Investigation by physical methods of the possible role of telomeres in DNA in aging process

11 Pages·0.16 MB·English

by  Md. Ashrafuzzaman

Investigation by physical methods of the possible role of telomeres in DNA
in aging process
Md. Ashrafuzzaman and Ahmed Shafee∗
Institut de Physique, Universit´e de Neuchˆatel,
Rue A.L.Breguet, 2000 Neuchˆatel, Switzerland
*Department of Physics,
University of Dhaka, Bangladesh
contact: [email protected]
3
0
The interaction energies between thedifferent typesof bases of a single strand of DNAmolecule
0
havebeen calculated. Using theseoriginal values of energies theharmonic behaviorof a numberof
2
base patterns of DNA has been studied. In view of the great interest aroused by the discovery of

n the role of the telomere segment of the DNA in the replication process and its possible link with
a theagingprocess,wehaveinvestigated,withsimplemodels,theharmonicbehaviorofthetelomeric
J
patternofbasesaswellasthethermodynamicresponseinthebiological system. Withtheseresults

5 a conclusion on the probable role of the telomeric pattern on aging has also been drawn. Here the
1 calculated values of harmonic frequencies of the telomeric pattern of bases and of other possible
patternsshowthatthetelomericpatternisassociatedwiththehighestvibrationalfrequencyamong
]
all patterns of base combinations at the replication end of DNA. This seems to suggest that due
h
p to the existing telomeric pattern being closest to the frequencies of the electromagnetic radiation
- comingfrom sunlight, resonance of thetelomeric frequencywith such radiation mayberesponsible
o fordamagetothereproductiveabilityofthecellsandconsequentagingandotherproblems. Onthe
i other hand in the last part of this work we have calculated the thermal vibrational amplitudes of
b
the telomeric pattern and other possible patterns which show that the amplitude for the telomeric
.
s patternistheleast,andthissuggeststhatthetelomericpatternismoremechanicallyandthermally
c
stablethanotherpossiblepatternsinthebiologicalenvironmentagainstdamagefromordinaryheat
i
s and mechanical effects.
y
h PACSnumbers:
p
[

I. INTRODUCTION energyconsiderations. Molecularbiophysics,therefore,is
1
anintegralpartofman’squestforcompletecontrolofhis
v
1 Most of the activities of the different parts of a liv- inner world.
3 ing system arecontrolledin nucleic acids DNA (deoxyri- For a long time biochemists and biologists have been
0 bonucleic acids) and RNA (ribonucleic acids). The nu- tryingtogathermoreinformationonstructuralandfunc-
1
cleic acids are made of some combinations of purine and tionalbehaviorofbiomoleculesintermsofenzymaticac-
0
pyrimidine bases called genetic codons. The behavior tivities. They met some success in certain areas but the
3
0 and functioning of a living system are all controlled by complete ideas of the behavior of the molecules are to
/ differentcombinations ofgenetic codons. The possibility be established. The nature of biochemical or enzymatic
s
c ofthecontrolofgeneticcharacteristicsisthemostimpor- approachtoknowthe structuralandfunctionalbehavior
i tantareaofthelatestgenomeresearch. Peoplearetrying of biomolecules is biological aspects and the limitations
s
y to find out how the genetic codes arrange themselves to of these methods force the scientists to find other ways
h make DNA and how they have evolved with time. Since to explain the cause of stability or instability and some
p the central dogma of biology is that genetic changes are functional behavior of biomolecules. Therefore scientists
v: broughtaboutby changesinthe macromolecules,itis of are trying to impose the physical methods to explain
i great importance also to investigate the stability of the the structural and functional behavior of biomolecules.
X moleculesandtheirpatternsresponsibleforthegenotyp- In this new process to learn the behavioral aspects of
r icalvariations. Itcanofcoursebe expectedthatsomeof biomolecules,theestablishedmethodsorsometimessome
a
the patterns of bases are more stable and they may be modifications of the existing methods according to the
more persistent in organisms. problem of real or imaginary structures of biomolecules
Attempts are being made to gain a full understand- and their functioning are used.
ing of the role of the different molecules involved in the Formorethantwodecadesphysicistshavebeenstudy-
passing of genetic information to succeeding generations ing the structure-function relationship of the proteins.
