Juan Fernando Gomez-Molina. (International Group of Neuroscience, IGN (USA, Colombia, India)) . Mauricio Corredor.
Computer simulation for ions under electric and magnetic fields: from random walks in aqueous solutions to stochastic manifolds for calcium location probabilities in microbes and neurons. Juan Fernando Gomez-Molina (International Group of Neuroscience, IGN (USA, Colombia, India))
Mauricio Corredor (Instituto de Biologia PhD GEBIOMIC group, University of Antioquia, Medellin, Colombia)
Alberto Antonio Restrepo-Velasquez (Informatica y Sistemas, Universidad EAFIT, Medellin, Colombia)
Ulises M Ricoy (Department of Biology, Chemistry and Env. Science, Northern New Mexico College, Española, NM, USA)
Organizadores Universidad de Antioquia Universidad EAFIT Instituto Tecnológico Metropolitano – ITM Universidad Pontificia Bolivariana Sede Medellín Universidad CES Corporación para Investigaciones Biológicas – CIB Medellin, Colombia, South America. 16 al 18 de septiembre de 2015. http://ccbcol.co/
INTRODUCTION
How to stimulate electrically the excitable tissue in a noninvasive and “friendly” way?
Enrouting Calcio ions with a field…
Ions move in a random walk (sequences of steps in which they change direction in a probabilistic form) toward certain targets (a membrane protein, a vesicle sensor…).
Recent optical techniques (BRAIN Initiative 2013-2015) show that ion movement differs from a random walk. This suggests that the cell microenvironment affects the encounter with the target.
Simple Random Walk
vs.
Radious: Probability for angles. Color: probability for distances
Non-Random Walk
Probability of taking a particular angle (direction)
Probability of taking a particular distance
Variables in the microenvironment that modify the ionic motion:
The field represents: membrane Buffer Macromolecular net Electric or magnetic field. The field involves any factor that affects the probability of the ion: Direction of next step, Length of next step And/or duration of next step.
We modify the field of simple electrochemical scenarios, in two aims…
1. Integrate principles of Ca-dynamics: NEURONS
HOMOLOGS Cav (4 repeats of 6 Transm Domain, selectivity filters)
MICROBES Fungal Cch1 protein Mid1 stretch activated Ca-channel
Ca2+-reléase-Activated cannel (CICR)
Stromal interaction molecule (STIM) Sense Ca and activates Orai
Ca-ATPases: IIA sarco/ER (SERCA) IIB plasma membrane PMCA
Ca-ATPases: PMR1 en fungi - Golgi PMC1 fungal vacuole Ca-ATPase
NCKX: K-Dependent Na/Ca exchanger
CAX: Fungal-type Ca/H exchanger -Vacuole
P2X (extracelular signaling) Ligand-gated permeable to Ca activated by ATP
P2X in fungi and amoeba (intracelular vacuola)
Transient Receptor Potential Channels TRPC (Ca-permeable. Regulate temp, osmolarity…)
Fungal TRPY1
Years of Evolution (after two billion years)
Number of Organic Messanger Molecules
Variety of Ca-Responses to them
Ca-binding proteins (based on DNA sequences)
Ca-signaling networks
2. Search for more appropriate probabilistic algorithms able to describe possible interactions and distortions of ionic atmospheres for single ions in cell microenvironments.
In neurons, cytoskeletal and perineuronal networks can cause these hypothetical effects (Gomez, Ricoy, Escobar, Velez 2012).
METHODS
We simulated the diffusion of ions as a sequence of random steps in restricted spaces (e.g. between impermeable membranes). The effects of fields and ionic atmospheres are simulated as “directional preferences” which are generated by algorithms that use probability distributions.
Three populations of ions are considered:
P1: ions that bind to buffers in few steps P2: ions that stay free for the whole simulation
P3: ions that are released from buffers
We compare the results with: 1. Algorithms for directional effect of obstacles in (Anomalous) Diffusion-Reaction equations.
