
1
17.3
10.26
10.0
10
3
1.99
1.53
1.68
-Lactoglobulin (3BLG)
1
18.4
10.07
1.74
1.56
1.62
1.61
51
1
Cellulase (2ENG)
1
22.0
9.63
9.8
62
-2
1.50
1.37
1.41
Somatotropin (1HGU)
1
22.1
8.84
8.88
11
0
1.31
0.95
1.07
Trypsin (1TPO)
1
23.3
9.50
9.3
12
2
1.51
1.28
1.35
1.13
53
19
Trypsinogen (1TGN)
1
24.0
9.49
9.68
13
-2
1.49
1.28
1.35
Chymotrypsinogen A (2CGA)
1
25.7
9.04
9.23
14
-2
1.25
1.14
1.17
1.1
47
6
Elastase (1EST)
1
25.9
9.06
9.5
15
-5
1.28
1.13
1.18
Savinase (1SVN)
1
26.7
9.35
1.36
1.27
1.30
1.35
46
-4
Subtilysin (1SUP)
1
27.3
9.10
9.04
16
1
1.25
1.17
1.20
Carbonic Anhydrase B (2CAB)
1
28.7
8.84
8.89
17
-1
1.20
1.04
1.09
1.08
50
1
Taka - Amylase (6TAA)
1
54.0
7.22
7.37
18
-2
0.765
0.506
0.592
Human Serum Albumin (1AO6)
1
69.0
6.17
6.15
58
0
0.412
0.330
0.357
0.349
57
2
apo Ovotransferrin (1AIV)
1
75.4
5.86
6.14
52
-5
0.0408
0.0259
0.0309
0.0217
52
42
Transferrin (1H76)
1
76.0
5.96
5.73 - 6.0
19 - 21
1
0.422
0.259
0.313
0.3
61
0
Protein Transport
Dt(10-7cm2/s)
Dr(107s-1)
-Lactoglobulin (1BEB)
2
36.7
7.74
7.3
22 - 24
5
1.004
0.579
0.72
1
0.75
51
-4
Oxyhemoglobin (1HHO)
4
68.0
6.95
6.5 - 6.9
24 - 25
4
0.594
0.509
0.53
7
0.52
21
4
KDPG Aldolase (1EUN)
3
69.2
6.22
5.6
26
11
0.415
0.369
0.38
3
Alkaline Phosphatase
(1ALK)
2
94.7
5.92
5.7
27
4
0.439
0.269
0.32
5
Concanavalin (2CTV)
4
96.2
5.75
5.6
24, 28
4
0.303
0.290
0.29
5
Citrate Synthase (1CTS)
2
97.9
5.82
5.8
29
0
0.380
0.276
0.31
0
Glucose Oxidase (1GPE)
2
133.7
5.45
5.02 5.13
30, 59
7
0.297
0.238
0.25
8
Canavalin (2CAV)
3
141.0
5.32
5.10
24
4
0.243
0.215
0.22
5
Lactate Dehydrogenase
(6LDH)
4
145.2
5.08
4.99
31
2
0.216
0.201
0.20
6
0.20
55
5
Aldolase (1ADO)
4
156.0
4.66
4.29 4.8
32 - 35
3
0.166
0.147
0.15
3
Nitrogenase MoFe (2MIN)
4
220.0
4.41
4.0
36
10
0.166
0.120
0.13
5
Catalase (4BLC)
4
230.3
4.49
4.1
24, 37
10
0.156
0.138
0.14
4
Xanthine Oxidase (1FIQ)
6
270.0
3.94
3.9
38
0
0.133
0.0747
0.09
40
[] (cm3/g)
Protein
The Intrinsic Viscosity of Proteins.
Dt(10-7cm2/s)
Mass
kDa
Calc.
Exp.
Ref.
%Err
Calc.
Exp.
Ref.
%Er
.
