The biological cell exhibits a fantastic range of behaviors, but ultimately, these are governed by a handful of physical and chemical principles. Here, we explore a simple theory, known for decades and based on the simple thermodynamics of mixtures of ideal gases, that illuminates several key functions performed within the cell. Our focus is the free-energy-driven import and export of molecules, such as nutrients and other vital compounds, via transporter proteins. Complementary to a thermodynamic picture is a description of transporters via “mass-action” chemical kinetics, which lends further insights into biological machinery and free energy use. Both thermodynamic and kinetic descriptions can shed light on the fundamental non-equilibrium aspects of transport. On the whole, our biochemical-physics discussion will remain agnostic to chemical details, but we will see how such details ultimately enter a physical description through the example of the cellular fuel ATP.

1.
Philip
Nelson
,
Biological Physics
(
WH Freeman
,
New York
,
2014
).
2.
Terrell L.
Hill
,
Free Energy Transduction and Biochemical Cycle Kinetics
(
Dover
,
Mineola, NY
,
2004
).
3.
Douglas C.
Giancoli
, “
A course in biophysics: An integration of physics, chemistry, and biology
,”
Am. J. Phys.
39
(
7
),
739
741
(
1971
).
4.
John J.
Hopfield
, “
Kinetic proofreading: A new mechanism for reducing errors in biosynthetic processes requiring high specificity
,”
Proc. Natl. Acad. Sci. U. S. A.
71
(
10
),
4135
4139
(
1974
).
5.
Erwin
Schrödinger
,
What is Life? the Physical Aspect of the Living Cell and Mind
(
Cambridge U.P
.,
Cambridge
,
1944
).
6.
Rob
Phillips
,
Julie
Theriot
,
Jane
Kondev
, and
Hernan
Garcia
,
Physical Biology of the Cell
(
Garland Science
,
New York
,
2012
).
7.
Peter M.
Hoffmann
,
Life's Ratchet: How Molecular Machines Extract Order from Chaos
(
Basic Books
,
New York
,
2012
).
8.
Charles W.
Wolgemuth
, “
Trend: Does cell biology need physicists?
,”
Physics
4
,
4
(
2011
).
9.
Debashish
Chowdhury
, “
Resource Letter PBM-1: Physics of biomolecular machines
,”
Am. J. Phys.
77
(
7
),
583
594
(
2009
).
10.
Debashish
Chowdhury
, “
Stochastic mechano-chemical kinetics of molecular motors: A multidisciplinary enterprise from a physicist's perspective
,”
Phys. Rep.
529
(
1
),
1
197
(
2013
).
11.
Ken
Dill
and
Sarina
Bromberg
,
Molecular Driving Forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience
(
Garland Science
,
New York
,
2012
).
12.
Benjamin W.
Dreyfus
,
Benjamin D.
Geller
,
David E.
Meltzer
, and
Vashti
Sawtelle
, “
Resource letter TTSM-1: Teaching thermodynamics and statistical mechanics in introductory physics, chemistry, and biology
,”
Am. J. Phys.
83
(
1
),
5
21
(
2015
).
13.
Bruce
Alberts
,
Alexander
Johnson
,
Julian
Lewis
,
Martin
Raff
,
Keith
Roberts
, and
Peter
Walter
,
Molecular Biology of the Cell
, 4th ed. (
Garland Science
,
New York
,
2002
).
14.
Daniel M.
Zuckerman
,
Statistical Physics of Biomolecules: An Introduction
(
CRC Press
,
Boca Raton, FL
,
2010
).
15.
Jeremy M.
Berg
,
John L.
Tymoczko
, and
Lubert
Stryer
,
Biochemistry
, 5th ed. (
Freeman
,
New York
,
2002
).
16.
Simone
Weyand
,
Tatsuro
Shimamura
,
Shunsuke
Yajima
,
Shun'ichi
Suzuki
,
Osman
Mirza
,
Kuakarun
Krusong
,
Elisabeth P.
Carpenter
,
Nicholas G.
Rutherford
,
Jonathan M.
