Walker esa

Planetary Systems Biochemistry
Inferring the “Laws of Life”
at a Planetary Scale
Art by Michael Northrop (ASU)
Sara Imari Walker, PhD
Deputy Director, Beyond Center for Fundamental Concepts in Science
Associate Director, ASU-SFI Center for Biosocial Complex Systems
Associate Professor, School of Earth and Space Exploration
Arizona State University
External Faculty, Santa Fe Institute
Web: www.emergence.asu.edu
@Sara_Imari

“how can the events in space
and time which take place
within the spatial boundary of
a living organism be accounted
for by physics and chemistry?”
E. Schrödinger. What is Life? Cambridge University Press, 1944.

- Andrew Ellington
(American Chemical Society 2012)
- Jack Szostak
(J. Biomolecular Struc. Dyn. 29.4 (2012): 599-600.)

*this does not imply reality is a simulation, rather that
simulations are physical and arise by physical mechanisms

“… living matter, while not eluding
the “laws of physics” as established
up to date, is likely to involve
“other laws of physics” hitherto
unknown”
E. Schrödinger. What is Life? Cambridge University Press, 1944.

Walker 2016 “The Descent of Math” In Trick of Truth: The Mysterious Connection Between Physics and Mathematics? A. Aguirre, B. Foster and Z. Merali (ed.) Springer.
Life is what?

(w/ Michael Lachmann, Aeon magazine 2019)

0 0 1 0
1 0 0 1 1
0 0 1 0 1 0 0 1 1 0 0 0 0
00
10100110101
00 10100110000
001100
0 1
0
1
0
1
0 1
0
1
001
0
1
1
1
1 0
0
0
1
0
1
1 00001
0 1
0
1
1
1 0
1
1 0
0
1
00101001
00 1010011
001
1
0 1
1
1
001100
1 0
1
1
0
1
00
10100110101
00 10100110000
001100 1
0
0 1
1
1
001100
1 0
1
1 0
0
00
10100110101
1
0
0 1
1
0
0
0 1
1
001100
1 0
1
1 0
0
1
00
10100110101
00 10100110000
001100 1
0
0 1
1
1
001100
1
0
0
0
1 0
1
1 0
1
00
10100110101
00 10100110000
001100
1
1
0
1
0
0 1
1
1 001100
1 0
1
1 0
1
00
10100110101
00 10100110000
001100 1
1
0 1
0
1
0
0 1
1
1
1 0
1
1 0
1
00
10100110101
001100
1
001100
00 10100110000
Abiotic Biological Technological

Image from: Cronin and Walker “Beyond prebiotic
chemistry.” Science 352, no. 6290 (2016): 1174-1175.
‘Life’ is the where the physics of information is the dominant physics

0 0 1 0
1 0 0 1 1
0 0 1 0 1 0 0 1 1 0 0 0 0
00
10100110101
00 10100110000
001100
0 1
0
1
0
1
0 1
0
1
001
0
1
1
1
1 0
0
0
1
0
1
1 00001
0 1
0
1
1
1 0
1
1 0
0
1
00
101001
00 1010011
001
1
0 1
1
1
001100
1 0
1
1
0
1
00
10100110101
00 10100110000
001100 1
0
0 1
1
1
001100
1 0
1
1 0
0
00
10100110101
1
0
0 1
1
0
0
0 1
1
001100
1 0
1
1 0
0
1
00
10100110101
00 10100110000
001100 1
0
0 1
1
1
001100
1
0
0
0
1 0
1
1 0
1
00
10100110101
00 10100110000
001100
1
1
0
1
0
0 1
1
1 001100
1 0
1
1 0
1
00
10100110101
00 10100110000
001100 1
1
0 1
0
1
0
0 1
1
1
1 0
1
1 0
1
00
10100110101
001100
1
001100
00 10100110000
Finding the transition from non-living to living physics
Abiotic Biological

