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on - baryonic dark matter ) the basic dark matter particle properties ass , stability , darkness ) the similarity in cosmic abundance between ordinary and non - baryonic dark matter , @xmath0 ; ) large scale structure formation ; ) microlensing ( macho ) events ; ) asymptotically flat rotation curves in spiral galaxies ) the impressive dama / nai annual modulation signal . mirror matter - type dark matter is capable of explaining ose of th to - date dark matter candidate

) the basic dark matter particle properties ) the similarity in cosmic abundance between ordinary and non - baryonic dark matter , @xmath0 ; ) large scale structure formation ; ) microlensing ( macho ) events ; ) asymptotically flat rotation curves in spiral galaxies ) the impressive dama / nai annual modulation signal . mirror matter - type dark matter is capable of explaining

there is a very strong scientific case that most of the matter in the universe consists of non - baryonic stable particles . since the standard model of particle physics does not contain any heavy stable non - baryonic particles new particle physics is required . but what is this new physics ? it is widely assumed that the particles comprising non - baryonic dark matter are weakly interacting in the sense that they interact with ordinary matter via exchange of w , z gauge bosons , higgs bosons or more exotic heavy particles . from collider bounds ( e.g. lack of new particles in decays of the w and z gauge bosons ) , the masses of any new weakly interacting particles should be ( typically ) greater than about 30 - 45 gev , unless indicated otherwise . ] depending on the model . however , such heavy weakly interacting particles should decay with a lifetime of order @xmath1 seconds ( for @xmath2 ) about 41 orders of magnitude too short - lived to be suitable as dark matter candidates seconds . ] . thus , one must make additional ad hoc assumptions in order to stabalize such hypothetical particles . in the end , theories with such particles require multiple unrelated assumptions and become very ugly from a particle physics point of view . a well known example is the popular neutralino model which requires at least three independent hypothesis : a ) broken low energy supersymmetry exists which provides wimp candidates , b ) an exact unbroken r - parity symmetry is proposed to prevent the lightest superpartner from decaying and c ) the lightest superpartner is hypothesised to be neutral to make it suitable for dark matter . it seems to me that a more plausible candidate for this new physics arises from the hypothesis of exact unbroken mirror symmetry [ @xmath3 . it is more plausible because it involves only a single well motivated hypothesis . improper space - time symmetries , such as parity and time reversal symmetries , stand out as the only obvious symmetries which are not respected by the interactions of the known elementary particles . it is an interesting and non - trivial fact that these symmetries can be exact , unbroken symmetries of nature if a set of mirror particles exist . even more interesting is that the mirror particles have the right broad properties to be identified with the non - baryonic dark matter in the universe . the ordinary and mirror particles form parallel sectors each with gauge symmetry @xmath4 ( where @xmath5 in the simplest case ) so that the full gauge group is @xmath6 . mathematically , mirror symmetry has the form:@xcite @xmath7 where @xmath8 are the standard @xmath9 gauge particles , @xmath10 are the standard leptons and quarks ( @xmath11 is the generation index ) and the primes denote the mirror particles . there is also a standard higgs doublet @xmath12 with a mirror higgs doublet partner , @xmath13 . importantly , there is a large range of parameters of the higgs potential for which mirror symmetry is _ not _ spontaneously broken by the vacuum ( i.e. @xmath14 ) so that it is an exact , unbroken symmetry of the theory@xcite . ) , but the simplest models of this type are disfavoured for a variety of reasons@xcite . [ more complicated models with broken mirror symmetry are still possible and have been studied in the literature , see e.g. ref.@xcite ] . ] interestingly , despite doubling the number of particle types the number of free parameters have not ( yet ! ) been increased ; mirror symmetry implies that the masses and couplings of the particles in the mirror sector are exactly the same as the corresponding ones in the ordinary sector . ordinary and mirror particles couple with each other via gravity and possibly by new interactions connecting ordinary and mirror particles together . constraints from gauge invariance , mirror symmetry and renormalizability , suggest only two types of new interactions@xcite : a ) higgs - mirror higgs quartic coupling ( @xmath15 ) , and b ) via photon - mirror photon kinetic mixing : ) . however , compared to other ideas beyond the standard model , many of which have literally hundreds of new parameters , mirror symmetry _ is _ a fairly minimal extension of the standard model . also note , if the neutrinos have mass , mass mixing between ordinary and mirror neutrinos is also possible@xcite and might be implicated by the observed atmospheric , solar and lsnd neutrino anomalies . however , the experimental situation is still not clear@xcite . ] @xmath16 where @xmath17 ( @xmath18 ) is the field strength tensor for electromagnetism ( mirror electromagnetism ) . gauge bosons , since only for abelian @xmath19 symmetry is the mixing term , @xmath20 , gauge invariant@xcite . therefore there is both @xmath21 and @xmath22 kinetic mixing . [ however , experiments are much more sensitive to @xmath23 kinetic mixing which is why it is more important ] . in the case of theories without @xmath19 gauge symmetries , such as guts , the @xmath21 mixing can arise radiatively provided that there exists a mixed form of matter carrying both ordinary and mirror electric charges@xcite . interestingly , there is a class of such models@xcite where @xmath24 vanishes at one and two loop level , and therefore naturally of the order of @xmath25 . ] the effect of the higgs - mirror higgs quartic coupling is to modify the properties of the standard higgs boson@xcite . this interaction will be tested if / when scalar particles are discovered . one effect of photon - mirror photon kinetic mixing is to cause mirror charged particles ( such as the mirror proton and mirror electron ) to couple to ordinary photons with effective electric charge @xmath26@xcite . as we will see , this non - gravitational interaction between ordinary and mirror particles provides a key way to experimentally test the theory . to summarize : the only obvious space - time symmetries that are not respected by the interactions of the known elementary particles are the improper lorentz symmetries ( such as parity and time reversal ) . these symmetries can be unbroken symmetries of nature provided that the universe contains both ordinary and mirror particles . the mirror particles have identical masses to the corresponding ordinary particles and have identical , but separate gauge interactions ( the gauge group is @xmath27 ) . the mirror particles couple to the ordinary ones via gravity and possibly via higgs - mirror higgs interactions and photon - mirror photon kinetic mixing . it turns out that the mirror particles lead to an elegant explanation for the inferred non - baryonic dark matter component of the universe , as we will explain in more detail in the following sections . 0.3 cm 0.3 cm there is a substantial range of evidence for non - baryonic dark matter in the universe . we have already emphasised in the introduction that a basic requirement is that the massive particles comprising dark matter need to be stable and have no or small coupling to ordinary photons . there are other desirable features that are also required , including ( in random order ) : * an explanation for @xmath28 . * it should be capable of explaining the large scale structure of the universe . * asymptotically flat rotation curves in spiral galaxies suggest that dark matter is ( roughly ) spherically distributed in a ` halo ' in spiral galaxies . this is in contrast to ordinary matter which is distributed in the disk and bulge . * a substantial fraction ( @xmath29 ) of the mass of the halo appears to be in the form of massive ( @xmath30 ) compact invisible objects ( machos ) . what are the machos and why are they invisible ? * the direct experimental detection of halo dark matter particles has been achieved by the dama / nai collaboration . other experiments report only negative results . we now examine each of these items from a mirror matter perspective . precision cosmic microwave background measurements ( culminating with the recent wmap results@xcite ) have established that the universe is spatially flat , i.e. @xmath31 . furthermore , the wmap results , together with observations of high redshift type 1a supernovae@xcite , and other measurements , suggest that the universe consists predominately of three components : ordinary matter ( @xmath32 ) , non - baryonic dark matter ( @xmath33 ) and dark energy ( @xmath34 ) . it is striking that each of these three different components should have energy densities of the same order of magnitude . since @xmath35 scales differently in time with @xmath36 and @xmath37 , the similarity between @xmath35 and @xmath38 might simply be a coincidence . however , the similarity in magnitude of the ordinary and dark matter densities : @xmath39 is expected to be constant in time until a very early epoch . this means that the amount of dark matter produced in the early universe is of the same order of magnitude as the ordinary matter , despite their apparent disparate properties . the similarity in the abundances of ordinary and dark matter hints at an underlying similarity between the microscopic properties of the elementary particles comprising the ordinary matter and the dark matter . clearly , the standard exotic weakly interacting dark matter scenarios offer no hope in explaining this cosmic coincidence because these particles have completely different properties ( different masses and interactions ) from the ordinary baryons . a priori , a dark matter / ordinary matter ratio of , say , @xmath40 would appear to be equally likely in these scenarios . however if dark matter is identified with mirror baryons , then it seems to be possible to explain the similarity of @xmath36 and @xmath37 because the microscopic properties of the mirror particles mirror those of the ordinary particles . in fact , @xmath41 would occur if the initial conditions of the universe were also mirror symmetric and no macroscopic asymmetry ( such as a temperature difference ) was produced during the early evolution of the universe . however , the success of standard big bang nucleosynthesis ( bbn)@xcite does suggest that @xmath42 was somewhat less than @xmath43 during the bbn epoch , @xmath44 in order for the expansion rate of the universe to have been within an acceptable range then the energy density at the bbn epoch would be double the standard value significantly increasing the expansion rate of the universe at that time . the equilibration of the three mirror neutrinos , mirror electron / positron and mirror photons is equivalent to an extra @xmath45 neutrino species . more generally , @xmath46 , so that demanding @xmath47 would imply @xmath48 . ] . if the temperatures are different , then this means that either the initial conditions of the universe were asymmetric or that the asymmetry was induced during the early evolution of the universe . actually , within the inflation paradigm it is quite easy to generate the required temperature asymmetry@xcite . in particular , it is natural to have an ` ordinary inflaton ' coupling to ordinary matter , and a ` mirror inflaton ' coupling to mirror matter . if inflation is triggered by some random fluctuation , then it can occur in the two sectors at different times , leading to @xmath49 after reheating in the two sectors . in such a scenario , one expects the baryon number and mirror baryon number to be unequal ( since baryogenesis or leptogenesis depends on the temperature and expansion rate ) . provided that the temperatures of the two sectors are not too different this might explain the fact that @xmath37 is within an order of magnitude of @xmath36 . clearly , the details will depend on the precise model for baryogenesis used by nature , which is of course not known ( see the first paper of ref.