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Journal of Theoretical Biology 230 (2004) 261–270
Propagation of electromagnetic radiation in mitochondria?
Roland Thar*, Michael K.uhl
Marine Biological Laboratory Helsingør, University of Copenhagen, Strandpromenaden 5, Helsingør 3600, Denmark
Received 20 February 2004; received in revised form 12 May 2004; accepted 13 May 2004
Available online 17 July 2004
Abstract
Mitochondria are the main source of ultra-weak chemiluminescence generated by reactive oxygen species, which are continuously
formed during the mitochondrial oxidative metabolism. Vertebrate cells show typically filamentous mitochondria associated with
the microtubules of the cytoskeleton, forming together a continuous network (mitochondrial reticulum). The refractive index of
both mitochondria and microtubules is higher than the surrounding cytoplasm, which results that the mitochondrial reticulum can
act as an optical waveguide, i.e. electromagnetic radiation can propagate within the network. A detailed analysis of the inner
structure of mitochondria shows, that they can be optically modelled as a multi-layer system with alternating indices of refraction.
The parameters of this multi-layer system are dependent on the physiologic state of the mitochondria. The effect of the multi-layer
system on electromagnetic radiation propagating along the mitochondrial reticulum is analysed by the transfer-matrix method. If
induced light emission could take place in mitochondria, the multi-layer system could lead to lasing action like it has been realized in
technical distributed feedback laser. Based on former reports about the influence of external illumination on the physiology of
mitochondria it is speculated whether there exists some kind of long-range interaction between individual mitochondria mediated by
electromagnetic radiation.
r2004 Elsevier Ltd. All rights reserved.
Keywords: Ultra-weak chemiluminescence; Optical waveguide; Mitochondrial reticulum; Reactive oxygen species (ROS); Refractive index
1. Introduction
The internal organization of eukaryotic cells is
characterized by the compartments of diverse organelles
(e.g. nucleus, endoplasmic reticulum, mitochondria,
microsomes), which are related to specific physiological
functions. The compartments are generally enclosed by
one or two membranes consisting of a lipid bilayer. The
membranes show diverse morphologies, ranging from
simple spherical to highly complex configurations.
Mitochondria consist of an outer membrane enclosing
an inner membrane, which exhibits a complex pattern of
invaginations called cristae. Different cell types show a
wide variety of cristae morphologies, e.g. tubular,
lamellar, helical, or even triangular cristae (Fawcett,
1981;Tandler and Hoppel, 1972). Vertebrate tissues
typically show lamellar or tubular cristae, which are
arranged perpendicular to the mitochondrial long axis
yielding to a cross-striated appearance of the mitochon-
drion (Fawcett, 1981;Perkins and Renken, 1997;Riva
et al., 2003;Tandler and Hoppel, 1972). The basic
structure of mitochondria is closely related to their
physiological function as the ‘‘power-house’’ of the cell.
The oxidation of reduced substrates with molecular
oxygen builds up a proton motive force across the inner
membrane. The proton motive force is in turn utilized
by membrane bound enzymes (Mitchell, 1977), which
phosphorylate adenosine diphosphate (ADP) to adeno-
sine triphosphate (ATP) the latter being the universal
energy-providing molecule for biochemical reactions. In
recent years mitochondria regained much research
interest as their central role in programmed cell death
(apoptosis) and in many diseases became evident (for a
review see Nieminen, 2003;Ohta, 2003).
Despite the general ‘‘text book’’-appearance of
mitochondria as ovoid organelles of about 0.5 mmin
diameter and 1 mm in length which originated from
observations on isolated mitochondria, improved tech-
niques in light microscopy such as differential inter-
ference contrast (DIC) and the application of fluorescent
probes (Bereiter-Hahn, 1990; Bereiter-Hahn and V .
oth,
ARTICLE IN PRESS
*Corresponding author. Tel.: +45-4921-3344; fax: +45-4926-1165.
E-mail address: rthar@zi.ku.dk (R. Thar).
