Mitochondrial fusion through membrane automata

K. Giannakis T. Andronikos

Department of InformaticsIonian University

tkgiann, andronikosu@ionio.gr

1st World Congress on Geriatrics and NeurodegenerativeDisease Research

Corfu, Greece,April 13, 2014

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Outline of our work

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What biological function and model we investigated.• Mitochondrial fusion described by Alexiou et al.

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Our tool• Membrane automata and brane calculus.

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Why• The importance of biomolecular functions for human’s

health.• It’s innovative.

• Combining P automata and BioAmbients calculus.• Use of P automata notions in describing a mitochondrial

model.• More “friendly" visualization, prosperous and well

established framework.

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Why mitochondria

• Key role in various biological processes.• e.g. ATP production, cell life cycle control etc.

• Connection among malfunctions in mitochondrial dynamicsand neurodegenerative diseases.

• Population regulation through fusion and fission.• Mitochondrial fusion: a parallel structure where several

units operate concurrently.

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Existing approaches

• Stochastic processes• e.g. Markov processes.

• Based on differential equations.

• Process calculi• Simulation platforms (e.g. SpiM)• BioAmbient calculus

• Brane calculus

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Membrane computing

• Known as P systems with several proposed variants.• Evolution depicted through rewriting rules on multisets of

the form uÑv• imitating natural chemical reactions, u, v are multisets of

objects.

• The hierarchical status of membranes evolves byconstantly creating and destroying membranes, bymembrane division etc.

• Represented either by a Venn diagram or a tree.• Types of communication rules:

• symport rules (one-way passing through a membrane)• antiport rules (two-way passing through a membrane)

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Examples

˝ Membranes create hierarchical structures.˝ Each membrane contains objects and rules.

(a) Hierarchical nestedmembranes

(b) With simple objects andrules

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DFAs and finite-state machines

• Model of computation.• An abstract machine being in one of a (finite) number of states.• Transition among states according to a transition function.• Represented through transition matrices or graphs.• Many variants and classes of accepted languages.• It takes an input (word) and decides either to accept or reject.

Theory of computation

• What can be computed.

• How it is computed.

• How long does it take to be computed.

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P systems evolution and computation

• Via purely non deterministic, parallel rules.

• Characteristics of membrane systems: the membranestructure, multisets of objects and rules.

• They can be represented by a string of labelled matchingparentheses.

• Use of rules ùñ transitions among configurations.• A sequence of transitions is interpreted as computation.• Accepted computations are those which halt and a

successful computation is associated with a result.

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P automata

• Variants of P systems with automata-like behaviour.• Computation starts from an initial configuration.• Acceptance is defined by a set of final states.

• They define a computable set of configurations satisfyingcertain conditions.

• The set of accepted input sequences forms the acceptedlanguage.

• A configuration of a P automaton with n membranes isdefined as a n-tuple of multisets of object in eachmembrane.

• A run of a P automaton is defined as a process of alteringits configurations in each step.

• Transition function depends on the computational mode(maximally parallel mode, sequential mode, etc).

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The case study we used

• A biological model of mitochondrial fusion by Alexiou et al,expressed in BioAmbient calculus.

• Cell is divided into hierarchically nested ambients.• 3 proteins are required (Mfn1, Mfn2 and OPA1) for the

successful fusion.• Fusion can occur:

• by the merging of two membrane-bounded segments.• when segments may enter or exit one another.

• Synchronized capabilities that can alter ambients’ state areentry, exit, or merge of other compartments.

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The biological model in brief

..1 Mfn1, Mfn2 and OPA1 are initially created.• Transcription of DNA into mRNA to create Mfn1-Mfn2.• RNAMfn1-Mfn2 reacts with Transl.• mRna translation is completed in two steps.• The production of OPA1 follows a similar process.• The above production processes are independent.

..2 Mfn1 and Mfn2 activate OPA1.

..3 Two independent mitochondria merge ù successfulfusion.

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Combining membranes and calculus

◃ Membrane computing is a computing model motivatedfrom the biological cell.

• Brane calculi focus on the fidelity of the biological reality.◃ In membrane computing, membranes are separators of

compartments and the multiset of abstract objects is themain data structure.

• In brane calculi the structure, properties, and evolution ofmembranes themselves matter.

◃ Most of the activation processes are independent to eachother ùñ use of a mechanism with intrinsic parallel,non-deterministic behaviour.

Different variants of P systems simulates different aspects ofthe cellular biology depending on their behaviour andcharacteristics (types of rules, attention on skin’s boundariesetc.).

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Our approach

• Every ambient ” membrane subsystem.• Hierarchical structure of ambients ” membrane-like

segments.• Biomolecular rules from Bioambient calculus to P

automata rewriting rules.• Actions altering ambients’ state (entry, exit, or merge).

Initial configuration:

rrrrrrsAO1rsK sPM1M2sRM1M2sGM1M2sOMOM1M2 rrrrrsBO1sPO1sRO1sGO1sIMOM1M2sskin{cell

Final configuration:

rrsPM1M2rsRM1M2rsGM1M2rsOMOM1M2rsPO1rsRO1rsGO1rsIMOM1M2rsK rsAO1rsBO1sskin{cell

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The production of the the protein Mfn1-Mfn2

Initial config. consecutive use of appropriate ruleÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÑ final config. and halt.

• Initial configuration: rrrrsPM1M2sRM1M2sGM1M2sOMOM1M2

• Final configuration: rsPM1M2rsRM1M2rsGM1M2rsOMOM1M2

• Halting configuration through consecutive exo operations.

rrrrsPM1M2sRM1M2sGM1M2sOMOM1M2exo

ÝÝÑ rrrsPM1M2sRM1M2sGM1M2rsOMOM1M2exo

ÝÝÑ

rrsPM1M2sRM1M2rsGM1M2rsOMOM1M2exo

ÝÝÑ rsPM1M2rsRM1M2rsGM1M2rsOMOM1M2

• Similarly for the rest parts of the model.

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Schematic view

Figure: The step by step process through consecutive uses of the exooperation.K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 15 / 19

Discussion

X Inherent compartmentalization, easy extensibility anddirect intuitive appearance for biologists.

X Suitable in cases when few number of objects are involvedor slow reactions.

X Need for deeper understanding of mitochondrial fusion˝ Connections with neurodegenerative diseases and

malfunctions.

X Probability theory and stochasticity (many biologicalfunctions are of stochastic nature).

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Future work

♢ Wealth of membrane computing models ùñ ample spacefor future work.

♢ Our approach can be adapted to other similar models˝ More case studies.

♢ They can potentially act as computation devices.♢ The intrinsic infinite behaviour of similar biomolecular

functions should be investigated by implementing andusing elements from the computation theory on infiniteobjects.

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Key References

ALEXIOU, A. T., PSIHA, M. M., REKKAS, J. A., AND VLAMOS, P. M.A stochastic approach of mitochondrial dynamics.World Academy of Science, Engineering and Technology 55 (2011).

CARDELLI, L., AND PAUN, G.An universality result for a (mem) brane calculus based on mate/drip operations.International Journal of Foundations of Computer Science 17, 01 (2006), 49–68.

CSUHAJ-VARJÚ, E., AND VASZIL, G.(mem) brane automata.Theoretical Computer Science 404, 1 (2008), 52–60.

REGEV, A., PANINA, E. M., SILVERMAN, W., CARDELLI, L., AND SHAPIRO, E.Bioambients: an abstraction for biological compartments.Theoretical Computer Science 325, 1 (2004), 141–167.

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Any Questions?

Thank you for your attention!

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