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Sabine Peres, Mario Jolicœur, Cécile Moulin, Philippe Dague, Stefan Schuster
How important is thermodynamics for identifying elementary flux modes?
www.plosone.org
www.plosone.org
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()Tj
/F7 1 Tf
-0.004 Tc
0.9922 0 Td
(1)Tj
0.6973 0 Td
(and,)Tj
1.9559 0 Td
(at)Tj
0.9524 0 Td
(least)Tj
1.9842 0 Td
(theoretically,)Tj
5.3632 0 Td
(we)Tj
1.3322 0 Td
(see)Tj
1.423 0 Td
(that,)Tj
2.0069 0 Td
(if)Tj
0.7767 0 Td
(the)Tj
1.4684 0 Td
(concentrations)Tj
6.1794 0 Td
(of)Tj
1.0148 0 Td
(external)Tj
-33.5619 -1.491 Td
(metabolites)Tj
4.8018 0 Td
(are)Tj
1.4513 0 Td
(imposed)Tj
3.6454 0 Td
(such)Tj
2.0579 0 Td
(that)Tj
ET
Q
q
1 j
1 J
0 w
337.3795 617.5559 m
344.9764 617.5559 l
344.9764 617.1591 l
337.3795 617.1591 l
f*
5.9998 0 0 5.9998 338.1732 620.7307 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
-0.1322 -0.2173 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 341.9716 617.9527 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 338.1732 612.737 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
-0.1322 -0.2173 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 341.9716 609.959 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 347.7543 614.8346 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(<)Tj
/F8 1 Tf
1.0488 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 364.7055 612.3401 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 368.2204 614.8346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 374.6834 612.3401 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 378.3685 614.8346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
/F7 1 Tf
-0.004 Tc
0.7199 0 Td
(,)Tj
0.4422 0 Td
(then)Tj
2.0183 0 Td
(the)Tj
1.4683 0 Td
(thermodynamical)Tj
7.3247 0 Td
(feasibility)Tj
4.0365 0 Td
(condi-)Tj
-33.8453 -1.542 Td
(tion)Tj
0.83 0.64 0.02 0 k
1.8425 0 Td
(Eq)Tj
1.2926 0 Td
(\(1\))Tj
0 g
1.3776 0 Td
(is)Tj
0.8447 0 Td
(satisfied)Tj
3.4526 0 Td
(for)Tj
1.3833 0 Td
(reactions)Tj
3.8551 0 Td
(1)Tj
0.6973 0 Td
(and)Tj
/F8 1 Tf
1.7291 0 Td
[()]TJ
/F7 1 Tf
0.7484 0 Td
(in)Tj
1.0317 0 Td
(forward)Tj
3.4072 0 Td
(direction,)Tj
4.0762 0 Td
(whatever)Tj
3.8381 0 Td
(the)Tj
1.4683 0 Td
(direction)Tj
3.8551 0 Td
(of)Tj
1.0148 0 Td
(any)Tj
-35.9146 -1.3606 Td
(of)Tj
1.0148 0 Td
(the)Tj
/F8 1 Tf
1.4683 0 Td
[()]TJ
/F13 1 Tf
0.7483 0 Td
[()]TJ
/F7 1 Tf
0.7881 0 Td
(2)Tj
0.6973 0 Td
(other)Tj
2.3471 0 Td
(reactions)Tj
/F8 1 Tf
3.8551 0 Td
[()]TJ
/F7 1 Tf
(,)Tj
0.7029 0 Td
(2)Tj
/F16 1 Tf
0 Tc
0.6917 0 Td
()Tj
/F8 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F16 1 Tf
0 Tc
0.4762 0 Td
()Tj
/F8 1 Tf
-0.004 Tc
0.9922 0 Td
[()]TJ
/F13 1 Tf
0.7483 0 Td
[()]TJ
/F7 1 Tf
0.788 0 Td
(1.)Tj
0.9241 0 Td
(In)Tj
1.1054 0 Td
(the)Tj
1.474 0 Td
(same)Tj
2.2564 0 Td
(way,)Tj
2.0182 0 Td
(if)Tj
/F15 1 Tf
0 Tc
0.8901 0.2154 Td
()Tj
/F8 1 Tf
-0.1134 -0.2154 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 456.0377 583.3133 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 460.6866 587.9622 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
-0.119 -0.2154 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 466.8661 583.3133 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 473.159 585.8078 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(<)Tj
/F8 1 Tf
1.0488 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 490.1102 583.3133 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
/F16 1 Tf
0.5858 1.1055 Td
( )Tj
/F15 1 Tf
0.7654 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 501.7322 585.8078 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 508.1952 583.3133 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 511.8803 585.8078 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
/F7 1 Tf
-0.004 Tc
0.7199 0 Td
(,)Tj
0.83 0.64 0.02 0 k
0.4422 0 Td
(Eq)Tj
1.2983 0 Td
(\(1\))Tj
0 g
1.3776 0 Td
(is)Tj
0.8448 0 Td
(sat-)Tj
-35.8693 -1.3039 Td
(isfied)Tj
2.3527 0 Td
(for)Tj
1.389 0 Td
(reaction)Tj
3.4922 0 Td
(1)Tj
0.6917 0 Td
(in)Tj
1.0375 0 Td
(backward)Tj
4.0988 0 Td
(direction)Tj
3.8551 0 Td
(and)Tj
1.7292 0 Td
(reaction)Tj
/F8 1 Tf
3.4922 0 Td
[()]TJ
/F7 1 Tf
0.7484 0 Td
(in)Tj
1.0374 0 Td
(forward)Tj
3.4016 0 Td
(direction,)Tj