0022-5193/$ - see front matter r2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jtbi.2004.05.021
1994) have shown that vertebrate mitochondria within
intact cells of muscular, neuronal, or connective tissue
are predominantly filamentous. Single filamentous
mitochondria are typically about 100–500 nm in dia-
meter and up to 10 mm in length, and they are associated
with microtubules in the cytoskeleton (Ball, 1982;
Heggeness et al., 1978). Microtubules and filamentous
mitochondria form together complex reticula (networks)
radiating from the centrosome (Fig. 1). Mitochondrial
reticula have been observed in cell cultures of mammal
fibroblasts, rat smooth muscle cells, rat sensory neurons,
rat kidney cells, mouse macrophages, monkey myocar-
dial cells, and Xenopus endothelial cells (Bakeeva et al.,
1978;Bereiter-Hahn and V .
oth, 1994;De Giorgi et al.,
2000;Dedov and Roufogalis, 1999;Kirkwood et al.,
1986;Poot et al., 1996;Shimada et al., 1984). Within
muscle tissue these reticula actually extend across
neighbouring cells resulting in a supracellular mitochon-
drial network as e.g. observed in the rat diaphragm
muscle (Bakeeva et al., 1978).
Ultra-weak chemiluminescence appears as a general
feature of all living organisms. It appears as a permanent
weak light emission throughout the ultra-violet (UV),
visible, and near-infrared (NIR) parts of the electro-
magnetic spectrum, which can be only detected by highly
sensitive photo-multiplier-tubes (Cadenas, 1988;Inaba,
1988;Mei, 1994). Generally it is assumed that this light
emission is linked to radical production accompanying
the cell’s metabolism (Adam and Cilento, 1982;Cilento
and Adam, 1995). Radical production takes predomi-
nantly place in mitochondria, where redox-reactions of
the mitochondrial respiration chain permanently produce
reactive oxygen species (ROS) (Barja, 1999;Møller, 2001;
Turrens, 2003). It was estimated that under normal
conditions 1–2% of the cell’s oxygen consumption is
converted into ROS (Turrens, 2003). This level of ROS-
production is essential for the physiological control of a
variety of cell functions (Droge, 2002), whereas patholo-
gical increased levels of ROS cause oxidative damage to
many cell compounds (Turrens, 2003). Several chemical
mechanisms have been proposed to explain how ROS can
generate electronic excited compounds (e.g. singlet
oxygen or excited carbonyls), which are the source of
chemiluminescence (Adam and Cilento, 1982;Cadenas,
1988;Cilento and Adam, 1995). Ultra-weak chemilumi-
nescence has been directly measured from respiring
isolated mitochondria, where peroxidation of mitochon-
drial membrane lipids was the presumable light-produ-
cing mechanism (Hideg et al., 1991). Specific substrates
were shown to increase mitochondrial chemiluminescence
significantly, as was demonstrated for the aerobic
oxidation of aldehydes (Boh et al., 1982;Nantes et al.,
1995).
There is an ongoing debate in the scientific commu-
nity whether ultra-weak chemiluminescence bears any
functional relevance in biological organisms. The
majority regards ultra-weak chemiluminescence as a
waste product of the cell’s metabolism. In contrast,
some groups speculated whether ultra-weak chemilumi-
nescence could trigger photochemical reactions within
the cell (Cilento, 1982). Others even postulated that
ultra-weak chemiluminescence is used for some kind of
signalling or information transport in organisms,
designating ultra-weak chemiluminescence as ‘‘biopho-
tons’’ (e.g. Mei, 1994).
Most studies on ultra-weak chemiluminescence have
investigated the nature of the light-generating chemical
reactions (Allen, 1982;Cadenas, 1988;Cilento and
Adam, 1995) and how diverse parameters (e.g. specific
substrates, temperature) influence the quantity and
quality of ultra-weak chemiluminescence (Boh et al.,
1982;Hideg and Bj .
orn, 1996;Nantes et al., 1995).
However, to our knowledge no studies about the
propagation of emitted light within cells has been
published. In the following, we present a theoretical
analysis of the optical properties of different cell
compartments. Based on this analysis, we propose a
new view on the propagation of electromagnetic
radiation und thus also ultra-weak chemiluminescence
within biological tissues. We will focus on filamentous
mitochondria with cross-striated cristae morphologies,
which are typical for vertebrates. First we show that
filamentous mitochondria and microtubules can act as
optical waveguides (Section 2), then we analyse the
optical properties of the different mitochondrial com-
partments (Section 3) and show the implications for the
light propagation of intramitochondrial-generated che-
miluminescence (Section 4). A general discussion con-
cludes the article (Section 5).