and of the pitfalls which lie in the path. That structure People now have a fairly good idea about how muscle
and function of macromolecules are interrelated is fully filaments work or how some of the simpler enzymes per-
established at present. Hence any effort to understand formtheir catalytic activities. Proteincrystallographyis
biologicalprocessesatthe molecularlevelrequiresa rea- anestablishedscienceandusingthismethodcoordinates
sonable understanding of their structure, which in turn, of the atoms of the smaller proteins, such as dihydro-
canonlybeachievedbyathoroughstudyofstabilityand folate reductase (DHFR), are known accurately. Many
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researchgroupsallovertheworldareactiveintheambi- the so-called telomere, to ends of nuclear DNA. Here A
tioustaskofdesigningmoleculeswhichwillaccelerateor is for adenine, G for guanine and T for thymine. After
inhibit the actionof enzymes by attaching themselves to this, underreplication of the linear DNA molecule only
the enzyme at the active site. While this approach does shortens this nontranscribed sequence of the telomeric
remain a promising field, more recently it is becoming fragment of the chromosome without damaging the ge-
attractive to try to do the same with nucleic acids, i.e., netic information or the mechanism that reads it. At
to suppress or promote specific genes. Genes that cause certainstagesofdevelopmentinearlyembryogenesis,the
diseasesshouldberepaired,andifthatisnotpossible,at gene encoding telomerase in the majority of human so-
leastthosecausingproductionofharmfulproteinsshould matic cells is switched off, thereby making the genome
be inhibited. Some antibiotics prevent bacterial growth susceptible to shortening. The telomere shortens at a
by stopping nucleic acid (NA) synthesis, others attempt low but appreciable rate which impairs the functioning
to arrest the growth of cancer cells. However present of the chromosome. This impairment begins long before
methods donotallowchoiceofspecific targets,e.g.,bac- the disappearance of the whole telomere, which removes
terial NA or the NA of cancer cells. More knowledge protection from genetic information contained in tran-
is required about the conformational structures of the scribed regions. This role is still poorly understood.
NAs, about their flexibility and their binding to differ- Thereisclosecorrelationbetweenshorteningoftelom-
ent ligands. Here too energy considerations are of vital eric DNA regions and Hayflick’s limit [1,2]. To surpass
importance. this limit and continue reproduction, the cell should ac-
Recentlyscientistshavebecomeawareofthe existence tivate its telomerase gene.
ofthelink betweenagingandNAs. Itiswellknownthat The most remarkable feature is that switching off the
cells can not replicate indefinitely in vivo. It is possible telomerase gene is an ontogenetic stage that occurs at a
that despite the high accuracy of the process of replica- distincttimepointinthelifeofanorganismandinvolves
tion, with proofreading arrangements to correct errors, onlysomeofitscelltypes. Thiseventseemstoperforma
it is impossible to eliminate errors altogether. The bio- specific function and cannotbe regardedas a disorderin
logicalprocesscontinuesindependentlyandmancannot the living system or a kind of unpredictable age-related
control any biological activity completely. Any disorder defect, although it clearly promotes aging. In this con-
initiatedinsidethebiologicalsystemthereforesometimes text, we are reminded of an observation made in exper-
growsmulti-dimensionally. Therandomnoiseisaccumu- iments with barley germs. During the development of
lated and eventually replication stops. the germ,the telomere suddenly loses 50kb (kilo bases).
Veryrecentlyscientistshavebeguntolookintoanother It loses an additional 20 kb during growth of the spike
possible source of loss of replicability of nucleic acids. [6]. The mechanism responsible for this event remains
The DNAmolecule containsa tailcalledtelomere,acer- unknown. If the arrest of telomerase synthesis is consid-
tainpatternofbaseswhichdonotcodeforanygene,but ered as an accidental fault, telomere shortening in cells
on which the DNA polymerase has to stand when per- containingnofunctionaltelomeraseappearstobe anact
formingreplication. Ithasbeensuspectedthatwitheach ofdeliberatedamagetothe organism. Analternativein-
new cell generation in an organism, i.e., in the replica- terpretationis that the inhibition of the telomerase gene
tion of somatic cells, parts of the telomere gets lost. As and the telomere shortening are biologically important
the telomere keeps shrinking with age,eventually a time events. To understand the meaning of this process, one
comes when they can no longer replicate. As dying cells should remember that telomerase genes of somatic cells
are not replaced by new cells, the organism decays or are switched off only in sexually reproducing organisms,
’getsold’andfinallyfacesdeath. Thisbiologicalactivity but not in vegetatively reproducing organisms. It is ex-
of DNA [1,2] is known to scientists but they don’t know actly in the former case that the appearance of a new
why and how this activity occurs. trait, which can result from a combination of parental
M. Olovnikov formulated the problem of terminal un- genomes,becomes the most probable event. However,in
der replication of linear DNA molecules in 1971[3]; this vegetatively reproducing organisms,the appearance of a
phenomenon is caused by the inability of DNA poly- newtraitresultsfromrandommutationsoccurringinthe
merasestoreplicateseveralnucleotidesat3endsofDNA same cell.
