Exploring structural and dynamical properties of microtubules by means of Artificial Neural Networks

Department of Computer Science
Universitas Studiorum Mediolanensis
Milan, Italy
Rita Pizzi
Exploring structural and dynamical properties
of microtubules by means of
Artificial Neural Networks

Aim of the project
In our previous experiments we found evidence of a
sensitivity of neurons to extremely weak magnetic fields.
We aimed to verify if this sensitivity could be due to
Microtubules.
We prepared ad hoc experimental procedures to test
the reaction of Microtubules and tubulin to
electromagnetic fields:
•Resonance
•Birefringence

Aim of the project
• Comparison between Microtubules and tubulin,
and between these structures and
nanotubes/buckyballs, that have similar
structure and dimension and interesting optical,
electrical and quantum properties.
• Synergetic use of computational methods for the
analysis of data from the biophysical
experiments, aiming at the understanding of the
anomalous properties of microtubules.

A particular biophysical behavior is functional to
some specific property of the studied material.
Observed differences between samples of tubulin
and MTs under controlled biophysical conditions
suggests that the structural configuration of MTs
could be the reason of such differences and could
be suitable for specific cellular functionalities.
Working Hypothesis

Tubulin
Tubulin is a globular
protein and the
fundamental component
of microtubules.
Microtubules (MTs)
constitute the
cytoskeleton of all the
eukaryotic cells and are
supposed to be involved in
many key cellular
functions
M a t e r i a l s

Microtubules are cylindrical polymers composed by
aligned tubulin dimers, alpha and beta-tubulins, that
polymerize in a helix that creates the microtubule
Microtubules (MT)
M a t e r i a l s

MTs could have optical,
electrical and quantum
properties that might explain
long-distance intracellular
communication processes
MTs diameter is around 15 nm and their length can vary
from a few nm up to some centimeters
Microtubules (MT)

Carbon nanotubes (CNT) have the same tubular
structure and the same dimensions as MTs
Buckyballs (BB) have a globular structure that can be
compared to the tubulin structure
Carbon Nanotubes (CNT) and Buckyballs (BB)

• A fullerene is any molecule composed entirely of carbon, in
the form of a hollow sphere, ellipsoid or tube. Spherical
fullerenes are also called buckyballs (C60).
• The structure of C60 is a truncated icosahedron, which
resembles an association football ball of the type made of
twenty hexagons and twelve pentagons, with a carbon atom
at the vertices of each polygon and a bond along each
polygon edge.
• Buckyballs have been used by the Zeilinger’s group as the
biggest structures that show a quantum wave behavior in a
double-slit experiment with a source of single buckyballs.
• The van der Waals diameter of a C60 molecule is about 1.1
nanometers (nm).

• Nanotubes (CNTs) are cylindrical fullerenes. These tubes of carbon
are usually only a few nanometres wide, but they can range from less
than a micrometer to several millimeters in length, and are 0.4-1 nm
in diameter.
• Because of the symmetry and unique electronic structure of
graphene, the structure of a nanotube strongly affects its electrical
properties. For a given (n,m) nanotube, if n = m, the CNTs behave as
a conductor; if n>m they are semiconductors.
• Because of their nanoscale cross-section, electrons propagate only
along the tube's axis and electron transport involves quantum effects.
CNTs are considered one-dimensional conductors that carry single
electrons, so that their quantum conductance is easily measurable
thanks to the Heisenberg principle.
• Other researches report intrinsic superconductivity in CNTs

Electromagnetic Wave absorption
•One of the more recently researched properties of carbon nanotubes is
their wave absorption characteristics, specifically microwave absorption.
•The narrow selectivity in the wavelength makes nanotubes properties
extremely useful in photonics technologies.
•It has been shown that CNT behave as antennas for extremely high
frequencies, receiving and transmitting nanoscale waves

Antennas and Resonance
•Antennas transform an electromagnetic field into an electric signal or
viceversa.
•When fed by an electrical signal they absorb it and return it in the shape
of electromagnetic waves (transmitting antennas), or absorb energy from
an electromagnetic wave and generate a voltage to their ends (receiving
antennas).
•Any conductive object behave as an antenna, and if it is tubular and the
frequency corresponds to the resonance frequency, it resonates
mechanically (cavity antenna) amplifying the signal.
•Oscillations increase their extent and this corresponds to an increase of
energy within the oscillator.
•Resonance is a physical condition that occurs when a damped oscillating
system is subjected to a periodic solicitation with a frequency equal to
the system oscillation.

