Stochastic chains represent a key variety of phenomena in many branches of science within the context of information theory and thermodynamics. They are typically approached by a sequence of independent events or by a memoryless Markov process. Stochastic chains are of special significance to molecular biology, where genes are conveyed by linear polymers made up of molecular subunits and transferred from DNA to proteins by specialized molecular motors in the presence of errors. Here, we demonstrate that when memory is introduced, the statistics of the chain depends on the mechanism by which objects or symbols are assembled, even in the slow dynamics limit wherein friction can be neglected. To analyze these systems, we introduce a sequence-dependent partition function, investigate its properties, and compare it to the standard normalization defined by the statistical physics of ensembles. We then apply this theory to characterize the enzyme-mediated information transfer involved in DNA replication under the real, non-equilibrium conditions, reproducing measured error rates and explaining the typical 100-fold increase in fidelity that is experimentally found when proofreading and edition take place. Our model further predicts that approximately 1 kT has to be consumed to elevate fidelity in one order of magnitude. We anticipate that our results are necessary to interpret configurational order and information management in many molecular systems within biophysics, materials science, communication, and engineering.

1.
J. R.
Arias-Gonzalez
,
Integr. Biol.
6
,
904
(
2014
).
2.
C.
Bustamante
,
C.
Cheng
, and
Y. X.
Mejia
,
Cell
144
,
480
(
2011
).
3.
A.
Bérut
,
A.
Arakelyan
,
A.
Petrosyan
,
S.
Ciliberto
,
R.
Dillenschneider
, and
E.
Lutz
,
Nature
483
,
187
(
2012
).
4.
R.
Landauer
,
IBM J. Res. Develop.
5
,
261
-
269
(
1961
).
5.
C. E.
Shannon
,
Bell Syst. Tech. J.
27
,
379
(
1948
).
6.
C. H.
Bennett
,
Int. J. Theor. Phys.
21
,
905
(
1982
).
7.
F. G. S. L.
Brandão
and
M. B.
Plenio
,
Nat. Phys.
4
,
873
(
2008
).
8.
B.-H.
Liu
,
L.
Li
,
Y.-G.
Huang
,
C.-F.
Li
,
G.-C.
Guo
,
E.-M.
Laine
,
H.-P.
Breuer
, and
J.
Piilo
,
Nat. Phys.
7
,
931
(
2011
).
9.
R. K.
Pathria
and
P. D.
Beale
,
Statistical Mechanics
, 3rd ed. (
Academic Press
,
Boston
,
2011
).
10.
D.
Chandler
,
Introduction to Modern Statistical Mechanics
(
Oxford University Press
,
1987
).
11.
J. R.
Arias-Gonzalez
, e-print arXiv:1511.06139 [cond-mat.stat-mech] (
2015
).
12.
M. C.
Wang
and
G. E.
Uhlenbeck
,
Rev. Mod. Phys.
17
,
323
(
1945
).
13.
S.
Pressé
,
J.
Lee
, and
K. A.
Dill
,
J. Phys. Chem. B
117
,
495
(
2013
).
14.
H.-P.
Breuer
,
J. Phys. B: At., Mol. Opt. Phys.
45
,
154001
(
2012
).
15.
A.
Rivas
,
S. F.
Huelga
, and
M. B.
Plenio
,
Rep. Prog. Phys.
77
,
094001
(
2014
).
16.
T. A.
Kunkel
and
K.
Bebenek
,
Annu. Rev. Biochem.
69
,
497
(
2000
).
17.
L. A.
Loeb
and
T. A.
Kunkel
,
Annu. Rev. Biochem.
51
,
429
(
1982
).
18.
H. R.
Lee
and
K. A.
Johnson
,
J. Biol. Chem.
281
,
36236
(
2006
).
19.
F.
Bernardi
and
J.
Ninio
,
Biochimie
60
,
1083
(
1978
).
20.
J. R.
Arias-Gonzalez
,
PLoS One
7
,
e42272
(
2012
).
21.
D.
Andrieux
and
P.
Gaspard
,
Proc. Natl. Acad. Sci. U. S. A.
105
,
9516
(
2008
).
22.
D.
Andrieux
and
P.
Gaspard
,
J. Chem. Phys.
130
,
014901
(
2009
).
23.
C. H.
Bennett
,
Biosystems
11
,
85
(
1979
).
25.
J. J.
Hopfield
,
Proc. Natl. Acad. Sci. U. S. A.
71
,
4135
(
1974
).
26.
T. M.
Cover
and
J. A.
Thomas
,
Elements of Information Theory
(
John Wiley & Sons
,
1991
).