2. Filamentous mitochondria and microtubules act like
optical waveguides
An important optical property for the propagation
of light within media is the index of refraction n.It
ARTICLE IN PRESS
Fig. 1. Schematical drawing of a fibroblast in cell culture showing the
radial organisation of microtubules and mitochondria centered around
the centrosome. (a) Cell nucleus, (b) cytoplasm, (c) oval mitochon-
drion, (d) filamentous mitochondria, (e) microtubules, (f) centrosome.
R. Thar, M. Ku
¨hl / Journal of Theoretical Biology 230 (2004) 261–270262
determines the propagation velocity vof electromagnetic
waves within these media as v=n
1
c, where crepresents
the vacuum propagation velocity. Phase microscopy
allows the measurement of the index of refraction for
different intracellular components (Spencer, 1982).
Measurements yielded values of n
cyto
=1.35 (Johnsen
and Widder, 1999) for the cytoplasm and n
mito
=1.4 for
whole mitochondria (Beuthan et al., 1996). For
comparison, pure water has an index of refraction of
1.33. The optical geometry of a typical filamentous
mitochondrion can thus be regarded as an elongated
cylinder with a diameter of 300 nm, which is surrounded
by a medium with a lower index of refraction.
This configuration is analogous to fiber-optic wave-
guides, which allow the transmission of light along bent
paths (Lipson et al., 1995). Fiber-optic waveguides
consist of a cylindrical inner core surrounded by the
cladding, which shows a lower index of refraction than
the core material (Fig. 2A, B). The working principle of
fiber-optic waveguides is based on total internal reflec-
tion, which is given if light approaches an interface
towards a region with a lower index of refraction at an
angle y, which is smaller than the critical angle y
total
given as
sin ytotal ¼1n2
core
n2
clad
1=2
;ð1Þ
where n
core
and n
clad
are the indices of refraction of the
core and the cladding, respectively (Lipson et al., 1995).
A detailed theoretical analysis of the propagation of
light within waveguides shows, that there exists only a
discrete set of electromagnetic field patterns—termed
‘‘modes’’—for high transmittance of electromagnetic
waves through waveguides. The number of modes
decreases with decreasing core diameter, but there
remains always at least a single mode. Consequently,
even waveguides with a core diameter much smaller than
the wavelength of the light are able to guide light
efficiently. For a given core diameter a cut-off wave-
length (all wavelengths are regarded as vacuum wave-
length), l
c
, can be calculated as
lc¼1:305 Dðn2
core n2
clad Þ1=2;ð2Þ
where Drepresents the core diameter. There exists only
a single mode for wavelengths longer than the cut-off
wavelength l
c
(Lipson et al., 1995).
Electromagnetic radiation which is transmitted
along fiber-optic waveguides is not totally confined to
the inner core, but it is partly also located as an
‘‘evanescent field’’ in the surrounding cladding. The
intensity Iof the evanescent field decreases exponentially
with increasing distance to the core center (Fig. 2C)as
given by
IBexpð2brÞ;ð3Þ
where ris the distance from the core center and blies in
the range of
2pncorel1obo2pnclad l1;ð4Þ
where lis the wavelength of the transmitted light.
In order to assure a high transmittance of radiation
along the fiber-optic waveguide, the radius Rof the
cladding has to be large enough in order to contain
several decay lengths (2b)
1
of the evanescent field
ARTICLE IN PRESS
Fig. 2. Fiber-optic waveguide. (A) Longitudal cross-section. (B)
Transversal cross-section. (C) Radial dependence of the electromag-
netic field intensity.
R. Thar, M. Ku
¨hl / Journal of Theoretical Biology 230 (2004) 261–270 263
(Lipson et al., 1995):
Rbð2bÞ1:ð5Þ
All the mentioned considerations, which are well
established in the theory for light propagation in fiber-
optic waveguides, can also be applied to mitochondria.
Filamentous mitochondria themselves correspond to the
fiber core with a typical diameter of D=300 nm and
n
core
=n
mito
=1.4. The cytoplasm surrounding the mito-
chondria corresponds to the cladding with n
clad
=n
cy-
to
=1.35. Using Eqs. (1) and (2) this gives a critical angle
y
total
=15.4and a cut-off wavelength of l
c
=145 nm.