Our hypothesis is that MTs can behave as oscillators as well as CNTs do,
becoming superreactive receivers and trasmitters able to amplify the signals.
•After preparing MT and tubulin in suitable buffers (Taxol for MTs and General
Tubulin Buffer for tubulin), and control solutions for both MT and tubulin, we
started the resonance experiment.
•Two dipole antennas (1/4 wave) are spaced 1.6 in., and the test tube with the
MT, tubulin and control solutions are in turn put in a mu-metal box between the
antennas.

• The first antenna is connected to a Microwave Signal Generator (Polarad
mod. 1105) generating frequencies between 0.8 and 2.5 GHz. The second
antenna is connected with a Spectrum Analyzer (Avantest mod. TR4131).
• If the peak of the tested material results lower in amplitude than the resonance
reference peak , the sample is absorbing, if it is higher the sample is emitting
electromagnetic energy.

The experimental results are the following:
With tubulin and control samples no changes were detected in the signal
amplitude.
In the MT sample analysis we observed at 1510 MHz a sharp (0.3 dB)
lowering of the reference peak (absorption), and another lowering between
2060 and 2100 MHz.
It is possible that the observed peak is related to a harmonic frequency of
the main higher resonance characteristic frequency, that depends on the MT
dimensions.

The fact that the control buffer did not affect the
reference signal peak means that the observed effects
depend exclusively on the molecular structure contained
in the sample
The MT tubular structure can be responsible for the
observed variation of the signal

Birefringence
A polarimeter is a scientific instrument used to measure the angle of
rotation caused by passing polarized light through an optically active
substance.
Some chemical substances are optically active, and polarized
(unidirectional) light will rotate either to the left (counter-clockwise) or
right (clockwise) when passed through these substances. The amount
by which the light is rotated is known as the angle of rotation.
There are different kinds of polarimeter. The most classical is the Nicol
prism-based polarimeter, based on the birefringence properties of the
Nicol prism.
Birefringence is an optical property of materials that arises
from the interaction of light with oriented molecular and
structural components.

Birefringence
A Nicol prism consists of a rhombohedral crystal of Iceland spar (a
variety of calcite) that has been cut at an angle of 68° with respect to
the crystal axis, cut again diagonally, and then rejoined as shown
using, as a glue, a layer of transparent Canada balsam.
Unpolarized light enters through the left face of the crystal, as shown in
the diagram, and is split into two orthogonally polarized, differently
directed, rays due to the birefringence property of the calcite.

Birefringence
•The experiment was carried out at the Department of Physics of our
University.
•A polarimeter was prepared with a monochromatic source of light
(633 nm) sent to two Nicol prisms that, for they birefringence
properties, polarize it on two different planes.
•The beam then crosses the cuvettes containing the control solution
and the test solution which, if optically active, rotates the polarization
planes of light. Then the light passes a rotable polarizing filter that by
comparison detects the rotation angle.
•Finally the beam is directed to a photodiode and sampled for a
suitable signal analysis software.

A : He-Neon Laser (Hughes 3222H-P, 633 nm; np 5 nW max); Nicol polarizer;
beam splitter per
B : Cuvette and coil, 610.1 Hz , for the reference sample
C : Cuvette and coil, 632 Hz, for the solution sample
D : electric field cell
E : polarizing filter
F : focusing lens focusing to the photodiode
G : photodiode with amplifier
HP : spectrum analyzer (HP 3582°)
COMP : signal acquisition system for off-line processing

Birefringence
We applied magnetic and electric field to
evaluate the sensitivity of the test solutions to
the fields measuring the Faraday and Pockels
effects.
The Faraday effect ( or Faraday rotation ) is a
magneto-optical phenomenon, ie an interaction
between light and a magnetic field in a
(dielectric liquid) medium. The Faraday effect
causes a rotation of the plane of polarization,
which is linearly proportional to the component
of the magnetic field in the direction of
propagation.
The Pockels effect, or Pockels electro-optic
effect, produces birefringence in an optical
medium induced by a constant or varying
electric field

Birefringence
We executed four different test sessions, preparing 4 different cuvettes
containing:
• Tubulin in tubulin buffer;
• MTs in MT buffer;
• tubulin in MT buffer;
• MT buffer without MTs.
And applying to each cuvette
• a transverse electric field (1 V/cm)
• a transverse magnetic field
• a longitudinal magnetic field
• no field.

Birefringence
•For each test the polarimeter measures the current coming to the
photodiode: in presence of scattering due to the Faraday effect, the
signal intensity decreases.
•We use simultaneously also a distilled water cuvette to have a
reference signal, knowing that a Faraday effect due to the water was
to be expected and evaluated.
•After normalizing by the value of the distilled water sample, the
signals (sampled at 8000 Hz) were submitted to FFT procedures with
Hamming and Hann windowing systems, with and without smoothing.

