This document is a slide presentation by Hector Zenil on information theory and programmable medicine. It discusses using information theory and a behavioral approach to computation to map how molecular stimuli relate to the conformational spaces of biological systems. It provides an example of simulating the self-assembly of porphyrin molecules under different binding energies to demonstrate how this approach could help program biological behaviors and inform treatments. The goal is to work towards programmable medicine by introducing molecular arrays that can release payloads based on certain biological conditions being met.

1. Information Theory and Programmable Medicine
Hector Zenil
hector.zenil@ki.se
Unit of Computational Medicine, Stockholm, Sweden
Invited Talk
IEEE International Conference on Bioinformatics and Biomedicine
(BIBM 2013) December 20, 2013, Shanghai, China
Hector Zenil
Information and Programmable Medicine
1 / 27

2. Complexity and Computation in Nature
Natural computing
Contents
What is computation
Small computing machines and emergent properties
The Turing test and what is (artificial) life
Information theory and spatial molecular computation
Kolmogorov complexity and programmable medicine
Hector Zenil
Information and Programmable Medicine
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3. Complexity and Computation in Nature
Natural computing
The origins of modern computation
J. von Neuman’s self-replication interest (1950s).
von Neumann (with S. Ulam) started the field of Cellular Automata
Hector Zenil
Information and Programmable Medicine
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4. Complexity and Computation in Nature
Natural computing
Cellular Automata
Hector Zenil
Information and Programmable Medicine
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5. Complexity and Computation in Nature
Natural computing
Rule 30 continuation
Hector Zenil
Information and Programmable Medicine
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6. Complexity and Computation in Nature
Natural computing
von Neumann’s universal constructor
Hector Zenil
Information and Programmable Medicine
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7. Complexity and Computation in Nature
Natural computing
Life as self-replication?
Langton’s loop shows that self-replication does not require Turing
universality.
But crystals self-replicate too, so it cannot be a sufficient condition for life.
Hector Zenil
Information and Programmable Medicine
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8. Complexity and Computation in Nature
Natural computing
What is life?
An informational definition (Gerald F. Joyce, Bit by Bit: The Darwinian Basis of
Life, PloS, Bio. 2012) of life:
A genetic system that contains more bits than the number that
were required to initiate its operation.
A computational view (John Hopfield, J. Theor. Biol. 171, 53-60, 1994):
All biological systems perform some kind of computation.
Computation is inherent to adaptive systems and makes biology
different from physics.
A mechanistic view (Leroy Cronin, TED conference, 2011) proposes that:
Life is anything that can undergo evolution (survival of the
fittest). Matter that can evolve is alive.
Borderline case: Virus evolve (not exactly by their own though) yet they are
only matter (encapsulated genetic material).
Hector Zenil
Information and Programmable Medicine
8 / 27

9. Complexity and Computation in Nature
A behavioural approach to computation
A behavioural approach to what is computation
(and life)
The Turing test is a reformulation of a question of non-factual character into a
measurable one: something is intelligent if it behaves like so. It is a clever strategy
to tackle difficult questions!
Figure : A Turing-test like test strategy to the question of life (instead of machine
intelligence)
[Zenil, Philosophy & Technology, Springer (2013)]
Hector Zenil
Information and Programmable Medicine
9 / 27

10. Complexity and Computation in Nature
A behavioural approach to computation
A Turing test like approach to computation and life
[Zenil in Computing Nature, & SAPERE Series, Springer (2013)]
How to chemically recognize artificial life? (Cronin, Krasnogor, et al, Nature
Biotechnology 2006). Talking to the cells with chells.
How closely simulators emulate the properties of real data (e.g. in silico reconstruction
of genetic networks from synthetically generated gene expression data) (Maier et al., A
Turing test for artificial expression data, Bioinformatics (2013) 29 (20): 2603-2609, 2013).
Hector Zenil
Information and Programmable Medicine
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11. Complexity and Computation in Nature
A behavioural approach to computation
Algorithmic information theory to the rescue?
Which string looks more random?
(a) 1111111111111111111111111111111111111111
(b) 0011010011010010110111010010100010111010
(c) 0101010101010101010101010101010101010101
Definition
KU (s) = min{|p|, U(p) = s}
(1)
Compressibility and algorithmic randomness
A string with low Kolmogorov complexity is c-compressible if |p| + c = |s|. A
string is random if K(s) ≈ |s|.
[Kolmogorov (1965); Chaitin (1966)]
Hector Zenil
Information and Programmable Medicine
11 / 27

