The Simpson-Elsasser-Wolfram Framework
for Modeling the Living Cell
Sungchul Ji
Department of Pharmacology and Toxicology, Rutgers University
sji@rci.rutgers.edu
(Seminar at The DIMACS Center, Rutgers University, 4/17/2006)
The Simpson-Elsasser-Wolfram Framework for Modeling
the Living Cell
•
Introductory Remarks
•
Simpson, Elsasser, & Wolfram
All Laws, Principles, and Concepts Apply.
Physics and Chemistry are Necessary but Not Sufficient.
Complex Systems Can Be Modeled with Simple Programs on a Computger.
•
The Bhopalator
Dissipative Structures
Conformons
•
Application to Budding Yeast
Transcript Levels (TL)
Tranascription Rate (TR)
Transcript Degradation Rate (TD)
•
Conclusion
Structure
Conformons
Energy
Dissipative Structures
(TL = aTR - bTD )
Function
Budding Yeast, Saccharomyces cerevisiae
Developmental options of S. cerevisiae (budding yeast) cell type.
[H. Madhani, PNAS 97(25):13461-13463 (2000)].
The Living Cell
The Cytoskeleton
(Mouse Embryonic 3T3 cell)
The Simpson-Elsasser-Wolfram Framework
George G. Simpson
Walter Elsasser
(1902-1984)
( 1904 - 1991)
Steven Wolfram
(1959 -
)
• G. Simpson: Physicists study the principles
that apply to all phenomena: Biologists study
phenomena to which all principles apply.
• S. Wolfram: All structures and phenomena, whether
internal or external, can be modeled on the computer
as fractals, namely, the structures and patterns that
emerge as the consequences of iterating the
application of sets of simple rules n times, where n
can be a large number (103 - 106).
• G. Simpson: Physicists study the principles
that apply to all phenomena: Biologists study
phenomena to which all principles apply.
Additional Principles:
1.
General relativity & metabolic spacetime
(H. A. Smith & G. R. Welch, 1991)
“Just as matter tells spacetime how to
curve and curved spacetime tells matter
how to move, so biopolymers tells
chemistry how , when and where to
proceed and spatiotemporally organized
chemical concentrations (IDSs) tell
biopolymers how to move.”
2. Double articulation (1997)
Covalent & noncovalent interactions
3. Rule-governed creativity (1997)
Novel behaviors of cells are possible
although cells depend on a finite
number of chemicals and rules of
interactions.
4. Semiotics of Peirce (2005)
Biopolymers are molecular signs used in
cell language
5. Soft-state physics (2006)
Biopolymers are soft-state semiconductors
of conformons.
[S. Ji, BioSystems 44:17-39 (1997) ]
6. Biopolymers are coincidence detector s
implementing the rule: If A and B, then C.
(2006)
DNA as the carrier of both genetic information and free
energy.
Figure 1. Supercoiled DNA duplexes.
(Above) The electron micrograph of two circular
DNA duplexes, one supercoiled into a compact
shape and the other relaxed. (Right) Three
shapes of DNA duplexes – a linear form (left), a
circular form with one strand nicked (or cut)
(middle), and a circular form that is closed and
supercoiled (right).
Visualization of Conformons
Conformons = Mechanical energy stored in biopolymers as conformational
strains localized at sequence-specific sites.
The relaxed and supercoiled conformations of DNA: Supercoiled DNA harbors
mechanical strains at sequence-specific sites, i.e., conformons .
L. Stryer, Biochemistry, Fourth Ed., W. H. Freeman and Co., New York, 1995, p. 795
The Flame of a Candle as a Dissipative
Structure
•
Like the Belousov-Zhabotinsky
reaction run in a petri dish, the flame
of a candle is a self-organizing
chemical reaction-diffusion system, or
a dissipative structure. Different
reactions characterized by differently
colored chemical species and
temperatures occur in different
regions in space.
•
The only major difference between
the self-organizing chemical reactiondiffusion processes occurring in a
candle flame and those proceeding in
a living cell is that the former occur at
high temperatures and the latter at
low temperatures due to enzymic
catalysis.
•
Therefore, the living cell can be
viewed as supporting a cold flame
vis-à-vis a hot flame of a candle.
Thermal energy gradients and accompanying chemical
concentration gradients in a candle flame
•
A candle flame embodies
regions with different
temperatures, ranging
from 600 to 1,200 ºC.
•
Different temperatures are
due to different chemical
reactions proceeding in
different regions in space
that involve intermediates
exhibiting different colors.
Self-Organization
•