@xcite for a couple of examples ) . even if there is a large hierarchy in temperatures for the two sectors , similar abundances of ordinary and mirror particles can be achieved if there are interactions which can transfer lepton or baryon asymmetry between the two sectors@xcite . the simplest such interaction is given by the dimension 5 operator : @xmath50 where @xmath51 is a left - handed ordinary lepton doublet , @xmath52 is its mirror partner , @xmath12 is the ordinary higgs doublet and @xmath13 is its mirror partner ( @xmath53 hermitian conjugate ) . with such operators and some plausible assumptions about the physics governing the early evolution of the universe , it is even possible@xcite to _ quantitatively _ explain the inferred non - baryonic dark matter proportion , @xmath54 . we will not discuss much more about the very early universe ( the era prior to bbn ) . these were the cosmic dark ages where much is speculated but little is known . a more recent development ( in the history of the universe ) was the formation of large scale structure , which is also the next topic . we know from measurements of the cosmic microwave background that the universe was extraordinarily homogeneous in the past . at the present epoch , however , the universe is no longer particularly homogeneous : it contains galaxies , clusters of galaxies , superclusters etc . this large scale structure is believed to arise from small primordial inhomogeneities that grow via gravitational instability . however ordinary baryonic density perturbations can not begin to grow until photon decoupling occurs at a temperature of around @xmath55 ev , corresponding to a red shift of @xmath56 . [ prior to photon decoupling , the radiation pressure prevents the growth of perturbations ] . but this is too late : perturbations which have amplitude of order @xmath57 ( as inferred from the anisotropies of the cosmic microwave background ) do not have enough time to grow into galaxies , where @xmath58 . this suggests that inhomogeneities begin to grow prior to photon decoupling . this is one role that non - baryonic dark matter is expected to fill : it should be weakly coupled to the ordinary particles in the plasma so that density perturbation growth can begin prior to photon decoupling . mirror particles are weakly coupled to the ordinary ones . however , mirror baryonic density perturbations can only begin to grow after mirror photon decoupling occurs ( roughly when @xmath59 ev ) . the key point is that if @xmath60 [ which we infer from bbn , see eq.([4 ] ) ] then mirror photon decoupling necessarily occurs _ earlier _ than ordinary photon decoupling . thus , we expect that mirror baryonic structure formation should begin earlier than ordinary baryonic structure . according to refs.@xcite , they find that for @xmath61 , large scale structure formation with mirror matter - type dark matter closely resembles the standard cold dark matter scenario ( but with some intriguing differences ) and would provide a successful framework to understand the large scale structure of the universe@xcite . a consequence of @xmath60 , required for successful big bang nucleosynthesis and large scale structure formation , is that mirror bbn occurs earlier than ordinary bbn . this will mean that the proportion of mirror helium ( @xmath62 ) to mirror hydrogen ( @xmath63 ) synthesised in the early universe will be different to their ordinary matter counterparts . in fact , since the expansion rate of the universe is faster at earlier times the mirror neutron / mirror proton ratio should be closer to unity c.f . ordinary bbn . this means that the @xmath64 ratio is expected to be significantly greater than the corresponding ordinary @xmath65 ratio@xcite . this chemical imbalance between the ordinary and mirror sectors will no doubt have important effects . for example , the initial mass function for mirror stars can be quite different than for ordinary stars . ultimately , this chemical imbalance might even be responsible for the different distribution of ordinary and mirror matter in galaxies , as we will now discuss . 0.3 cm 0.3 cm we have briefly mentioned cosmological evidence for non - baryonic dark matter in sections 2.1 and 2.2 . there is also strong astrophysical evidence for a large amount of dark matter in galaxies and galaxy clusters . asymptotically flat rotation curves in spiral galaxies , illustrated in figure 1 , imply that there must exist invisible ` halos ' in galaxies such as our own milky way . these halos are , roughly , spherical distributions of invisible matter which dominate the mass of the galaxy . for example , the mass of the invisible halo of the milky way galaxy is estimated to be @xmath66 , which is about an order of magnitude more than the estimated mass of the galactic disk component@xcite . 0.2 cm 0.8 cm figure 1 : the observed rotation curve for the the spiral galaxy m33 superimposed on its optical image . [ figure from ref.@xcite ] . 1.2 cm there is strong evidence that this galactic halo dark matter must be something exotic ; ordinary baryons simply can not account for it@xcite . taking the case of white dwarfs as an example , these would be dim enough to escape detection ( unless they are very young ) . however , in the collapse process where they are formed the outer layers of the star are ejected into space . this ejected material is rich in heavy elements such as oxygen and nitrogen . if such material were present in the halo it would have been revealed from characteristic absorption / emission lines . alternatively , if the ejected material were to collapse onto the galactic disk due to collisional processes , its estimated abundance would be greater than the entire mass of the disk . thus , old ( ordinary ) white dwarfs can not provide a consistent picture for halo dark matter . all other conventional candidates for galactic dark matter run into similar severe difficulties . obviously a ( roughly ) spherical halo containing mirror stars , mirror planets , mirror dust and mirror gas would be much less problematic since any absorption / emission lines would be absent ( and @xmath67 given the fit of the dama / nai experiment , see later discussion in section 2.5 ) . ] . of course , there is still the important problem of explaining the roughly spherical mirror matter distribution in the galaxy , with ordinary matter collapsed onto the disk . a priori this is possible : although ordinary and mirror matter have identical microscopic interactions , _ there is no macroscopic mirror symmetry_. recall this macroscopic asymmetry is necessary to explain a ) different abundance of ordinary and mirror matter in the universe ( @xmath68 , but @xmath69 ) and b ) the different temperatures of the ordinary and mirror sector ( in the early universe ) required by successful bbn and large scale structure ( as discussed earlier ) . because of this macroscopic asymmetry , the evolution of the ordinary and mirror sectors can be significantly different . assuming that the halo is dominated by a mirror gas component which is approximately spherical and isothermal , its distribution can be obtained from the condition of hydrostatic equilibrium : @xmath70 where @xmath71 is the pressure and @xmath72 is the local acceleration at a radius @xmath73 . for a dilute gas , the pressure is related to the mass density , @xmath74 , via @xmath75 , where @xmath76 is the average mass of the particles in the gas ( @xmath77 is the proton mass ) . the local acceleration can be simply expressed in terms of the energy density , via : @xmath78 where @xmath4 is newton s constant . the solution of eq.([pr],[fin ] ) is @xmath79 : @xmath80 the rotational velocity at a radial location @xmath81 , @xmath82 , can be obtained from @xmath83 which implies : @xmath84 clearly , @xmath85 , implied by a spherically symmetric self gravitating gas in hydrostatic equilibrium , gives the required asymptotically flat rotation curve ( a well - known result ) . furthermore , from the above equation , @xmath86 , which means that we can express @xmath74 and @xmath43 in terms of @xmath87 : @xmath88 henceforth we focus on the milky way galaxy , for which @xmath89 km / s . since @xmath43 is much greater than the ionization energy for the light mirror elements ( @xmath90 ) , these elements should be ionized . it follows that bremsstrahlung and other processes will radiate off energy at a rate per unit volume of@xcite : @xmath91 where @xmath92 is the ( free ) mirror electron number density and @xmath93 is a calculable function ( which depends on cross section , temperature , composition etc ) . for a temperature of @xmath94 ev , @xmath95 ( see ref.@xcite for details ) . note that @xmath96 ( for @xmath62 mass dominated halo ) , which implies [ using eq.([wed ] ) ] @xmath97 because @xmath98 , the total halo luminosity , @xmath99 is divergent as @xmath100 . however , the inner region of the galaxy should contain a high density of mirror dust , stars , supernova , blackholes etc which will make things very complicated . energy sources ( such as supernova ) can heat the inner region . this effect , as well as the effect of mirror dust particles ( which can potentially make the inner region opaque to mirror radiation ) could potentially lead to an increasing temperature towards the galactic centre breaking the isothermal approximation . this would be consistent with observations which imply that the rotation curves in spiral galaxies fall in the inner region ( as shown in the example of figure 1 ) , suggesting that the mass density is not increasing , but roughly constant there@xcite . in other words , the observations themselves imply that the halo density appears to be heated up"@xcite , inexplicable in the standard cold dark matter scenario , but possible for mirror matter - type dark matter . in view of the above discussion , we introduce a phenomenological cutoff , @xmath101 , and consider only the energy produced at @xmath102 . in this case , the energy radiated from the halo is roughly @xmath103 the above calculation assumes that the halo contains only a gas component . from general considerations , as well as specific evidence from microlensing studies ( as will be discussed in the following subsection ) , a significant component of the halo will be in the form of compact mirror objects : mirror stars , planets etc . furthermore compact mirror objects can potentially dominate the mass in the inner regions of the galaxy which would alleviate the cooling problem to some extent . still , a heat source of order @xmath104 erg / s seems to be required to compensate for the energy lost due to radiative cooling . supernova offer promising candidate heat sources . an obvious possibility is that mirror supernova can heat the halo ; during an explosion the outer layers of the star are ejected into interstellar space , with energy of order @xmath105 erg per explosion . in order to achieve a rate of around @xmath106 erg / s would require a mirror supernova rate in our galaxy of around one every few years , which is about an order of magnitude greater than the rate of ordinary supernova . presumably this is possible given the uncertainties in the mirror sector . for example , as discussed at the end of the previous subsection , it is possible that the initial mass function for mirror stars is very different to ordinary stars because of the different chemical composition ( different light element ratios etc ) . this would mean that the rate of ordinary supernova could be quite different to mirror supernova . a more subtle , but equally promising possible energy source might come from ordinary supernova explosions . due to the effects of photon - mirror photon kinetic mixing , eq.