templates. Olovnikov also suggested that a specific bi- The above mentioned properties of the telomere make
ological mechanism should normally prevent this phe- understanding the cause of its instability is an exciting
nomenon. This mechanism was expected to be active in problem. Again, it is possible that evolution has chosen
gametes,cancercells,aswellasincellsofvegetativelyre- the most stable pattern. This may be investigated by
producing organisms. In most other cases, e.g., in many studying the energyof the telomere portionof the DNA.
human somatic cells, this mechanism is suppressed. We can try to interpret this stability with respect to ra-
Further studies revealed the enzyme telomerase [4,5] diation, vibration etc i.e., by using physical rather than
(whose existence had been predicted by Olovnikov)that biological methods. If the energies involved between the
compensates for DNA shortening in the mentioned cell basesofDNAs canbedeterminedandifusingthesehar-
types. Thefunctionoftelomeraseistoaddarepeatedse- monic behaviors of the telomere can be calculated (i.e.,
quence(thehexamerTTAGGGinhumans),whichforms the harmonic frequenciesand thermalvibrationalampli-
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tudes of bases) it can probably be possible to get some II. ENERGY CALCULATION FOR BASE
ideas about the stability of this all important tail which SEQUENCES IN DNA
needstoberetainedforgoodhealthandtocontinuenor-
mal living behavior. Application of quantum mechanics A. Introduction
can give a very good solution of energies and other nec-
essary parameters to explain the states of a single body
InDNAthesuccessivebasesexistinenergeticallyequi-
or in some cases two or three body problems. The ab-
librium state. The most important energies between the
solutely correct way of carrying out such investigations
successive bases are stacking energy and van der Waals
wouldbetosolvetheSchrodingerequationforthe entire
interaction. Stacking energy is due to interaction be-
DNA, which is, of course, quite impossible. Even small
tween the magnetic moments of the helical structure of
molecules can not be solved quantum mechanically, ex-
bases and van der Waals interaction is the well known
actly or even by approximation methods. However, one
6-12 potential that arises when the two bases come very
can, as a zeroth order approximation, completely ignore
neartoeachother. Inthis workthese twotypes ofinter-
thedetailsoftheinteractionsandstudyonlythesymme-
actions between the bases of DNA have been calculated
try aspects of the problem by taking square well poten-
using the well known formulae.
tialsorharmonicbehavior,asis oftendoneincondensed
matterphysics. Theharmonicattitudehasbeenadopted
in this work and the telomere has been studied as a spe-
B. Energy Modeling
cificpatternofbasesrepresentedbyharmonicoscillators.
For this work the bases are considered as simple atoms
AcomputermodelhasbeenconstructedtomakeDNA
connectedtothe nearestatom(base)byaforceconstant
double helices according to whatever base pattern se-
’k’ i.e., between the bases linear restoring forces are in-
quence we required. This was done by smoothly fitting
volved. We believethatevenwithsuchadrasticapprox-
experimental data for each base pair configuration with
imation a meaningful beginning can be made in trying
one another to form a straight double helical structure
to understand the stability problem of the telomere and
. However some flexibility were also retained so as to
the response of the pattern with the thermal, electro-
vary the inter base separation to some extents. While
magnetic and other agents involved in environment. We
lengtheningthe doublehelix bystretchingit ourmethod
have also introduced the thermodynamics effect on the
alsochangesthetwistanglestosomeextendssothatthe
telomere molecules in this work which would represent
interbaseangleswhicharenormally36o for10basepairs
the dependence of structure and function of biological
per turn per piece can vary to some extends in keep-
molecules,especially oftelomere onthermalconditionof
ing with the inter base separation h which is normally
the biological system.
0.36 nm [7-12]. It is well known that the most impor-
tant energy in forming double helix is stacking energy.