27.
M.
Fisz
,
Probability Theory and Mathematical Statistics
(
Krieger Publishing Company
,
1980
).
28.
P.
Schindler
,
D.
Nigg
,
T.
Monz
,
J. T.
Barreiro
,
E.
Martinez
,
S. X.
Wang
,
S.
Quint
,
M. F.
Brandl
,
V.
Nebendahl
,
C. F.
Roos
,
M.
Chwalla
,
M.
Hennrich
, and
R.
Blatt
,
New J. Phys.
15
,
123012
(
2013
).
29.
S.
Kamtekar
,
A. J.
Berman
,
J.
Wang
,
J. M.
Lázaro
,
M.
de Vega
,
L.
Blanco
,
M.
Salas
, and
T. A.
Steitz
,
Mol. Cell
16
,
609
(
2004
).
30.
S. J.
Johnson
and
L. S.
Beese
,
Cell
116
,
803
(
2004
).
31.
O. O.
Brovarets’
and
D. M.
Hovorun
,
RSC Adv.
5
,
99594
(
2015
).
32.
B.
Ibarra
,
Y. R.
Chemla
,
S.
Plyasunov
,
S. B.
Smith
,
J. M.
Lázaro
,
M.
Salas
, and
C.
Bustamante
,
EMBO J.
28
,
2794
(
2009
).
33.
H.
Echols
and
M. F.
Goodman
,
Annu. Rev. Biochem.
60
,
477
(
1991
).
34.
J.
SantaLucia
, Jr.
and
D.
Hicks
,
Annu. Rev. Biophys. Biomol. Struct.
33
,
415
(
2004
).
35.
D. A.
Erie
,
T. D.
Yager
, and
P. H.
von Hippel
,
Annu. Rev. Biophys. Biomol. Struct.
21
,
379
(
1992
).
36.
J.
SantaLucia
, Jr.
,
Proc. Natl. Acad. Sci. U. S. A.
95
,
1460
(
1998
).
37.
C. R.
Calladine
,
H. R.
Drew
,
B. F.
Luisi
, and
A. A.
Travers
,
Understanding DNA: The Molecule and How It Works
, 3rd ed. (
Elsevier
,
2004
).
38.
O. O.
Brovarets’
and
D. M.
Hovorun
,
Phys. Chem. Chem. Phys.
17
,
15103
(
2015
).
39.
O. O.
Brovarets’
and
D. M.
Hovorun
,
J. Biomol. Struct. Dyn.
33
,
2297
(
2015
).
40.
O. O.
Brovarets’
and
D. M.
Hovorun
,
J. Biomol. Struct. Dyn.
33
,
2710
(
2015
).
41.
O. O.
Brovarets’
and
D. M.
Hovorun
,
RSC Adv.
5
,
66318
(
2015
).
42.
O. O.
Brovarets’
and
D. M.
Hovorun
,
Phys. Chem. Chem. Phys.
17
,
21381
(
2015
).
43.
R.
Guajardo
and
R.
Sousa
,
J. Mol. Biol.
265
,
8
(
1997
).
44.
H.
Yin
,
M. D.
Wang
,
K.
Svoboda
,
R.
Landick
,
S. M.
Block
, and
J.
Gelles
,
Science
270
,
1653
(
1995
).
45.
J.
Saturno
,
L.
Blanco
,
M.
Salas
, and
J. A.
Esteban
,
J. Biol. Chem.
270
,
31235
(
1995
).
46.
G. J. L.
Wuite
,
S. B.
Smith
,
M.
Young
,
D.
Keller
, and
C.
Bustamante
,
Nature
404
,
103
(
2000
).
47.
J. A.
Morin
,
F. J.
Cao
,
J. M.
Lázaro
,
J. R.
Arias-Gonzalez
,
J. M.
Valpuesta
,
J. L.
Carrascosa
,
M.
Salas
, and
B.
Ibarra
,
Proc. Natl. Acad. Sci. U. S. A.
109
,
8115
(
2012
).
48.
J. A.
Morin
,
F. J.
Cao
,
J. M.
Lázaro
,
J. R.
Arias-Gonzalez
,
J. M.
Valpuesta
,
J. R.
Carrascosa
,
M.
Salas
, and
B.
Ibarra
,
Nucleic Acids Res.
43
,
3643
(
2015
).
49.
R. R.
Iyer
,
A.
Pluciennik
,
V.
Burdett
, and
P. L.
Modrich
,
Chem. Rev.
106
,
302
(
2006
).
You do not currently have access to this content.