Actin Networks Voltage Circuits

Filaments of the cellular protein actin can form bundles, which can conduct ionic currents as well as mechanical and voltage solitons. These inherent properties can be utilized to generate computing circuits solely based on self-assembled actin bundle structures. Starting with experimentally observed networks of actin bundles, we model their network structure in terms of edges and nodes. We compute and discuss the main electrical parameters, considering the bundles as electrical wires with either low or high filament densities. A set of equations describing the network is solved with several initial conditions. Input voltages, which can be considered as information bits, are applied in a set of points and output voltages are computed in another set of positions. We consider both an idealized situation, where pointlike electrodes can be inserted in any points of the bundles and a more realistic case, where electrodes lay on a surface and have typical dimensions available in the industry. We find that in both cases such a system can implement the main logical gates and a finite state machine.

[1]  Willy Wriggers,et al.  Like-charge attraction between polyelectrolytes induced by counterion charge density waves , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[2]  C. Heussinger,et al.  Motor-free actin bundle contractility driven by molecular crowding , 2015, 1503.02929.

[3]  Fumio Oosawa,et al.  Interaction between particles suspended in solutions of macromolecules , 1958 .

[4]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[5]  J. Käs,et al.  Synthetic Transient Crosslinks Program the Mechanics of Soft, Biopolymer‐Based Materials , 2018, Advanced materials.

[6]  Francisco Casacuberta,et al.  Probabilistic finite-state machines - part I , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Andrew Adamatzky,et al.  Boolean gates on actin filaments , 2015, ArXiv.

[8]  M. Zivanov,et al.  Solitonic Ionic Currents Along Microtubules , 2010 .

[9]  Fumio Oosawa,et al.  On Interaction between Two Bodies Immersed in a Solution of Macromolecules , 1954 .

[10]  H. Cantiello,et al.  Ionic Waves Propagation Along the Dendritic Cytoskeleton as a Signaling Mechanism , 2006 .

[11]  Awad Aubad,et al.  Towards a framework building for social systems modelling , 2020 .

[12]  S. Hameroff,et al.  Quantum computation in brain microtubules: decoherence and biological feasibility. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Selim G. Akl,et al.  From Parallel to Emergent Computing , 2019 .

[14]  Jian Wang,et al.  Weakly Nonlinear AC Response: Theory and Application , 1997, cond-mat/9712060.

[15]  J. Käs,et al.  Semiflexible Biopolymers in Bundled Arrangements , 2016, Polymers.

[16]  Michal Cifra,et al.  Electric field generated by axial longitudinal vibration modes of microtubule , 2010, Biosyst..

[17]  Jack A. Tuszynski,et al.  Ferroelectric behavior in microtubule dipole lattices: Implications for information processing, signaling and assembly/disassembly* , 1995 .

[18]  Jack Tuszynski,et al.  Conduction pathways in microtubules, biological quantum computation, and consciousness. , 2002, Bio Systems.

[19]  Florian Huber,et al.  Counterion-Induced Formation of Regular Actin Bundle Networks , 2012 .

[20]  Cameron M. Hough,et al.  Response to Alternating Electric Fields of Tubulin Dimers and Microtubule Ensembles in Electrolytic Solutions , 2017, Scientific Reports.

[21]  J. Käs,et al.  Self-assembly of hierarchically ordered structures in DNA nanotube systems , 2016 .

[22]  H. Cantiello,et al.  Ionic wave propagation along actin filaments. , 2004, Biophysical journal.

[23]  Jian Wang,et al.  Nonlinear quantum capacitance , 1999 .

[24]  M. Sataric,et al.  Ionic Pulses along Cytoskeletal Protophilaments , 2011 .

[25]  A. Priel,et al.  A nonlinear cable-like model of amplified ionic wave propagation along microtubules , 2008 .

[26]  Mark Bathe,et al.  Transiently crosslinked F-actin bundles , 2010, European Biophysics Journal.

[27]  J. Tuszynski,et al.  Behavior of α, β tubulin in DMSO-containing electrolytes , 2019, Nanoscale advances.

[28]  Andrew Adamatzky,et al.  Actin droplet machine , 2019, Royal Society Open Science.

[29]  Andrew Adamatzky,et al.  Towards Cytoskeleton Computers. A proposal , 2018, From Parallel to Emergent Computing.

[30]  J. Tuszynski,et al.  DIPOLE INTERACTIONS IN AXONAL MICROTUBULES AS A MECHANISM OF SIGNAL PROPAGATION , 1997 .

[31]  John D. Hunter,et al.  Matplotlib: A 2D Graphics Environment , 2007, Computing in Science & Engineering.

[32]  Andrew Adamatzky,et al.  Computing on actin bundles network , 2019, Scientific Reports.

[33]  F. Huber,et al.  Emergent complexity of the cytoskeleton: from single filaments to tissue , 2013, Advances in physics.

[34]  Steen Rasmussen,et al.  Information Processing in Microtubules: Biomolecular Automata and Nanocomputers , 1989 .

[35]  Steen Rasmussen,et al.  Computational connectionism within neurons: a model of cytoskeletal automata subserving neural networks , 1990 .

[36]  J. Tuszynski,et al.  Nonlinear ionic pulses along microtubules , 2011, The European physical journal. E, Soft matter.

[37]  J. Käs,et al.  Formation of regularly spaced networks as a general feature of actin bundle condensation by entropic forces , 2015 .

[38]  R C Watt,et al.  Information processing in microtubules. , 1982, Journal of theoretical biology.

[39]  Jack A. Tuszynski,et al.  The Dendritic Cytoskeleton as a Computational Device: An Hypothesis , 2006 .

[40]  Jack A. Tuszynski,et al.  Nonlinear calcium ion waves along actin filaments control active hair–bundle motility , 2018, bioRxiv.

[41]  J. Tuszynski,et al.  Tubulin Polarizability in Aqueous Suspensions , 2019, ACS omega.