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.

Antennas and Resonance

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.

BirefringenceA 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 sampleC : Cuvette and coil, 632 Hz, for the solution sampleD : electric field cellE : polarizing filterF : focusing lens focusing to the photodiodeG : photodiode with amplifierHP : spectrum analyzer (HP 3582°)COMP : signal acquisition system for off-line processing

BirefringenceWe 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

BirefringenceWe 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

610Hz

632Hz

610Hz 632Hz

610Hz

632Hz

610Hz

632Hz

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

610Hz

632Hz

610Hz

632Hz

610Hz

632Hz

610Hz

632Hz

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

1.3EF TMF LMF NF

610Hz

632Hz

610Hz

632Hz

610Hz

632Hz

610Hz

632Hz

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.

Statistical Analysis

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 fields1° 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 fieldC o m p u t a t i o n a l A n a l y s i s

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:

Occupancynumber of patterns mapped onto the same neuron,indicating similarities in the input domain

Conflictsneurons 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

Occupancy:37Conflict:676

TUBULIN

Occupancy:53Conflict:1020 Occupancy:38

Conflict:117

Occupancy:35

Conflict:780

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 organizationMicrotubules: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 organization

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

MicrotubulesShow 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

Technology

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