EF TMF LMF NF
610Hz 632Hz 610Hz 632Hz 610Hz 632Hz 610Hz 632Hz
Mt in MT buffer 927.41 24.75 1257.95 101.44 1232.30 2253.10 1148.0 9.87
Tb in MT buffer 2229.97 39.46 2013.46 200.63 2047.91 4827.94 2146.92 6.13
MT buffer 2996.69 29.72 2842.10 262.97 2893.39 6758.69 2878.20 16.83
Tb in Tb buffer 3445.27 8.65 884.68 79.21 834.54 1928.90 940.53 3.32
EF TMF LMF NF
Mt in MT buffer 286.7 8.1 391.7 32.8 385.5 712.4 356.5 n/d
Tb in MT buffer 694.9 13.7 627.8 63.9 646.7 1525.1 669.8 n/d
MT buffer 934.3 11.5 885.6 84.4 902.1 2133.8 897.6 n/d
A- Hamming windowing (home made sw)
B - Hann windowing – Hann smoothing (SigView)

EF TMF LMF NF
Mt in MT buffer 1141.8 27.2 1547.0 185.0 1517.5 2628.3 1412.1 5.5
Tb in MT buffer 2750.1 4.7 2477.4 234.3 2555.9 5629.3 2610.9 2.3
MT buffer 3690.6 30.8 3498.0 305.1 3564.8 7883.4 3547.3 8.7
Tb in Tb buffer 4247.7 7.7 1089.7 92.5 1028.5 2250.7 1158.5 1.3
EF TMF LMF NF
Mt in MT buffer 748.7 18.68 1015.4 79.3 994.8 1762.5 926.4 9.91
Tb in MT buffer 1800.1 31.58 1625.5 157.1 1674.8 3775.6 1733.0 2.34
MT buffer 2418.6 21.64 2294.1 204.8 2335.2 5284.8 2323.1 8.19
C - Hann windowing without smoothing
D - Hamming windowing - Hamming smoothing

The tabled values have been normalized with respect to
the reference value (632 value/610 value).
Tab. A EF Tab. B EF Tab. D EF Tab. E EF
Mt in MT buffer 0.0267 0.0283 0.0238 0.0249
Tb in MT buffer 0.0177 0.0197 0.0169 0.0175
MT buffer 0.0099 0.0123 0.0083 0.0089
ELECTRICAL FIELD
Under electrical field the solution with MTs has always
bigger values both than the solution with tubulin, and
than the buffer alone

Tab. A TMF Tab. B TMF Tab. C TMF Tab. D TMF
MT in MT
buffer
0.0810 0.0837 0.0766 0.0781
Tb in MT
buffer
0.0996 0.1018 0.0946 0.0966
MT buffer 0.0925 0.0953 0.0872 0.0893
TRANSVERSE MAGNETIC FIELD
The magnetic transverse field affects the various solutions
virtually in the same way.
.

LONGITUDINAL MAGNETIC FIELD
With longitudinal magnetic field the solution with MTs has
always a value that is minor than both the solution with
tubulin and the solution alone.
Tab. X LMF Tab. Y LMF Tab. Z LMF Tab. K LMF
Mt in MT buffer 1.828 1.8480 1.7320 1.7717
Tb in MT buffer 2.327 2.3567 2.2025 2.2544
MT buffer 2.336 2.3654 2.2115 2.2628

Tab. X NF Tab. Y NF Tab. Z NF Tab. K NF
Mt in MT buffer 0.00860 No peak in 632 0.00389 0.01069
Tb in MT buffer 0.00285 No peak in 632 0.00088 0.00135
MT buffer 0.00585 No peak in 632 0.00245 0.00353
NO FIELD
•Without electromagnetic field the solution with MTs has
always a value bigger than the value of the solution with
tubulin.
•In this case the value of the solution with tubulin is
minor than the value of the solution alone.

Statistical Analysis
• Given the substantial equivalence between parameterizations, the
statistical analysis was performed checking the significance of data
processed with Hamming windowing and Hamming smoothing (5 pts).
• The chosen procedure was a Paired T-test.
• Among all the tests, just the Paired T-test which compares tubulin in
microtubules buffer and buffer alone subjected to electric field, shows a
value above the 5% threshold.
• All the other comparisons show an extremely high statistical
significance, with p-Value always <0.0005.

Results
MTs react to electromagnetic fields in a different way than tubulin
and control sample: birefringence effect is always sharply different
in MTs with respect to tubulin and control, with very high
statistical significance
(p<<0.001).
This suggests again that the molecular structure of MTs
could be the cause of their reaction to electromagnetic
fields
The uniformity of the results through the different parameterizations
after normalization suggests that the measured effects are not due to
noise or chance.