Themodeldescribedherehasbeenusedtocalculatethis
stacking energy for different base pair neighbors. The
pyrimidine(CytosineandThymine)havesinglearomatic
six side a ring pattern whereas for the ring in purine
(Adenine and Guanine) eachhas adjoining six sided and
In sec.II, the energies between the different bases in afivesidedaromaticrings. Theseringscontentelectrons
DNA have been calculated. For this some established that contribute magnetic moments. The energy between
methods of energy calculation have been used and the two rings i.e., between two such magnetic moments is
values of some parameters needed for this work of cal- given by
culating the energies involved in DNA have also been
calculated. In sec.III, a method of calculating the har- U(r ,r )= µo[ µ1·µ2 −3µ1·(r1−r2)µ2·(r1−r2)]
monic frequency of telomere and other possible patterns 1 2 4π |r1−r2|3 |r1−r2|5
taking fourpurines andtwo pyrimidinesandalsofor few (1)
other imaginary patterns of bases has been developed. Whentakingintoaccounttheorthogonalityofthes(i.e.,
Forthisamatrixhasbeendevelopedandusingtheener- the base planes) with the helical axis, this reduces to
giesinvolvedbetweenthebasesinDNAtheharmonicfre-
quency of telomere has been calculatedand a conclusion µ (lg)2 d2
U(|r −r |)= o [1−3 ] (2)
onthestabilityoftelomerepatterninthereplicationend 1 2 4π s2
of DNA has been drawn. In sec.IV, the thermodynamic
behaviorofDNAmoleculesespeciallythetemperatureef- where µ = 4π ×10−7 SI unit, is the magnetic perme-
o
fectonthestabilityoftelomerehasbeendiscussed. Here ability in free space,s is the actual distance between the
it is tried to find the effect of the environmentespecially centers of the two rings and d is the 2 dimensional pro-
the biological environmentwhere the DNA exists on the jection of the separation in the plane of the base l is a
structure and function of telomere. Finally in sec.V, the no. and r’s are coordinates. µ1 and µ2 are proportional
results are discussed and the conclusions are presented. to the angular momentum of electrons by the usual gy-
4
romagneticratio(g) andcanbe takenidenticalforother those between purine pyrimidine and pyrimidine pyrim-
rings because always π electrons are involved. idine bases. This is because pyrimidine (Cytosine and
It is to be mentioned the part of energy that can Thymine ) have single aromatic six side a ring pattern
countertheDNAtobecollapsedbytheattractivestack- whereas for the ring in purine (Adenine and Guanine)
ing energy. This type of energy is the van der Waals each has adjoining six sided and a five sided aromatic
interaction which is given by rings. So for purine purine interaction extra stacking
for extra rings exists and therefore the stacking energy
A B
betweenpurinepurinebasesismuchhigherthanthatbe-
U(i,j)=− + (3)
r6 r12 tween pyrimidine pyrimidine bases. When the two rings
ij ij
comecloseduetotheirattractionbystackingenergythey
whereAandB arevanderWaalsconstants. Thevander shouldcollapseasthestackinginteractionis onlyattrac-
Waals interactionsbecomes dominating whentwo atoms tive. So in lieu of being stable the whole DNA molecule
come within van der Waals limit distance. This type of should collapse. But this type of collapsing is encoun-
interaction is also called the 6-12 potential. teredbyvanderWaalshighrepulsive12potentialwhich
Special feature for DNA double helix is that all the becomesdominatingwhenthechargedistributionsoftwo
baseringsareperpendiculartotheaxisofthedoublehe- atoms overlap. So the attractive interaction of stacking
lix. This feature is included in the energy calculation. It energyisthuscompensatedbythehighrepulsivevander
has also been takenin the termthe rotationofthe bases Waals interaction.
asthe helixgoesdownasisalreadymentioned. Combin-
ing the two energies mentioned above the equation for
the calculation of the total interaction energy [13] be-
III. FREQUENCY CALCULATION FOR
tween the two bases of DNA is being calculatedwhich is DIFFERENT BASE SEQUENCES IN DNA
as follows
A B z2 A. Introduction
V = + (1−3 ) (4)
ij (z2+r2)6 (z2+r2)3/2 z2+r2
DNA bases are considered as molecules those are at-
where z represents the variable separationbetween the i tached to each other by intermolecular forces that are
th and j th bases and r represents the radius. harmonic. So between two bases there exists force con-
In the real configuration of DNA the average separa- stants. The values of force constants k between different
tion of two successive bases is about 0.36 nm and in the pairs e.g., purine-purine, pyrimidine-pyrimidine, purine-
calculation of the total energy here this separation has pyrimidine etc. are different. Due to this force DNA
been used as the minimum energy state and thus this molecules follow the harmonic behavior and therefore
stateismorestable. Usingthisminimumenergystateat they vibrate with some harmonic frequencies.