4.0818 0 Td
(whatever)Tj
3.838 0 Td
(the)Tj
-35.2456 -1.3493 Td
(direction)Tj
3.8551 0 Td
(of)Tj
1.0148 0 Td
(any)Tj
1.6554 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
/F8 1 Tf
1.4683 0 Td
[()]TJ
/F13 1 Tf
0.7484 0 Td
[()]TJ
/F7 1 Tf
0.788 0 Td
(2)Tj
0.6973 0 Td
(other)Tj
2.3471 0 Td
(reactions.)Tj
4.0818 0 Td
(This)Tj
1.9843 0 Td
(means)Tj
2.8063 0 Td
(that)Tj
1.7801 0 Td
(choosing)Tj
3.8268 0 Td
(for)Tj
1.3889 0 Td
(example)Tj
/F15 1 Tf
0 Tc
3.6623 0.2155 Td
()Tj
/F8 1 Tf
-0.1134 -0.2155 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 537.3921 556.7811 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 543.685 559.2755 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F15 1 Tf
1.0488 0 Td
(1)Tj
/F7 1 Tf
-0.004 Tc
-35.4158 -1.3606 Td
(and)Tj
/F15 1 Tf
0 Tc
1.8482 0.2098 Td
()Tj
/F8 1 Tf
-0.1191 -0.2098 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 224.674 543.1181 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 230.9669 545.6692 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(<)Tj
/F8 1 Tf
1.0488 0 Td
[()18()12()]TJ
/F16 1 Tf
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 267.5338 543.1181 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 271.0488 545.6692 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(;)Tj
/F8 1 Tf
0.4365 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 281.8771 543.1181 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
/F16 1 Tf
0.5858 1.1149 Td
( )Tj
/F15 1 Tf
0.7654 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 293.4992 545.6692 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 303.8173 543.1181 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 307.5023 545.6692 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
/F7 1 Tf
-0.004 Tc
0.941 0 Td
(satisfies)Tj
0.83 0.64 0.02 0 k
3.2769 0 Td
(Eq)Tj
1.2982 0 Td
(\(1\))Tj
0 g
1.3777 0 Td
(for)Tj
1.3833 0 Td
(reaction)Tj
/F8 1 Tf
3.4922 0 Td
[()]TJ
/F7 1 Tf
0.7484 0 Td
(in)Tj
1.0374 0 Td
(forward)Tj
3.4016 0 Td
(direction,)Tj
4.0819 0 Td
(whatever)Tj
3.838 0 Td
(the)Tj
-35.6255 -1.3095 Td
(direction)Tj
3.8551 0 Td
(of)Tj
1.0148 0 Td
(any)Tj
1.6555 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
/F8 1 Tf
1.4683 0 Td
[()]TJ
/F13 1 Tf
0.7483 0 Td
[()]TJ
/F7 1 Tf
0.7881 0 Td
(1)Tj
0.6972 0 Td
(other)Tj
2.347 0 Td
(reactions.)Tj
4.0819 0 Td
(Conversely,)Tj
4.8982 0 Td
(the)Tj
1.4684 0 Td
(same)Tj
2.2563 0 Td
(reasoning)Tj
4.1499 0 Td
(shows)Tj
2.6589 0 Td
(that)Tj
1.7802 0 Td
(choos-)Tj
-34.8829 -1.3607 Td
(ing)Tj
/F15 1 Tf
0 Tc
1.6158 0.2155 Td
()Tj
/F8 1 Tf
-0.1134 -0.2155 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 222.3496 516.4724 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 228.6425 518.9669 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F15 1 Tf
1.0488 0 Td
(1)Tj
/F7 1 Tf
-0.004 Tc
0.72 0 Td
(and)Tj
/F15 1 Tf
0 Tc
1.8481 0.2154 Td
()Tj
/F8 1 Tf
-0.1134 -0.2154 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 270.9921 516.4724 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 277.285 518.9669 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(>)Tj
/F8 1 Tf
1.0488 0 Td
[()18()12()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 303.5338 522.5952 cm
BT
/F16 1 Tf
1 TL
0 0 Td
( )Tj
/F15 1 Tf
0.7748 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 311.6976 518.9669 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 322.0157 516.4724 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 325.5307 518.9669 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(;)Tj
/F8 1 Tf
0.4365 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 336.359 516.4724 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
/F16 1 Tf
0.5858 1.1055 Td
( )Tj
/F15 1 Tf
0.7654 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 347.9811 518.9669 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 358.2992 516.4724 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 361.9842 518.9669 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 369.1842 522.5952 cm
BT
/F16 1 Tf
1 TL
0 0 Td
( )Tj
/F15 1 Tf
0.7653 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 379.5023 518.9669 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(satisfies)Tj
0.83 0.64 0.02 0 k
3.2824 0 Td
(Eq)Tj