([km ] ) , in the core of the supernova a significant fraction , @xmath107 , of an ordinary supernova s total energy , @xmath108 , can be converted into mirror photons and mirror electrons / positrons , which can provide a significant heat source for the halo . the amount of energy going into the halo from ordinary supernova explosions , is of order@xcite : particles which are potentially observable . in fact , they may have already been observed in the form of gamma ray bursts and positron annihilation radiation from the galactic bulge@xcite ( this will be briefly reviewed in section 3.1 ) . ] @xmath109 evidently , ordinary supernova s can potentially supply about the right amount of energy to replace the energy lost in radiative cooling , if ordinary supernova s occur at a rate , @xmath110 , of order once per hundred years and of order @xmath111 of the supernova s energy is converted into mirror @xmath112 . presumably the heating of the mirror sector and ordinary sector needs to be different in order to explain why ordinary matter has collapsed onto the disk and mirror matter has not . this is not impossible given the lack of macroscopic mirror symmetry , leading to e.g. asymmetric ordinary and mirror supernova rates . it seems therefore that asymmetric heating of the ordinary and mirror sectors is feasible and we conclude that mirror matter - type dark matter is capable of explaining the dark matter halo in spiral galaxies . in one sense the existence of a dark halo is more directly explained within the standard wimp paradigm . wimps being collisionless are non - dissipative and could not collapse onto the disk . however this cure has serious side - effects which are potentially fatal . wimps being collisionless particles are relatively simple , macroscopically , and their distribution can be predicted . the result is a dark matter density profile that goes like@xcite @xmath113 , with @xmath114 . this prediction is in clear disagreement with the observations ( see e.g. ref.@xcite ) . in other words , the standard wimp paradigm can simply explain the existence of dark matter in galaxies , but fails to explain the detailed distribution of dark matter within the halo . this ` fact ' seems to support the idea that the dark matter is , macroscopically , more complicated than collisionless wimps . more evidence for the complexity of the dark halo is provided by microlensing surveys of stars in nearby galaxies , which brings us to the next topic . if non - baryonic dark matter is identified with mirror matter , then a substantial fraction of the non - baryonic dark matter should be in the form of compact bodies such as mirror stars . this leads naturally to an explanation@xcite for the mysterious massive astrophysical compact halo objects ( or macho s ) discovered by the macho collaboration . the macho collaboration@xcite has been studying the nature of halo dark matter with the gravitational microlensing technique@xcite , using source stars in the large magellanic cloud . this australian - american experiment has collected 5.7 years of data and provided statistically strong evidence for dark matter in the form of invisible star sized objects which is what you would expect if there is a significant amount of mirror matter in our galaxy . the macho collaboration@xcite has done a maximum likelihood analysis which implies a macho halo fraction of @xmath115 for a typical halo model with a @xmath116 confidence interval of @xmath117 their most likely macho mass is between @xmath118 and @xmath119 depending on the halo model . on the other hand , the eros team@xcite studying microlensing towards the small magellanic cloud did not find evidence for a significant population of compact halo objects . this yielded a constraint which was however consistent with the @xmath115 halo mass fraction reported by the macho collaboration . more recently , a new survey@xcite has begun examining stars across the face of m31 . they find significant evidence for a population of halo microlensing dark matter objects , inferring a halo mass fraction of @xmath120 . this result is consistent with the positive results of the macho collaboration and provides important independent confirmation of their positive signal . furthermore , they find significant evidence for an asymmetry in the distribution of microlensing events across the face of m31 , which is expected if their events are correctly interpreted as a large population of invisible massive compact halo objects . it is important to realize that the inferred macho halo fraction , @xmath115 , is consistent with a mirror matter halo ; the entire halo need not be in the form of mirror stars . mirror gas and dust would also be expected as they are a necessary consequence of stellar evolution and can significantly populate the halo . as we have just seen , the results of the microlensing surveys suggest a macho halo fraction of @xmath115 . within the mirror matter theory , this gets a natural interpretation in terms of mirror stars , mirror white dwarfs etc . the remaining fraction , @xmath121 should presumably be in the form of mirror gas . assuming a roughly spherical and isothermal distribution for this ionized gas , it would have a mass density ( at our location , @xmath122 kpc ) and temperature [ using eq.([wed ] ] : @xmath123 considering a particular chemical element , @xmath124 ( e.g. @xmath125 etc ) , the velocity distribution for these halo mirror particles is then : @xmath126 \nonumber \\ & \equiv & exp[-v^2/v_0 ^ 2]\ , \label{fr5}\end{aligned}\ ] ] where @xmath127 . using eq.([wed2 ] ) , we have : @xmath128 recall , @xmath76 is the mean mass of the particles comprising the mirror ( gas ) component of the halo and @xmath129 km / s is the local rotational velocity . evidently the characteristic velocity , @xmath130 , for a particular halo component element , @xmath124 , depends on the chemical composition of the halo ( through the dependence on @xmath76 ) . mirror bbn will generate @xmath90 and , possibly , heavier mirror elements as well , quite unlike the ordinary matter case . and also if @xmath131 , then the number density of mirror nucleons present during the mirror bbn epoch can be several orders of magnitude greater than the number density of ordinary nucleons at the time of ordinary bbn . the greater mirror nucleon number density can dramatically increase the rate of three - body processes such as the triple alpha process . thus , it seems to be an interesting possibility that a significant abundance of heavy mirror elements ( such as @xmath132 ) could be generated in the early universe . ] heavy mirror elements can also be generated in mirror stars . in any case , we consider two representative possibilities : first that the mass of the halo is dominated by @xmath62 and the second is that the halo is dominated by @xmath63 . the mean mass of the particles in the halo are then ( taking into account that the light halo mirror atoms should be fully ionized ) : @xmath133 the @xmath134 values can then be easily obtained from eq.([z3 ] ) : @xmath135 it is important to realize that halo atoms can potentially be detected in conventional dark matter experiments via the nuclear recoil signature@xcite . the reason is that the photon - mirror photon kinetic mixing interaction , eq.([km ] ) , gives the mirror nucleus , with ( mirror ) atomic number @xmath136 , a small effective ordinary electric charge of @xmath137 . this means that ordinary and mirror nuclei can elastically scatter off each other ( essentially rutherford scattering ) . the basic feynman diagram for this process is given in the figure 2 ( on the following page ) . for a mirror atom of mass @xmath138 and ( mirror ) atomic number @xmath136 scattering on an ordinary target atom of mass @xmath139 and atomic number @xmath140 , the differential cross section is given by : @xmath141 where @xmath142 ( the @xmath143 are the nuclear form factors ) . in eq.([cs ] ) @xmath144 is the velocity of the mirror nucleus relative to the earth and @xmath145 is the recoil energy of the ordinary ( target ) nucleus . 0.7 cm 0.3 cm figure 2 : ordinary and mirror nuclei can elastically scatter via the photon - mirror photon kinetic mixing interaction ( indicated by a ` cross ' in this feynman diagram ) . 0.9 cm in dark matter direct detection experiments ( such as dama / nai@xcite ) , the measured quantity is the recoil energy , @xmath145 , of the target nucleus . the differential interaction rate is @xmath146 where @xmath147 is the number of target atoms per kg of detector ( for detectors with more than one target element we must work out the interaction rate for each element separately and add them up to get the total interaction rate ) . in the above equation @xmath148 is the velocity distribution of the mirror element ( @xmath149 is the normalization factor ) , @xmath124 , and @xmath150 is the earth velocity relative to the galaxy . since @xmath151 is the velocity of the mirror particles relative to the galaxy , it follows from eq.([fr5 ] ) , that @xmath152 $ ] . in eq.([55 ] ) the lower velocity limit , @xmath153 , is the minimum velocity for which a mirror atom of mass @xmath138 impacting on a target atom of mass @xmath154 can produce a recoil energy of @xmath145 for the target atom . this minimum velocity satisfies the kinematic relation : @xmath155 interestingly , most of the existing dark matter experiments are not very sensitive to mirror matter - type dark matter because @xmath156 [ eq.([v ] ) ] turns out to be too high . this is because they either use target elements which are too heavy ( i.e. large @xmath154 ) and/or have a @xmath145 threshold which is too high . the dark matter experiment most sensitive to halo mirror matter - type dark matter is the dama / nai experiment@xcite . the aim of the dama / nai experiment is to measure the nuclear recoils of @xmath157 atoms due to the interactions of halo dark matter particles . because of the dependence of the interaction rate , eq.([55 ] ) , on @xmath150 , the interaction rate of halo dark matter with a detector depends on the earth s velocity relative to the halo . because of the earth s annual motion , its velocity satisfies : @xmath158 where @xmath159 km / s is the sun s velocity with respect to the galaxy and @xmath160 km / s is the earth s orbital velocity around the sun ( @xmath161 , with @xmath162 year ) . the inclination of the earth s orbital plane relative to the galactic plane is @xmath163 , which means that @xmath164 km / s . thus , the differential interaction rate in an experiment will thus contain an annual modulation term : @xmath165 where @xmath166 according to the dama analysis@xcite , they indeed find an annual modulation over 7 annual cycles at more than @xmath167 c.l . their data fit gives @xmath168 year and @xmath169 , consistent with the expected values . [ the expected value for @xmath170 is 152 ( 2 june ) , where the earth s velocity , @xmath150 , reaches a maximum with respect to the galaxy ] . their signal occurs in the energy range @xmath171 kevee , which is related to the actual energy , @xmath145 , by @xmath172 , where @xmath173 is the quenching factor corresponding to a given target element , @xmath174 . for the dama / nai experiment , @xmath175.