0.36nmseparationtheconstantsAandB havebeencal-
culated. In calculating the values of the force constants
the value of energy has been taken from the deviated B. Derivation of Expression for Frequency
portion from this minimum level.
Thevaluesofk’sarecalculatedfromthevanderWaals
interaction and stacking interaction [7,11,12] between
C. Results
bases of different types e.g., purine-purine, pyrimidine-
pyrimidine,purine-pyrimidineetc. Usingthesevaluesthe
The results for the stacking energies and the total harmonic frequencies of the telomere in DNA are calcu-
energies including the van der Waals energy with re- lated. To illustrate the technique for obtaining the res-
spect to the different distances between the bases in onant frequencies and normal modes it is considered in
DNA are shownin Fig.2 and Fig.3 respectively. In these detail a model based on a linear symmetrical six atomic
calculations the stacking energies between purine-purine molecule. All these six atoms are considered to be on
bases at different separations are seen to be higher to- one straight line, the equilibrium distances apart being
wards negative than those between purine-pyrimidine denoted by b. For simplicity it is considered that only
andpyrimidine-pyrimidinebasesrespectively. Similarse- vibrations along the line of the molecule, and the actual
quenceisalsoseenforthecalculationoftotalinteraction complicated interatomic potential are approximated by
energies between the bases. two spring of two different or similar force constants on
both sides of an atom. There are six obvious coordi-
nates marking the position of the six atoms on the line.
D. Discussion The atomic arrangement then repeats for the telomere
in DNA like AGGGTT then again AGGGTT and so on
The stacking energy calculation between the bases uptoahugenumberofrepeatation. Ifthemeanpositions
shows that the stacking energies for different order of oftheatomsareconsideredasx1,x2,x3,x4,x5,x6 then
separation between purine purine bases are higher than the positions of the atoms repeat and thus the arrange-
5
mentcompletesacyclicarrangement. Intelomeresystem Hence the V matrix has the form,
it is assumed that there exists two types of atoms: four
purine(oneAdenineandthreeGuanine)andtwopyrimi- k1+k2 −k1 0 0 0 −k2
dine(twoThymine). ItistruethatAdenineandGuanine  −k1 2k1 −k1 0 0 0 
haveabout the same mass whichis consideredas M and V = 0 −k1 2k1 −k1 0 0 
themassofpyrimidine(ThymineandCytocine)isdiffer- m  0 0 −k1 k1+k2 −k2 0 
entfromthat ofpurine andlet this be m. Boththese M  0 0 0 −k2 k2+k3 −k3 
andmhavebeencalculatedfromthetotalatomicweights  −k2 0 0 0 −k3 k2+k3 
oftheirconstituentatoms. Inthearrangementtheremay (11)
existthesequenceslikepurine-purine,purine-pyrimidine, The kinetic energy T has the form
pyrimidine-pyrimidine and the force constants for these
1 1
arrangements are considered k1, k2, k3 respectively. If a T = M(y˙2+y˙2+y˙2+y˙2)+ m(y˙2+y˙2) (12)
force constant k in between two atoms of mass M each, 2 1 2 3 4 2 5 6
the potential energy in this system is given by Potential
The T matrix is diagonal which is of the form,
energy
M 0 0 0 0 0
1
V2 = k(x2−x1−b)2 (5)  0 M 0 0 0 0 
2
0 0 M 0 0 0
T =  (13)
For a three atoms system this potentialenergy becomes m  0 0 0 M 0 0 
 0 0 0 0 m 0 
 
V3 = 1k(x2−x1−b)2+ 1k(x3−x2−b)2 (6)  0 0 0 0 0 m 
2 2
Combining these two matrices, the secular equation
with the atomic arrangement as follows
appears as
m(x1)−k−M(x2)−k−m(x3)
|V −ω2T |=0 (14)
m m
Similarly if we increase the number of atoms ac-
cording to our real problem of telomere (AGGGTT) or,
inDNAwithsixatomsthearrangementbecomeslikethis
k1+k2 −k1 0 0 0 −k2
M(x1)−k1 −M(x2)−k1−M(x3)−k1−M(x4)−  −Mk1 2Mk1 −k1 0 0 M0 
M M M
k2−m(x5)−k3−m(x6)−k2−M(x1)  0 −k1 2k1 −k1 0 0 
 0 M0 −Mk1 k1M+k2 −k2 0 =0 (15)
For this system of atoms the total potential energy V  0 0 M0 −Mk2 k2M+k3 −k3 
is  −k2 0 0 m0 −mk3 k2m+k3 
m m m
1 1
V = + k1(x2−x1−b)2+ k1(x3−x2−b)2 Eigen values of this matrix give the square of the
2 2
1 1 frequencies(iω). Herethevaluesfork’s(attheseparation
+ k1(x4−x3−b)2+ k2(x5−x4−b)2 0.36nmbetweenbases)areusedfromthecalculatedval-
2 2
ues from the total energies (stacking and van der Waals
1 1
+ k3(x6−x5−b)2+ k2(x1−x6−b)2 (7) interaction) between the bases of DNA. The masses of
2 2
purine and pyrimidine are the total mass of their con-
Now we introduce coordinates relative to the equilib- stituent atoms.