1.2926 0 Td
(\(1\))Tj
0 g
1.3777 0 Td
(for)Tj
1.3833 0 Td
(reaction)Tj
/F8 1 Tf
3.4979 0 Td
[()]TJ
/F7 1 Tf
0.7483 0 Td
(in)Tj
1.0318 0 Td
(backward)Tj
4.0989 0 Td
(direc-)Tj
-34.6617 -1.3549 Td
(tion,)Tj
2.0636 0 Td
(whatever)Tj
3.8381 0 Td
(the)Tj
1.4683 0 Td
(direction)Tj
3.8551 0 Td
(of)Tj
1.0148 0 Td
(any)Tj
1.6611 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
/F8 1 Tf
1.4683 0 Td
[()]TJ
/F13 1 Tf
0.7484 0 Td
[()]TJ
/F7 1 Tf
0.788 0 Td
(1)Tj
0.6972 0 Td
(other)Tj
2.3471 0 Td
(reactions.)Tj
4.0762 0 Td
(So,)Tj
1.4286 0 Td
(with)Tj
/F15 1 Tf
0 Tc
2.1147 0.2154 Td
()Tj
/F8 1 Tf
-0.1191 -0.2154 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 492.0377 502.9228 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 498.3307 505.4173 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F15 1 Tf
1.0488 0 Td
(1)Tj
/F7 1 Tf
-0.004 Tc
0.72 0 Td
(and)Tj
1.7347 0 Td
(depending)Tj
-33.3351 -1.3606 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(value)Tj
2.3074 0 Td
(of)Tj
/F15 1 Tf
0 Tc
1.1339 0.2155 Td
()Tj
/F8 1 Tf
-0.1191 -0.2155 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 268.044 489.3165 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 271.5023 491.811 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(either)Tj
2.5342 0 Td
(smaller)Tj
3.1181 0 Td
(than)Tj
/F8 1 Tf
0 Tc
2.0296 0 Td
[()18()12()]TJ
/F16 1 Tf
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 378.8787 489.3165 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 382.3937 491.811 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(;)Tj
/F8 1 Tf
0.4365 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 393.222 489.3165 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
/F16 1 Tf
0.5858 1.1055 Td
( )Tj
/F15 1 Tf
0.7748 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 404.844 491.811 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 415.1622 489.3165 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 418.9039 491.811 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
/F7 1 Tf
-0.004 Tc
0.9354 0 Td
(or)Tj
1.0998 0 Td
(greater)Tj
3.0047 0 Td
(than)Tj
/F8 1 Tf
0 Tc
-26.9288 -1.3719 Td
[()18()12()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 215.7732 481.7196 cm
BT
/F16 1 Tf
1 TL
0 0 Td
( )Tj
/F15 1 Tf
0.7748 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 223.8803 478.0913 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 234.1984 475.5968 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 237.7133 478.0913 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(;)Tj
/F8 1 Tf
0.4365 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 248.5417 475.5968 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
/F16 1 Tf
0.5858 1.1055 Td
( )Tj
/F15 1 Tf
0.7748 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 260.2204 478.0913 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 270.5385 475.5968 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 274.2236 478.0913 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 281.3669 481.7196 cm
BT
/F16 1 Tf
1 TL
0 0 Td
( )Tj
/F15 1 Tf
0.7748 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 291.685 478.0913 cm
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/F7 1 Tf
1 TL
-0.004 Tc
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(\(both)Tj
2.4037 0 Td
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4.4731 0 Td
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3.8097 0 Td
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0 Tc
1.0148 0 Td
[()18()12()]TJ
/F16 1 Tf
()Tj
/F8 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 489.8267 475.5968 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 493.3417 478.0913 cm
BT
/F17 1 Tf
1 TL
0 0 Td
(;)Tj
/F8 1 Tf
0.4365 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 504.17 475.5968 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
/F16 1 Tf
0.5858 1.1055 Td
( )Tj
/F15 1 Tf
0.7748 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 515.7921 478.0913 cm
BT
/F16 1 Tf
1 TL
0 0 Td
()Tj
0.6633 0 Td
()Tj
/F15 1 Tf
1.0488 0 Td
(1)Tj
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0.72 0 Td
(and)Tj
/F8 1 Tf
-34.0098 -1.3039 Td
[()]TJ
/F16 1 Tf
0 Tc
0.8617 0 Td
()Tj
/F7 1 Tf
-0.004 Tc
0.9921 0 Td
(1\),)Tj
1.2586 0 Td