12. Complexity and Computation in Nature
A behavioural approach to computation
Behavioural classes of abstract computing
machines
Wolfram’s computational classes of behaviour:
Class I: system evolves into a homogeneous state.
Class II: system evolves in a periodic state.
Class III: system evolves into random-looking states.
Class IV: system evolves into localised complex structures.
Living systems clearly fall in class IV systems.
[Wolfram, (1994)]
Hector Zenil
Information and Programmable Medicine
12 / 27

13. Complexity and Computation in Nature
A behavioural approach to computation
Asymptotic behaviour of compressed evolutions
[Zenil, Complex Systems (2010)]
Hector Zenil
Information and Programmable Medicine
13 / 27

14. Complexity and Computation in Nature
A behavioural approach to computation
A behavioural approach to computation (and life
recognition)
A Turing-test like test strategy to the question of life (instead of Turing’s
original question of artificial intelligence):
[Zenil, Philosophy & Technology and SAPERE, (2013)]
Hector Zenil
Information and Programmable Medicine
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15. Complexity and Computation in Nature
A behavioural approach to computation
Answering Chalmer’s rock question
Figure : ECA R4 has a low Ct value for any n and t (it doesn’t react much to external
n
stimuli).
[Zenil, Philosophy & Technology, (2013)]
Hector Zenil
Information and Programmable Medicine
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16. Complexity and Computation in Nature
A behavioural approach to computation
Turing universality
Figure : ECA R110 has large asymptotic coefficient Ct value for large enough choices
n
of t and n, which is compatible with the fact that it is Turing universal (for particular
semi-periodic initial configurations).
Hector Zenil
Information and Programmable Medicine
16 / 27

17. Complexity and Computation in Nature
A behavioural approach to computation
A hierarchical view of computing systems (and life?)
The measure can be applied to other than computers.
Programmability of physical and biological entities sorted by variability
versus controllability:
The diagonal determines the degree of programmability.
[Zenil, Ball, Tegn´ r, ECAL MIT Press Proceedings, (2013)]
e
Hector Zenil
Information and Programmable Medicine
17 / 27

18. Complexity and Computation in Nature
A behavioural approach to computation
Proof of concept: The EMBL-EBI BioModel’s
Database
The EMBL-EBI BioModel DB is a curated database of mathematical published
(about 400) models related to living organisms.
Hector Zenil
Information and Programmable Medicine
18 / 27

19. Complexity and Computation in Nature
A behavioural approach to computation
Cell cycle versus metabolic pathways
Variability analysis: Models cluster by their role in living processes.
[Zenil, Ball, Tegn´ r, ECAL MIT Press Proceedings, (2013)]
e
Hector Zenil
Information and Programmable Medicine
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20. Complexity and Computation in Nature
A behavioural approach to computation
Variability and controllability of biological
models
Information content trajectories
(from EMBL-EBI model simulations):
Programmability is a combination of variability and controllability
[Zenil, Ball, Tegn´ r, ECAL MIT Press Proceedings, (2013)]
e
Hector Zenil
Information and Programmable Medicine
20 / 27

21. Complexity and Computation in Nature
A behavioural approach to computation
The main challenges in biology
Parameter to conformational space mapping in biological systems from the
fact that shape is function in biology!
DNA sequence → protein structure mapping / Signalling → cells
self-organization
Environmental conds. → virus mutations / drugs → diseases reaction
I call it the conformational space problem in biology.
Hector Zenil
Information and Programmable Medicine
21 / 27

22. Complexity and Computation in Nature
A behavioural approach to computation
Case study: Phorphyrin molecules simulation with
Wang tiles
Porphyrin interaction dynamics are extensively well known and accurate
mathematical models exist. We ran a kinetic Monte Carlo simulation on 2
different porphyrin molecules deposited on a solid substrate. Porphyrins
self-assemble in structures depending on the binding energy between:
molecules of the same functional type
molecules of different (2) functional type
molecules and the substrate
(They give red color to blood. They envelop hemes in hemoglobin that deliver
nutrients (in particular oxygen!).)
[Terrazas, Zenil and Krasnogor, Exploring programmable self-assembly in non-DNA
based molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]
Hector Zenil
Information and Programmable Medicine
22 / 27

23. Complexity and Computation in Nature
A behavioural approach to computation
Self-assembly of porphyrin molecules
How to map stimuli (energy binding) to conformational space?
With information theory and Kolmogorov complexity.
[Terrazas, Zenil and Krasnogor, Exploring programmable self-assembly in non-DNA
based molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]
Hector Zenil
Information and Programmable Medicine
23 / 27