•
•
•
The proto-typical example of selforganization is provided by the BelosovZhabotinsky (BZ) reaction discovered by
the Russian chemist, B. P. Belousov in
1958. A few years later A. M. Zhabotinski
confirmed and further elaborated on the
the reaction.
The BZ reaction is characterized by the
organization of chemical concentrations
in space (2- and 3-dimensions) and time
(i.e., oscillating concentrations).
The spatial patterns of chemical
concentrations can evolve with time.
‘Patterns of chemical concentrations’ is
synonymous with ‘chemical
concentration gradients’.
The organization of chemical
concentration gradients in space and
time in the BZ reaction is driven by the
exergonic (i.e., free energy-releasing)
chemical reactions constituting the BZ
reaction itself.
The Living Cell as a Dissipative Structure
•
The intracellular calcium ion gradient (an example of intracellular
dissipative structures, IDSs) human neutropohils during phagocytosis
[D. W. Sawyer et al., Science 230:663-666 (1985)]
The florescent indicator called Quin2 is
used to visualize intracellular calcium ion in
human neutrophils during chemotaxis
towards, and phagocytosis, of opsonized
(i.e., coated with proteins that promote
phagocytosis, or ingestion by cells)
zymosan particles.
•
The pictures in the first column are brightfield images. The pictures in the second
column are fluorescent images showing
intracellular calcium ion distribution (white
= high calcium; dark = low calcium). The
pictures in the third column represent the
color-coded ratio images of the same cells
as in the second column.
•
Cells on the first row = Unstimulated
neutrrophils.
Cells on the second row = Neutrophils
migrating toward an opsonized particle.
Cells on the third row = Neutrophils with
pseudopods surrounding an opsonized
particle.
Cells on the fourth row = Neutrophils after
having ingested several opsonized
particles.
Take-home lesson = Dissipative structures in
the form of ion gradients can form inside
the cell without any membranes.
The Action Potential as a Dissipative Structure
•
•
•
•
The action potential is the
transient depolarization of the
neuronal membrane due to the
equilibration followed by active
transport of ions (Na+, K+, Ca++)
across cell membrane in
appropriate directions.
The action potential is a
heritable property of the neuron
and hence must be encoded in
the nucleotide sequences of
DNA.
How is such a dynamic
properties of the cell encoded in
the nucleus and how such
encoded information is retrieved
when needed are fundamental
questions not yet fully
answered.
Three different kinds of ion
movements are involved in the
generation of the action
potential: (1) primary active
transport, (2) secondary active
transport, and (3) passive
transport.
The Mikula-Niebur equation for the output rate of a coincidence detector
[S. Mikula and E. Niebur, “The Effects of Input Rate and Synchrony on a Coincidence Detector: Analytical
Solution. Neural Computat. 5(3):539-547 (2003)]
“The coincidence detector is a computational unit that fires if the number of input
spikes received within a given time bin equals or exceeds the threshold, Θ .”
Nout = the output rate, firing per mint.
p = the probability of a spike occurring within a time bin Δt.
m = the number of input spike trains, each having n time bins.
Θ = the threshold number of spikes that must be exceeded by the
summed input spikes before the coincidence detector fires or is
activated.
q = the correlation coefficient between spike trains 1, . . . , m.
j
= the number of coincident spike trains.
The Enzyme as a Coincidence Detector
S. Ji, Ann. N. Y. Acad. Sci. 227:419-437 (1974)
The Ca++ Ion Pump as a Coincidence Detector
20
1
/ \
/
\
2
/ \
/
4
/ \
/
21
3
/ \
\
/
5 6
\
7
22
9 10 11 12 13 14 15
23
\
8
/ \
/
16
\
17 18 19 20 21 22 23 24 25 . . .
24
P = mCj pj (1 – p)m-j , where mCj = m!/j!(m – j)!
Figure 1. A temporal hierarchy composed of a set of coincidence-detecting
events (CDEs), each constructed from a set of three nodes, j-i-k,
where the simultaneous occurrence of events j and k leads to (or
causes) event i.
• W. Elsasser: Physicists study objects that belong
to pure classes to which mathematical methods
can be applied; biologists study objects that
belong to heterogeneous classes to which logic,
but not mathematics, can be applied.
A Comparison between the Living Cell and the Atom
0.1 nm
Dissipative Structure
Equilibrium Structure
Table 1. The different levels of description (granularity) involved in modeling
the living cell
Granularity
Objects
Number
Emergent
Properties
Discipline
Methods
VII
Cells
1030 ?
Biological
Functionality
Cell Biology &
Computer Science
Wolfram’s Simple
programs (Algorithmic
Math?)
VI
Networks of
Complexes
1020 ?
Dissipative
Structures &
Mol. Logic
Holistic Biology
Bioinformatics
(Discrete
Mathematics)
V
Complexes
1015 ?
Enhanced
Coincidence
Detection
Biochemistry &
Molecular Biology
X-ray, TEM,
SEM, etc.
IV
Macromolecules
1012 ?
Coincidence
Detection &
Information
Biochemistry &
Molecular Biology
Single Molecule
Mechanics
(C.M.)
III
Small
Molecules
109 ?
Diversity
Chemistry
Chemical Kinetics
(C.M.)
II
Atoms
~ 102
Diversity
Quantum
Mechanics
Molecular Dynamics
(C.M.)
I
Subatomic
Particles
(e-, p+, n)
3
-
Quantum
Mechanics
Molecular Dynamics
(Cont. Math.)
• S. Wolfram: All structures and phenomena, whether
internal or external, can be modeled on the computer
as fractals, namely, the structures and patterns that
emerge as the consequences of iterating the
application of sets of simple rules n times, where n
can be a large number (103 - 106).
Shell shapes
generated by the
simple model and
found in nature.
Two parameters are
systematically changed:
(a) the overall factor by which
the size increases in the
course of each revolution;
(b) the relative amount by
which the opening is
displaced downward at
each revolution.
[S. Wolfram, A New Kind of
Science, 2002, p. 416.]
The Bhopalator