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2.0183 0 Td
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7.3191 0 Td
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1.6611 0 Td
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1.1452 0 Td
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1.474 0 Td
[()]TJ
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[()]TJ
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2.0183 0 Td
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5.9753 0 Td
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1.0319 0 Td
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1.661 0 Td
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3.8551 0 Td
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4.3483 0 Td
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4.1442 0 Td
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1.6271 0 Td
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2.228 0 Td
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1.1792 0 Td
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0 Tc
4.9095 0.2154 Td
()Tj
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-0.1191 -0.2154 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 562.9039 436.0818 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 425.1401 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(and)Tj
/F15 1 Tf
0 Tc
1.8481 0.2097 Td
()Tj
/F8 1 Tf
-0.119 -0.2097 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 224.674 422.5889 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 228.1889 425.1401 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4422 0 Td
(and)Tj
1.7291 0 Td
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3.8551 0 Td
(1)Tj
0.6973 0 Td
(and)Tj
/F8 1 Tf
1.7291 0 Td
[()]TJ
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1.3153 0 Td
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1.9842 0 Td
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-34.6277 -1.3039 Td
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3.05 0 Td
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1.1792 0 Td
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1.7121 0 Td
(the)Tj
1.4683 0 Td
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5.6693 0 Td
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2.3811 0 Td
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1.9105 0 Td
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2.2054 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 400.5354 416.5795 cm
BT
/F8 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 406.6582 412.1007 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(to)Tj
1.0261 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 421.6818 416.5795 cm
BT
/F8 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F13 1 Tf
0.8239 0 Td
[()]TJ
/F7 1 Tf
0.8617 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 437.8393 412.1007 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4478 0 Td
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1.2529 0 Td
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5.2044 0 Td
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1.4683 0 Td
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-32.1559 -1.2982 Td
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0.83 0.64 0.02 0 k
4.1159 0 Td
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1.2926 0 Td
(\(15\))Tj
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1.8538 0 Td
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3.4753 0 Td
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1.7801 0 Td
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4.4447 0 Td
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1.0261 0 Td
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1.1509 0 Td
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3.4752 0 Td
(that)Tj
1.7802 0 Td
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1.1452 0 Td
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1.0262 0 Td
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1.0374 0 Td
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3.0614 0 Td
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1.9786 0 Td