Thus, mitochondria could in principle act like single
mode fibers for electromagnetic radiation with wave-
lengths >145 nm, which comprises UV, visible, and
NIR radiation. If we assume a typical wavelength in the
visible region of l=500 nm, the decay lengths (2b)
1
of
the evanescent field will be ca. 30 nm following Eqs. (3)
and (4). Filamentous mitochondria observed in the
different cell types listed in the introduction are
generally surrounded within several micrometer distance
by cytoplasm, which means that Eq. (5) is satisfied.
Therefore, filamentous mitochondria should in principle
be able to act like waveguides along their long axis.
The same considerations also hold for the micro-
tubules, which are composed of tubulin proteins ar-
ranged in a hollow cylinder 24 nm in diameter. The
refractive index of microtubules was measured to be
n
mt
=1.51 (Sato et al., 1975). Following the same
reasoning as for light propagation in mitochondria,
microtubules should also act as single mode waveguides.
The transmittance of light within mitochondria is in
principle not confined to a single mitochondrion.
Filamentous mitochondria forming an intracellular
reticulum are often observed to be in close connection
to each other, i.e. several mitochondria are arranged in
a cable-like structure (Fig. 1)(Bakeeva et al., 1978;
Bereiter-Hahn and V .
oth, 1994;De Giorgi et al., 2000;
Dedov and Roufogalis, 1999;Kirkwood et al., 1986;
Poot et al., 1996;Shimada et al., 1984). The distance
between neighbouring mitochondria is often much less
than the wavelength of visible light and this would allow
radiation propagating through a mitochondrion to cross
the gap to a neighbouring mitochondrion where it can
propagate further (Lipson et al., 1995). Additionally,
the attachment of filamentous mitochondria with the
microtubules of the cytoskeleton (Ball, 1982;Heggeness
et al., 1978) can be optically described as two parallel
waveguides in close proximity. The above calculated
decay length of the evanescent field of ca. 30 nm enables
electromagnetic waves propagating within a mitochon-
drion to be coupled via the evanescent field into the
microtubule. Thus, even if filamentous mitochondria are
not in close contact to each other, microtubules could
provide light guiding along the cellular network of
microtubules and filamentous mitochondria.
3. Mitochondria as an optical multi-layer system
The outer and inner membranes divide a mitochon-
drion into two compartments: the intramembrane space
and the matrix (Fig. 3). The inner mitochondrial
membrane in vertebrate cells generally exhibits cristae
perpendicular to the long axis of the mitochondrion
with fairly regular distances dbetween neighbouring
ARTICLE IN PRESS
Fig. 3. (A) Internal organisation of filamentous mitochondrion with lamellar cristae. The left side shows state 3-, the right side state 4-configuration
(B) Model of filamentous mitochondrion used for optical calculations. Llength, Ddiameter of mitochondrion, d
1
/n
1
thickness and refractive index of
matrix space between two cristae, d
2
/n
2
thickness and refractive index of cristae, Nnumber of double layers, Rreflectance, Ttransmittance.
R. Thar, M. Ku
¨hl / Journal of Theoretical Biology 230 (2004) 261–270264
cristae. A filamentous mitochondrion thus appears in
electron microscopic images as cross-striated with
alternating layers of matrix and intramembrane space.
A typical value for the distance dis about 100 nm, and
this value will be used in the following calculations,
although especially mitochondria in heart muscle tissue
show values as low as 50 nm (Fawcett, 1981;Tandler
and Hoppel, 1972). Advanced electron microscopy
techniques have recently revealed that the actual
morphology of the cristae is more complicated than
given in the schematical drawing of Fig. 3 (Frey and
Manella, 2000;Perkins and Frey, 2000). However, for
our optical considerations the simplified model should
give results, which are also valid for the actual more
complex morphology.
The ratio between the volume of the matrix and the
one of the intramembrane space is dependent on the
physiological state of the mitochondrion. Provided that
the mitochondrion is supplied with sufficient organic
substrate and molecular oxygen, two states can be
distinguished. At low ADP concentrations the mito-
chondria are in a resting state with low oxygen
consumption, whereas at high ADP concentrations the
mitochondria respire oxygen at their full capacity. Both
states are traditionally termed state 4 and state 3,
respectively (Hackenbrock, 1972). During state 4 the
matrix occupies about 90% of the mitochondrial
volume, i.e. the cristae appear as thin infoldings. On
the transition to state 3 the cristae swell until the matrix
volume is finally almost halved, i.e. mitochondria in
state 3 show an approximately equal distribution
between the matrix and the intramembrane space
volume (Halestrap, 1989;Srere, 1980). The resultant
state dependent thicknesses for the matrix layers, d
1
, and
for the intramembrane space layers, d
2
, of a typical
mitochondrion are listed in Table 1.