rium positions:
yi =x−xoi (8) C. Results
where
The eigenvaluesofthe derivedmatrix givesthe square
ofthefrequencies(iω). Hencenegativevaluesoftheeigen
xo2−xo1 =b=xo3−xo2, etc. (9)
values give the real parts of the frequencies and positive
values give the imaginary parts of the frequencies. From
The potential energy then reduces to
theeigenvaluesofthematrixthevaluesofthefrequencies
1 1 ofthe harmonicoscillatoroftelomericpatternhavebeen
V = +2k1(y2−y1)2+ 2k1(y3−y2)2 calculated. Similarlyrearrangingthepatternsofthema-
1 1 trices for other patterns of base combinationof telomere
+2k1(y4−y3)2+ 2k2(y5−y4)2 and for some imaginary patterns taking all purine or all
1 1 pyrimidinestheeigenvaluesandthusthefrequencieshave
+ k3(y6−y5)2+ k2(y1−y6)2 (10) been calculated.
2 2
6
The highest values of the frequencies [13] of telomere tern is the lowest among all other patterns which shows
and other different patterns of base combinations are as that the pattern to be unstable and this is also proved
follows: fromtherealdataoflowerenergyofinteractionbetween
the bases TA or AT where one exists in one strand and
Telomere (AGGGTT) pattern: the other in the other strand than that of CG or GC.
ω =-3.104028110062502×1012 Hz Hence to continue the normal living behavior of biologi-
ω =+3.104028110062502×1012 Hz calmoleculestelomerepatternshouldthethemoststable
pattern at the replication end of DNA.
AGTGGT pattern:
ω =-2.586737456962528×1012 Hz
ω =+2.586737456962528×1012 Hz IV. AMPLITUDE OF VIBRATION IN
THERMAL EQUILIBRIUM
AGTGTG pattern:
ω =-2.944491229994985×1012 Hz A. Introduction
ω =+2.944491229994985×1012 Hz
Human body exists at a particular temperature. This
AAAAAA or GGGGGG pattern: temperature is at an averageabout 37oC. The tempera-
ω =-3.333518830239974×1012 Hz turenormallydoesnotchangewiththechangeoftheex-
ω =+3.333518830239974×1012 Hz ternalorenvironmentaltemperature. DNAmoleculesex-
ist inside this temperature state. The telomeres in DNA
TTTTTT or CCCCCC pattern: thus exist in the thermodynamic state of temperature
ω =-1.668814797430148×1012 Hz 37oC. The telomere pattern AGGGTT has been con-
ω =+1.668814797430148×1012 Hz sidered as an oscillator that vibrates with some frequen-
cies. This vibration should create some thermodynamic
motion of these molecules due to the thermal state. It
is known from the well known kinetic interpretation of
D. Discussion temperature an atom being in the thermal state of tem-
perature T has an average translational kinetic energy
which is equal to 3kT. Here k is the Boltzmann con-
In the calculation of the frequencies of the oscillators 2
stant that is equalto 1.38×10−23 joule/molecule K and
of the telomere pattern of bases and the other patterns
T is the absolute temperature of the environment i.e.,
itisseenthatthe valueofthefrequencyforthe telomere
T = 273+t, where t is in oC and T is in oK. For one
pattern is the highest among those patterns having four
dimentionalmotiontheaverageenergyisonethirdofthe
purine and two pyrimidine bases. So the frequency of
previousthatisequalto 1kT. Nowanyatomormolecule
the telomere pattern is close to the frequencies available 2
ofmassM andvibratingwiththe frequencyshouldhave
in the sunlight. So a resonance of this frequency with
the total energy that is equal to 1Ma2ω2 where a is the
the frequencies of the infrared rays existing in the lower 2
amplitude of the vibration. In this problem it is con-
side of the band of light coming from the sun may oc-
sidered for DNA telomere bases (purine and pyrimidine)
cur. Most of the people stay under shade most of the
time of their life. The infrared light of the frequency of
the order of the frequency of telomere are in the lower 1 1
end of the band of light coming from the sunlight and Ma2ω2 = kT (16)
2 2
staying in the shade (in most time) people experience
this infraredlights. Theinterferenceofthisinfraredrays The calculated values of the frequencies for telomere
with the frequency of the telomere may be one of the pattern AGGGTT and other possible random patterns
causes of the aging i.e., the shrinking of the skin and have been used here. The calculation has given us the
decaying of the normal activities of the cells of human following results for the amplitudes of vibration.