Self-Organizing Chemical Reaction-Diffusion System = City Name + ator .
(e.g., the Brusselator = the Belousov-Zhabotinsky reaction)

The first molecular model of the living cell.

Proposed in an international biological conference held in Bhopal, India, in
1983.

The cell as a coincidence detector of coincidence detectors (2006)
[S. Ji, J. theoret. Biol. 116:399-426 (1985)]
Output
Input
10
9
Gradients
5
6
4
Proteins
Amino
Acids
3
7
2
RNA
Ribonucleotides
1
8
Genes
A Simplified Representation of the
Bhopalator
[S. Ji, J. theoret. Biol. 116:399-426 (1985)].
DNA Microarrays
•
There are two kinds of DNA
microarrays – cDNA or EST
microarray and the Gene Chips.
cDNA/EST microarrays are discussed
first.
•
One microarray can measure 104
mRNA levels simultaneously
•
Each square can recognize one kind
of mRNA molecules.
•
mRNA levels in the cell are
determined by mRNA synthesis (Vsyn)
and mRNA hydrolysis (Vhyd), because
the rate of change in mRNA levels
inside the cell is always:
dR/dt = Vsyn - Vhyd
•
Only when certain kinetic conditions
are met (to be discussed later) can
the DNA microarray technique
measure rates of gene expression.
How DNA Microarray Experiments are Done
1
1.
2.
3
2
3.
4
4.
5.
5
6.
6
5
Isolate mRNA from broken cells.
Synthesize fluorescently labeled cDNA
from mRNA using reverse transcriptase
and fluorescent nucleotides.
Prepare a microarray either with EST or
oligonucleotides (synthesized right on
the microarray surface by
Affimetric,Inc.).
Pour the fluorescently labeled cDNA
preparations over the microarray
surface to effect hybridization. Wash
off excess debris.
Measure fluorescently labeled cDNA
using a computer-assisted microscope.
The final result is a table of numbers,
each number registering the fluorescent
intensity which is in turn proportional to
the concentration of cDNA (and
ultimately mRNA) located at row x and
column y, row indicating the identity of
genes, and y the conditions under which
the mRNA levels are measured.
Cluster Analysis

The changes in mRNA levels of human fibroblasts (cells
of connective tissues that synthesize and secrete fibrillar
procollagen, fibronectin, and collagenase) measured
with DNA microarrays over a time period of 24 hours.

Green represents a decrease in mRNA levels (or
“genes”, which term is strictly speaking incorrect; see
below), black no change, and red an increase.

Each mRNA molecule is represented by a single row of
colored boxes, and each column represents measuring
time point.