Cytochrome c (1HRC)
1
12.4
3.04
2.74
1
12
11.63
11.1 - 11.6
29 - 31
3
Ribonuclease (7RSA)a
1
13.7
3.52
3.30 - 3.50
2, 38
3
10.84
10.68
32
2
Lysozyme (2CDS)
1
14.3
3.22
2.98 - 3.00
3, 4
8
11.04
10.9
33 – 36
1
a-Lactalbumin (1HFX)
1
14.4
3.38
3.4
5
0
10.84
10.57
45
2
Myoglobin (1MBO)
1
17.2
3.37
3.15 - 3.25
6, 7
5
10.24
10.4
46
-2
Trypsinogen (1TGN)
1
24.0
3.00
2.96
8
1
9.49
9.68
47
-2
Chymotrypsinogen A (2CGA)
1
25.7
3.23
3.12
10
3
9.04
9.23
48
-2
Carbonic Anhydrase B (2CAB)
1
28.7
3.08
2.76 - 3.2
11, 44
3
8.84
8.89
49
-1
Taka - Amylase A (6TAA)
1
51.2
3.23
3.3
12
-2
7.22
7.37
50
-2
Human Serum Albumin (1AO6)
1
66.2
3.92
3.9
41, 42
0
6.17
6.15
43
0
Ovotransferrin (1OVT)
1
75.5
3.86
3.8
13
2
6.03
5.72
51
5
Transferrin (1H76)
1
76.0
3.85
4.0
14
-4
5.96
5.73 – 6.0
52, 53
1
6.4
3.15
2.9
66
9
14.45
2
Insulin (9INS)
-Lactoglobulin (1BEB)
2
36.7
3.65
4.0
16 – 18
-9
7.74
7.3
54
5
α-Chymotrypsin (5CHA)
2
49.7
3.27
4.1
39
-20
7.24
7.40
40
-2
Ricin (2AAI)
2
61.7
3.35
2.96
67
14
6.61
6.0
68
10
Oxyhemoglobin (1HHO)
4
68.0
2.87
3.6 - 4.0
19, 21
-18
6.95
6.5 – 6.9
55, 56
7
Alkaline Phosphatase (1ALK)
2
94.7
3.17
3.4
23
-7
5.92
5.7
57
4
Citrate Synthase (1CTS)
2
97.9
3.20
3.95
24
-20
5.82
5.8
58
0
Glucose Oxidase (1GPE)
2
133.7
2.83
4.0
25
-29
5.45
5.13
59
6
Lactate Dehydrogenase (6LDH)
4
145.2
3.21
3.8
26
-16
5.08
4.99
60
2
Aldolase (1ADO)
4
156.0
3.87
4.0
27, 36
-3
4.66
4.29 - 4.8
61 - 64
5
Catalase (4BLC)
4
230.3
3.15
3.9
28, 37
-19
4.49
4.1
65
10
The Ubiquitin Problem
Translational and rotational diffusion
coefficients calculated for ubiquitin, ubiquitin
modified and ubiquitin clipped with a hydration
layer of 1.5 Å.
Dt and Dr experimental are 14.9 x107 cm2/s and
4.02x107 s-1
Protein
Dt 107 cm2/s
Dr 107 s-1
UBQ
12.58
3.10
UBQ modified
12.96
3.46
UBQ clipped
13.32
3.76
DNA oligomer tessellation
Uniform hydration
Non-uniform hydration
Table IV: Uniform Hydration of a
DNA oligomer
Table V: Non-uniform Hydration of a
DNA oligomer
Nitrogen Inflation
8.00
7.00
6.00
% Error
5.00
Nitrogen
inflation of 2.6
A yields a 1%
error in both
Dt and Dr.
4.00
3.00
% error rotation
2.00
% error translation
1.00
0.00
-1.00 0
1
2
3
-2.00
-3.00
Inflation to Nitrogens(A)
4
Conclusions I
• Extrapolation is needed for high accuracy.
