Mitochondrial Fusion Through Membrane Automata

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  • 1. Mitochondrial fusion through membrane automata K. Giannakis T. Andronikos Department of Informatics Ionian University tkgiann, andronikosu@ionio.gr 1st World Congress on Geriatrics and Neurodegenerative Disease Research Corfu, Greece, April 13, 2014 K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 1 / 19
  • 2. Outline of our work Ä What biological function and model we investigated. • Mitochondrial fusion described by Alexiou et al. Ä Our tool • Membrane automata and brane calculus. Ä 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. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 2 / 19
  • 3. Why mitochondria • Key role in various biological processes. • e.g. ATP production, cell life cycle control etc. • Connection among malfunctions in mitochondrial dynamics and neurodegenerative diseases. • Population regulation through fusion and fission. • Mitochondrial fusion: a parallel structure where several units operate concurrently. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 3 / 19
  • 4. Existing approaches • Stochastic processes • e.g. Markov processes. • Based on differential equations. • Process calculi • Simulation platforms (e.g. SpiM) • BioAmbient calculus • Brane calculus K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 4 / 19
  • 5. 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 by constantly creating and destroying membranes, by membrane 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) K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 5 / 19
  • 6. Examples ˝ Membranes create hierarchical structures. ˝ Each membrane contains objects and rules. (a) Hierarchical nested membranes (b) With simple objects and rules K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 6 / 19
  • 7. 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. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 7 / 19
  • 8. P systems evolution and computation • Via purely non deterministic, parallel rules. • Characteristics of membrane systems: the membrane structure, multisets of objects and rules. • They can be represented by a string of labelled matching parentheses. • 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. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 8 / 19
  • 9. 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 satisfying certain conditions. • The set of accepted input sequences forms the accepted language. • A configuration of a P automaton with n membranes is defined as a n-tuple of multisets of object in each membrane. • A run of a P automaton is defined as a process of altering its configurations in each step. • Transition function depends on the computational mode (maximally parallel mode, sequential mode, etc). K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 9 / 19
  • 10. 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 are entry, exit, or merge of other compartments. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 10 / 19
  • 11. 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 successful fusion. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 11 / 19
  • 12. Combining membranes and calculus ◃ Membrane computing is a computing model motivated from 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 the main data structure. • In brane calculi the structure, properties, and evolution of membranes themselves matter. ◃ Most of the activation processes are independent to each other ùñ use of a mechanism with intrinsic parallel, non-deterministic behaviour. Different variants of P systems simulates different aspects of the cellular biology depending on their behaviour and characteristics (types of rules, attention on skin’s boundaries etc.). K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 12 / 19
  • 13. 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 K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 13 / 19
  • 14. The production of the the protein Mfn1-Mfn2 Initial config. consecutive use of appropriate rule ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÑ final config. and halt. • Initial configuration: rrrrsPM1M2sRM1M2sGM1M2sOMOM1M2 • Final configuration: rsPM1M2rsRM1M2rsGM1M2rsOMOM1M2 • Halting configuration through consecutive exo operations. rrrrsPM1M2sRM1M2sGM1M2sOMOM1M2 exo ÝÝÑ rrrsPM1M2sRM1M2sGM1M2rsOMOM1M2 exo ÝÝÑ rrsPM1M2sRM1M2rsGM1M2rsOMOM1M2 exo ÝÝÑ rsPM1M2rsRM1M2rsGM1M2rsOMOM1M2 • Similarly for the rest parts of the model. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 14 / 19
  • 15. Schematic view Figure: The step by step process through consecutive uses of the exoK. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 15 / 19
  • 16. Discussion Inherent compartmentalization, easy extensibility and direct intuitive appearance for biologists. Suitable in cases when few number of objects are involved or slow reactions. Need for deeper understanding of mitochondrial fusion ˝ Connections with neurodegenerative diseases and malfunctions. Probability theory and stochasticity (many biological functions are of stochastic nature). K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 16 / 19
  • 17. Future work ♢ Wealth of membrane computing models ùñ ample space for 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 and using elements from the computation theory on infinite objects. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 17 / 19
  • 18. 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 P ˘AUN, 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. K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 18 / 19
  • 19. Any Questions? Thank you for your attention! K. Giannakis and T. Andronikos Mitochondrial fusion through membrane automata 19 / 19