Poisson vs. Power-law Distributions
Figure 4.4
(d)
(b)
(a)
(c)
(a) Comparing a Poisson function with a
power-law function ( = 2.1) on a linear plot.
Both distributions have k = 11.
(b) The same curves as in (a), but shown on a
log-log plot, allowing us to inspect the dif-
ference between the two functions in the
high-k regime.
(c) A random network with k = 3 and N = 50,
illustrating that most nodes have compara-
ble degree k k .
(d) A scale-free network with =2.1 and k =
3, illustrating that numerous small-degree
nodes coexist with a few highly connected
hubs. The size of each node is proportional
to its degree.
The Largest Hub
All real networks are finite. The size of the WWW is estimated to be N
1012
nodes; the size of the social network is the Earth’s population, about N
7 × 109
. These numbers are huge, but finite. Other networks pale in com-
parison: The genetic network in a human cell has approximately 20,000
genes while the metabolic network of the E. Coli bacteria has only about
a thousand metabolites. This prompts us to ask: How does the network
size affect the size of its hubs? To answer this we calculate the maximum
degree, kmax
, called the natural cutoff of the degree distribution pk
. It rep-
resents the expected size of the largest hub in a network.
It is instructive to perform the calculation first for the exponential dis-
tribution
For a network with minimum degree kmin
the normalization condition
provides C = e kmin
. To calculate kmax
we assume that in a network of N
nodes we expect at most one node in the (kmax
, ∞) regime (ADVANCED TOPICS
3.B). In other words the probability to observe a node whose degree exceeds
(4.15)
∫ =
∞
p k dk
( ) 1
kmin
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
p(k) = Ce k
.
Figure 4.4
(d)
(b)
(a)
(c)
high-k regime.
ble degree k k .
to its degree.
The Largest Hub
1012
7 × 109
degree, kmax
. It rep-
It is instructive to perform the calculation first for the exponential dis-
tribution
For a network with minimum degree kmin
the normalization condition
provides C = e kmin
. To calculate kmax
we assume that in a network of N
nodes we expect at most one node in the (kmax
, ∞) regime (ADVANCED TOPICS
3.B). In other words the probability to observe a node whose degree exceeds
kmax
is 1/N:
(4.16)
(4.15)
∫ =
∞
p k dk
( ) 1
kmin
∫ =
∞
p k dk
N
( )
1
.
kmax
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
p(k) = Ce k
.
Statistical approaches to
characterizing life’s chemistry
Universal Signatures of Life
Life as the physics of information
The nature of intelligence
HFSP Form RGP-A (2020)
Cherry tree buds (Fig. 4C), and will confirm the functional connectivity between cells. The p
EB lab will travel to RB lab to perform these latter experiments using live hybrid aspen buds.

Biosignatures:
Where do we go from here?
Agnostic
Biosignatures
Big Data and
Statistical Metrics
Consensus Biosignature
Assessments

Assessments

OPLANET BIOSIGNATURES: OVERVIEW
Kiang et al. 2018 “Exoplanet Biosignatures: At the Dawn of a New Era of Planetary Observations” Astrobiology 18(6): 619- 629.
Detecting Life Statistically
OPLANET BIOSIGNATURES: OVERVIEW

Likelihood of observation
on Non-living worlds
Stellar environment
Climate and Geophysics
Geochemical Environment
Likelihood of observation on Living
Worlds
Black box approaches
Probabilistic biosignatures
Co-evolution of life and planets
Universal biology: scaling laws, information-
theoretic and network biosignatures
Posterior Likelihood of
Life
Statistical Inference and
Ensemble statistics
Prior Probability of Life
origins of life
biological innovations
observational constraints
P(life|data) =
P(data|life)P(life)
P(data|life)P(life) + P(data|abiotic)(1 P(life))
<latexit sha1_base64="syds/iddc1OMXO+gxKdmH3wnBfQ=">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</latexit>
Inferring life Bayesian
Framework for Life Detection
Figure courtesy of N. Kiang, adopted
from Walker et al. 2018 “Exoplanet
Biosignatures: Future Directions”
Astrobiology 18(6): 779-824

What statistical
patterns characterize
life in chemical space?
Are there molecules uniquely
producible by life?
Can we move to studying statistical
patterns and distributions of properties
that distinguish life from non-life?
• Molecules
• Reactions
• Pathways
• Networks

Pathway Assembly
for Probabilistic Biosignatures
Marshall SM, Murray AR, Cronin L. A probabilistic framework for identifying biosignatures using Pathway Complexity. Philosophical Transactions of the Royal
Society A: Mathematical, Physical and Engineering Sciences. 2017 Dec 28;375(2109):20160342.
Marshall, S.M., Moore, D., Murray, A.R., Walker, S.I. and Cronin, L., 2019. Quantifying the pathways to life using assembly spaces. arXiv preprint arXiv:1907.04649.