The numerous enzymes present in mitochondria result
in a high protein concentration. The mitochondrial
compartments differ considerably in their respective
protein content. The matrix together with the inner
membrane contain up to 90% of total mitochondrial
protein, i.e. less than 10% are located in the intramem-
brane space (Schnaitman and Greenawalt, 1968). Thus,
the matrix of mitochondria in state 4 show protein
concentrations of up to 0.5 g ml
1
(Hackenbrock, 1968;
Srere, 1980), as can be anticipated by the electron dense
appearance of the matrix in electron microscopic
images. The almost two-fold contraction of the matrix
volume during state 3 of respiring mitochondria
increases the protein concentration further to up to
1gml
1
(Srere, 1980). It can be calculated that such a
high protein concentration approaches the densest
possible packaging possible for protein molecules with
minimal water content (Srere, 1980). The protein
content influences the optical properties of the compart-
ments. The index of refraction nis linearly dependent on
the protein concentration as given by
n¼1:33 þ0:19 cprotein;ð6Þ
where c
protein
is the protein concentration in units of
gml
1
(Spencer, 1982). This dependency can now be
applied to the known protein concentration of the
different mitochondrial compartments (Table 1).
Mitochondria in the resting state 4 show no sig-
nificant differences in the refractive indices of the
intramembrane space and the matrix. Thus, they will
act like homogeneous fiber-optic waveguides as de-
scribed in the previous section. But the picture is
different for actively respiring mitochondria in state 3.
The matrix shows now an index of refraction as high as
1.5, which is comparable to values measured for certain
glass types. In contrast, the index of refraction of the
intramembrane space is about 1.35.
Based on the obtained information about the dimen-
sions and the optical properties of the mitochondrial
compartments during state 3, we formulated a one-
dimensional optical model of an ideal mitochondrion. A
mitochondrion can be represented as a multi-layer
system of two alternating layers L
1
and L
2
with a
thickness of d
1
and d
2
and an index of refraction of n
1
and n
2
, respectively (Fig. 3B). Such an optical config-
uration corresponds to interference mirrors, which in
case of perpendicular incident light show highest
reflectivity for the wavelength
l¼ðn1þn2Þd;ð7Þ
where d=d
1
+d
2
is the thickness of a single double layer
(Fig. 3). Following the values given in Table 1,
ARTICLE IN PRESS
Table 1
Protein content, refractive index, and thickness for the different compartments of the model mitochondrion with lamellar cristae as used for the
optical calculations
State 4 (resting) State 3 (respiring)
Matrix + inner membrane Intramembrane space Matrix + inner membrane Intramembrane space
Protein concentration (g ml
1
) 0.5 0.5 0.9 0.1
Index of refraction n
1
=1.43 n
2
=1.43 n
1
=1.50 n
2
=1.35
Thickness (nm) d
1
=90 d
1
=10 d
1
=50 d
1
=50
R. Thar, M. Ku
¨hl / Journal of Theoretical Biology 230 (2004) 261–270 265
mitochondria in state 3 should possess highest reflectiv-
ity at a wavelength of ca. 285 nm, if the incident light is
directed as indicated in Fig. 3B. The absolute value of
the reflectance Rfor this wavelength is dependent on the
number of double layers and can be calculated by
R¼n2
n1
2N
1
!
2n2
n1
2N
þ1
!
2
;ð8Þ
where Nis the number of double layers. A filamentous
mitochondrion L=1 mm in length (N=10) shows a
reflectivity of R=61.34%, which increases to
R=99.99% for a length of L=5 mm(N=50) (Table 2).
4. Spectral analysis of light propagation in mitochondria
The spectral dependencies of the transmittance Tand
the reflectance Rin the one-dimensional optical model
(Fig. 3B) can be analysed by the transfer-matrix method
(see Appendix) (Lipson et al., 1995), which is generally
applied for analysing optical multi-layer systems, e.g.
interference filters. Additionally, we assumed a possible
light amplification mechanism, i.e. electromagnetic
waves travelling the distance Dxwithin the multi-layer
system are amplified by the factor exp(aDx), where ais
the amplification constant (Eq.(A.4)). The intention
behind this will be discussed later. The transfer-matrix
method was implemented in a Mathematica program
(Wolfram Research Inc.), which calculates the reflec-
tance Rand transmittance Tfor 200 different equidi-
stant wavelengths lwithin the interval of 200–800 nm.