Derivatives difference equations y(k)-y(k-1) Second derivative Undesirable edge effects? Runge-Kutta algorithm Discretization errors
2. Kernels of integrodifference equations. Expected location of an individual at a given time, is associated to a redistribution kernel: f() Input Integrals to sum
3. Tortuosity and Diffusion-tensor models. ADC = D (free dif coef) / Tortuosity ^ n ; Principal Diffusion Direction: PDD
RESULTS
The outcomes are presented as visualizations showing the final position of each calcium ion in different conditions: in absence of an electric field and in presence of it at different time intervals.
Final position of the particles after time t=T/3 (.) after t =T (+) T are the total steps of the simulation. (a) Without electrical field. (b) With an electrical field between 0 and T. (c) With an electrical field only between 0 and T/3.
The available space reduced by half. (a)Final position of calcium ions without electrical field. (b)Field applied from 0 to T (c)Field applied only the first T/5 msec (d)Field applied only from the T/5 to T.
Preliminary analysis suggests…
1. The strength of the field determines the population of calcium ions that is going to respond more strongly.
2. As the angle between the electric field and the buffer-target vector increases the probability that P3-ions find the target decreases (for angles less than 180 degrees).
CONCLUSIONS
1. Probabilistic algorithms for single-particles present unique properties respect to collective (average) approaches. Average: Aprox, Discretization error Single-particle
2. Because the number of calcium ions is small, probabilities might not be interpreted as averages.
3. Weak Electric fields can change the final location probabilities of P2-ions, allowing neuromodulation of synaptic connections.
4. In order to visualize the trajectory of a random walker with probabilistic location, the use of a “stochastic manifold” is suggested. Generalized surface in 4D Det. : stochastic 1. [Ca]i: Prob. location 2. Vm: Po 3. Recovery variable
4. Field Limit cycles: Oscilat. (3D Proj. Artistic comp.)
For non-invasive electric stimulation we need to define… 1. Subpopulation of Ca2+ 2. Parameters of electric field 3. Time-interval for stimulation – max(Po).
not control but interact amicably…
Acknowledgment International Advisors and Coauthors of: International Group of Neuroscience (IGN) Institutions, Professors and Researchers for support of this IGN-initiative: Deg. Biology, University of Antioquia- Informatica y Sistemas EAFIT Univ Dep Biology, Northern New Mexico Univ Medical School CES Univ
REFERENCES Anwar H, Roome CJ, Chen W, Kuhn B, Nedelescuy H, Schutter E (2015) Dendritic diameters affect the spatial variability of intracellular calcium dynamics in computer models. Front. Cell. Neurosci., 23 July 2014 Blackwell (2013) Approaches and tools for modeling signaling pathways and calcium dynamics in neurons. J Neurosci Methods. 220(2):131-40 Gomez JF (2013) Ionic channels and long-range electrical signals: a probabilistic interaction. medical Hypothesis. Gomez-Molina JF, Ricoy UM, J. Velez-M.D., D. Sepulveda-Falla (2014) Reestablishing Ca2+ amplitude and speed during deep sleep in Alzheimer´s disease with EEG-triggered TES/TMS: Neuromodulation of abnormal columnar states. Abstract Society for Neuroscience Meeting. Santamaria F, Wils S, De Schutter E, Augustine GJ (2011) The diffusional properties of dendrites depend on the density of dendritic spines. Eur. J. Neurosci. 1460-9568. Wieder N, Rainer HA, Wegner F (2011) Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics J Biomed Biotechnol. 2011; 2011: 572492. PMCID: PMC3216318 Williams R.J.P. (2006) The evolution of calcium biochemistry. Biochimica et Biophysica Acta 1763 1139– 1146 Xinjiang Cai, and David E. Clapham. (2012) Ancestral Ca21 Signaling Machinery in Early Animal and Fungal Evolution. Mol. Biol. Evol. 29(1):91–100. doi:10.1093/molbev/msr149
Thank you! …questions or comments?
