Transcript Vida, Proteínas e Demônios de Maxwell

A Física da
Vida
H. M. Nussenzveig
UFRJ
How Does Life Work?
Darwin (1859) Evolution by natural selection:
removal of least fit.
Physics also has history (Cosmology), but crucial
difference:
Teleology – living organisms have a project: to
reproduce (“selfish gene”).
Nothing in biology makes sense but in the light of
evolution (Th. Dobzhansky)
Ex.: sensitivity of eye and ear
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Schrödinger (1947): Explain gene stability: as an
“aperiodic crystal” —› biopolymer.
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Watson & Crick (1953): Double helix: the secret
of life?
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Part of it (GENOTYPE):
1. Program (“software”) = genome.
2. Replication ability, allowing (rare!) mutations, for
natural selection. Dual role of chance and necessity.
But (PHENOTYPE):
3. Growth, Metabolism: chain of chemical reactions:
open system far from equilibrium, feeding on order
(“negentropy”) resulting from interaction with the
environment. Source: Sun. Fuel: ATP —› ADP + Pi
Catalysis: Enzymes (highly specific) increase the
speed of reactions by many orders of magnitude.
4. Self-organization (Homeostasis): organism is a
complex adaptive system. (Minimum: hundreds of
genes; thousands of reactions). Regulation: control of
gene expression; intracellular transport; repairs.
Life’s Pyramid
Genome  Transcriptome  Proteome  Metabolome
Natural selection acts at top (on populations)
Two complementary approaches:
Bottom-Up (reductionist):
MOLECULAR CELL BIOLOGY
Top-Down (system):
MODULAR CELL BIOLOGY
Need both, in combination.
Molecular: start from PROTEOME
Proteins
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Responsible for phenotype. Main actors in cell
behavior. Multiple functions:
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B. Alberts
Structure: cytoskeleton.
Catalysis: enzymes.
Motility: motor proteins.
Defense: antibodies, repair.
Regulation: hormones.
Transport: ionic channels.
Communication: signal transduction.
Control: cell-cycle control.
They are macromolecules, polymers of 20
aminoacids. Typical: ~ 300 units.
Of ~20300 possible proteins, only ~105 used in
cells – by natural selection.
Function of a protein is determined by its
shape (geometry!).
Cell proteins, once formed, fold to correct
shape spontaneously.
How can one explain the “intelligence”
shown by proteins in fulfilling so many
different functions?
Brownian Motion
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Robert Brown (1827): pollen in water. Life?
Einstein (1905): fluctuations, diffusion.
Typical protein: ~ 10 to 100 X size of water
molecules.
Maxwell’s Demon (1871)
Szilard (1929): unimolecular “gas” .
Brillouin (1949): entropy increases when
demon acquires information.
Landauer (1961), Bennett (1982): entropy
increases when information is erased, to
reset memory.
Brownian Ratchet
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Smoluchowski (1912), Feynman (1966):
automatic Maxwell demon
Pawl requires spring + damping.
For T1 = T2, would violate 2nd law.
  energy for engage/release
p1  probab. of advancing = exp –  kT1 
p2  probab. of going back = exp –  kT2 
Motor only runs for T1  T2 ; obeys 2 nd law
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With load: torque L, rotation q for each tooth,
work Lq
p2 unchanged. The rotation speed Ω is
proportional to p1 – p2 . For T1 = T2,
p1  exp   Lq kT1
  e kT eLq kT 1
Rectification of fluctuations
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A brownian ratchet rectifies brownian
fluctuations, generating unidirectionality.
Proteins behave like Maxwell demons
(Monod, 1970: insight, greatly expanded since).
Protein folding model: analogous to spin glass search
on free energy landscape, assisted by brownian
fluctuations (+ chaperones).
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Motor proteins are molecular machines that directly
convert chemical energy work
Entropy can decrease over sufficiently small spatial
regions during sufficiently small time intervals
Fluctuation theorem (Evans & Searles 1994)
Resolves Loschmidt reversibility paradox
Verified experimentally with optical tweezers
Ex. 1: Polymerization Motor
Polymerization of actin filaments (from monomers in
solution) by brownian ratchet mechanism can
propel object
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Diffusion creates gap. Insertion and elastic tension
push object.
Aplication to Listeria
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Theoretical simulation
Similar (generalized) mechanism applies to many
other cell motility systems.
Experimental Tool: Optical Tweezers
Nd:YAG laser (1.064 mm) : no damage for in-vivo use (~
102 mW). Force range: up to ~ 102 pN on a ~ mm object
– just right for cell biology
Can detect ~ 0.3 nm displacements (single base pair
resolution in RNAP) in real time (ms).
Manipulate transparent microspheres as handles (the
Glass Bead Game)
Ex. 2: Walking Proteins
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http://www.fbs.leeds.ac.uk/research/contractility/
ATP, the fuel of life
Hidrolysis of ATP (~100% of weight/day!)