@xcite ] and the amplitude of their signal is @xmath176 cpd / kg / kevee [ cpd @xmath177 counts per day ] . these are extremely impressive results . the self consistency of their signal is highly non - trivial : there is simply no reason why their data should contain a periodic modulation or why it should peak near june 2 . in fact , the known systematic errors are several orders of magnitude too small to account for the signal@xcite . it therefore seems probable that dama has indeed discovered dark matter . interestingly the interpretation of the dama / nai signal in terms of standard wimps appears to be disfavoured by a number of experiments@xcite , the most impressive of which is the recent null cdmsii / ge results@xcite . however , if we interpret the dama / nai signal in terms of mirror matter - type dark matter then the positive dama / nai signal and the negative results of the other experiments can be reconciled@xcite . the dama experiment is not particularly sensitive to very light dark matter particles such as mirror hydrogen and mirror helium . impacts of these elements ( typically ) do not transfer enough energy to give a signal above the detection threshold@xcite . if stellar nucleosynthesis in the mirror sector is sufficiently similar to the ordinary sector , then the next most abundant element should be mirror oxygen . in the analysis of ref.@xcite the spectrum of heavy mirror elements were approximated by just two components , @xmath178 . naturally this is just a crude approximation : in general there will be a distribution of mirror elements which is very difficult to theoretically predict ( because of e.g. unknown initial mass function for mirror stars etc ) . of course , it may turn out that approximating the spectrum in terms of the two components , @xmath178 , will be insufficient in the future as more detailed data is obtained . anyway , interpreting the dama / nai annual modulation signal in terms of @xmath178 , it was found that@xcite : @xmath179 where the errors denote a 3 sigma allowed range and @xmath180 is the @xmath124 proportion ( by mass ) of the halo dark matter ( at the earth s location ) . suggested by the dama experiment , eq.([dama55 ] ) , would also have important implications for the orthopositronium system@xcite . the current experimental situation , summarized in ref.@xcite , implies that @xmath181 , which is easily consistent with eq.([dama55 ] ) . importantly , a new orthopositronium experiment has been proposed@xcite which can potentially cover much of the @xmath24 parameter space suggested by the dama experiment . such an experiment is very important not just as a check of the mirror matter explanation but also because dark matter experiments are sensitive to @xmath182 and an independent measurement of @xmath24 would allow the extraction of @xmath183 values . ] this fit to the data is shown in figure 3 . -0.1 cm 0.2 cm figure 3 : dama / nai annual modulation signal ( taking data from the second paper of ref.@xcite ) together with the mirror matter prediction ( initial time is august @xmath184 ) . 1.1 cm in ref.@xcite it was found that a dama / nai annual modulation signal dominated by an @xmath185 component , is experimentally disfavoured for three independent reasons : a ) it predicts a mean differential energy spectrum rate larger than the measured dama / nai rate b ) potentially leads to a significant diurnal effect ( sidereal daily variation ) and c ) should have been observed in the cdmsi experiment . thus it is probable that lighter mirror elements , such as a mirror oxygen component , dominates the dama annual modulation signal . from eq.([dama55 ] ) this means that @xmath186 . recently , a more stringent limit of @xmath187 was obtained in ref.@xcite using the recent cdmsii / ge result@xcite . if the dama signal is dominated by @xmath188 , then things depend on only one parameter , @xmath189 . this parameter is fixed from the annual modulation signal , eq.([dama55 ] ) , which means that the event rate ( due to @xmath188 interactions ) can be predicted for other experiments . it turns out that , with the exception of one experiment ( cressti@xcite ) , all of the other experiments are not sensitive to @xmath188 interactions . for example , the predicted rate for cdmsii / ge due to @xmath188 interactions is given in figure 4 ( taken from ref.@xcite ) . 0.3 cm 0.4 cm figure 4 : predicted differential event rate , @xmath190 , ( binned into 10 kev bins ) due to @xmath188 dark matter with @xmath191 ( dama / nai annual modulation best fit ) for the cdmsii / ge experiment . the solid line corresponds to a standard halo model with @xmath62 dominated halo while the dashed line assumes a @xmath63 dominated halo . 1.4 cm as the figure shows , the event rate is predicted to be very low . for the cdmsii / ge experiment the predicted event rate is just 1 event per @xmath192 kg - days for @xmath62 dominant halo and 1 event per @xmath193 kg - days if @xmath63 dominates the halo . given that cdmsii has only 52.6 kg - day raw exposure in ge , this implies a predicted number of events of just @xmath194 ( assuming @xmath62 dominant halo ) and even less if @xmath63 dominates the mass of the halo . clearly this prediction is nicely consistent with the null result of cdmsii / ge , it is much more sensitive to interactions of heavier mirror elements such as @xmath185 . future cdms data may well find a positive signal due to these heavier elements because they should be there at some level . ] . in the case of standard spin independent wimps , the cdmsii experiment is more sensitive than the dama / nai experiment . however , as we have discussed above , this is clearly not the case for @xmath188-type dark matter ( with dominant @xmath64 component ) . the diverse behaviour of the two types of dark matter candidate has to do with their basic differences : * the mass of @xmath188 is only 15 gev , while standard wimps are typically assumed to have masses which are greater than @xmath195 gev ( depending on the model ) . * for @xmath188-type dark matter in an @xmath64 dominated halo , @xmath196 km / s [ eq.([19y ] ) ] , while the characteristic velocity of standard wimps are assumed to be approximately 220 km / s . * the differential cross section for mirror matter - type dark matter is inversely proportional to the square of the recoil energy , while that for standard wimps is energy independent ( excepting the energy dependence of the form factors ) . these three key differences mean that experiments with low threshold energy and light target elements are much more sensitive ( to @xmath188-type dark matter ) than experiments with higher threshold energy and/or heavy target elements . in the case of dama / nai , the event rate for mirror matter - type dark matter is dominated by interactions with the light @xmath197 component . the actual threshold energy of 6.7 kev ( for @xmath197 ) , implies a threshold impact velocity , obtained from eq.([v ] ) , of 290 km / s for @xmath188 impacts . in the case of cdmsii / ge , the threshold energy of 10 kev and heavy ge target gives a threshold impact velocity of 450 km / s ( see ref.@xcite for a table of threshold velocities for the various experiments ) . given the low value of @xmath198 [ using eq.([19y ] ) , @xmath199 km / s ( @xmath200 km / s ) for @xmath62 ( @xmath63 ) dominated halo ] the number of @xmath188 atoms with impact velocity above threshold is clearly much lower for cdmsii / ge compared with dama / nai ( in fact it is exponentially suppressed ) . note that the edelweiss i / ge ( ref.@xcite ) and zeplin i / xe ( ref.@xcite ) experiments are even less sensitive than cdmsii / ge because the threshold impact velocity of those experiments is even higher@xcite . there is one experiment , besides dama / nai , which was potentially sensitive to mirror matter interactions , namely the cresst i experiment@xcite . that experiment had a target consisting of sapphire crystals ( @xmath201 ) , with a low recoil energy threshold of @xmath202 kev . however , the results of that experiment turned out to be roughly consistent with the mirror matter prediction ( i.e. with parameters fixed by the dama / nai annual modulation signal)@xcite , providing tentative support for the mirror matter interpretation of the dama / nai experiment . unfortunately , this experiment did not collect enough data to do an annual modulation analysis ( it has now been discontinued , replaced by a new experiment , cresst ii , which will use a @xmath203 target , and has an expected threshold energy of 10 kev , which will be less sensitive than cresst i , but should still be useful ) . 0.3 cm 0.3 cm in section 2 we have examined the conventional cosmological and astrophysical implications of mirror matter - type dark matter including direct experimental evidence from the dama / nai experiment . however mirror matter - type dark matter is an unconventional dark matter candidate with numerous unconventional implications . included among these is the possibility of binary ordinary / mirror systems , possible manifestations of mirror matter in our solar system , implications for supernova etc . we now briefly examine some of these applications . photon - mirror photon kinetic mixing , eq.([km ] ) , of magnitude @xmath204 ( as suggested by the dama annual modulation signal ) will lead to important implications for core collapse supernova both ordinary and mirror types . recall , that in the core of ordinary supernova , the temperature reaches , @xmath205 mev , leading to a plasma of @xmath206 ( @xmath207 ) . because of the photon - mirror photon kinetic mixing , mirror @xmath208 can also be produced via a variety of processes ( the most obvious being @xmath209 ) . actually the main production process for mirror particles in the core of a mirror supernova is expected to be the plasmon decay process ( see e.g. ref.@xcite for a review ) . the energy loss rate for production of minicharged particles has been calculated in ref.@xcite : @xmath210 where @xmath211 is a factor of order unity . @xmath212 is comparable to the energy loss rate due to neutrino emission for@xcite @xmath213 thus , the production of mirror particles in the core of ordinary supernova must lead to important effects as a significant part of the emission of ordinary supernova s will be in the form of @xmath214 . one of these effects is that the @xmath215 produced in the core will help supernova s to explode as we will now explain . supernova explosions of massive stars are believed to be driven by the convectivelly supported neutrino - heating mechanism@xcite . but refined simulations have shown@xcite that there is insufficient neutrino energy transfer behind the stalled supernova shock to produce the explosion . this is actually a long standing problem in supernova dynamics . it suggests some missing piece of physics , which might well be photon - mirror photon kinetic mixing : the @xmath215 produced in the core will interact and heat the matter behind the shock ( adding to the effect of neutrino - heating ) thereby producing the explosion . for this to be possible we require that the cross section for mev @xmath216 ( and/or large angle @xmath208 ) scattering with ordinary electrons ( i.e. @xmath217 and @xmath218 ) to be of roughly the same magnitude as the neutrino nucleon cross section . the mirror particle cross section is : @xmath219 where @xmath220 is the classical radius of the electron . the neutrino nucleon cross section is @xmath221 where @xmath222 is the energy of the neutrino . evidently the cross sections for the two completely different processes are indeed comparable ! importantly , the energy dependence is different : compared with neutrino interactions , the mirror particle interactions with ordinary matter are larger at lower energies . it follows that the heating effect of the mirror particle interactions on the ordinary matter just behind the shock is expected to be comparable to or may even exceed the neutrino effect . a significant portion of the @xmath215 will escape the supernova , however direct detection of these particles seems to be very difficult for ordinary matter observers . even if we can not directly detect this emission it does not mean that it is unimportant ; as we discussed earlier in section 2.3 , these mirror particles may have an important role in heating the galactic halo to compensate for the energy lost due to radiative cooling . in the case of a _ mirror _ type ii supernova is also very interesting . in this case , the core of the mirror supernova would be a source of ordinary electrons , positrons and gamma rays making such an event easily detectable for ordinary matter observers . in fact , they may have already been detected ! provided that the number of ordinary baryons is sufficiently low the @xmath223 ` fireball ' will lead to a gamma ray burst ( grb)@xcite . of course , grb s have been observed for some time , and their origin has been a long standing puzzle . it is certainly interesting that the mirror supernova , with photon - mirror photon kinetic mixing interaction has roughly the right characteristics ( energy release , time scale , and potentially small baryon load ) to be identified with the observed gamma ray bursts . in addition to being a source of photons , grb will also eject electrons and positrons into the interstellar medium . this might explain@xcite the 511 kev photon emission from the galactic bulge . this emission was first detected more than 30 years ago@xcite and studied in a number of experiments culminating in the recent integral - spi measurements@xcite . while grbs and galactic positron emission are certainly rather spectacular possible manifestations of the mirror world , something even more tantalizing would be the discovery of a mirror world itself . if mirror matter exists in our galaxy , then binary systems consisting of ordinary and mirror matter should also exist . while systems containing approximately equal amounts of ordinary and mirror matter are very unlikely due to e.g. differing rates of collapse for ordinary and mirror matter ( due to different initial conditions such as chemical composition , temperature distribution etc ) , systems containing predominately ordinary matter with a small amount of mirror matter ( and vice versa ) should exist . remarkably , there is interesting evidence for the existence of such systems coming from extra - solar planet astronomy . in 1995 , the first planet orbiting another star was discovered@xcite . since that time the field of extra - solar planet astronomy has been moving at a rapid pace . to - date , more than 100 extra - solar planets have been discovered orbiting nearby stars@xcite . they reveal their presence because their gravity tugs periodically on their parent stars leading to observable doppler shifts . several transiting planets have been observed allowing for an accurate determination of the planet s size and mass in those systems . one of the surprising characteristics of the extrasolar planets is that there are a class of large ( @xmath224 ) close - in planets with a typical orbital radius of @xmath225 ( which is about eight times closer than the orbital radius of mercury ) . ordinary ( gas giant ) planets are not expected to form close to stars because the high temperatures do not allow them to form . theories have been invented where they form far from the star where the temperature is much lower , and migrate towards the star@xcite . a fascinating alternative possibility presents itself in the mirror world hypothesis . the close - in planets may be mirror worlds composed predominately of mirror matter@xcite . they do not migrate significantly , but actually formed close to the star which is not a problem for mirror worlds because they are not significantly heated by the radiation from the star . this hypothesis can potentially explain the opacity of transiting planets because mirror worlds would accrete ordinary matter from the solar wind which accumulates in the gravitational potential well of the mirror world . it turns out that the effective radius , @xmath226 at which the planet becomes opaque to ordinary radiation depends sensitively on the mass of the planet , with ref.@xcite providing a prediction : @xmath227 where @xmath228 is the surface temperature of the planet and @xmath229 is the mass of the planet . this was only a rough prediction ( especially the dependence on @xmath228 ) but a prediction nevertheless . heuristically it is very easy to understand : increasing the planet s mass increases the force of gravity which causes the gas of ordinary matter to become more tightly bound to the mirror planet ( thereby decreasing the effective size , @xmath226 ) , while increasing the temperature of the gas increases the volume that the gas occupies ( thereby increasing @xmath226 ) . of these two effects we expect that the dependence on @xmath229 should be the more robust prediction . because the size of ordinary gas giant planets ( i.e. planets made mostly of ordinary matter ) depends quite weakly on their mass , the dependence on @xmath229 which is significant according to eq.([1new ] ) should allow a decisive test of the mirror planet hypothesis . there are currently four extrasolar planets for which measurements of @xmath226 and @xmath229 are available : hd209458b@xcite , ogle - tr-56b@xcite , ogle - tr-113b@xcite and ogle - tr-132b@xcite . we summarize their properties in the following table : -0.1 cm -0.15 cm these measurements ( ignoring ogle - tr-132b because of its huge uncertainty in @xmath226 ) , together with the 2001 prediction , eq.([1new ] ) , are shown in figure 5 ( from ref.@xcite ) . the solid line is the prediction , eq.([1new ] ) , where we have used hd209458b to fix the proportionality constant . 0.4 cm ( 1500,900)(0,0 ) = cmr10 at 10pt ( 181.0,123.0 ) ' '' '' ( 161,123)(0,0)[r ] 0 ( 1419.0,123.0 ) ' '' '' ( 181.0,215.0 ) ' '' '' ( 161,215)(0,0)[r ] 0.2 ( 1419.0,215.0 ) ' '' '' ( 181.0,307.0 ) ' '' '' ( 161,307)(0,0)[r ] 0.4 ( 1419.0,307.0 ) ' '' '' ( 181.0,399.0 ) ' '' '' ( 161,399)(0,0)[r ] 0.6 ( 1419.0,399.0 ) ' '' '' ( 181.0,492.0 ) ' '' '' ( 161,492)(0,0)[r ] 0.8 ( 1419.0,492.0 ) ' '' '' ( 181.0,584.0 ) ' '' '' ( 161,584)(0,0)[r ] 1 ( 1419.0,584.0 ) ' '' '' ( 181.0,676.0 ) ' '' '' ( 161,676)(0,0)[r ] 1.2 ( 1419.0,676.0 ) ' '' '' ( 181.0,768.0 ) ' '' '' ( 161,768)(0,0)[r ] 1.4 ( 1419.0,768.0 ) ' '' '' ( 181.0,860.0 ) ' '' '' ( 161,860)(0,0)[r ] 1.6 ( 1419.0,860.0 ) ' '' '' ( 181.0,123.0 ) ' '' '' ( 181,82)(0,0 ) 0 ( 181.0,840.0 ) ' '' '' ( 410.0,123.0 ) ' '' '' ( 410,82)(0,0 ) 0.2 ( 410.0,840.0 ) ' '' '' ( 638.0,123.0 ) ' '' '' ( 638,82)(0,0 ) 0.4 ( 638.0,840.0 ) ' '' '' ( 867.0,123.0 ) ' '' '' ( 867,82)(0,0 ) 0.6 ( 867.0,840.0 ) ' '' '' ( 1096.0,123.0 ) ' '' '' ( 1096,82)(0,0 ) 0.8 ( 1096.0,840.0 ) ' '' '' ( 1325.0,123.0 ) ' '' '' ( 1325,82)(0,0 ) 1 ( 1325.0,840.0 ) ' '' '' ( 181.0,123.0 ) ' '' '' ( 1439.0,123.0 ) ' '' '' ( 181.0,860.0 ) ' '' '' ( 29,595)(0,0)@xmath230 $ ] ( 810,21)(0,0)@xmath231 ( 181.0,123.0 ) ' '' '' ( 1325.0,759.0 ) ' '' '' ( 1315.0,759.0 ) ' '' '' ( 1315.0,805.0 ) ' '' '' ( 1090.0,616.0 ) ' '' '' ( 1080.0,616.0 ) ' '' '' ( 1080.0,763.0 ) ' '' '' ( 950.0,588.0 ) ' '' '' ( 940.0,588.0 ) ' '' '' ( 940.0,653.0 ) ' '' '' ( 1285.0,782.0 ) ' '' '' ( 1285.0,772.0 ) ' '' '' ( 1365.0,772.0 ) ' '' '' ( 1033.0,690.0 ) ' '' '' ( 1033.0,680.0 ) ' '' '' ( 1147.0,680.0 ) ' '' '' ( 866.0,620.0 ) ' '' '' ( 866.0,610.0 ) ' '' '' ( 1033.0,610.0 ) ' '' '' ( 181.0,123.0 ) ' '' '' ( 161,123)(0,0)[r ] 0 ( 1419.0,123.0 ) ' '' '' ( 181.0,215.0 ) ' '' '' ( 161,215)(0,0)[r ] 0.2 ( 1419.0,215.0 ) ' '' '' ( 181.0,307.0 ) ' '' '' ( 161,307)(0,0)[r ] 0.4 ( 1419.0,307.0 ) ' '' '' ( 181.0,399.0 ) ' '' '' ( 161,399)(0,0)[r ] 0.6 ( 1419.0,399.0 ) ' '' '' ( 181.0,492.0 ) ' '' '' ( 161,492)(0,0)[r ] 0.8 ( 1419.0,492.0 ) ' '' '' ( 181.0,584.0 ) ' '' '' ( 161,584)(0,0)[r ] 1 ( 1419.0,584.0 ) ' '' '' ( 181.0,676.0 ) ' '' '' ( 161,676)(0,0)[r ] 1.2 ( 1419.0,676.0 ) ' '' '' ( 181.0,768.0 ) ' '' '' ( 161,768)(0,0)[r ] 1.4 ( 1419.0,768.0 ) ' '' '' ( 181.0,860.0 ) ' '' '' ( 161,860)(0,0)[r ] 1.6 ( 1419.0,860.0 ) ' '' '' ( 181.0,123.0 ) ' '' '' ( 181,82)(0,0 ) 0 ( 181.0,840.0 ) ' '' '' ( 410.0,123.0 ) ' '' '' ( 410,82)(0,0 ) 0.2 ( 410.0,840.0 ) ' '' '' ( 638.0,123.0 ) ' '' '' ( 638,82)(0,0 ) 0.4 ( 638.0,840.0 ) ' '' '' ( 867.0,123.0 ) ' '' '' ( 867,82)(0,0 ) 0.6 ( 867.0,840.0 ) ' '' '' ( 1096.0,123.0 ) ' '' '' ( 1096,82)(0,0 ) 0.8 ( 1096.0,840.0 ) ' '' '' ( 1325.0,123.0 ) ' '' '' ( 1325,82)(0,0 ) 1 ( 1325.0,840.0 ) ' '' '' ( 181.0,123.0 ) ' '' '' ( 1439.0,123.0 ) ' '' '' ( 181.0,860.0 ) ' '' '' ( 29,595)(0,0)@xmath230 $ ] ( 810,21)(0,0)@xmath231 ( 181.0,123.0 ) ' '' '' ( 181,123 ) ( 181.00,123.59)(0.950,0.485)11 ' '' '' ( 181.00,122.17)(11.251,7.000)2 ' '' '' ( 194.00,130.59)(0.758,0.488)13 ' '' '' ( 194.00,129.17)(10.547,8.000)2 ' '' '' ( 206.00,138.59)(0.950,0.485)11 ' '' '' ( 206.00,137.17)(11.251,7.000)2 ' '' '' ( 219.00,145.59)(0.950,0.485)11 ' '' '' ( 219.00,144.17)(11.251,7.000)2 ' '' '' ( 232.00,152.59)(0.824,0.488)13 ' '' '' ( 232.00,151.17)(11.443,8.000)2 ' '' '' ( 245.00,160.59)(0.874,0.485)11 ' '' '' ( 245.00,159.17)(10.369,7.000)2 ' '' '' ( 257.00,167.59)(0.950,0.485)11 ' '' '' ( 257.00,166.17)(11.251,7.000)2 ' '' '' ( 270.00,174.59)(0.824,0.488)13 ' '' '' ( 270.00,173.17)(11.443,8.000)2 ' '' '' ( 283.00,182.59)(0.874,0.485)11 ' '' '' ( 283.00,181.17)(10.369,7.000)2 ' '' '' ( 295.00,189.59)(0.950,0.485)11 ' '' '' ( 295.00,188.17)(11.251,7.000)2 ' '' '' ( 308.00,196.59)(0.824,0.488)13 ' '' '' ( 308.00,195.17)(11.443,8.000)2 ' '' '' ( 321.00,204.59)(0.874,0.485)11 ' '' '' ( 321.00,203.17)(10.369,7.000)2 ' '' '' ( 333.00,211.59)(0.950,0.485)11 ' '' '' ( 333.00,210.17)(11.251,7.000)2 ' '' '' ( 346.00,218.59)(0.950,0.485)11 ' '' '' ( 346.00,217.17)(11.251,7.000)2 ' '' '' ( 359.00,225.59)(0.824,0.488)13 ' '' '' ( 359.00,224.17)(11.443,8.000)2 ' '' '' ( 372.00,233.59)(0.874,0.485)11 ' '' '' ( 372.00,232.17)(10.369,7.000)2 ' '' '' ( 384.00,240.59)(0.950,0.485)11 ' '' '' ( 384.00,239.17)(11.251,7.000)2 ' '' '' ( 397.00,247.59)(0.824,0.488)13 ' '' '' ( 397.00,246.17)(11.443,8.000)2 ' '' '' ( 410.00,255.59)(0.874,0.485)11 ' '' '' ( 410.00,254.17)(10.369,7.000)2 ' '' '' ( 422.00,262.59)(0.950,0.485)11 ' '' '' ( 422.00,261.17)(11.251,7.000)2 ' '' '' ( 435.00,269.59)(0.824,0.488)13 ' '' '' ( 435.00,268.17)(11.443,8.000)2 ' '' '' ( 448.00,277.59)(0.950,0.485)11 ' '' '' ( 448.00,276.17)(11.251,7.000)2 ' '' '' ( 461.00,284.59)(0.874,0.485)11 ' '' '' ( 461.00,283.17)(10.369,7.000)2 ' '' '' ( 473.00,291.59)(0.824,0.488)13 ' '' '' ( 473.00,290.17)(11.443,8.000)2 ' '' '' ( 486.00,299.59)(0.950,0.485)11 ' '' '' ( 486.00,298.17)(11.251,7.000)2 ' '' '' ( 499.00,306.59)(0.874,0.485)11 ' '' '' ( 499.00,305.17)(10.369,7.000)2 ' '' '' ( 511.00,313.59)(0.824,0.488)13 ' '' '' ( 511.00,312.17)(11.443,8.000)2 ' '' '' ( 524.00,321.59)(0.950,0.485)11 ' '' '' ( 524.00,320.17)(11.251,7.000)2 ' '' '' ( 537.00,328.59)(0.950,0.485)11 ' '' '' ( 537.00,327.17)(11.251,7.000)2 ' '' '' ( 550.00,335.59)(0.758,0.488)13 ' '' '' ( 550.00,334.17)(10.547,8.000)2 ' '' '' ( 562.00,343.59)(0.950,0.485)11 ' '' '' ( 562.00,342.17)(11.251,7.000)2 ' '' '' ( 575.00,350.59)(0.950,0.485)11 ' '' '' ( 575.00,349.17)(11.251,7.000)2 ' '' '' ( 588.00,357.59)(0.758,0.488)13 ' '' '' ( 588.00,356.17)(10.547,8.000)2 ' '' '' ( 600.00,365.59)(0.950,0.485)11 ' '' '' ( 600.00,364.17)(11.251,7.000)2 ' '' '' ( 613.00,372.59)(0.950,0.485)11 ' '' '' ( 613.00,371.17)(11.251,7.000)2 ' '' '' ( 626.00,379.59)(0.874,0.485)11 ' '' '' ( 626.00,378.17)(10.369,7.000)2 ' '' '' ( 638.00,386.59)(0.824,0.488)13 ' '' '' ( 638.00,385.17)(11.443,8.000)2 ' '' '' ( 651.00,394.59)(0.950,0.485)11 ' '' '' ( 651.00,393.17)(11.251,7.000)2 ' '' '' ( 664.00,401.59)(0.950,0.485)11 ' '' '' ( 664.00,400.17)(11.251,7.000)2 ' '' '' ( 677.00,408.59)(0.758,0.488)13 ' '' '' ( 677.00,407.17)(10.547,8.000)2 ' '' '' ( 689.00,416.59)(0.950,0.485)11 ' '' '' ( 689.00,415.17)(11.251,7.000)2 ' '' '' ( 702.00,423.59)(0.950,0.485)11 ' '' '' ( 702.00,422.17)(11.251,7.000)2 ' '' '' ( 715.00,430.59)(0.758,0.488)13 ' '' '' ( 715.00,429.17)(10.547,8.000)2 ' '' '' ( 727.00,438.59)(0.950,0.485)11 ' '' '' ( 727.00,437.17)(11.251,7.000)2 ' '' '' ( 740.00,445.59)(0.950,0.485)11 ' '' '' ( 740.00,444.17)(11.251,7.000)2 ' '' '' ( 753.00,452.59)(0.824,0.488)13 ' '' '' ( 753.00,451.17)(11.443,8.000)2 ' '' '' ( 766.00,460.59)(0.874,0.485)11 ' '' '' ( 766.00,459.17)(10.369,7.000)2 ' '' '' ( 778.00,467.59)(0.950,0.485)11 ' '' '' ( 778.00,466.17)(11.251,7.000)2 ' '' '' ( 791.00,474.59)(0.824,0.488)13 ' '' '' ( 791.00,473.17)(11.443,8.000)2 ' '' '' ( 804.00,482.59)(0.874,0.485)11 ' '' '' ( 804.00,481.17)(10.369,7.000)2 ' '' '' ( 816.00,489.59)(0.950,0.485)11 ' '' '' ( 816.00,488.17)(11.251,7.000)2 ' '' '' ( 829.00,496.59)(0.824,0.488)13 ' '' '' ( 829.00,495.17)(11.443,8.000)2 ' '' '' ( 842.00,504.59)(0.874,0.485)11 ' '' '' ( 842.00,503.17)(10.369,7.000)2 ' '' '' ( 854.00,511.59)(0.950,0.485)11 ' '' '' ( 854.00,510.17)(11.251,7.000)2 ' '' '' ( 867.00,518.59)(0.824,0.488)13 ' '' '' ( 867.00,517.17)(11.443,8.000)2 ' '' '' ( 880.00,526.59)(0.950,0.485)11 ' '' '' ( 880.00,525.17)(11.251,7.000)2 ' '' '' ( 893.00,533.59)(0.874,0.485)11 ' '' '' ( 893.00,532.17)(10.369,7.000)2 ' '' '' ( 905.00,540.59)(0.950,0.485)11 ' '' '' ( 905.00,539.17)(11.251,7.000)2 ' '' '' ( 918.00,547.59)(0.824,0.488)13 ' '' '' ( 918.00,546.17)(11.443,8.000)2 ' '' '' ( 931.00,555.59)(0.874,0.485)11 ' '' '' ( 931.00,554.17)(10.369,7.000)2 ' '' '' ( 943.00,562.59)(0.950,0.485)11 ' '' '' ( 943.00,561.17)(11.251,7.000)2 ' '' '' ( 956.00,569.59)(0.824,0.488)13 ' '' '' ( 956.00,568.17)(11.443,8.000)2 ' '' '' ( 969.00,577.59)(0.950,0.485)11 ' '' '' ( 969.00,576.17)(11.251,7.000)2 ' '' '' ( 982.00,584.59)(0.874,0.485)11 ' '' '' ( 982.00,583.17)(10.369,7.000)2 ' '' '' ( 994.00,591.59)(0.824,0.488)13 ' '' '' ( 994.00,590.17)(11.443,8.000)2 ' '' '' ( 1007.00,599.59)(0.950,0.485)11 ' '' '' ( 1007.00,598.17)(11.251,7.000)2 ' '' '' ( 1020.00,606.59)(0.874,0.485)11 ' '' '' ( 1020.00,605.17)(10.369,7.000)2 ' '' '' ( 1032.00,613.59)(0.824,0.488)13 ' '' '' ( 1032.00,612.17)(11.443,8.000)2 ' '' '' ( 1045.00,621.59)(0.950,0.485)11 ' '' '' ( 1045.00,620.17)(11.251,7.000)2 ' '' '' ( 1058.00,628.59)(0.874,0.485)11 ' '' '' ( 1058.00,627.17)(10.369,7.000)2 ' '' '' ( 1070.00,635.59)(0.824,0.488)13 ' '' '' ( 1070.00,634.17)(11.443,8.000)2 ' '' '' ( 1083.00,643.59)(0.950,0.485)11 ' '' '' ( 1083.00,642.17)(11.251,7.000)2 ' '' '' ( 1096.00,650.59)(0.950,0.485)11 ' '' '' ( 1096.00,649.17)(11.251,7.000)2 ' '' '' ( 1109.00,657.59)(0.758,0.488)13 ' '' '' ( 1109.00,656.17)(10.547,8.000)2 ' '' '' ( 1121.00,665.59)(0.950,0.485)11 ' '' '' ( 1121.00,664.17)(11.251,7.000)2 ' '' '' ( 1134.00,672.59)(0.950,0.485)11 ' '' '' ( 1134.00,671.17)(11.251,7.000)2 ' '' '' ( 1147.00,679.59)(0.758,0.488)13 ' '' '' ( 1147.00,678.17)(10.547,8.000)2 ' '' '' ( 1159.00,687.59)(0.950,0.485)11 ' '' '' ( 1159.00,686.17)(11.251,7.000)2 ' '' '' ( 1172.00,694.59)(0.950,0.485)11 ' '' '' ( 1172.00,693.17)(11.251,7.000)2 ' '' '' ( 1185.00,701.59)(0.824,0.488)13 ' '' '' ( 1185.00,700.17)(11.443,8.000)2 ' '' '' ( 1198.00,709.59)(0.874,0.485)11 ' '' '' ( 1198.00,708.17)(10.369,7.000)2 ' '' '' ( 1210.00,716.59)(0.950,0.485)11 ' '' '' ( 1210.00,715.17)(11.251,7.000)2 ' '' '' ( 1223.00,723.59)(0.950,0.485)11 ' '' '' ( 1223.00,722.17)(11.251,7.000)2 ' '' '' ( 1236.00,730.59)(0.758,0.488)13 ' '' '' ( 1236.00,729.17)(10.547,8.000)2 ' '' '' ( 1248.00,738.59)(0.950,0.485)11 ' '' '' ( 1248.00,737.17)(11.251,7.000)2 ' '' '' ( 1261.00,745.59)(0.950,0.485)11 ' '' '' ( 1261.00,744.17)(11.251,7.000)2 ' '' '' ( 1274.00,752.59)(0.824,0.488)13 ' '' '' ( 1274.00,751.17)(11.443,8.000)2 ' '' '' ( 1287.00,760.59)(0.874,0.485)11 ' '' '' ( 1287.00,759.17)(10.369,7.000)2 ' '' '' ( 1299.00,767.59)(0.950,0.485)11 ' '' '' ( 1299.00,766.17)(11.251,7.000)2 ' '' '' ( 1312.00,774.59)(0.824,0.488)13 ' '' '' ( 1312.00,773.17)(11.443,8.000)2 ' '' '' ( 1325.00,782.59)(0.874,0.485)11 ' '' '' ( 1325.00,781.17)(10.369,7.000)2 ' '' '' ( 1337.00,789.59)(0.950,0.485)11 ' '' '' ( 1337.00,788.17)(11.251,7.000)2 ' '' '' ( 1350.00,796.59)(0.824,0.488)13 ' '' '' ( 1350.00,795.17)(11.443,8.000)2 ' '' '' ( 1363.00,804.59)(0.874,0.485)11 ' '' '' ( 1363.00,803.17)(10.369,7.000)2 ' '' '' ( 1375.00,811.59)(0.950,0.485)11 ' '' '' ( 1375.00,810.17)(11.251,7.000)2 ' '' '' ( 1388.00,818.59)(0.824,0.488)13 ' '' '' ( 1388.00,817.17)(11.443,8.000)2 ' '' '' ( 1401.00,826.59)(0.950,0.485)11 ' '' '' ( 1401.00,825.17)(11.251,7.000)2 ' '' '' ( 1414.00,833.59)(0.874,0.485)11 ' '' '' ( 1414.00,832.17)(10.369,7.000)2 ' '' '' ( 1426.00,840.59)(0.824,0.488)13 ' '' '' ( 1426.00,839.17)(11.443,8.000)2 ' '' '' 0.2 cm figure 5 : the measured effective size , @xmath226 , of the transiting planets ( from top to bottom ) hd209458b , ogle - tr-56b and ogle - tr-113b versus @xmath231 ( in units where @xmath232 for hd209458b ) . the solid line is the prediction , eq.([1new ] ) , which assumes that the planets are composed predominately of mirror matter . 1.5 cm evidently the 2001 prediction , eq.([1new ] ) , is in reasonable agreement with the observations . this appears to be non - trivial : in the case of ordinary matter planets , increasing the mass does not significantly affect the radius , and does not generally lead to a decreasing radius ( for example , jupiter is three times heavier than saturn , but is 15% _ larger _ ) . however , it is possible that the apparent agreement with the rough prediction , eq.([1new ] ) is coincidental so more data would be welcome . especially decisive would be the discovery of a much heavier transiting planet , @xmath233 , which should have a radius less than @xmath234 if it is a mirror world . 0.2 cm 0.2 cm if this mirror world interpretation of the close - in planets is correct then it is very natural that the dynamical mirror image system of a mirror star with an ordinary planet could also exist . such a system would appear to ordinary observers as an isolated " ordinary planet . remarkably , such isolated " planets have been identified in the @xmath235 orionis star cluster@xcite . these planets have estimated mass of @xmath236 and appear to be gas giants which do not seem to be associated with any visible star . given that the @xmath235 orionis cluster is estimated to be less than 5 million years old , the formation of these isolated " planets must have occurred within this time ( which means they ca nt orbit faint stellar bodies such as old white dwarfs ) . zapatero osorio et al@xcite argue that these findings pose a challenge to conventional theories of planet formation which are unable to explain the existence of numerous isolated planetary mass objects . thus , the existence of these planets is surprising if they are made of ordinary matter , however there existence is natural from the mirror world perspective since they can be interpreted as ordinary planets orbiting mirror stars@xcite . furthermore , if the isolated planets are not isolated but orbit mirror stars then there must exist a periodic doppler shift detectable on the spectral lines from these planets . this represents a simple way of testing this hypothesis@xcite . 0.2 cm 0.2 cm perhaps the most fascinating possible implication of mirror matter - type dark matter is that our solar system contains mirror matter space - bodies ( sb)@xcite . there is not much room for a large amount of mirror matter in our solar system . for example , the amount of mirror matter within the earth has been constrained to be less than @xmath237@xcite . however , we do nt know enough about the formation of the solar system to be able to exclude the existence of a large number of space bodies made of mirror matter if they are small like comets and asteroids . the total mass of asteroids in the asteroid belt is estimated to be only about 0.05% of the mass of the earth . a similar or even greater number of mirror bodies , perhaps orbiting in a different plane or even spherically distributed like the oort cloud is a fascinating possibility . in fact , the comets themselves and hence the oort cloud itself might actually be composed of mirror matter ( as we will discuss in the following subsection ) . anyway , collisions of such bodies with themselves and ordinary bodies would generate a solar system population of mirror gas and dust particles and larger bodies . the impact velocity of such solar system objects ( relative to the earth ) would be in the range : @xmath238 if such small mirror matter bodies do in fact exist and happen to collide with the earth , what would be the consequences ? if the only force connecting mirror matter with ordinary matter is gravity , then the consequences would be minimal . the mirror matter space body would simply pass through the earth and nobody would know about it unless the body was so heavy as to gravitationally affect the motion of the earth . however , if there is photon - mirror photon kinetic mixing of magnitude , @xmath239 , as indicated by the dama / nai experiment , then the mirror nuclei of the space body can interact with the ordinary nuclei in the earth via elastic rutherford scattering ( see figure 2 ) . small dust particles could thereby be detectable in simple surface experiments . in particular , experiments such as the st . petersburg experiment@xcite are sensitive to solar system mirror dust particles@xcite . such particles can produce a burst of photons in a scintillator due to elastic collisions between the mirror atoms of the dust particle and the ordinary scintillator atoms . not only can these photons be detected via a photomultiplier ( pm ) tube , but the velocity of the mirror dust particle can be determined if the pm tubes are appropriately arranged . this is important because ordinary cosmic rays should be travelling close to the speed of light , and can thereby be distinguished from relatively slow moving mirror dust particles . petersburg experiment finds a positive signal consistent with a flux of about 1 mirror dust particle per square meter per day . impacts of larger bodies should be less frequent , nevertheless there is a fascinating range of evidence for their existence . the largest recorded impact event was the 1908 tunguska event . remarkably no significant asteroid or cometary remnants were recovered from the tunguska site@xcite . people have _ assumed _ that the impacting body was made of ordinary matter , however there is ( literally ! ) no solid evidence to support this claim . the tunguska body may have been made out of dark matter which is a logical possibility if mirror matter is identified with the dark matter of the universe . in fact , this hypothesis seems to provide a better explanation for the known features of the tunguska event@xcite . there are also many other ` anomalous ' impact events , on smaller scales@xcite , and evidence for anomalous impact events on larger scales . included among the latter are the impact events responsible for strange glass fields such as edeowie glass@xcite , libyan desert glass , tektites etc . all of these impact related phenomena share a common feature which is the remarkable lack of clearly defined extraterrestrial material or even chemical traces ( such as iridium excess ) . this fact is obviously explicable if the events were due to the impact of a mirror matter space body . other solar system evidence for mirror matter also exists coming from the lack of small craters on the asteroid eros@xcite and also from the anomalous slow - down of _ both _ pioneer spacecraft@xcite . the overall situation is summarized in figure 6 . 0.4 cm 0.3 cm figure 6 : favoured range of @xmath24 from various experiments / observations . also shown are the current direct experimental bound , @xmath240 which comes from orthopositronium lifetime studies@xcite and also the limit , @xmath241 , suggested by early universe cosmology ( successful bbn ) @xcite . 