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6.0321 0 Td
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3.7417 0 Td
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1.0999 0 Td
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4.0988 0 Td
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1.7348 0 Td
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1.9332 0 Td
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1.7064 0 Td
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3.4129 0 Td
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3.8097 0 Td
( \( \) 0 V)Tj
/F7 1 Tf
(,)Tj
2.8063 0 Td
(and)Tj
-34.5087 -1.2983 Td
(thus)Tj
1.9332 0 Td
(dividing)Tj
3.5433 0 Td
(by)Tj
1.1849 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 271.3889 364.5354 cm
BT
/F8 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F13 1 Tf
0.8163 0 Td
[()]TJ
/F7 1 Tf
0.8618 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 289.7574 360.1133 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(the)Tj
1.4683 0 Td
(configuration)Tj
5.6749 0 Td
(space)Tj
2.3754 0 Td
(size,)Tj
1.9106 0 Td
(from)Tj
2.2053 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 430.8661 364.5354 cm
BT
/F8 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 437.0456 360.1133 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(to)Tj
1.0204 0 Td
(2.)Tj
0.9241 0 Td
(Adding)Tj
3.2428 0 Td
(the)Tj
1.4684 0 Td
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4.0308 0 Td
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1.0261 0 Td
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1.4684 0 Td
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4.8869 0 Td
(condition)Tj
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4.4674 0 Td
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0.83 0.64 0.02 0 k
1.2755 0 Td
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1.2983 0 Td
(\(1\))Tj
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3.0218 0 Td
( \( \) 0)Tj
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2.2564 0 Td
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[()]TJ
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1.8425 0 Td
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5.5104 0 Td
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3.4356 0 Td
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1.6837 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 350.9291 266.9669 cm
BT
/F8 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 356.5984 268.6677 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
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2.2053 0 Td
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4.9266 0.2097 Td
()Tj
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[()]TJ
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1 j
1 J
0 w
5.9998 0 0 5.9998 468.3968 266.1732 cm
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/F8 1 Tf
1 TL
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[()]TJ
ET
Q
q
1 j
1 J
0 w
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1 TL
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1.0261 0 Td
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Q
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1 j
1 J
0 w
5.9998 0 0 5.9998 555.5338 258.8598 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
0 -1.3323 Td
[()]TJ
/F16 1 Tf
()Tj
/F15 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 566.9291 253.644 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 571.748 251.1496 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 238.3937 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(reactions,)Tj
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0 Tc
4.0761 0.7483 Td
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ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 251.3196 243.5527 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
0 -1.3228 Td
[()]TJ
/F16 1 Tf
()Tj
/F15 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 262.7149 238.3937 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 267.5338 235.8992 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 271.8425 238.3937 cm
BT
/F16 1 Tf
1 TL
0 0 Td
( )Tj
/F8 1 Tf
0.9977 0 Td
[()]TJ
