Information Theory and Programmable Medicine

Information Theory and ProgrammableMedicine

Hector Zenil

[email protected]

Unit of Computational Medicine, Stockholm, Sweden

Invited TalkIEEE International Conference on Bioinformatics and Biomedicine

(BIBM 2013) December 20, 2013, Shanghai, China

Hector Zenil Information and ProgrammableMedicine 1 / 27

Complexity and Computation in Nature Natural computing

Contents

What is computationSmall computing machines and emergent propertiesThe Turing test and what is (artificial) lifeInformation theory and spatial molecular computationKolmogorov complexity and programmable medicine



The origins of modern computation

J. von Neuman’s self-replication interest (1950s).

von Neumann (with S. Ulam) started the field of Cellular Automata



Cellular Automata



Rule 30 continuation



von Neumann’s universal constructor



Life as self-replication?

Langton’s loop shows that self-replication does not require Turinguniversality.

But crystals self-replicate too, so it cannot be a sufficient condition for life.



What is life?

An informational definition (Gerald F. Joyce, Bit by Bit: The Darwinian Basis ofLife, PloS, Bio. 2012) of life:

A genetic system that contains more bits than the number thatwere 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 biologydifferent from physics.

A mechanistic view (Leroy Cronin, TED conference, 2011) proposes that:

Life is anything that can undergo evolution (survival of thefittest). Matter that can evolve is alive.

Borderline case: Virus evolve (not exactly by their own though) yet they areonly matter (encapsulated genetic material).


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 ameasurable one: something is intelligent if it behaves like so. It is a clever strategyto tackle difficult questions!

Figure : A Turing-test like test strategy to the question of life (instead of machineintelligence)

[Zenil, Philosophy & Technology, Springer (2013)]Hector Zenil Information and ProgrammableMedicine 9 / 27


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, NatureBiotechnology 2006). Talking to the cells with chells.

How closely simulators emulate the properties of real data (e.g. in silico reconstructionof genetic networks from synthetically generated gene expression data) (Maier et al., ATuring test for artificial expression data, Bioinformatics (2013) 29 (20): 2603-2609, 2013).



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 randomnessA string with low Kolmogorov complexity is c-compressible if |p| + c = |s|. Astring is random if K(s) ≈ |s|.

[Kolmogorov (1965); Chaitin (1966)]Hector Zenil Information and ProgrammableMedicine 11 / 27


Behavioural classes of abstract computingmachines

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)]



Asymptotic behaviour of compressed evolutions

[Zenil, Complex Systems (2010)]Hector Zenil Information and ProgrammableMedicine 13 / 27


A behavioural approach to computation (and liferecognition)A Turing-test like test strategy to the question of life (instead of Turing’soriginal question of artificial intelligence):

[Zenil, Philosophy & Technology and SAPERE, (2013)]Hector Zenil Information and ProgrammableMedicine 14 / 27


Answering Chalmer’s rock question

Figure : ECA R4 has a low Ctn value for any n and t (it doesn’t react much to external

stimuli).

[Zenil, Philosophy & Technology, (2013)]Hector Zenil Information and ProgrammableMedicine 15 / 27


Turing universality

Figure : ECA R110 has large asymptotic coefficient Ctn value for large enough choices

of t and n, which is compatible with the fact that it is Turing universal (for particularsemi-periodic initial configurations).



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 variabilityversus controllability:

The diagonal determines the degree of programmability.

[Zenil, Ball, Tegner, ECAL MIT Press Proceedings, (2013)]Hector Zenil Information and ProgrammableMedicine 17 / 27


Proof of concept: The EMBL-EBI BioModel’sDatabase

The EMBL-EBI BioModel DB is a curated database of mathematical published(about 400) models related to living organisms.



Cell cycle versus metabolic pathways

Variability analysis: Models cluster by their role in living processes.



Variability and controllability of biologicalmodels

Information content trajectories(from EMBL-EBI model simulations):

Programmability is a combination of variability and controllability



The main challenges in biology

Parameter to conformational space mapping in biological systems from thefact that shape is function in biology!

DNA sequence→ protein structure mapping / Signalling→ cellsself-organization

Environmental conds. → virus mutations / drugs→ diseases reaction

I call it the conformational space problem in biology.Hector Zenil Information and ProgrammableMedicine 21 / 27


Case study: Phorphyrin molecules simulation withWang tilesPorphyrin interaction dynamics are extensively well known and accuratemathematical models exist. We ran a kinetic Monte Carlo simulation on 2different porphyrin molecules deposited on a solid substrate. Porphyrinsself-assemble in structures depending on the binding energy between:

molecules of the same functional typemolecules of different (2) functional typemolecules and the substrate

(They give red color to blood. They envelop hemes in hemoglobin that delivernutrients (in particular oxygen!).)

[Terrazas, Zenil and Krasnogor, Exploring programmable self-assembly in non-DNAbased molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]Hector Zenil Information and ProgrammableMedicine 22 / 27


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-DNAbased molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]



Phorphyrins: mapping behaviour to stimuli

Binding energies induced by chemical reactions with highest behaviouralimpact can be tested and programmed in silico and verified in the wet lab.

(Hemes in hemoglobin. They give the red color to blood)




Capturing and clustering behaviour

The compressibility test retrieved phase transitions corresponding to changesin qualitative behaviour. Qualitative behaviour is captured by a quantitativemeasure.

Corresponding to different stimuli

[Terrazas, Zenil and Krasnogor, Exploring programmable self-assembly in non-DNAbased molecular computing, Natural Computing, vol 12(4), pp 499–515, 2013.]Hector Zenil Information and ProgrammableMedicine 26 / 27


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 totreatments releasing a payload if expressing certain conditions (e.g. cancermarkers) are met.



H. Zenil, Compression-based Investigation of the Dynamical Properties ofCellular Automata and Other Systems, Complex Systems, Vol. 19, No. 1, pages1-28, 2010.

H. Zenil, What is Nature-like Computation? A Behavioural Approach and aNotion of Programmability, Philosophy & Technology (special issue on Historyand Philosophy of Computing), 2013.

H. Zenil, On the Dynamic Qualitative Behavior of Universal ComputationComplex Systems, vol. 20, No. 3, pp. 265-278, 2012.

G. Terrazas, H. Zenil and N. Krasnogor, Exploring Programmable Self-Assemblyin 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 Complexityin Cellular Automata Rule Spaces, Journal of Bifurcation and Chaos (in press).

H. Zenil, G. Ball and J. Tegner, Testing Biological Models for Non-linearSensitivity with a Programmability Test. In P. Lio, O. Miglino, G. Nicosia, S. Nolfiand 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),



Historical and Contemporary Research in Logic, Computing Machinery andArtificial Intelligence, Proceedings published by the Royal Flemish Academy ofBelgium for Science and Arts, 2013.

A Behavioural Foundation for Natural Computing and a Programmability Test. InG. Dodig-Crnkovic and R. Giovagnoli (eds), Computing Nature: Turing CentenaryPerspective, SAPERE Series vol. 7, Springer, 2013.

H. Zenil, Turing Patterns with Turing Machines: Emergence and Low-levelStructure Formation, Natural Computing, 12(2): 291-303 (2013), 2013.

J.-P. Delahaye and H. Zenil, Numerical Evaluation of the Complexity of ShortStrings: A Glance Into the Innermost Structure of Algorithmic Randomness,Applied Mathematics and Computation 219, pp. 63-77, 2012.


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