bodyandfinallyleadingtodeath. Thefrequenciesofthe
two imaginary patterns of bases e.g., all purine and all
pyrimidines are different from the original pattern with B. Results and Discussions
four purines and two pyrimidines. For all purines the
value of the frequency is higher than that for telomeric The following results show the amplitudes of thermal
pattern which supports for being more stable than the vibrationfor purine (Adenine and Guanine) and pyrimi-
telomeric pattern but there may arise some problem in dine (Uracil and Thymine) in DNA.
replicability of DNA due to the heavy attraction of the
pattern GGGGGG in the first strand with CCCCCC in TELOMERE:
the second strand because GC has very high attraction Pyrimidine: a=+/−0.0311nm
between two strands. On the other hand if all purines Purine: a=+/−0.0292nm
like AAAAAA pattern exists the frequency for this pat-
7
AGTGTG pattern: frequencies for the telomeric pattern (AGGGTT) and
Pyrimidine: a=+/−0.0328nm other patterns have been calculated. Here the results
Purine: a=+/−0.0308nm show that the highest frequency exists in the telomeric
patternamongthedifferentpossiblepatterns,takingfour
AGTGGT pattern: purines andtwo pyrimidines. The value ofthe frequency
Pyrimidine: a=+/−0.0374nm for telomeric pattern is close to the infrared band of the
Purine: a=+/−0.0351nm frequencies available in sunlight. The frequency of the
telomeric pattern may have thus a resonance with the
AAAAAA pattern: infraredraysexistingbelowthelowerendofvisiblespec-
Pyrimidine: a=+/−0.0290nm trum of sunlight. Human beings can not avoid exposure
Purine: a=+/−0.0272nm todirectorindirectsunlightduringmostoftheirlifetime,
andarethereforevulnerabletothe effects ofthe infrared
TTTTTT pattern: frequencies. The possible resonance of the telomeric fre-
Pyrimidine: a=+/−0.0579nm quencywiththe infraredfrequenciesmayplayanimpor-
Purine: a=+/−0.0543nm tantroleinthe agingprocessandothermaladiessuchas
cancer in the lives of human beings.
The least values for amplitudes for purine and pyrim- On the other hand this frequency for the telomeric
idine are found in the telomere pattern (AGGGTT) pattern may be the cause of the thermal and mechan-
among the patterns having two pyrimidine and four ical stability of the pattern AGGGTT in the replication
purine base sequences in DNA. The higher the values end of DNA and therefore the pattern repeats such a
of the thermodynamic vibrational amplitudes from the large number of times. In this work the frequencies for
mean position of rest the higher the possibility of the some imaginary patterns with all purines and with all
breaking of the biological structure. Hence the lowest pyrimidines in a single helix are also calculated where
values of the amplitudes of thermodynamic vibrational the results show that the frequency of the pattern with
for telomere structure support for the stability of telom- allpurines(AdenineorGuanine)isthehighestamongall
ere pattern from the thermodynamic point of view. the patterns and the frequency for the pattern with all
pyrimidines (Thymine orCytosine)is the lowest. There-
forethe patternAAAAAA orGGGGGGshowmoststa-
V. DISCUSSION AND CONCLUSIONS ble than other patterns. Here only a single strand of the
DNA is considered. When both strands are considered
together, of course there is an equality of the purines
In this work some basic parameters involved in DNA,
and pyrimidines. A problem may arise here due to the
the biggestmolecule,havebeencalculated. Indoingthis
anomalyofattractionofthesepatternswiththeircounter
some approximations are considered but these approxi-
strandinDNA as GC hashigher attractionthan AT.So
mationsdonotaffecttherealityoftheproblem. Though
ifallGsexistinthe1stcoiltheninthe2ndcoiltherewill
the method of calculation is fairly simple, using some-
be all Cs. So highest binding between GC bonding may
times somewhatdrasticapproximations,itis remarkable
beacauseofstoppingofthereplicationofDNA,butthat
that the results which are achieved here are either in
would be impossible for continuing the living activity of
agreementwithexperimentalobservations,or,whenthat
human beings, or any other organism. So, for stabil-
is lacking, in agreement with the idea of molecular evo-
ity of the telomeric pattern (AGGGTT) there should be
lution, viz. the approach to states of stability or lower
anoptimizationbetweenthestabilityandreplicabilityof
energy in molecular configurations that presumably are
DNAandthatmightbe areasonwhythe specific telom-
less susceptible to perturbations of the environment.