Conclusions
The experimental results confirm the working hypothesis
that Microtubules could be the structure inside neurons
responsible for their sensitivity to extremely weak
electromagnetic field and that this behavior could be due
to their peculiar tubular structure, that allow them to
behave like cavity antennas.

Computational Analysis
C o m p u t a t i o n a l A n a l y s i s
Synergetic use of different computational methods to validate and
analyze the experimental results
Molecular Dynamics
Self-organizing artificial neural networks
Study of the evolution of the dynamic organization of the examined
structures under the influence of electromagnetic fields
Analysis of the resulting network configuration:
occupancy – conflicts method

Molecular Dynamics software
Ascalaph
- Very flexible tool with many possible
parameterizations for the force fields
- Various dynamical optimization
techniques
- Graphical interface with many
interactive methods for the
development of molecular models
- Quantum computation
- Possibility to apply electric field

Tertiary structures of MTs and tubulin obtained from Protein Data
Bank (PDB) and NANO_D INRIA group
Tertiary structures of nanotubes and buckyballs included in Ascalaph
Validation of the experimental results using molecular dynamics on
MT, tubulin, CNT and BB under different level of electro-magnetic
fields
1° simulation: absence of electric field
2° simulation: EF = 2 V/cm, f = 90 Hz
3° simulation: EF = 90 V/cm, f = 90 Hz
Molecules in implicit water at 298,15°K
AMBER64 force field
Molecular Dynamics simulations

TUBULIN MICROTUBULES
Tubulin and Microtubules Simulation

CNT Simulation
No Field 90 V/cm field

CNT Simulation
BBs show to be insensible the to electric field.
CNTs tend to move with a dynamic axial motion, which
becomes a real regular pulse in the presence of electric
field.
The movement of Tubulin and MTs is slower due to their
computational complexity.

Simulation results were submitted to two different self-
organizing artificial neural networks:
SONNIA for the evaluation of specific output
parameters
ITSOM for the evaluation of the cahotic attractors of the
dynamical systems constituted by the molecular
structures
The xyz values of the molecules after dynamic simulation
(energy minimization) are used as input values for the
ANNs

A Self-Organizing Map is an Artificial Neural Network able to classify streams
of input data by mapping them by vector quantization into a smaller
dimension. The weights of the network adapt themselves to the input after
a number of recursions (self-organization) and represent the classification
itself.

Any Artificial Neural Network can be considered as a dynamic
system of n-dimensional differential equations describing the
dynamics of n neurons. Each neuron is mathematically defined by its
state x (i) and by its gain function gi=gi(xi) (tipically the logistic
function).
In particular, a Self-Organized Map (SOM) can be expressed as a
non-linear dynamic model.
The SOM dynamical evolution shows the typical self-organizing and
chaotic behavior of the complex dynamic systems.
SONNIA and ITSOM are SOM networks and highlight a
self-organized and chaotic dynamic evolution in presence
of organized data.
Artificial Neural Networks (ANN) are effective non-linear classifiers,
useful for complex patterns

SONNIA
SONNIA is a computational environment for the development and analysis of
self-organizing neural networks
Very useful in the field of drug discovery and protein prediction.
It allows to classify a series of data sets, providing both supervised and
unsupervised learning. In particolar, SONNIA can classify new molecules of
known structure but unknown function, or viceversa
In this research project we have instead decided to use the analysis
tools provided by SONNIA to assess the degree of dynamic
organization reached by the examined molecules when subjected to
electromagnetic fields

SONNIA
Two parameters were represented:
Occupancy
number of patterns mapped onto the same neuron,
indicating similarities in the input domain
Conflicts
neurons corresponding to inputs belonging to different classes
For our case study we developed a Kohonen rectangular network
structure with 9x6 neurons and a random initialization.

Occupancy:55 Conflict:251
No Field
Occupancy: 51 Conflict: 384
EF=2V/cm f=90Hz
EF=90V/cm f=90Hz
TUBULIN
Occupancy:53 Conflict:1020 Occupancy:38 Conflict:117
MICROTUBULES Tubulin:
•No field: high values of
occupancy (high regularity)
and conflicts
•Weak electric field: same
occupancy and conflicts
•Increasing the electric field the
number of conflicts increases,
showing a decrease in structural
organization
Microtubules:
No field: less occupancy
compared to tubulin,
demonstrating that MTs have a
more complex spatial
conformation.
Weak electric field: there are
no changes.
Increasing the electric field the
conflicts decrease
dramatically, showing an
increase in structural

BUCKYBALL NANOTUBES
O: 8 C: 0
C: 0O: 7 O: 13 C: 0
O: 6 C: 0
O: 7 C: 0
No Field
EF=2V/cm f=90Hz
EF=90V/cm f=90Hz
C: 0O: 4
Buckyballs and
nanotubes have low
values of occupancy
and no conflicts,
because of their
limited number of
component and their
stable configuration
Nanotubes have a more
complex structure, but
their occupancy is still
low. Zero conflicts
mean good dynamical
stability.
Occupancy increases
with the growing of the
electric field,
improving regularity.