1.3 cm direct detection of mirror matter fragments in the ground is also possible at these impact sites . the photon - mirror photon kinetic mixing interaction will lead to a static force which can keep small mirror matter fragments ( of size @xmath242 ) near the earth s surface , provided that@xcite @xmath243 such fragments can be experimentally detected via the centrifuge technique@xcite and through the thermal effects of the embedded mirror matter on the surrounding ordinary matter@xcite . note however that impacts of galactic halo mirror ions / electrons will vaporize these small fragments over time . the flux of halo mirror electrons is roughly @xmath244 and defining @xmath245 to be the mean number of mirror atoms evaporated from the impact of each halo mirror electron ( @xmath246 ) , then the rate at which a mirror matter fragment would evaporate would be of order @xmath247 ( where @xmath248 is the atomic number density of mirror atoms in the mirror fragment ) . this suggests that mirror matter fragments probably could not be recovered from the remnants of old impact events , such as edeowie glass , libyan desert glass , tektites etc ( which are of order 1 myr old or older ) but might be recovered from relatively recent anomalous impact events such as the tunguska event@xcite and small anomalous impact events@xcite . if mirror matter space - bodes do exist in our solar system , then one might expect other unconventional scientific implications . below we mention just a few more of these things . comets are believed to originate from an approximately spherically symmetric cloud extending out about half way to the nearest star . this comet cloud , called the oort cloud , is reminisant of the dark halo of our galaxy . both are largely invisible , are distributed differently to the ` visible ' matter , and are also hypothetical . of course , this analogy is very simplistic and should not be taken very seriously . nevertheless , it is also true that comets seem to have a number of puzzling features and are not altogether well understood . one interesting feature of comets is that they seem to contain a very dark nucleus . for example , the nucleus of halley s comet has an albedo of only 0.03 making it one of the darkest objects in the solar system darker even than coal ! this has led to the suggestion@xcite that the nucleus could be composed predominately of mirror matter . of course , pure mirror matter would be transparent , but if it contained a small admixture of ordinary matter embedded within , it might appear opaque and dark . if the ordinary matter had a volatile component such as water ice , then this would explain the large head and tail observed when the comet passed close to the sun . furthermore , such a picture would simply explain the long standing comet fading problem : that many comets lose a large factor ( 100 - 1000 ) in average brightness after approaching the sun for the first time . if this interpretation is correct , then comets may simply become dimmer and dimmer over time rapidly losing all of their volatile ordinary matter component . they may effectively become invisible . of course , the rate that this occurs will depend on many things such as the proportion of ordinary to mirror matter , the chemical composition , details of the orbit etc . interestingly , a recent study@xcite has concluded that many old comets must have either become invisible or have somehow disintegrated . the number of cometary remnants ( assumed to be asteroid - like objects ) is 100 times less abundant than theoretically expected!@xcite . clearly , this seems to support ( or at least , encourage ) the mirror matter interpretation of the comets . of course , if comets are predominately made of mirror matter then this fits - in nicely with the mirror matter interpretation of the anomalous small impact events ( and tunguska event ) , which was discussed in the previous subsection . it might also be connected with atmospheric anomalies . to explain the anomalous small impact events we require that some of the mirror matter space - bodies to survive and hit the ground without completely melting and vaporizing in the atmosphere . detailed studies@xcite have shown that this is possible , especially for non - volatile mirror matter ( such as mirror iron ) . sometimes , it could happen that a mirror space - body would heat up enough to completely vaporize in the atmosphere . after vaporizing , the mirror atoms interact with the air atoms by rutherford scattering . although initially the mirror matter will heat up the ordinary matter because of its large kinetic energy ( since its initial velocity is at least 11 km / s ) , after a short time , the mirror matter will cool the atmosphere . the mirror atoms will draw in heat from the surrounding ordinary atoms and radiate it away into mirror photons . since the mirror atoms are not absorbing mirror photons from the environment , heat will be lost from the system . the net effect is a localized rapid cooling of the atmosphere which might lead to the formation of unusual clouds and other strange atmospheric phenomena . this might explain the remarkable observations of falling ice blocks@xcite and maybe even the observations of atmospheric ` holes'@xcite . it seems that the answer may indeed be ` blowing in the wind ' but only for a sort time ! historically , imposing symmetries of particle interactions has led to the prediction and subsequent discovery of a variety of ` new ' fundamental particles including : * antiparticles predicted to exist by imposing proper lorentz symmetry ; * neutrino predicted to exist by imposing time translational symmetry ( energy conservation ) ; * top quark predicted to exist from @xmath249 electroweak gauge symmetry ( to partner the bottom quark ) ; * the @xmath250 baryon predicted from @xmath251 flavour symmetry in the quark model . mirror matter is also an offspring of this methodology ; it is an attempt to follow this historically successful approach . in fact it appears to be theoretically unique , arising from a single well motivated hypothesis : the improper lorentz symmetries ( such as parity and time reversal invariance ) stand out as the only space - time symmetries which are not respected by the interactions of the known elementary particles , but can be exact unbroken symmetries of nature if a set of mirror particles exist . mirror matter is thus very well motivated from a particle physics point of view . furthermore it seems to have the right properties to be identified with the inferred non - baryonic dark matter in the universe . specifically , mirror dark matter seems to provide a consistent explanation for : a ) the basic dark matter particle properties ( mass , stability , darkness ) ; b ) the similarity in cosmic abundance between ordinary and non - baryonic dark matter , @xmath0 ; c ) large scale structure formation ; d ) microlensing ( macho ) events ; e ) asymptotically flat rotation curves in spiral galaxies and f ) the impressive dama / nai annual modulation signal . of course , any theory of dark matter should also be measured against the standard paradigm that non - baryonic dark matter consists of hypothetical weakly interacting particles i.e. essentially collisionless particles . however this comparison is actually favourable . in the standard wimp hypothesis : the basic dark matter properties ( stability , darkness ) require ad hoc hypothesis ; macho events can not be explained ; @xmath252 is mysterious ; dama / nai annual modulation signal is difficult to understand consistently with other experiments such as cdmsii . perhaps the only thing that wimps might explain better is the existence of the halo in galaxies . this is because wimps are non - dissipative . however this success is significantly eroded by the facts ; standard collisionless dark matter predicts@xcite overly dense cores in galaxies and over abundance of small scale structures within halos which are _ not _ consistent with the observations@xcite . thus , by either comparing mirror matter - type dark matter with experiments and observations or with the standard wimp paradigm , it is clear that it is a strong candidate for the non - baryonic dark matter in the universe , deserving of serious consideration and further study . 0.4 cm * acknowledgements * 0.1 cm it is a pleasure to thank my collaborators , sergei gninenko , sasha ignatiev , henry lew , saibal mitra , zurab silagadze , ray volkas and t. l. yoon . i would also like to thank s. mitra , z. silagadze and r. volkas for their comments on a draft of this article . this work was supported by the australian research council . r. foot , h lew and r. r. volkas , phys . b272 , 67 ( 1991 ) . the idea that exact unbroken parity symmetry can be respected by the fundamental interactions if a set of mirror particles exist was earlier discussed , prior to the advent of the standard model of particle physics , in t. d. lee and c. n. yang , phys . rev . 104 , 256 ( 1956 ) ; i. kobzarev , l. okun and i. pomeranchuk , sov . j. nucl . phys . 3 , 837 ( 1966 ) ; m. pavsic , int . j. theor . 9 , 229 ( 1974 ) . the first application to non - baryonic dark matter was given in : s. i. blinnikov and m. yu . khlopov , sov . 36 , 472 ( 1982 ) ; sov . 27 , 371 ( 1983 ) . r. foot , phys . b496 , 169 ( 2000 ) [ hep - ph/0007065 ] ; r. foot and r. r. volkas , phys . b543 , 38 ( 2002 ) [ hep - ph/0204265 ] ; r. foot , mod . a18 , 2079 ( 2003 ) [ hep - ph/0210393 ] ; mod . a18 , 2071 ( 2003 ) [ hep - ph/0303005 ] . e. w. kolb , d. seckel and m. s. turner , nature 314 , 415 ( 1985 ) ; h. m. hodges , phys . d47 , 456 ( 1993 ) ; z. g. berezhiani , a. d. dolgov and r. n. mohapatra , phys . b375 , 26 ( 1996 ) [ hep - ph/9511221 ] ; v. berezinsky and a. vilenkin , phys . d62 , 083512 ( 2000 ) [ hep - ph/9908257 ] . r. foot and r. r. volkas , phys . rev . d68 , 021304 ( 2003 ) [ hep - ph/0304261 ] ; phys . d69 , 123510 ( 2004 ) [ hep - ph/0402267 ] see also : l. bento and z. berezhiani , phys . 87 , 231304 ( 2001 ) [ hep - ph/0107281 ] ; hep - ph/0111116 . z. k. silagadze , acta phys . b32 , 99 ( 2001 ) [ hep - ph/0002255 ] ; r. foot and z. k. silagadze , acta phys . b32 , 2271 ( 2001 ) [ astro - ph/0104251 ] ; z. k. silagadze , acta phys . pol . b33 , 1325 ( 2002 ) [ astro - ph/0110161 ] . r. foot , acta phys . b32 , 3133 ( 2001 ) [ hep - ph/0107132 ] ; r. foot and t. l. yoon , acta phys . 33 , 1979 ( 2002 ) [ astro - ph/0203152 ] ; r. foot and s. mitra , astropart . 19 , 739 ( 2003 ) [ astro - ph/0211067 ] ; z. k. silagadze , astro - ph/0311337 . m. morawska - horawska and a. manechi , przeglad geofizyczny 40 , 335 ( 1995 ) ; j. a. docobo _ et al_. , meteoritics & planetary science 33 , 57 ( 1998 ) ; a. olkhovatov , http://olkhov.narod.ru/gr1997.htm . the 2001 jordan event , http://www.jas.org.jo/mett.html . http://tierra.rediris.es/megacryometeors/index2.html and j. martinez - frias _ et al . _ , compositional heterogeneity of hailstones : atmospheric conditions and possible environmental implications , ambio vol . 30 ( 2001 ) .

on - baryonic dark matter ) the basic dark matter particle properties ass , stability , darkness ) the similarity in cosmic abundance between ordinary and non - baryonic dark matter , @xmath0 ; ) large scale structure formation ; ) microlensing ( macho ) events ; ) asymptotically flat rotation curves in spiral galaxies ) the impressive dama / nai annual modulation signal . mirror matter - type dark matter is capable of explaining

on - baryonic dark matter ) the basic dark matter particle properties ass , stability , darkness ) the similarity in cosmic abundance between ordinary and non - baryonic dark matter , @xmath0 ; ) large scale structure formation ; ) microlensing ( macho ) events ; ) asymptotically flat rotation curves in spiral galaxies ) the impressive dama / nai annual modulation signal . mirror matter - type dark matter is capable of explaining

there are six main things which any non - baryonic dark matter theory should endeavour to explain : ( 1 ) the basic dark matter particle properties [ mass , stability , darkness ] ; ( 2 ) the similarity in cosmic abundance between ordinary and non - baryonic dark matter , @xmath0 ; ( 3 ) large scale structure formation ; ( 4 ) microlensing ( macho ) events ; ( 5 ) asymptotically flat rotation curves in spiral galaxies ; ( 6 ) the impressive dama / nai annual modulation signal . only mirror matter - type dark matter is capable of explaining all six of these desirable features . the purpose of this article is to provide an up - to - date and pedagogical review of this dark matter candidate .