eric pattern continues in human DNA at the replication
A possible cause of the stability of the telomeric pat-
end.
tern in the replication end of DNA has been suggested
in this work. Before that the interaction energies in- Withthevaluesofthefrequenciesofthetelomericpat-
volvedbetweenthesuccessivebasesinaDNAsinglehelix tern andother possible patterns of DNA bases with four
have been calculated. With these energies the values of purines and two pyrimidines, the thermodynamic vibra-
the forceconstantshave beencalculatedfor the different tionalamplitudeshavebeencalculatedinthiswork. Here
patterns of base combinations i.e., between the purine- too telomeric pattern shows the lowest value of the am-
purine, purine-pyrimidine and pyrimidine-pyrimidine se- plitude of vibration, which supports the stability of the
quence. Itis seenthatthe minimum energystatefor the configuration with this pattern (AGGGTT) in the ther-
sequence purine-purine is lower than all other sequences mal environment of human cells. For purines (A or G)
i.e.,purine-pyrimidineandpyrimidine-pyrimidine. Inre- the amplitudesaresmallerthanthatofpyrimidine(T or
ality too it should be so, because in purine there exists C) because purines are more massive than pyrimidines
one additional ring than the single ring in pyrimidine due to the presence of extra ring in purines.
base. In this work some physical methods are used and
Usingthevaluesofforceconstantsk’s[13]fromslightly some mathematical formulas have been developed for
deviated portions of the minimum energy positions, the calculating the interaction energies and frequencies of
8
DNA molecules. Calculations have been performed (Russ.).
with these formulas and appropriate conclusions have 3.Olovnikov, A. M. (1971) Dokl. Akad. Nauk SSSR, 201,
been drawn. In future when more crystallographic data 1496-1498.
become available for base sequences of DNA for human 4.Melek, M., Greene, E. C., and Skippen, D. E. (1996) Mol.
genomeorotherlivingorgans,the workcanbe extended Cell Biol.,16,3437-3445.
to test this hypothesis about the association between 5.Harley,C.B. (1991)Mutat. Res., 256,271-282.
lowerenergyandpreferredmolecularconfigurationswith 6.Kim, N. W., Piatyszek, M. A., Prowse, K. R., Harley, C.
moleculararrangements. Thustheworkcanbeextended B., West, M. D., Ho, P. L. C., Coviello, G. M., Wright, W.
to a level which can explain the most important causes E., Weinrich, S. L., and Shay, J. W. (1994) Science, 266,
of aging and other phenomena involved in living bodies, 2011-2015.
not only for human beings but also for other living 7.Fengelman,M.et al.: Nature London175,834(1955)
systems. 8.Biophysics by Walter Hoppe, Lohmann, H. Markl, H.
Ziegler, ed. 2nd p25,t2.2
Acknowledgment 9.G.N. Ramachandran and V. Sasisekharan, Adv. Protein
This research was partly supported by the Min- Chem. 23(1968)283-437
istry of Science and Technology, Peoples’ Republic of 10.G.N. Ramachandran, C. Ramakrisanan and V. Sasisekha-
Bangladesh and Bangladesh University of Engineering ran,J. Mol.,7(1963)95-99
and Technology. The authors are grateful to Prof. Gias 11.Volkenshtein, M.V.: Molecules and Life. New York-
uddin Ahmad, Department of Physics, Bangladesh Uni- London,PlenumPress 1970
versity of Engineering and Technology, for his valuable 12.Biophysics by Walter Hoppe, Lohmann, H. Markl, H.
suggestions. Ziegler, ed. 2nd p24,s2.2.4
13. M.Phil. thesis, submitted by Md. Ashrafuzzaman,
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9
FIG. 1: Sequence of bases in DNA single strand are
shown. Here it is seen that the aromatic rings of the
bases are parallel to each other.
10
FIG. 2: Stacking Energy versus Separation plot be-
tween bases in DNA. Different curves from upper to
lowerareforsuccessivepyrimidinepyrimidine,purine
pyrimidine, purine purine bases in DNA.