Notice that the mRNA molecules belonging to cluster A
started to decrease around 12 hours after beginning
experiment.

The mRNA molecules belonging to cluster E began to
increase at around 8 hours after the beginning of the
experiment.

It is postulated that mRNA clusters represent dissipative
structures of Prigogine produced by time-correlated
activities of transcriptosomes and degradasome.
A
1.2
1
1
0.8
0.6
0.4
0.2
0
6
0
fTL-fTR Plot 3
1.2
1
1
1
0.8
0.6
0.4
6
0.2
0
0.5
1
1.5
Fold Changes in TL
0
2
4
Fold Changes in TL
D
fTL-fTR Plot 10
C
6
fTL-fTR 19
2
1.2
1
Fold Changes in
TR
Fold Changes in TR
B
Fold Changes in TR
Fold Changes in
TR
fTL-fTR Plot 1
1
0.8
0.6
6
0.4
0.2
6
1.5
1
1
0.5
0
0
0
1
2
Fold changes in TL
3
0
0.5
1
1.5
Fold Changes in TL
Plots of fold changes in transcription rates (TR) and transcript levels (TL) of budding yeast
during metabolic transitions caused by glucose-galactose shift. These three examples (for
genes #1, #3, #10, and #19) were chosen randomly out of the 5,184 genes investigated by
Perez-Ortin and his coworkers in Valencia, Spain. Each plot shows the results of 6
measurements at t = 0, 5, 120, 360, 450, and 850 minutes after glucose was replaced with
galactose in the growth medium.
Tim e - v_S plots
= Glycolysis;
= Oxphos
Average m RNA Levels
= Glycolysis;
= Oxphos
b
mRNA, molecules/cell
a
50
30
20
10
0
-200
1
0.8
0.6
0.4
0.2
0
v_S,
molecules/cell/min
40
0
200
400
600
800
-200
1000
0
200
400
600
800
1000
Tim e, m in
Tim e, m in
Degradation/Transacription (D/T) Ratios vs Tim e
= Glycolysis;
= Oxphos
c
D/T Ratios
4.0
3.0
2.0
1.0
0.0
0
200
400
600
800
Tim e, m in
Figure 1. The kinetics of mRNA level and transcription rate changes following glucose-galactose shift. (a) The time
courses of the glycolytic and respiratory mRNA level changes. (b) The time courses of the glycolytic and respiratory
transcription rate changes. (c) The time courses of the changes in the transcript degradation (D) to transcription (T) ratios.
mRNA-Processor as a Coincidence Detector
mRNA Synthesis
(dnS/dt)
Transcriptosome
(> 50 proteins)
0<T<a
Degradasome
mRNA Level
(dn/dt)
(~ 10 proteins?)
mRNA
Degradation
(dnD/dt)
Dissipative Structures
Cell Functions
1. Steady state (dn/dt = 0), if dnS/dt = dnD/dt
2. On-the-way-up state (dn/dt >0), if dnS/dnD > dnD/dt
3. On-the-way-down state (dn/dt <0), if dnS/dt < dnD/dt
Table 9. An analogy between atomic physics and cell biology based on the similarity
between line spectroscopy in atomic physics and cDNA array technology in cell biology.
Parameter
Atomic Physics
Cell Biology
1. Time
19th-20th Century
20th-21st Century
2. Experimental
Technique
Atomic Absorption/Emission
Spectroscopy (19th C)
cDNA Array Technology
(‘ribonoscopy’ ?)(1995)
3. Experimental Data
Atomic Line Spectra
mRNA Levels in the Cell
4. Regularities
Lyman Series
Balmer Series
Ritz-Paschen Series
Brackett Series
Pfund Series
RNA Metabolic Modules (‘ribons’)
Genetic networks
Cell Metabolic Networks
5. Theoretical Model
Bohr’s Atom (1913)
The Bhopalator (1985)
6. Basic Concepts
Quantum of Action (1900)
The Conformon (1972)
IDSs (1985)
Cell LanguageTheory (1977)
7. Theory
Quantum Theory (1925)
The Conformon Theory of Molecular Machines (1974)
Cell Language Theory (1997)
Molecular Information Theory (2004)
8. Philosophy
Complementarity (1915)
Complementarism (1993)
9. A Unified Theory of
Physics, Biology, and
Philosophy
The Tarragonator (2005)
[For references, see http://www.grlmc.com, under Publications]