Theory of Ageing

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Attribute Exploration with Proper Premises and Incomplete Knowledge Applied to the Free Radical

Theory of Ageing

Johannes Wollbold, R¨udiger K¨ohling and Daniel Borchmann

Systems Biology and Bioinformatics, University of Rostock [email protected]

Oscar Langendorff Institute of Physiology, University Medicine, Rostock, Germany Institute of Theoretical Computer Science, Technische Universitt Dresden, Germany

ICFCA 2014, 10 - 13 June 2014

Johannes Wollbold (SBI Rostock) PP-Exploration of the FRTA June 2014 1 / 25

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Outline

1 The free radical theory of ageing

2 Assembling a knowledge base of ripple down rules

3 Validation and completion by attribute exploration

4 Attribute exploration with proper premises and incomplete knowledge

5 Outlook

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Free radicals

Free radicals have unpaired electrons.

One subclass of reactive oxygen species (ROS), highly oxidative small molecules capable of damaging organic molecules.

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ROS generation in the mitochondrial respiratory chain

Figure: [Tim Vickers. In: en.wikipedia.org, Electron transport chain.]

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Mitochondria get damaged with age.

Figure: Liver mitochondria from young and old rats. [Jose Vina. Antioxidant &

Redox Signaling, 19 (8), 2013, Figure 2]

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Vicious cycle of ROS generation and molecular damage

[Aubrey de Grey. The Mitochondrial Free Radical Theory of Aging, 1999, Fig. 6.1]

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Outline

5 Outlook

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The workflow

A collection of Ripple Down Rules (RDR) and cornerstone cases is converted to a complete knowledge base of implications.

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Rules from literature

Knowledge¹ is collected in a tree of general and exceptional rules (Ripple Down Rules, RDR).

Observed cases, defined by attributes m∈M\C, are classified by classes C ⊆ {ROS.old.+,ROS.old.−,Lifespan.+,Lifespan.−} ⊆M.

Iterative process of knowledge base construction: 1. >→ ROS.old.+, Lifespan.–

1.1. AntiOx1.+→ROS.old.–, Lifespan.+

1.1.1. AntiOx1.+, AntiOx2.–→ROS.old.+

1.3. AntiOx2.–, Mouse→ROS.old.+ 1.3. AntiOx2.–, CElegans→ ROS.old.+

Background knowledge for later exploration: AntiOx2.– →ROS.old.+

1Kirkwood, TBL and Kowald, A. The free-radical theory of ageing – older, wiser and still alive: Modelling positional effects of the primary targets of ROS reveals new support. BioEssays 2012, p. 1f.

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Rules from literature

Iterative process of knowledge base construction:

1. >→ ROS.old.+, Lifespan.–

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Rules from literature

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Rules from literature

1.1.1. AntiOx1.+, AntiOx2.–→ROS.old.+ 1.3. AntiOx2.–, Mouse→ROS.old.+ 1.3. AntiOx2.–, CElegans→ ROS.old.+

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Rules from literature

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Rules from literature

1.3. AntiOx2.–, Mouse→ROS.old.+

1.3. AntiOx2.–, CElegans→ ROS.old.+

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Rules from literature

1.3. AntiOx2.–, Mouse→ROS.old.+

1.3. AntiOx2.–, CElegans→ ROS.old.+

Background knowledge for later exploration:

AntiOx2.– →ROS.old.+

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Mutations of respiratory chain molecules are studied in the ROSAge project

Figure: [Tim Vickers. In: en.wikipedia.org, Electron transport chain.]

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A rule derived from ROSAge data

Figure: Basal ROS measurements by Dept. of Hematology Rostock.

Mouse, Mut-ETC,→∅

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A conflicting rule derived from ROSAge data

Figure: Basal ROS measurements by Institute of Physiology Rostock for the mouse strain NOD (mutation in complex IV of the respiratory chain). A significant increase of free radicals in 24 month old mice is measured, compared to 3 month.

Mouse, Mut-ETC →ROS.old.+

⇒ Mut-ETC, Mouse →∅ not accepted as background knowledge.

Both cases are stored in the formal context of cornerstone cases.

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The tree of rules and exceptions

1.2. Mouse, AntiOx2.–→ROS.old.+

1.3. CElegans, AntiOx2.–→ ROS.old.+

1.4. Mouse, Mut-ETC→ ⊥

2. OxStress →... 2.1. ...

3. ATP.old.–→... 3.1. ...

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The tree of rules and exceptions

1.4. Mouse, Mut-ETC→ ⊥ 2. OxStress →...

2.1. ...

3. ATP.old.–→... 3.1. ...

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The tree of rules and exceptions

1.4. Mouse, Mut-ETC→ ⊥ 2. OxStress →...

2.1. ...

3. ATP.old.–→...

3.1. ...

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The incomplete formal context of cornerstone cases

AntiOx1.+ AntiOx1.− AntiOx2.+ AntiOx2.− CElegans Mouse Mut-ETC ROS.old.+ ROS.old.− Lifespan.+ Lifespan.−

1. ? ? ? ? × × ? × ×

1.1. × ? ? × × × ×

1.1.1. × × × × × ? ?

1.2.-1.3. ? ? × × × × ? ?

1.4a ? ? ? ? ? × × ? ?

1.4b ? ? ? ? ? × × × ? ?

Table: Examples (cornerstone cases) related to the RDR knowledge base: Certain context K+ and possible contextK?.

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Outline

5 Outlook

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Confirmed rules (some logical juggling)

AntiOx1.–, AntiOx2.+ →⊥(background) implies that AntiOx2.+ does not hold.

As RDR, we had already the stronger rule AntiOx1.+, AntiOx2.– → ROS.old.+.