Biochemical Space Defined by Chemical
Complexity
Leroy Cronin private communication

Big Data and Statistical
Metrics

Universality in Biochemistry
“… it seems likely that the basic building blocks of life
anywhere will be similar to our own, in the generality
if not in the detail.”
-Norman Pace, PNAS, 2001
N. Pace “The Universal Nature of Biochemistry” PNAS 2001

“Phenomena with the same set of critical exponents are said to form a universality class”
Universality in Physics
|⇢+ ⇢ | / |T Tc| Liquid-gas critical point
M / (T Tc) Ferromagnetic critical point
N. Goldenfeld “Lectures on Phase Transitions and the Renormalization Group”

Does life have a universality class?

The Chemical Space of Life on Earth

Ecosystems
5,545 metagenomes
Individual Species
21,637 bacteria, 845 archaea, 77 eukarya genomes
Sampling the Ensemble of Biochemical Networks
Biosphere
8,658 cataloged, enzymatically catalyzed reactions

Kim, Smith, Mathis, Raymond & Walker. 2019 Universal scaling across biochemical networks on Earth. Science Advances, 5(1), p.eaau0149; Jeong H, Tombor B, Albert R, Oltvai ZN,
Barabási AL. The large-scale organization of metabolic networks. Nature. 2000 Oct;407(6804):651-4. Albert R, Barabási AL. Statistical mechanics of complex networks. Reviews of
modern physics. 2002 Jan 30;74(1):47.
Planetary Systems Biochemistry: Determining Universal
Patterns as New Predictive Tools
regularities in Earth’s biochemistry across
levels are statistically distinguishable from
non-living chemistry

Universal scaling in network topology across
individuals and ecosystems
Kim, Smith, Mathis, Raymond & Walker. 2019 Universal scaling across biochemical networks on Earth. Science Advances, 5(1), p.eaau0149.

Random sampling of biochemical space does not
recover universality class of biochemistry
Kim, Smith, Mathis, Raymond & Walker. 2019 Universal scaling across biochemical networks on Earth. Science Advances, 5(1), p.eaau0149.

Explaining scaling for network topology requires
universal set of shared reactions

Life exists in chemical space
What are the properties of life
in chemical space, are they
universal?

Universality and Coarse-graining
|⇢+ ⇢ | / |T Tc|
Liquid-gas critical point
T

Enzyme Commission Numbers
Coarse Grain Chemical Reaction Space
Class
Sub-class
Sub-subclass
Serial number
EC 1.x.x.x Oxioreductases
EC. 1.1.x.x CH-OH groups as donors
EC 1.1.1.x NAD+ or NADP+ as electron
acceptors
EC 1.1.1.1 alcohol dehydrogenase

Coarse Graining Chemical Reaction Space by
major categories of enzyme function
Class EC x
EC Class Name Function
EC1 Oxidoreductas
e
Transfer e
-
EC2 Transferase Transfer functional groups
EC3 Hydrolase Cleave bonds via hydrolysis
EC4 Lyase Cleave bonds not via
hydrolysis
EC5 Isomerase Molecular rearrangement
EC6 Ligase Join large molecules

Scaling of Enzyme Class with Network Size
Gagler, Karas et al. In prep

Scaling regimes suggest different
universality classes
Archaea Bacteria Eukarya Metagenomes
Oxidoreductase
1.175+/-0.023 1.239+/-0.006 1.327+/-0.037 1.291+/-0.004
Transferase 0.937+/-0.013 0.868+/-0.003 0.864+/-0.021 0.911+/-0.003
Hydrolase 1.195+/-0.033 1.196+/-0.006 1.344+/-0.046 1.015+/-0.003
Lyase 1.303+/-0.022 1.158+/-0.005 1.014+/-0.046 0.995+/-0.003
Isomerase 0.820+/-0.028 0.959+/-0.006 0.959+/-0.066 0.887+/-0.004
Ligase 0.733+/-0.021 0.722+/-0.006 0.462+/-0.032 0.573+/-0.003
Super-linear Linear Sub-linear