• A single calculation yields a transport property
within 2% of the extrapolated value.
• Numerical accuracy is better than 0.1%
• Precision is 0.1 % for Dt and 0.3% for Dr with
extrapolation.
• Hydration content and specific volumes are
obtainable, in good agreement with experiment
• Using 1.1 A hydration, we can match transport
properties for a broad range of proteins within their
experimental error.
Conclusions II
• Uniform hydration layer describes hydrodynamic
transport of proteins well.
• We appear to be detecting a difference between the
crystal and solution structures for multi-subunit
proteins.
• Nucleic acids are better described by non-uniform
hydration, with more water in the grooves.
• This work demonstrates the effectiveness of the
boundary element method for the calculation of
the transport properties of biomolecules, and their
intrinsic advantage over traditional bead methods.
References
1.Antiosewicz,J. and Porschke,D. J. Phys.Chem. 93,5301-5305 (1989)
2.Youngren,G.K. and Acrivos,A,J. Fluid. Mech. 69,377-402 (1975)
3.Connolly,M.L., J. Mol. Graphics 11, 139-141 (1993)
4.Zhou,H-X.,Biophys.J. 69, 2286-2297 (1995)
5.Squire,P.G. and Himmel,M.E. Arc. Bioc. Bioph.,196,165-177 (1979)
6.Kuntz,I.D. and Kauzman, W. Ad. Protein Chem.,28,239-345 (1974)
7.Bull,H.B. and Breese,Arch.Biochem. Biophys.,128,497-502 (1968)
8. Eimer, W. and Pecora, R., J.Chem.Phys., 94, 2324 (1991)
ARAGON GROUP
Martin Perez, M.S. 2003, Ph.D.
candidate, UC San Diego
Chris Potter, B.S. Chem
Tilman Rosales. M.S. 2002,
Ph.D. candidate, U.
Maryland/NIH
Heather Harding, B.S.
Chem
Chris Zimmer, M.S. 2003, Ph.D.
candidate, UC Davis.
Ryan Moffet, B.S. 2002, Ph.D.
candidate, UC San Diego
David Hahn, Ph.D.
Postdoctoral Fellow
Visualization & Interactive
Computation Projects
1. Triangulation Visualization & smart triangulator?
Rotate a triangulation real time to visualize shape.
Generate a smart triangulator to make Coalesce obsolete.
2. Manually assisted hydration program
Need to avoid a very very expensive computation first.
3. Web based interactive computation.
Integration of fortran and visualization via a web accesible
user interface. Enable non-expert to perform high precision
hydrodynamic computations.
Fig. 2 Lysozyme: Explicit
Hydration
256 waters are
included within a
cutoff distance of
3.25 A from the
molecular surface.
[Solvate Program]
Table III. Comparison of Uniform Hydration and
Explicit Hydration for Lysozyme
A^2
A*3
10^6 cm^2/s 1/s
Hydration
lysozyme
molec surface volume
dt
dr1
dr2
dr3
patches
h
# Waters
1.3
5837.369 24663.206
11.31 1.967E+07 2.018E+07 2.843E+07 2950
1.4
5868.519 25354.493
11.23 1.927E+07 1.973E+07 2.772E+07 2814
1.5
5909.729 25990.992
11.17 1.903E+07 1.950E+07 2.719E+07 2812
0.445
354
Dt Expt:
11.2
Explicit hydration
cutoff distance
lysozyme 3.24
7195.532 22867.055
11.06 1.867E+07 1.937E+07 2.622E+07 3921
0.301
245
lysozyme 3.25
7200.115 23188.109
11.36 1.894E+07 1.968E+07 2.622E+07 4001
0.315
256
lysozyme 3.26
7265.007 23444.381
11.04 1.844E+07 1.911E+07 2.706E+07 3942
0.327
266
lysozyme 3.25
7200.115
23188.109
11.14 1.896E+07 2.020E+07 2.842E+07
4653
0.315
256