Assuming an ideal filamentous mitochondrion
(D=300 nm, L=5 mm, N=50) in the respiring state 3
(Table 1) and no amplification (a=0), the resultant
reflectance and transmittance spectra show a stop-band
with almost unity reflectance (RE100%) at the wave-
lengths of 270–290 nm (Fig. 4A), which is in accordance
to the results of the previous section. In contrast, the
wavelength region 300–800 nm shows almost unity
transmittance (TE100%) and an ideal filamentous
mitochondria in both metabolic states 3 and 4 should
for these wavelengths act like fiber-optic waveguides if
neither light amplification nor absorption is assumed.
A different result is obtained if we assume that the
electromagnetic waves can be amplified when propagat-
ing through the mitochondrion, i.e. a>0 (Eq. (A.4)).
Assuming otherwise the same parameters as before, the
resultant reflectance and transmittance spectra show a
series of peaks within the range of visible light (Fig. 4B).
For example if we choose a=0.6 mm
1
(unfortunately,
there are no experimental data so far available in order
ARTICLE IN PRESS
Table 2
Reflectance R(see Fig. 2) of model mitochondrion with varying length Land number of double layers N
L(mm) 0.1 0.2 0.5 1 2 3 4 5
N12 51020304050
R(%) 1.10 4.31 23.32 61.34 94.26 99.28 99.91 99.99
Fig. 4. Spectral reflectance and transmittance as calculated for model mitochondrion measuring 5 mm in length. (A) No amplification (a=0).
(B) With amplification (a=0.6 mm
1
).
R. Thar, M. Ku
¨hl / Journal of Theoretical Biology 230 (2004) 261–270266
to obtain a quantitative estimate for a), light of unity
intensity entering the ideal mitochondrion from the left
side is amplified at the peak wavelengths up to 10000
times and is emitted almost symmetrical towards both
sides of the mitochondrion as can be anticipated from
the transmittance and reflectance spectra. Most of the
emitted light energy now originate from the amplifica-
tion mechanism inside the ideal mitochondrion, as the
incident light intensity measures only a fraction of the
emitted one.
The latter results were obtained by assuming an
external incident light source of unity intensity from the
left side (Fig. 3B), which initiated the amplification
process. In case the external light source is replaced by
an internal light source within the first layer to the left
side, this source would initiate still the same amplifica-
tion process, i.e. it will result in emission spectra to the
left and the right end of the multi-layer system which are
identical to the reflectance and transmittance spectra in
Fig. 4B, respectively. Furthermore, the almost symme-
trical shape of both spectra indicates that the actual
position of the internal source should not affect the
qualitative shape of the resultant emission spectra. Thus,
an ideal filamentous mitochondrion in state 3, which
generates chemiluminescence and additionally exhibits
the proposed amplification mechanism could emit light
at both ends with characteristic peaks in the spectral
light composition.
Chemiluminescence from mitochondria originates
generally from excited molecules generated by the
oxidative metabolism of mitochondria. There exist two
principal mechanisms for photon emission from an
excited molecule: spontaneous and induced emission
(Lipson et al., 1995). In the first case, the excited
molecules emit the photons with a certain decay rate.
Assuming that the excited molecules have a random
spatial orientation, the emitted photons will not exhibit
a preferred propagation direction, i.e. the emission is
isotropic. The angle, y, between the propagation
direction and the long axis of an ideal mitochondrion
determines whether the emitted photon is actually
‘‘captured’’ within the mitochondrion and guided by
the optical properties of the mitochondrion (see Section
2). According to Eq. (1), only photons with an angle y
smaller than the critical angle y
total
will be captured and
propagate along an ideal mitochondrion. Assuming an
isotropic emission characteristic, the fraction fof
captured photons can be calculated as
f¼ð1cos ytotal Þð9Þ
which gives f=0.036 if we assume y
total
=15.4(Section
2). Thus, only 3.6% of the emitted photons are actually
captured within an ideal mitochondrion and guided
towards both its ends.