Enzyme universality classes are not
explained by enzyme universality
Area Under the
Curve
(AUC) scores
EC1 EC2 EC3 EC4 EC5 EC6
Archaea 0.152 0.244 0.158 0.228 0.248 0.461
Bacteria 0.156 0.249 0.210 0.233 0.284 0.431
Eukarya 0.253 0.337 0.303 0.233 0.214 0.522
Metagenomes
0.431 0.451 0.508 0.479 0.518 0.663
Pan-taxa
0.270 0.311 0.330 0.320 0.357 0.526

What about symmetries?
503
Ising Universality Class

Fraction of chiral molecules scales with
network size
Kim et al. In prep

Biosignatures:
Building an Integrated Theory-
Driven Framework Across
Astrobiology
Agnostic
Biosignatures
Big Data and
Statistical Metrics
Assessments

Statistical patterns in technologically
produced molecules and networks
Reaxys Network

Statistically exploring the origins of life and
the role of planetary context
Surman, Andrew J., Marc Rodriguez-Garcia, Yousef M. Abul-Haija, Geoffrey JT Cooper, Piotr S. Gromski, Rebecca Turk-MacLeod, Margaret Mullin, Cole Mathis, Sara I. Walker, and Leroy Cronin.
(2019) "Environmental control programs the emergence of distinct functional ensembles from unconstrained chemical reactions." Proceedings of the National Academy of Sciences 116 (12) :
5387-5392. Shipp JA, Gould IR, Shock EL, Williams LB, Hartnett HE. Sphalerite is a geochemical catalyst for carbon− hydrogen bond activation. Proceedings of the National Academy of Sciences.
2014 Aug 12;111(32):11642-5.

Astrobiologists need ‘big data’ approaches to
answer complex problems

Figure 4.4
(d)
(b)
(a)
(c)
high-k regime.
ble degree k k .
to its degree.
The Largest Hub
1012
7 × 109
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
Figure 4.4
(d)
(b)
(a)
(c)
power-law function ( = 2.1) on a linear pl
(b) The same curves as in (a), but shown on
log-log plot, allowing us to inspect the d
ference between the two functions in t
high-k regime.
(c) A random network with k = 3 and N = 5
illustrating that most nodes have compar
ble degree k k .
(d) A scale-free network with =2.1 and k
3, illustrating that numerous small-degr
nodes coexist with a few highly connect
hubs. The size of each node is proportion
to its degree.
The Largest Hub
1012
7 × 109
degree, kmax
. It rep-
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
100
0 10 20 30 40 50
0.05
0.1
0.15
10-6
100
10-1
10-2
10-3
10-4
10-5
101
102
103
POISSON
k
k
pk
pk
pk
~ k-2.1
POISSON
pk
~ k-2.1
Grid of Jovian atmospheres,
with observational uncertainties
Statistical characterization
of Jovian atmospheres
Grid of Terrestrial atmospheres,
with observational uncertainties
Statistical characterization of
Terrestrial atmospheres, with
implications for biosignatures
From Networks to Observables

Network measures from forward modeling of
hot Jupiter atmospheres
See poster by Tessa Fisher

Inferring atmospheric properties : Combining
statistics, networks, and machine learning
Forward Models
See poster by Tessa Fisher
Increased
uncertainty Increased temperature
Inferred Kzz

“Base metals can be transmuted into gold by stars, and by intelligent
beings who understand the processes that power stars, and by nothing
else in the universe”
-David Deutsch
University of Oxford
“The Beginning of Infinity”

Walker SI, Bains W, Cronin L, DasSarma S, Danielache S,
Domagal-Goldman S, Kacar B, Kiang NY, Lenardic A, Reinhard CT,
Moore W, Schweiterman, EW, Shkolnik EL, Smith HB. Exoplanet
biosignatures: future directions. Astrobiology. 2018 Jun 1;18(6):779-
824.
Walker SI, Cronin L, Drew A, Domagal-Goldman S, Fisher T, Line
M, Millsaps C. Probabilistic Biosignature Frameworks. Planetary
Astrobiology. 2020 Jun 16:477.

Visit us on the web: www.emergence.asu.edu
Thank you
Lab Members working on projects presented:
Hyunju Kim
Doug Moore
Alexa Drew
Dylan Gagler
Tessa Fisher
Bradley Karas
John Malloy
Pilar Vergeli
Veronica Mierzejewski
Harrison Smith (now at ELSI)
Collaborators:
Lee Cronin (Glasgow)
Aaron Goldman (Oberlin)
Chris Kempes (SFI)

Walker esa

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