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thales of miletus ( 6th century b.c . ) made the first observations of electricity by rubbing pieces of amber being biological in origin , thanks to macroscopic charge separation .
spontaneous charge separation appears also with ferroelectric materials , where at the molecular level the positive charge center is shifted relative to the negative charge distribution .
the perfect alignment of these individual electric dipoles gives rise to the ferroelectricity .
thus , the ferroelectric state exhibits spontaneously a macroscopic electric dipole moment even in the absence of an external electric field .
this occurs below a characteristic temperature , the curie temperature t@xmath0 , where the individual electric dipoles of the molecules get spontaneously aligned ; for comparison , to polarize a dielectric material to a similar value , one needs electric fields of the order mv / cm to gv / cm , and this distinguishes ferroelectricity .
the consequence of the coherent single dipole alignment is the appearance of unpaired positive and negative bound charges on the two end - faces along the direction of the spontaneous ferroelectric polarization @xmath1 . in the ideal case , a piece of ferroelectric material is equivalent to an empty capacitor of the same dimensions , each plate being charged with @xmath2 .
assuming @xmath3 values by factor @xmath4 below those encountered often with crystals , the associated surface charge density ( @xmath5 ) can still be as much as @xmath6 charges/@xmath7 charges/@xmath8m@xmath9 .
the maximum electric field strength inside matter is given by @xmath10 , with @xmath11 being the dielectric constant of the medium .
for example , for @xmath12=1 mc / m@xmath9 only , the associated electric field is of the order of @xmath13mv / cm .
such electric fields exist only transiently , and , they can give rise even to the self - emission of energetic electrons ( @xmath14 kev electrons have been measured ( s. gundel et al . , 1989 ) ) ; depending on the actual conditions those electrons might ionize the surrounding , or , they can cause other related effects .    in this section , we present in short the main properties of ferroelectricity ,
a phenomenon which is also described in the text books , but we also refer to a few related articles , which can be read actually by non - specialists ( zioutas @xmath15 daskaloyannis , 1985 , gundel et al . , 1989 , riege , 1994 ) , or , modern theoretical ones ( resta , 1997 ) .
it is worth remembering that ferroelectricity and ferromagnetism have at first sight many common properties . comparing both types of materials , the main difference comes from the ( at least practically ) non - existence of magnetic monopoles .
the ubiquitous electric charges compensate the large polarization electric fields , and , they determine the transient ferroelectric behaviour during polarization change .
thus , the ferroelectric state is completely described by its widely known static properties as well as its dynamical behaviour associated with a temperature change , or , applying externally pressure and/or electric pulses .
in fact , every ferroelectric material is also piezoelectric and pyroelectric , but not _ vice versa_.    obviously , any change of the intrinsic spontaneous ferroelectric polarization ( @xmath16 is associated with a corresponding surface charge change ( @xmath17 ) .
these bound polarization charges attract ( either from the surrounding or from the ferroelectric medium itself ) an equal number of charges , but opposite in sign , since no environment can stand those electric fields . in short , a ferroelectric in its static state
consists of a polarized crystal or polycrystalline medium , and , quasi free screening surface charges , which partly migrate into the bulk of the ferroelectric .
the time period needed , for this charge neutralization to be completed , defines the dynamical behaviour of ferroelectrics . in general , this transient time is much longer than the preceding switching time .
depending on the applying electric field , temperature and the ferroelctric compound itself , transient times can be in the @xmath18sec to sec region .
many ferroelectric properties during polarization change appear much more pronounced compared with those we know in the static case .
for example , the dielectric constant takes enormous values around the phase transition temperature .
in fact , a ferroelectric sample in its static state might remain unnoticed at first sight .
it is only the change of its spontaneous polarization vector ( @xmath1 ) , which makes actually ferroelectricity visible .
we mention here a few mostly encountered cases when working with such materials .