In the second case, induced emission provides a
possible mechanism for the proposed amplification of
the internal light field. Induced emission takes place
when an excited molecule is hit by a photon inducing the
emission of a second photon. Both photons have
identical propagation directions and phase relations,
which was the underlying assumption for the mathema-
tical formulation of the amplification process in
Eq. (A.4). If induced photon emission is predominant
over spontaneous emission, the fraction fof the
captured and guided light changes significantly. Cap-
tured photons, which are guided along an ideal
filamentous mitochondrion, would have a longer re-
sidence time within the mitochondrion than non-
captured photons. Thus, induced emission will predo-
minantly take place for captured photons. This results in
a self-amplification process providing that the fraction f
of captured photons approaches 100%. The emitted
light should show temporal coherence as photons
generated by induced emission have identical phases.
The spectra shown in Fig. 4B were calculated with the
assumption of a wavelength-independent amplification
constant a. In reality, the self-amplification mechanism
of induced photon emission will cause the amplification
process to select for specific peaks within these spectra.
Which peaks are actually selected depends on the
emission spectrum of the excited molecule. Chemilumi-
nescence from mitochondria has been detected within
the visible region of the electromagnetic spectrum (Boh
et al., 1982;Hideg et al., 1991;Nantes et al., 1995), thus,
it is likely that also peaks within this region are selected.
Consequently, if induced emission actually is the
dominant emission process within filamentous mito-
chondria in metabolic state 3, the internally generated
light will be emitted at both ends of the mitochondria
with high temporal coherence and high directivity, i.e.
mitochondria would act like lasers. The described lasing
principle has been technically realized in the design of
distributed feedback lasers, which consist of a similar
multi-layer system consisting of layers with different
indices of refraction (Kneub .uhl and Sigrist, 1999).
5. Discussion
Most of the presented considerations are well
supported by optical theory, but we are aware that the
assumption of induced light emission is very speculative.
The internal light intensity of technical lasers has to be
above a certain threshold in order for the induced light
emission to predominate the spontaneous one (Kneub-
.uhl and Sigrist, 1999). Typical threshold light intensities
are many orders of magnitude higher than the intensity
of ultra-weak chemiluminescence. Thus, it appears to be
very unlikely that induced light emission takes place in
mitochondria. However, there are some points to be
considered: Due to the optical waveguide properties of
the mitochondrial network, only a small fraction of the
ARTICLE IN PRESS
R. Thar, M. Ku
¨hl / Journal of Theoretical Biology 230 (2004) 261–270 267
internal light field might actually leave the network.
Thus, the actual light intensity inside the mitochondria
might be considerably higher than one would expect
from the measurements on ultra-weak chemilumines-
cence, which is generally measured macroscopically
several centimetres in distance from the tissue or cell
cultures (Cadenas, 1988;Inaba, 1988;Mei, 1994).
Furthermore, in recent years technical micro-lasers have
been manufactured approaching the small dimensions of
mitochondria. It has been shown that the threshold light
intensity for these micro-lasers is significantly lower than
observed for macroscopic lasers (e.g. Loncar et al.,
2002). Altogether, there are too many unknown para-
meters at the current stage in order to evaluate
quantitatively the possibility of induced light emission
within mitochondria.
Nevertheless, we have shown that the mitochondrial
network within eukaryotic cells possesses optical prop-
erties, which to our knowledge have so far not been
considered regarding the light propagation within
eukaryotic cells and tissues. Most treatise on this subject
are based on scattering theory, assuming that the light
propagation is mainly based on random absorption and
scattering events (e.g. Yamada, 2000). In contrast, the
demonstrated light guiding properties of the mitochon-
drial network indicate that the light propagation can be
essentially non-random. It is tempting to speculate
whether this is related to any biological function.
Cilento has pointed to the possibility that biochemi-
cally generated excited molecules could transfer their
energy to other molecules, where it in turn triggers
chemical reactions (Cilento, 1982). Whereas Cilento
considered interactions of molecules in close contact to
each other, the mechanism could be extended to long-
range interactions if the light guiding properties of the
mitochondrial network are additionally taken into
account. Chemiluminescent light generated in one
mitochondrion could propagate along the network
and, e.g., trigger some chemical reaction in another
mitochondrion. This picture would provide that the
physiology of mitochondria can be effected by light
illumination. Interestingly, there exists a wealth of
experimental data about the influence of low power
laser irradiation on cell cultures (e.g. Alexandratou et al.,
2002;Kaku, 1990;Karu et al., 2001;Schwartz et al.,
2002;Shefer et al., 2002). Typical experiments were
based on daily short-period illumination of cell cultures
with a certain visible light dose, which resulted in
significant changes in the physiology and proliferation
of cells. Pathologic effects could be excluded as the
observed effects were strictly dose-dependent, i.e. there
existed an optimum daily light dose, which showed the
most prominent effect on the cell cultures. It is presumed
that the site of the interaction between the light field and
the cells was located within the mitochondria, and
indeed experiments with isolated mitochondria demon-
strated that external illumination influenced their
physiology significantly (Breitbart et al., 1996;Gordon
and Surrey, 1960;Greco et al., 2001;Kato et al., 1981;
Morimoto et al., 1994;Passarella et al., 1984).