/F16 1 Tf
0.6917 0 Td
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(1)Tj
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3.3562 0 Td
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1.7292 0 Td
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1 j
1 J
0 w
536.5417 241.0583 m
554.4 241.0583 l
554.4 240.6614 l
536.5417 240.6614 l
f*
5.9998 0 0 5.9998 536.5417 242.9858 cm
BT
/F8 1 Tf
1 TL
0 0 Td
[()]TJ
/F16 1 Tf
()Tj
/F8 1 Tf
[()]TJ
/F16 1 Tf
( )Tj
/F15 1 Tf
2.0882 0 Td
(1)Tj
/F16 1 Tf
()Tj
/F15 1 Tf
-0.8504 -1.3323 Td
(2)Tj
ET
Q
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1 j
1 J
0 w
10 0 0 10 556.611 238.3937 cm
BT
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1 TL
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( \( \) 0 V)Tj
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1.1452 0 Td
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1.1679 0 Td
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4.8075 0 Td
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4.0422 0 Td
(12)Tj
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(metabolites)Tj
4.8076 0 Td
(\(see)Tj
0.83 0.64 0.02 0 k
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(Fig)Tj
1.4797 0 Td
(4)Tj
0 g
(\).)Tj
1.2642 0 Td
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2.5966 0 Td
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3.8267 0 Td
([)Tj
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(12)Tj
0 g
(],)Tj
2.0806 0 Td
(we)Tj
1.3266 0 Td
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3.7304 0 Td
(31)Tj
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1.1735 0 Td
( \( \) 0 V)Tj
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2.2337 0 Td
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(a)Tj
0.6576 0 Td
(matlab)Tj
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/F6 1 Tf
3.6283 0 Td
( \( \) 0 G U D Z)Tj
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4.3483 0 Td
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1.7802 0 Td
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1.3266 0 Td
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1.7121 0 Td
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-35.4838 -1.2983 Td
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2.5852 0 Td
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(and)Tj
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(if)Tj
0.7767 0 Td
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1.4683 0 Td
( \( \) 0 V)Tj
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1.9956 0 Td
(thermodynamics.)Tj
7.2283 0 Td
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1.7858 0 Td
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2.7439 0 Td
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3.6057 0 Td
(27)Tj
/F6 1 Tf
-36.6347 -1.2983 Td
( W \( \) 0 V)Tj
/F7 1 Tf
3.1691 0 Td
(at)Tj
/F8 1 Tf
0.9524 0 Td
[()]TJ
/F7 1 Tf
0.8107 0 Td
(=)Tj
0.7994 0 Td
(0)Tj
0.6973 0 Td
(and)Tj
1.7291 0 Td
(26)Tj
/F6 1 Tf
1.1735 0 Td
( W \( \) 0 V)Tj
/F7 1 Tf
3.1692 0 Td
(at)Tj
/F8 1 Tf
0.9524 0 Td
[()]TJ
/F7 1 Tf
0.8107 0 Td
(=)Tj
0.7994 0 Td
(48)Tj
/F8 1 Tf
[()]TJ
/F7 1 Tf
(,)Tj
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1.9048 0 Td
[()]TJ
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0.8107 0 Td
(=)Tj
0.7994 0 Td
(72)Tj
/F8 1 Tf
[()]TJ
/F7 1 Tf
1.6781 0 Td
(and)Tj
/F8 1 Tf
1.7291 0 Td
[()]TJ
/F7 1 Tf
0.8107 0 Td
(=)Tj
0.7994 0 Td
(96)Tj
/F8 1 Tf
[()]TJ
/F7 1 Tf
(.)Tj
1.9049 0 Td
(The)Tj
1.7801 0 Td
(non-thermodynamic)Tj
/F6 1 Tf
-27.2804 -1.2982 Td
( \( \) 0 V)Tj
/F7 1 Tf
2.5795 0 Td
(at)Tj
/F8 1 Tf
0.9524 0 Td
[()]TJ
/F7 1 Tf
0.8107 0 Td
(=)Tj
0.7994 0 Td
(0)Tj
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[()]TJ
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1.2018 0 Td
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1.6725 0 Td
([8)Tj
1.0375 0 Td
(16)Tj
1.1735 0 Td
(18)Tj
1.1679 0 Td
(23])Tj
1.5136 0 Td
(\(shown)Tj
3.1862 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
0.83 0.64 0.02 0 k
1.4684 0 Td
(Fig)Tj
1.4797 0 Td
(5)Tj
0 g
(\),)Tj
1.2642 0 Td
(whereas)Tj
3.4412 0 Td
(at)Tj
/F8 1 Tf
0.9525 0 Td
[()]TJ
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0.8107 0 Td
(=)Tj
0.7993 0 Td
(48,)Tj