* a ) *   let the temperature increase from the ferro- to the paraelectric state . during the phase transition ,
the intrinsic polarization disappears , and , one is left suddenly with the unpaired screening charges on each end - surface , which must be screened so to say , because of the associated strong electric fields .
since those charges are quasi - free , the result will be : either a current flow through the bulk of the ferroelectric material with both charge polarities compensating each other , or , for sufficient high intrinsic resistance of the sample , those almost unbound charges will be removed from each end - surface by their own repulsive coulomb force ( i.e. self - emission ) .  * b ) *   in the opposite process , i.e. by lowering the temperature from the paraelectric to the ferroelectric state , the onset of the spontaneous polarization attracts screening charges from the surrounding , because usually those transient electric fields are far above the electrical breakdown limit of any material , including the ferroelectric sample itself , if one should consider this to happen in space .  *
c ) *   reversal of the spontaneous polarization takes place , for example , by applying an external electric field ( @xmath19kv / cm is usually sufficient ) , being either alternating or pulsed .
thus , during a hysteresis loop measurement two polarization reversals occur per cycle . in a complete reversal of the intrinsic spontaneous polarization ,
the new bound polarization charges on each end - face of the sample have the same polarity as the previous screening charges .
this makes the associated transient electric fields even stronger than those appearing in the first two cases mentioned before .
the result is finally a complete rearrangement of the old screening charges , giving rise to a more pronounced dynamical behaviour , depending on the conductivity of the sample and other factors .
finally , we mention in short a few other known effects , which occur when changing the polarization vector by @xmath20 , or , much more enhanced during phase transition , which afterall can be of relevance for similar phenomena with the predicted _ biological _ ferroelectrics .
these are : the flow of pyroelectric current through the sample , which occasionally takes the form of spikes ( barkhausen pulses ) , similarly to the self - emission of energetic electrons , or , bursts of microwave radiation ( caspers , riege @xmath15 zioutas , 1988 ) .
we also like to mention here the antiferroelectric state , which is possibly of not minor importance .
this is a peculiar polarized state , since it consists of quasi infinite many 180@xmath21 domains of opposite alignment each , which does not require screening charges .
however , the transition ferroelectric@xmath22antiferroelectric gives also rise to a similar dynamical behaviour as for the mentioned paraelectric@xmath22ferroelectric phase transition .
we like to focus now on a very specific family of hydrated ferroelectric crystals , with the widely investigated potassium ferrocyanide trihydrate ( k@xmath23fe(cn)@xmath243h@xmath25o ) , in short kfct ( helwig , klpperpieper , @xmath15 mser , 1978 ) , taken to be a representative case .
we think that this type of ferroelectricity might serve as a model configuration in biology , with emphasis given to the microtubules , which no doubt play a fundamental rle in cell s functioning .
in fact , these subcellular constituents have attracted the recent years the particular interest of biophysicists .
microtubules have been predicted to posses oriented dipoles , assuming ferroelectric phase , which appears to be optimal for microtubule signaling and assembly / disassembly ( sataric et al . , 1993 , tuszynski et al . , 1995 ) .
such processes are obviously of basic importance . in the light of previous work ( mavromatos and nanopoulos 1997,1998 ) , relating the ferroelectric properties to the appearance of mesoscopic quantum - coherent states in internal regions of the microtubule cylinders , playing the rle of ( thermally isolated ) electromagnetic cavities
, ferroelectricity may also be important for quantum mechanical aspects of microtubular arrangements in the cell .
specifically , it was suggested in [ mavromatos and nanopoulos 1998 ] that ferroelectricity in the dimer medium , strengthens isolation of the ` cavity regions ' , thereby leading to a larger probability for the coherent states to form and live long enough , so as to transport information and energy across the microtubular arrangement .
the rle of the surrounding water molecules for the ferroelectricity in the dimer medium was emphasized .    in this latter respect
we now mention that the interesting property of kfct is the origin of its ferroelectricty .
in fact , the alignment of the water molecules by the surrounding crystalline structure ( @xmath26 ) causes the measured macroscopic spontaneous polarization @xmath27mc / m@xmath9 , which is compatible with the known microscopic water dipole configuration in kfct ( helwig , klpperpieper , @xmath15 mser , 1978 ) . to be more specific ,
the onset of ferroelectric behaviour is connected with the ordering of the hydrogen - bonded water - molecules ( taylor , mller , hitterman , 1970 ) .
thus , one is tempting to conclude from this particular ferroelectric crystal that a similar mechanism might be at work with the microtubules .
indeed , a typical microtubular arrangement consists of a quasi solid cylinder of tubulin dimers , which are arranged in 13 arrays ( protofilaments ) .
the interior of the microtubules , of cross - section diameter @xmath28 , is filled with water molecules , being ubiquitous in biology .
the dimers ( of extent @xmath29 in the direction of the protofilament axis ) are believed to have unpaired ( mobile ) electric charges , which lead to electric dipole moments ( sataric _ et al .
_ , 1993 , tuszynski _ et al .