Ex. 3: The motor of life
R. Feynman
1959
~ 1/2 mm electric motor.
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Evolution:
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FoF1ATPase
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In mitochondria/chloroplasts, uses cross- membrane
difference in [H+] (respiration/photosyntesis) to
produce ATP. Fo transports H+ and F1 catalyses
production. 1997 Nobel Chemistry Prizes (Paul
How it works (1)
How it works (2)
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Motor Fo (ionic turbine) produces rotation of F1,
which catalyses synthesis of ATP. Both are
reversible. Efficiency: ~ 90%!
Brownian ratchet: responsible for both
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Ex. 4: RNA Polymerase
2006 Nobel Chemistry Prize: R. Kornberg
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Ex. 5: DNA Helicase
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Top-Down: Scaling Laws
Basal metabolic rate scales as 3/4-power of mass, over
27 orders of magnitude, from molecular and intracellular
levels to the largest organisms
Law can be derived (G. B. West + al.) from 3 assumptions:
1) Metabolic nets (vascular, respiratory,…) structure is
hierarchical, fractal, branching, space-filling.
2) Their terminal units (e.g., capillaries) are invariants.
3) Performance is maximized (by evolution).
Other consequence:
Number of heartbeats per lifetime is  invariant, ~ 1,5  109.
Chemotaxis Network
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Gene Regulatory Network
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Biological Net Features
Small-world net: “6 degrees of separation”
Advantage: minimize transition and reaction times
Robustness  parameter fine-tuning not required
Biological networks are sparse, modular, scale-free and
hierarchical. Optimized for evolvability
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Bacterial chemotaxis net has exact adaptation: follows
from network architecture having integral feedback control
Advantage: returns to pre-stimulus sensitivity regardless
of absolute concentration of attractants or repellents
Modularity: minimizes effects of failure in one module
“Evolution is a tinkerer, not an engineer” (F. Jacob).
However, tinkering over ~ 109 years has led to optimization
in response to environment.
Proportion of cell components devoted to regulation
exceeds proportion devoted to other functions
Modular Approach to Biology
L. Kadanoff, Physics Today (september 2005).
Drosophila morphogenesis (von Dassow et al. 2000):
Model biochemical chain by 14 ODE, ~ 50 parameters
2  105 parameter sets tested. ~ 1 in 200 OK. Result:
Qualitative behavior robust w.r. to parameter variation
Similar results found valid in discrete Boolean model
of same system preserving net topology (connectivity
and activating or inhibiting nature), as well
as in model of cell cycle control in yeast.
Kadanoff’s conjecture: “Living
things can be described by
modules…Since our isolation
of modules only includes a
portion of the relevant
network,we cannot expect to
obtain fully quantitative
descriptions…But since it’s the
connections that matter, we
might…catch something of the
essence of what is going on.
The organism…is much more
complex, perhaps describable
as many such modules hooked
together…students of
biological dynamics are
beginning to catch what is
going on at the first level of
interconnection.”
Yeast Modules From Proteome
Gavin et al., Nature 440 (March 2006), 631
Conclusion:
Chaos, Order and Life
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Chaos: Plus ça change, plus c’est la même chose.
Order: Sub specie aeternitatis (clockwork).
Life: Plus ça change, plus c’est différent!
Living organisms make use of two kinds of
information (order) in their dynamical evolution, at
the border order/chaos: staying at this border
allows them to combine robustness with
adaptation. Requirements of natural selection:
(i) Reproduce fast in optimal conditions;
(ii) Survive (rare) extremal conditions.
Two kinds of order:
1) Stored in the genome;
2) Stored in the molecules on which they feed
(origin: Sun).
Chaos (producing fluctuations) plays an essential
role, when combined with natural selection :
1) In genome mutations;
2) In selection, by proteins, of favorable brownian
fluctuations: mechanism of Maxwell’s demon.
Boltzmann wanted to become “the Darwin of
matter”. The Brownian ratchet mechanism of
protein function may be regarded as “natural
selection of favorable fluctuations”
Gallery
Natural selection
Demon and
its author
Brownian motion
The program
Ratchet; nanoscience
Biological Net Features (1)
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Mathematical/physical tools
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Stochastic processes
Langevin equation
m&
x&(negligible) = F   x& 2 T  t ,
 t   0,
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 t  t     t  t  
Viscous force: Navier-Stokes
Soft matter, biopolymers, elasticity
Theory of chemical reactions
Reaction-diffusion equations
pi x,t  kT 2 pi   F x  
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 
pi 
2
t
 x
x  
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   k ji x  p j x,t   kij x  pi x,t 
j
pi  probab. for state i; k ij  transition rate i  j
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Statistical mechanics of far- fromequilibrium, small, open, highly
heterogeneous systems
Dynamical systems; complexity. “Edge of
chaos”: Lyapunov exponent around zero
Spin glass theory
Systems and control theory
BUT: Experimental biology prevails!