ITSOM network
ITSOM is an evolution of Kohonen SOM, that highlight the chaotic
dynamic evolution that the neural network follows in the presence of
organized data

ITSOM network
The sequence of winning neurons forms a series of numbers that are
repeated almost periodically (chaotic attractors).
Each attractor uniquely identifies the input pattern.
The graphical representation of the chaotic attractor provides a
graphical representation of the dynamic organization of the pattern
We developed in Matlab - Simulink a procedure that processes
in form of dynamic attractors the series of winning neurons
resulting from the output of ITSOM

BUCKYBALL NANOTUBES
No Field
EF=2V/cm f=90Hz
EF=90V/cm f=90Hz
Buckyballs:
Behavior not
modified by the
electric field
Nanotubes:
Increase of spatial
occupancy, with an
interesting increase
of order when
electric field is
applied

No field
EF=2V/cm f=90Hz
EF=90V/cm f=90Hz
Tubulin
Generates a stable
attractor in absence of
field, that tends to become
less structured when
applying E-M field
Microtubules
Show the same strong
organization as tubulin in
absence of field, but on
the contrary their
attractors tend to
become more compact
when electric field is
applied, focusing on a
restricted spatial
configuration, after a
short transition phase
TUBULIN MICROTUBULES

The MD simulation shows that BBs are insensible the to electric field,
as confirmed also by the Artificial neural Networks.
CNTs tend clearly to move with a dynamic axial motion, which
becomes a real regular pulse in the presence of electric field.
The behavior of the neural network reflects this trend, which shows
the extreme regularity of these nanostructures and an interesting
(known in literature) behavior of CNTs in the presence of electric
field, highlighted by the growing spatial regularity and extremely
regular dynamic attractors, that are also highlighted by the pulsing
behavior in the MD simulation.
C o n c l u s i o n s
Conclusions

Tubulin, despite its symmetric structure, seems to have
internal forces that tend to resist a dynamic stabilization,
and in the presence of electric field it does not show a
regular behavior.
Microtubules tend to stabilize their dynamical evolution
with the growing of the electrical field, again showing an
analogy with the CNT behavior.
Conclusions

Conclusions and Future Plans
The computational methods showed to be valuable for the analysis
of complex biophysical phenomena
The Artificial Intelligence approach supports the experimental
evidences at the microscopic level, allowing a more correct and
accurate interpretation of the results
It was possible to justify the experimental results in light
of structural and dynamic models, highlighting the actual
existence of substantial effects of electromagnetic fields
on the dynamic evolution of microtubules.

Conclusions and Future Plans
•The evidence of a specific behavior of MTs in presence of
electromagnetic field and its explanation in terms of dynamical
organization could be seen as a progress towards the study of the
role of MTs in long distance cellular communication: not only in the
neuronal system but also in the whole body cellular system.
•The positive results obtained from the synergetic approach
combining computational methods to biophysical experiments
encourage us to continue our experimental and computational
research.
•A possible future development consists of the evaluation of the
biophysical modifications of microtubules and tubulin due to
potential conformational changes upon interaction with different
ligands.

R. Pizzi, S. Fiorentini, G. Strini, and M. Pregnolato. “Exploring Structural
and Dynamical Properties of Microtubules by Means of Artificial Neural
Networks”. In: Complexity Science, Living Systems and Reflexing
Interfaces: New Models and Perspectives. p. 78-91, 2012, IGI Global
New York.
Publications
R. Pizzi, G. Strini, S. Fiorentini, V. Pappalardo and M. Pregnolato,
“Evidences of new biophysical properties of Microtubules”, in Focus on
artificial neural networks. p. 191-207, 2010, Nova Science New York.
R. Pizzi, S. Fiorentini, “Artificial Neural Networks Identify the Dynamic
Organization of Microtubules and Tubulin Subjected to Electromagnetic
Field”, Proc. 9th WSEAS Int Conf. On Applied Computer Science,
Genova 17-19 Oct. 2009, p. 103-106.
P u b l i c a t i o n s

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