1.4003 0 Td
(72,)Tj
1.3947 0 Td
(96)Tj
/F8 1 Tf
[()]TJ
/F7 1 Tf
1.6781 0 Td
(they)Tj
1.9275 0 Td
(are:)Tj
1.6725 0 Td
([8)Tj
1.0374 0 Td
(13)Tj
-36.4589 -1.2983 Td
(15)Tj
1.1678 0 Td
(16)Tj
1.1736 0 Td
(23])Tj
1.5136 0 Td
(\(shown)Tj
3.1862 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0374 0 Td
(Fig)Tj
1.4797 0 Td
(6)Tj
0 g
(\).)Tj
/F6 1 Tf
1.2586 0 Td
( \( \) 0)Tj
/F7 1 Tf
1.9899 0 Td
(8)Tj
0.6973 0 Td
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0.8504 0 Td
(most)Tj
2.2053 0 Td
(improbable)Tj
4.8189 0 Td
(because)Tj
3.3165 0 Td
(it)Tj
0.7881 0 Td
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0.8503 0 Td
(known)Tj
3.0047 0 Td
(that)Tj
1.7745 0 Td
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2.778 0 Td
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(mostly)Tj
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3.2484 0 Td
(from)Tj
2.2054 0 Td
(glucose)Tj
3.1748 0 Td
(and)Tj
1.7291 0 Td
(not)Tj
1.576 0 Td
(from)Tj
2.2054 0 Td
(glutamine)Tj
4.2519 0 Td
([)Tj
0.83 0.64 0.02 0 k
(42)Tj
0 g
(].)Tj
2.075 0 Td
(In)Tj
1.1111 0 Td
(the)Tj
1.4684 0 Td
(model,)Tj
2.9707 0 Td
(we)Tj
1.3266 0 Td
(only)Tj
1.9785 0 Td
(describe)Tj
3.5206 0 Td
(one)Tj
1.7008 0 Td
(pool)Tj
1.9956 0 Td
(of)Tj
-36.5383 -1.2983 Td
(pyruvate)Tj
3.702 0 Td
(\()Tj
/F8 1 Tf
[()]TJ
/F7 1 Tf
(.)Tj
/F8 1 Tf
[()]TJ
/F7 1 Tf
1.4456 0 Td
(the)Tj
1.4684 0 Td
(cytosolic)Tj
3.7077 0 Td
(pyruvate)Tj
3.702 0 Td
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0.8447 0 Td
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1.5761 0 Td
(differentiated)Tj
5.6069 0 Td
(from)Tj
2.2053 0 Td
(mitochondrial)Tj
5.9641 0 Td
(pyruvate\).)Tj
4.2689 0 Td
(It)Tj
0.8561 0 Td
(is)Tj
-35.3478 -1.2983 Td
(known)Tj
3.0047 0 Td
(that)Tj
1.7744 0 Td
(lactate)Tj
2.778 0 Td
(comes)Tj
2.7552 0 Td
(from)Tj
2.2054 0 Td
(cytosolic)Tj
3.7077 0 Td
(pyruvate)Tj
3.702 0 Td
(while)Tj
2.3697 0 Td
(alanine)Tj
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(from)Tj
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(mitochondrial)Tj
-30.3815 -1.3039 Td
(pyruvate)Tj
3.702 0 Td
(\(which)Tj
2.9877 0 Td
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2.4378 0 Td
(from)Tj
2.2053 0 Td
(glutamine\).)Tj
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(Moreover,)Tj
4.3936 0 Td
(after)Tj
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2.0353 0 Td
[()]TJ
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0.8107 0 Td
(=)Tj
0.7994 0 Td
(48)Tj
/F8 1 Tf
[()]TJ
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1.6781 0 Td
(the)Tj
1.4683 0 Td
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1.7291 0 Td
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0.8504 0 Td
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3.2201 0 Td
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1.0261 0 Td
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1.1509 0 Td
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4.8869 0 Td
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1.6214 0 Td
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1.474 0 Td
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2.2564 0 Td
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3.0897 0 Td
(the)Tj
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1.4684 0 Td
( \( \) 0)Tj
/F7 1 Tf
1.9899 0 Td
(13)Tj
1.1735 0 Td
(and)Tj
/F6 1 Tf
1.7291 0 Td
( \( \) 0)Tj
/F7 1 Tf
-35.4838 -1.2983 Td
(16)Tj
1.1678 0 Td
(cannot)Tj
2.982 0 Td
(be)Tj
1.1509 0 Td
(thermodynamically)Tj
8.022 0 Td
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3.3959 0 Td
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1.2019 0 Td
[()]TJ
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0.8107 0 Td
(=)Tj
0.7993 0 Td
(0,)Tj
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(the)Tj
1.4684 0 Td
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(phase.)Tj
2.7099 0 Td
(Therefore,)Tj
4.3937 0 Td
(the)Tj
/F6 1 Tf
1.4683 0 Td
( \( \) 0)Tj
/F7 1 Tf
1.9899 0 Td
(16)Tj
1.1735 0 Td
(makes)Tj
2.7496 0 Td
(no)Tj
1.2756 0 Td
(biological)Tj
4.0932 0 Td
(sense)Tj
2.3358 0 Td
(with)Tj
1.9955 0 Td
(ATP)Tj
2.075 0 Td
(consumption)Tj
5.5445 0 Td
(for)Tj
1.389 0 Td
(the)Tj
-36.2662 -1.2983 Td
(transformation)Tj
6.2701 0 Td
(of)Tj
1.0148 0 Td