24. Complexity and Computation in Nature
A behavioural approach to computation
Phorphyrins: mapping behaviour to stimuli
Binding energies induced by chemical reactions with highest behavioural
impact can be tested and programmed in silico and verified in the wet lab.
(Hemes in hemoglobin. They give the red color to blood)
[Terrazas, Zenil and Krasnogor, Exploring programmable self-assembly in non-DNA
based molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]
Hector Zenil
Information and Programmable Medicine
24 / 27

25. Complexity and Computation in Nature
A behavioural approach to computation
Phorphyrins: mapping behaviour to stimuli
Binding energies induced by chemical reactions with highest behavioural
impact can be tested and programmed in silico and verified in the wet lab.
(Hemes in hemoglobin. They give the red color to blood)
[Terrazas, Zenil and Krasnogor, Exploring programmable self-assembly in non-DNA
based molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]
Hector Zenil
Information and Programmable Medicine
25 / 27

26. Complexity and Computation in Nature
A behavioural approach to computation
Capturing and clustering behaviour
The compressibility test retrieved phase transitions corresponding to changes
in qualitative behaviour. Qualitative behaviour is captured by a quantitative
measure.
Corresponding to different stimuli
[Terrazas, Zenil and Krasnogor, Exploring programmable self-assembly in non-DNA
based molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]
Hector Zenil
Information and Programmable Medicine
26 / 27

27. Complexity and Computation in Nature
A behavioural approach to computation
Towards programmable medicine
Building on molecular such as porphyrin computation imagine, for example,
the introduction of an array of these molecules with a simple logic to
treatments releasing a payload if expressing certain conditions (e.g. cancer
markers) are met.
Hector Zenil
Information and Programmable Medicine
27 / 27

28. Complexity and Computation in Nature
A behavioural approach to computation
H. Zenil, Compression-based Investigation of the Dynamical Properties of
Cellular Automata and Other Systems, Complex Systems, Vol. 19, No. 1, pages
1-28, 2010.
H. Zenil, What is Nature-like Computation? A Behavioural Approach and a
Notion of Programmability, Philosophy & Technology (special issue on History
and Philosophy of Computing), 2013.
H. Zenil, On the Dynamic Qualitative Behavior of Universal Computation
Complex Systems, vol. 20, No. 3, pp. 265-278, 2012.
G. Terrazas, H. Zenil and N. Krasnogor, Exploring Programmable Self-Assembly
in Non DNA-based Computing, Natural Computing, vol 12(4): 499–515, 2013.
DOI: 10.1007/s11047-013-9397-2.
H. Zenil and E. Villarreal-Zapata, Asymptotic Behaviour and Ratios of Complexity
in Cellular Automata Rule Spaces, Journal of Bifurcation and Chaos (in press).
H. Zenil, G. Ball and J. Tegn´ r, Testing Biological Models for Non-linear
e
Sensitivity with a Programmability Test. In P. Lio, O. Miglino, G. Nicosia, S. Nolfi
`
and M. Pavone (eds), Advances in Artificial Intelligence, ECAL 2013, pp.
1222-1223, MIT Press, 2013.
H. Zenil, A Turing Test-Inspired Approach to Natural Computation. In G.
Primiero and L. De Mol (eds.), Turing in Context II (Brussels, 10-12 October 2012),
Hector Zenil
Information and Programmable Medicine
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29. Complexity and Computation in Nature
A behavioural approach to computation
Historical and Contemporary Research in Logic, Computing Machinery and
Artificial Intelligence, Proceedings published by the Royal Flemish Academy of
Belgium for Science and Arts, 2013.
A Behavioural Foundation for Natural Computing and a Programmability Test. In
G. Dodig-Crnkovic and R. Giovagnoli (eds), Computing Nature: Turing Centenary
Perspective, SAPERE Series vol. 7, Springer, 2013.
H. Zenil, Turing Patterns with Turing Machines: Emergence and Low-level
Structure Formation, Natural Computing, 12(2): 291-303 (2013), 2013.
J.-P. Delahaye and H. Zenil, Numerical Evaluation of the Complexity of Short
Strings: A Glance Into the Innermost Structure of Algorithmic Randomness,
Applied Mathematics and Computation 219, pp. 63-77, 2012.
Hector Zenil
Information and Programmable Medicine
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