_ , 1995 ) .
in ( mavromatos and nanopoulos , 1997 , 1998 ) it was further conjectured that there are thin layers in the interior of the cylinders , of a thickness ranging up to few atomic scales ( angstrms ) , fairly isolated from their environment , which operate as cavities sustaining mesoscopic quantum coherent modes . in this scenario ,
the importance of the water molecules lies in the provision of the necessary coupling with the quantized elecgromagnetic radiation in the cavity , via their electric dipole moments , so that : ( i ) coherent modes appear in the interior of the cavity ( dipole quanta ) ( del giudice _ et al
. _ 1988 ) , and ( ii ) a coupling exists between these coherent modes and the dimer dipole quantum oscillation modes ( mavromatos , nanopoulos , 1997 ) .
the latter leads to coherent solitonic modes along the protofilament dimer chains , which have been argued to be responsible for dissipationless energy transfer across the microtubule .    in view of the existence of the afore - mentioned hydrated ferroelectric compounds
, we may now conjecture that such configurations favour an alignment of the water molecules ( actually , not necessarily only those inside the tube ) .
then , the sofar speculated polar properties of microtubules , and their connection to quantum physics , might exist in reality .
because of the importance of such a ferroelectric property for these subcellular constituents , the next step is to establish or exclude it experimentally . a suggested sensitive experimental method to confirm the predicted ferroelectric behaviour of microtubules is via the four probe ac impedance spectroscopy ( z(@xmath30 ) )
. this technique is based on the measuremnt of the ac voltage to current ratio using 4-electrodes ( figure 1a ) in a quite broad frequency interval ( the so called _ frequency domain technique _ ( figure 1b ) ) .
the experimental set up for the ac impedance measurement of the microtubules in liquid suspension is shown in figure 2 .
this method has been recognised already as a valuable tool in the study of similar electrochemical systems ( macdonald , 1987 ) .
there are practical advantages of this technique compared to the more simple and old one working in the so called _ time domain _ , which applies either pulse or step source signals ( macdonald , 1987 , bottelberghs , 1978 ) .
in fact , the expected ferroelectric contribution of the suspended microtubules to the measured impedance z(@xmath30 ) can only be observed in the higher frequency domain ( s. figure 1b ) .
otherwise , low frequency electrochemical phenomena , being certainly present in such a liquid suspension of microtubules , complicate the whole measuring procedure , which will suppress the appearance of a ferroelectric component inside the sample .    in practice ,
working with a suspension of microtubules additional experimental modifications might well become necessary .
thus , in addition to a conventional dc polarization for the z(@xmath30 ) measurement one can also apply a pseudo - dc polarization , in order to avoid quasi - static complex electrochemical phenomena due to the electrode s polarization coming from slow and heavy ion transport inside the sample .
the onset of ferroelectricity can be identified due to a resonance - like response in the phase and the amplitude diagram of the impedance ( s. figure 1b ) .
we thank j. albers for discussions and for providing us with information on hydrated ferroelectrics . this work is based on presentations by n.e.m . and k. z. at the workshop ` biophysics of the cytoskeleton ' , banff , alberta , canada , august 18 - 22 1997 .
we thank j. tuszynski for his interest in our work .
the work of n.e.m . is supported by p.p.a.r.c .
( u.k . ) , and that of d.v.n . is supported in part by d.o.e .
grant de - f - g03 - 95-er-40917 .
bottelberghs , p. h. edits .
p. hagenmller and w. van gool ,                                              * figure 1*.   ac impedance measurement of a suspension of microtubules using : * ( a ) * a 4 probe electrode configuration in order to avoid electrode polarization phenomena , and * ( b ) * two main experimental regimes in the measured amplitude and phase of the complex impedance z(@xmath30 ) .      *
figure 2*.   experimental set - up for the ac impedance measurement of the microtubules in liquid suspension , using evaporated 4 pt or au electrical contacts on a glass substrate mounted on a cu temperature head , allowing measurements at different temperatures ( left ) .
the diagram of the experimental set - up with the possibility of a pseudo dc offset is also shown ( right ) .
we present the main properties of ferroelectricity , with emphasis given to a specific family of hydrated ferroelectric crystals , which can serve as model systems for corresponding configurations in biology like the microtubules . 
 an experimental method is described , which allows to establish the ferroelectric property of microtubules in suspension .    
 2.5 cm    _ presented at the workshop on the molecular biophysics of the cytoskeleton , august 18 - 22 , 1997 , banff , alberta , canada . 
 _    1.5 cm