(extracellular)Tj
5.1364 0 Td
(glutamine)Tj
4.2463 0 Td
(into)Tj
1.8425 0 Td
(extracellular)Tj
5.1306 0 Td
(alanine,)Tj
3.3449 0 Td
(while)Tj
2.3698 0 Td
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4.0422 0 Td
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-35.3194 -1.2983 Td
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(anabolic)Tj
3.5887 0 Td
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3.118 0 Td
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2.3868 0 Td
(intermediate)Tj
5.3234 0 Td
(metabolites)Tj
4.8076 0 Td
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1.0148 0 Td
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(well)Tj
1.8198 0 Td
(as)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(ATP)Tj
-34.6108 -1.3039 Td
(regenerated.)Tj
/F6 1 Tf
5.1533 0 Td
( \( \) 0)Tj
/F7 1 Tf
1.9899 0 Td
(18)Tj
1.1735 0 Td
(cannot)Tj
2.9821 0 Td
(be)Tj
1.1508 0 Td
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3.1691 0 Td
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1.0148 0 Td
(well)Tj
1.8199 0 Td
(as)Tj
1.0148 0 Td
(there)Tj
2.262 0 Td
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0.8504 0 Td
(no)Tj
1.2756 0 Td
(lactate)Tj
2.7779 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.474 0 Td
(medium)Tj
3.6057 0 Td
(but)Tj
1.5533 0 Td
(it)Tj
0.7824 0 Td
(can)Tj
-35.0813 -1.2982 Td
(be)Tj
1.1508 0 Td
(feasible)Tj
3.1691 0 Td
(thereafter)Tj
4.0762 0 Td
(because)Tj
3.3222 0 Td
(the)Tj
1.4683 0 Td
(concentration)Tj
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(of)Tj
1.0148 0 Td
(lactate)Tj
2.7779 0 Td
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/F6 1 Tf
4.0592 0 Td
( \( \) 0)Tj
/F7 1 Tf
1.9899 0 Td
(23)Tj
1.1679 0 Td
(comes)Tj
2.7552 0 Td
(down)Tj
2.4888 0 Td
(to)Tj
-35.2627 -1.2983 Td
(CO)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 214.0724 159.307 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 219.8551 161.0078 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(production)Tj
4.7168 0 Td
(and)Tj
1.7291 0 Td
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1.3209 0 Td
(infeasibility)Tj
4.8528 0 Td
(of)Tj
1.0148 0 Td
(this)Tj
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1.6725 0 Td
( \( \) 0)Tj
/F7 1 Tf
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(seems)Tj
2.6078 0 Td
(pertinent)Tj
3.9175 0 Td
(because)Tj
3.3222 0 Td
(a)Tj
0.6519 0 Td
(major)Tj
2.6079 0 Td
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3.6113 0 Td
(of)Tj
1.0148 0 Td
(this)Tj
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1.6781 0 Td
( \( \) 0)Tj
/F7 1 Tf
1.9899 0 Td
(is)Tj
0.8447 0 Td
(that)Tj
1.7802 0 Td
(the)Tj
-34.8772 -1.3039 Td
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4.2576 0 Td
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1.0261 0 Td
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2.965 0 Td
(leak)Tj
1.8198 0 Td
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3.7247 0 Td
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1.0148 0 Td
(a)Tj
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(time)Tj
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(48h,)Tj
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(the)Tj
1.4683 0 Td
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(the)Tj
1.4683 0 Td
(exponential)Tj
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(the)Tj
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1.4683 0 Td
( \( \) 0)Tj
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(15)Tj
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4.4674 0 Td
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(72h)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 107.1496 23.6976 re
W* n
q
107.0929 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 326.3811 745.7952 cm
BT
/F0 1 Tf
1 TL
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ET
Q
q
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36 48.0002 m
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576 47.5002 l
36 47.5002 l
f*
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
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(PLOS)Tj
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(ONE)Tj
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