Hadden
,
John
O'Reilly
 et al, “
Structure and molecular mechanism of a nucleobase–cation–symport-1 family transporter
,”
Science
322
(
5902
),
709
713
(
2008
).
17.
Salem
Faham
,
Akira
Watanabe
,
Gabriel Mercado
Besserer
,
Duilio
Cascio
,
Alexandre
Specht
,
Bruce A.
Hirayama
,
Ernest M.
Wright
, and
Jeff
Abramson
, “
The crystal structure of a sodium galactose transporter reveals mechanistic insights into Na+/sugar symport
,”
Science
321
(
5890
),
810
814
(
2008
).
18.
Athel
Cornish-Bowden
,
Fundamentals of Enzyme Kinetics
, 4th ed. (
Wiley-Blackwell
,
Hoboken, NJ
,
2012
).
19.
Daniel M.
Zuckerman
, Physical lens on the cell <www.physicallensonthecell.org>.
20.
Ryan K.
Henderson
,
Klaus
Fendler
, and
Bert
Poolman
, “
Coupling efficiency of secondary active transporters
,”
Curr. Opin. Biotechnol.
58
,
62
71
(
2019
).
21.
John D.
Chodera
,
Nina
Singhal
,
Vijay S.
Pande
,
Ken A.
Dill
, and
William C.
Swope
, “
Automatic discovery of metastable states for the construction of markov models of macromolecular conformational dynamics
,”
J. Chem. Phys.
126
(
15
),
155101
(
2007
).
22.
Frederick
Reif
,
Fundamentals of Statistical and Thermal Physics
(
McGraw-Hill
,
New York
,
1965
).
23.
Terrell L.
Hill
,
An Introduction to Statistical Thermodynamics
(
Dover
,
Mineola, NY
,
1986
).
24.
Daniel A.
Beard
and
Hong
Qian
,
Chemical Biophysics: Quantitative Analysis of Cellular Systems
(
Cambridge U. P
.,
Cambridge
,
2008
).
25.
David G.
Nicholls
,
Bioenergetics
(
Academic Press
,
Boston
,
2013
).
26.
Andre
Bazzone
,
Annas J.
Zabadne
,
Anastasia
Salisowski
,
M. Gregor
Madej
, and
Klaus
Fendler
, “
A loose relationship: Incomplete H+/sugar coupling in the MFS sugar transporter GlcP
,”
Biophys. J.
113
(
12
),
2736
2749
(
2017
).
27.
Anne E.
Robinson
,
Nathan E.
Thomas
,
Emma A.
Morrison
,
Bryan M.
Balthazor
, and
Katherine A.
Henzler-Wildman
, “
New free-exchange model of EmrE transport
,”
Proc. Natl. Acad. Sci. U. S. A.
114
(
47
),
E10083
E10091
(
2017
).
28.
Jacques
Ninio
, “
Kinetic amplification of enzyme discrimination
,”
Biochimie
57
(
5
),
587
595
(
1975
).
29.
Kevin Y.
Chen
,
Daniel M.
Zuckerman
, and
Philip C.
Nelson
, “
Stochastic simulation to visualize gene expression and error correction in living cells
,”
Biophysicist
(in press).
30.
Arvind
Murugan
,
David A.
Huse
, and
Stanislas
Leibler
, “
Discriminatory proofreading regimes in nonequilibrium systems
,”
Phys. Rev. X
4
(
2
),
021016
(
2014
).
31.
Donald A.
McQuarrie
,
Statistical Mechanics
(
University Science Books
,
Sausalito, CA, New York
,
2000
).
32.
Philip
Nelson
,
Physical Models of Living Systems
(
WH Freeman
,
New York
,
2015
).
33.
Daniel T.
Gillespie
, “
Stochastic simulation of chemical kinetics
,”
Annu. Rev. Phys. Chem.
58
,
35
55
(
2007
).
34.
Steven S.
Andrews
, “
Smoldyn: Particle-based simulation with rule-based modeling, improved molecular interaction and a library interface
,”
Bioinformatics
33
(
5
),
710
717
(
2016
).
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