AntiOx2.+ →ROS.old.–

AntiOx1.–, AntiOx2.+ →⊥(background) implies that AntiOx1.– does not hold.

Hence, AntiOx2.+, AntiOx1.– →ROS.old.+ (parallel to RDR 1.1.1) is the only exception.

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Confirmed rules (some logical juggling)

AntiOx1.–, AntiOx2.+ →⊥(background) implies that AntiOx2.+ does not hold.

As RDR, we had already the stronger rule AntiOx1.+, AntiOx2.– → ROS.old.+.

AntiOx2.+ →ROS.old.–

AntiOx1.–, AntiOx2.+ →⊥(background) implies that AntiOx1.– does not hold.

Hence, AntiOx2.+, AntiOx1.– →ROS.old.+ (parallel to RDR 1.1.1) is the only exception.

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Confirmed rules

AntiOx1.+, AntiOx2.+, CElegans →Lifespan.+

The strong conclusion can be assumed for the short living worm C.

elegans.²

AntiOx1.–, Mouse, Mut-ETC →Lifespan.–

Mutations (deletions) of the mitochondrial DNA can cause lifespan reducing damage for long-lived animals like mice.³

3Sohal R., Orr, W.Free Radical Biology and Medicine52(3), 539-555 (2012)

3Kirkwood TBL, Kowald A.BioEssays 2012, p. 6

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Confirmed rules

AntiOx1.+, AntiOx2.+, CElegans →Lifespan.+

The strong conclusion can be assumed for the short living worm C.

elegans.²

AntiOx1.–, Mouse, Mut-ETC →Lifespan.–

Mutations (deletions) of the mitochondrial DNA can cause lifespan reducing damage for long-lived animals like mice.³

3Sohal R., Orr, W.Free Radical Biology and Medicine52(3), 539-555 (2012)

3Kirkwood TBL, Kowald A.BioEssays 2012, p. 6

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Counterexamples

Mouse, CElegans, Mut-ETC, AntiOx1.+ →ROS.old.–

Counterexample:

AntiOx2.+ →ROS.old.– was accepted, but here AntiOx2.– is possible.

AntiOx2.+ →Lifespan.+

ROS are reduced, but this is not sufficient to extend lifespan. Counterexample:

(AntiOx1.+,) AntiOx2.+, (Mouse,) ROS.old.–, NOT Lifespan.+

3Fitzenberger E, Boll M, Wenzel U. Impairment of the proteasome is crucial for glucose-induced lifespan reduction in the mev-1 mutant of Caenorhabditis elegans. Biochim Biophys Acta, 2013 Apr, 1832(4), p. 565-73.

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Counterexamples

Mouse, CElegans, Mut-ETC, AntiOx1.+ →ROS.old.–

Counterexample:

AntiOx2.+ →ROS.old.– was accepted, but here AntiOx2.– is possible.

AntiOx2.+ →Lifespan.+

ROS are reduced, but this is not sufficient to extend lifespan.

Counterexample:

(AntiOx1.+,) AntiOx2.+, (Mouse,) ROS.old.–, NOT Lifespan.+

3Fitzenberger E, Boll M, Wenzel U. Impairment of the proteasome is crucial for glucose-induced lifespan reduction in the mev-1 mutant of Caenorhabditis elegans. Biochim Biophys Acta, 2013 Apr, 1832(4), p. 565-73.

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Outline

5 Outlook

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Implications with proper premises

Definition

For a given formal context (G,M,I) and a set of attributesP ⊆M, define P^• to be the set of those attributes inM\P that follow fromP but not from a strict subset of P, i.e.

P^• =P⁰⁰\ P ∪ [

S(P

S⁰⁰

P is called aproper premise ifP^• is not empty. It is called a proper premise for m ifm∈P^•.

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Exploration with incomplete counterexamples

PP-Implications are suited for disjoint basic sets for the premises and conclusions:

Decision of an implicationP →C by closure under all implications of the base: C ⊆ L(P)?

PP base is iteration free: Closure is reached in one step.

For disjoint implications, no iteration is possible.

⇒ Standard algorithm for the base construction of the whole context can be used, with iteration through the interesting m∈C (M. Implications have to be valid for any realizer of K+ andK?.

Proposition (Proposition 30 from Ganter/Obiedkov 2013⁴) A set P ⊆M possibly entails m∈M if and only if m∈P^+?.

4Ganter, B., Obiedkov, S.: Conceptual Exploration. Preprint, Dresden (2013)

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A new algorithm

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Outline

5 Outlook

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Result and open questions

The new method gives a structured overview on facts and open questions of the free radical theory of ageing.

”True“ exploration of RDR:

^

i∈I

α_i ∧^

j∈J

¬α_j →β

Easier thanrule exploration of general clauses? Two contexts with positive and negated attributes? Integration of insecure data - Fuzzy FCA?

Larger, biologically more relevant application.

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Result and open questions

^

i∈I

α_i ∧^

j∈J

¬α_j →β

Easier thanrule exploration of general clauses?

Two contexts with positive and negated attributes?

Integration of insecure data - Fuzzy FCA? Larger, biologically more relevant application.

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Result and open questions

^

i∈I

α_i ∧^

j∈J

¬α_j →β

Integration of insecure data - Fuzzy FCA?

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Result and open questions

^

i∈I

α_i ∧^

j∈J

¬α_j →β

Integration of insecure data - Fuzzy FCA?

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Acknowledgements

Christin Kretzschmar and Catrin Roolf Dept. of Hematology, Rostock

Gesine Reichart and Johannes Mayer Dept. of Phyisology, Rostock

Britta Burkhardt

Siegfried Weller Institut, Eberhard-Karls-Universit¨at T¨ubingen