Altogether, we know that mitochondria emit chemi-
luminescent light, we know that their physiology is
influenced by illumination, and our present study shows
that light can be guided along the mitochondrial
network. Thus, it is very tempting to speculate whether
there exists in reality some long-range interaction
between individual mitochondria, which is mediated
by electromagnetic radiation. The biological function
and relevance of this possible mechanism would be the
next question to be answered.
Acknowledgements
We would like to thank Willfried Staude for advice
regarding the transfer matrix method, and Ian Max
Møller for commenting an earlier version of the manu-
script. Andrea Wieland, Konstantin Boucke, and Karen
Willbrand inspired by fruitful discussions. This study
was supported by the EU-project PHOBIA (QRLT-
2001-01938) to RT and by the Danish Natural Science
Research Council (Contract 9700549) to MK.
Appendix. A
One-dimensional electromagnetic waves with wave-
length lin the optical multi-layer system (Fig. 3B) can
be described by the electric field Eof two waves
travelling in opposite direction (Lipson et al., 1995).
The electrical field Ealong the x-axis at time tis then
given as
Eðx;tÞ¼Re ðEþðxÞþEðxÞÞexp i2pc
lt
;ðA:1Þ
where i ¼ffiffiffiffiffiffiffi
1
p;cis the vacuum speed of light, and
Re{Z} returns the real part of its complex argument Z.
EþðxÞand EðxÞare the time-independent complex
amplitudes of the electric fields belonging to the waves
propagating into positive and negative x-direction,
respectively. The complex amplitude is defined as
E=Eexp(ij) where Eis the amplitude and jthe phase
of the electric field wave. We assume normal incident
waves and regard only one polarization direction. Thus,
the electromagnetic field at position xfor a given
wavelength lcan be described by the time-independent
complex state vector
~
EEðxÞ¼ EþðxÞ
EðxÞ
:ðA:2Þ
If the state vector is known at a single position x, the
state vectors at all other positions can be calculated by
ARTICLE IN PRESS
R. Thar, M. Ku
¨hl / Journal of Theoretical Biology 230 (2004) 261–270268
the transfer-matrix method. The state vector to the right
side x
R
of the multi-layer system is related to the one to
the left side x
L
by
~
EEðxRÞ¼ðT21 S2T12S1ÞN~
EEðxLÞ;ðA:3Þ
where Skis the transfer matrix for the transition of the
state vector inside a layer L
k
given by
Sk¼
exp ink
2p
ldk
expðadkÞ0
0 exp ink
2p
ldk
expðadkÞ
0
B
B
B
@
1
C
C
C
A
:
ðA:4Þ
The constant arepresents a possible amplification of
the electromagnetic wave crossing a layer L
k
with
thickness d
k
and an index of refraction n
k
. The
electromagnetic waves will be partially reflected at the
boarder of adjacent layers L
k
and L
l
due to their
different indices of refraction (n
k
an
l
). This process is
represented by the transfer matrix T
kl
:
Tkl ¼1
2
1þnk
nl
1nk
nl
1nk
nl
1þnk
nl
0
B
@1
C
A:ðA:5Þ
Assuming an incident wave of unity intensity from the
left side, the following boundary conditions can be
applied:
~
EEðxLÞ¼ 1
EðxLÞ
and ~
EEðxRÞ¼ EþðxRÞ
0
ðA:6Þ
which are satisfactory in order to solve Eq. (A.3) for
EðxLÞand EþðxRÞ:As the light intensities are propor-
tional to the square of the amplitude of the electric
fields, the reflectance Rand the transmittance Tare
given by
R¼ðEðxLÞÞ2and T¼ðEþðxRÞÞ2:ðA:7Þ
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