d by a ion of the p ally accessible conformation the protein s s a pro in this paper , structural origins of binding affinity and of binding two ca@xmath0ions domain of ca lmodulin ( cam ) through simulations of a simple coarse - grained . in this the protein s open and closed conformational ensembles are simulated explicitly and ligand binding and unbinding is within the grand canonical ensemble . al ensemble u pon binding . nod - wyman - changeux model of allostery with appropriate binding free energ the open and closed ensembles a ccurately describes the simulated s predict that the two domains of cam binding affinity and c - terminal domain n - terminal domain , the a on the l s structural compatibility with the ligand in the b as well as the the binding site in the un

structural origins of binding affinity and within the grand canonical ensemble . the open and closed ensembles a s structural compatibility with the ligand

conformational dynamics is essential for a protein s ability to exhibit allostery . the coupling between two distant binding sites is frequently accomplished by a conformational change between a `` closed '' ( apo ) to an `` open '' ( holo ) conformation upon ligation.@xcite although the end point conformations often give valuable insight into protein function , a detailed description of the allosteric mechanism for a particular protein requires one to consider a broader conformational ensemble . the landscape theory of binding@xcite acknowledges that a folded protein is inherently dynamic and explores the thermally accessible conformational states in its native basin.@xcite this conformational ensemble comprises the protein s `` functional landscape''.@xcite while only a small subset of the states comprising the folding energy landscape@xcite , the functional landscape determines how a protein responds to the changes in its local environment such as ligand interactions . due to the heterogeneous nature of the conformational ensemble , a ligand preferentially stabilizes some conformations more than others , causing the protein s thermal population to redistribute to a ligated ensemble which in general has distinct equilibrium properties.@xcite the ensemble nature of allostery accommodates a rich and diverse set of regulatory strategies and provides a general framework to understand binding thermodynamics and kinetics of specific proteins.@xcite even simple landscapes with a small number of well defined basins separated by kinetic barriers can have subtle binding mechanisms because they depend on ligand interactions to short - lived transient states . experimental progress on this challenging kinetics problem has appeared only very recently.@xcite in principle , affinities of metastable states can also be obtained from thermodynamic binding measurements , although such analysis may not always be practical . in this paper , we focus on the cooperative binding of two ca@xmath0ions to the binding loops of the domains of calmodulin ( cam ) through equilibrium coarse - grained simulations . in this minimal model , the conformational transition between the open and closed ensembles are simulated explicitly and the dynamic shift in population due to ligand binding and unbinding is approximated by discrete jumps between a ligated and unligated free energy surfaces.@xcite the protein dynamics are governed by a native - centric potential that couples the open and closed conformational basins while ligation is represented implicitly through ligand mediated protein contacts . this model , developed by takada and co - workers , has been used to investigate the kinetic partitioning of induced fit and conformational selection binding pathways@xcite as well as mechanical unfolding of calmodulin in the presence of ca@xmath0.@xcite here , we assume that the ligands bound to the protein are in equilibrium with a dilute solution and calculate binding thermodynamics as a function of ligand concentration . the model is parameterized so that the closed basin is more stable than the open basin in the unligated ensemble . ligands interact with all conformations in the ensemble , but the affinity is largest for conformations within the open basin due to their high structural compatibility with the ligand . thus , the population shifts towards the open ensemble with increasing ligand concentration ( see _ si _ fig.s1 ) . the simulated ensembles have significant molecular fluctuations which modulate ligand affinities and affect the coupling between the binding sites . when binding thermodynamics are dominated by the open and closed ensembles , this model provides a molecular realization of the celebrated monod - wyman - changeux ( mwc ) model of allostery.@xcite for binding a single ligand the mwc model has four states : unligated - open , unligated - closed , ligated - open , and ligated - closed . appealing to this simple four - state model allows us to extract binding free energies of the isolated sites in the simulated open and closed ensembles and to calculate the free energy associated with the cooperative coupling between the sites . the simulations connect the conformational ensemble underlying the protein s dynamics with the mwc phenomenological binding parameters.@xcite early work on binding thermodynamics of cam has revealed that the affinities and cooperativities of the n - terminal domain ( ncam ) and the c - terminal domain ( ccam ) are distinct despite their structural similarity.@xcite although some experimental data has been reanalyzed recently@xcite , the traditional analysis of thermodynamic binding data has not used a dynamic landscape ( or mwc ) framework.@xcite nuclear magnetic resonance experiments@xcite and all atom molecular dynamics simulations@xcite that show a dynamic equilibrium between the open and closed conformations of cam s domains in the absence of ca@xmath0support our approach . calmodulin ( cam ) is a small , 148 amino acid long protein consisting of two topologically similar domains . each domain consists of four @xmath1-helices and a pair of ef - hand ca@xmath0-binding loops . the n - terminal domain ( ncam ) has helices labeled a d with binding loops i and ii , and the c - terminal domain ( ccam ) has helices labeled e h with binding loops iii and iv . we simulate open / closed allosteric transitions of the isolated domains of cam using a native - centric model implemented in the @xmath2 simulation package developed by takada and co - workers.@xcite this model couples two energy basins , one biased to the open ( pdb : 1cll@xcite ) reference structure and the other biased to the closed ( pdb : 1cfd@xcite ) reference structure . the energy of a conformation , specified by the @xmath3 position vectors of the c-@xmath1 atoms of the protein backbone , @xmath4 , is given by @xmath5 where @xmath6 is the single basin potential defined by the open structure and @xmath7 is the single basin potential defined by the closed structure . the interpolation parameters , @xmath8 and @xmath9 , control the barrier height and the relative stability of the two basins . parameters defining the single energy basins are set to their default values with uniform contact strength . the simulation temperature is set below the folding transition temperature of each of the four conformations . specifically , the simulation temperature is set to @xmath10 where @xmath11 is the folding transition temperature corresponding to the closed ( apo ) state of ncam , the lowest transition temperature among the open and closed states of ncam and ccam . equilibrium trajectories of length @xmath12 steps are simulated using langevin dynamics with a friction coefficient of @xmath13 and a timestep of @xmath14 ( in coarse - grained units).@xcite calcium binding to the two ef - hand loops of each domain of cam is modeled implicitly by adding a potential defined from the ligand - mediated contacts in the ef - hand loops of the open ( holo ) conformation @xmath15.\ ] ] here , the sum is over pairs of residues that are each within 4.5 @xmath16 of a ca@xmath0ion and closer than 10.0 @xmath16 in the open ( holo ) conformation . the binding energy parameters @xmath17 , @xmath18 , and @xmath19 are taken to be the same for each ligand - mediated contact for simplicity . binding cooperativity is influenced by the relative stability of the unligated open and closed states determined by @xmath9 and the binding free energy determined by @xmath20 . in principle , these parameters can be adjusted to match measured binding properties . in the absence of clear measured constraints , we choose parameters so that the relative stability between the open and closed states are the same for each domain . the transition barrier height is determined by @xmath8 which is set to @xmath21 for ncam and @xmath22 for ccam . adjusting @xmath23 for ncam and @xmath24 for ccam while keeping other parameters fixed gives an energy difference between the unligated open and closed states , @xmath25 for both domains . experimentally , the folding temperatures of the n - terminal and c - terminal domains in intact cam are approximately @xmath26 and @xmath27 , respectively.@xcite connecting to the domain opening kinetics in the intact protein , our simulation temperature corresponds to approximately @xmath28 which is 95% of ncam s simulated folding temperature , and 98% of ccam s simulated folding temperature . for the results reported in this paper , the binding energy parameters are set to @xmath29 ( default value in @xmath2 ) , @xmath30 and @xmath31 where @xmath32 is the corresponding separation distance in the open ( holo ) reference conformation . we have performed additional simulations to explore the dependence of binding thermodynamics on the ligand - mediated contact strength and interaction range . at higher values of @xmath17 and @xmath33 , the affinities of ligand binding to individual loops increase . nevertheless , the slope of the titration curve at the midpoint of the transition ( a measure of binding cooperativity ) remains the same ( _ si _ fig.s2 ) . the simulated conformational ensembles are characterized structurally in terms of local and global order parameters based on the contacts formed in each sampled conformation . the set of native contacts in the open and closed conformations are separated into three groups : those that occur exclusively in either the open or the closed native structures , and those that are common to both states . a native contact in a given conformation is considered to be formed provided the distance between the two residues is closer than 1.2 times the corresponding distance in the native conformation . local order parameters @xmath34 and @xmath35 are defined as the fraction of native contacts involving the @xmath36 residue that occur exclusively in the open and closed native structures , respectively . overall native similarity is monitored by corresponding global order parameters , @xmath37 and @xmath38 , where the average is taken over the residues of the protein . we identify metastable conformational basins from minima in the free energy computed through the population histogram parameterized by @xmath39 and @xmath40 . ligand binding / unbinding events coupled with a conformational change of the protein is modeled within the grand canonical ensemble . throughout the protein s conformational transitions , the ligation state of each loop is determined stochastically through a monte carlo step attempted every 1000 steps in the langevin trajectory . if the loop is unligated , a ligand is introduced to the binding loop ( @xmath41 ) with probability @xmath42.\ ] ] if the loop is ligated , the ligand dissociates from the binding loop ( @xmath43 ) with probability @xmath44.\ ] ] here , @xmath45 is the chemical potential of a bound ligand . at equilibrium , @xmath45 equals the chemical potential of the ligand in solution , @xmath46 where @xmath47 is the ligand concentration , and @xmath48 and @xmath49 are the reference concentration and reference chemical potential , respectively . to compute binding curves , a series of simulations are preformed , each at a different value of the ligand chemical potential . these simulated titration curves are reported as function of the chemical potential , or equivalently , in terms of the relative ligand concentration defined through @xmath50 where @xmath51 . this approach with monte carlo acceptance rates given in eq . [ eq : metropolis1 ] and eq . [ eq : metropolis2 ] is oriented towards binding thermodynamics from the outset . takada and co - workers present a different choice motivated by ligand binding kinetics.@xcite instead of introducing a chemical potential , ligand concentration enters their model through a variable binding attempt rate , while the attempt rate of unbinding is fixed . binding titration curves can also be calculated in this model , but as a function of the binding attempt rate rather than the concentration directly.@xcite we first consider ca@xmath0binding exclusively to each individual loop by simulating the conformational change of the entire domain while permitting binding only to a single site . as shown in fig.[fig : ncam_ccam_affinity ] ( a ) and fig.[fig : ncam_ccam_affinity ] ( b ) , the bound population as a function of ligand concentration , @xmath52 , follows a typical sigmoidal profile connecting a fully unbound population at low concentration and a fully bound population at high concentration . the overall binding strength of the individual loops is reflected in the dissociation constant , @xmath53 , shown in table.[tab : single_loop_data ] . binding affinities of ncam s loops are nearly the same , whereas the affinities of ccam s loops are significantly different , with @xmath54 . comparing the binding strength of cam s loops , our simulations predict that @xmath55 . .number of ligand - mediated contacts , dissociation constants , and binding free energies for the loops of cam . [ cols="<,^,^,^,^",options="header " , ] [ tab : equil_const ] although the right hand side of eq.[eq : cab ] can be evaluated directly from simulated populations , it is convenient to take advantage of the parameterization provided by the mwc model since it accurately describes the simulated equilibrium populations . using eq.([eq : prob_only_1_bound][eq : prob_both_bound ] ) with @xmath56 leads to @xmath57 \left [ 1 + \exp(-\beta ( \epsilon + \delta\epsilon^{\mathrm{a } } + \delta\epsilon^{\mathrm{b}}))\right ] } { \left [ 1 + \exp(-\beta ( \epsilon + \delta \epsilon^{\mathrm{a}}))\right ] \left [ 1 + \exp(-\beta ( \epsilon + \delta \epsilon^{\mathrm{b}}))\right ] } , \ ] ] with @xmath58 and @xmath59 . the computed equilibrium constants , shown in table.[tab : equil_const ] , indicate that ca@xmath0-binding to ccam ( with @xmath60 ) is more cooperative than ca@xmath0-binding to ncam ( with @xmath61 ) in qualitative agreement with experiment.@xcite the cooperative free energy is estimated to be @xmath62 for ccam and @xmath63 for ncam . the cooperative free energy for ccam is 1.8 times that of ncam in agreement with the experimental measured range of relative free energies of 1.2 3 reported in ref . and ref .. binding thermodynamics determined from experiments that can not distinguish between binding to individual sites are often reported through the macroscopic equilibrium constants @xmath64 and @xmath65.@xcite the macroscopic equilibrium constants describing the simulated binding thermodynamics are shown in table.[tab : equil_const ] . the value of @xmath66 for ccam is greater than @xmath66 for ncam by a factor of 1.5 in agreement with the experimentally reported range of 1.2 2.2.@xcite the free energy of binding two ca@xmath0ions can be estimated from the macroscopic binding constants summarized in table.[tab : equil_const ] , @xmath67 . the simulated relative values of @xmath68 for ccam is approximately 1.5 times the value of @xmath68 for ncam , which is in agreement with experimentally reported value of approximately 1.1 1.3.@xcite taken together , the simulated values of the macroscopic binding constants for cam are in qualitative agreement with those reported from experiments . the simulations offer a detailed molecular description of ca@xmath0binding as well as insight into the conformational ensembles underlying the binding free energies , @xmath69 and @xmath70 . fig.[fig : ncam_ccam rms variation ] shows the root mean square fluctuations ( rmsf ) of each residue for the unligated ( closed ) ensemble at low ligand concentration and the fully saturated ( open ) ensemble at high ligand concentration . focusing on ncam , we see that helix a , the n - terminal end of helix b , and the b - c linker become more flexible upon ca@xmath0-binding , while helix c and helix d show little change in flexibility . the temperature factors of the corresponding regions in ccam show qualitatively similar behavior . all four binding loops , on the other hand , become more rigid upon ca@xmath0coordination . the difference in flexibility upon binding is largest for loop iv due to its large fluctuations in the unligated ensemble . greater entropic stabilization of loop iv in the unligated state explains its relatively small binding affinity.@xcite furthermore , accounting for differences in loop entropy completes the rationalization of the binding free energies to the loops of cam : while the value of @xmath70 is dominated by the energetic stabilization of binding to the open state , the value of @xmath69 reflects the degree of conformational entropy of the loop in the unligated ensemble . ( black curve ) . the rmsf curves are calculated for each ensemble after aligning to the open native conformation . ( aligning to the closed conformation give similar curves . ) also shown is the reference fluctuations given in eq.[eq : rms avg ] ( green curve ) . ] the flexibility of individual residues are local order parameters that characterizes residue - specific conformational changes upon ca@xmath0binding.@xcite to qualitatively understand cam s structural changes along the binding curve , we compare the fluctuations of the @xmath71 residue to a two state reference rmsf , @xmath72 , given by average @xmath73 where the rmsf of the open ensemble , @xmath74 , and the closed ensemble , @xmath75 , are weighted by the fractional occupancy of the binding sites @xmath76 . the structural ordering of a residue at any concentration can be characterized as early or late compared to mean flexibility @xmath72 evaluated at the corresponding value of @xmath77 . for example , fig.[fig : ncam_ccam rms variation ] shows the simulated rmsf of each residue at @xmath53 , as well as the reference fluctuations evaluated at @xmath78 . although the ca@xmath0occupancy of the binding loops is only 50% , the local environment of helix a and the b - c linker of ncam as well as corresponding helix e and f - g linker of ccam is already similar to that of the open state ensemble . this `` early '' transition to the open ensemble is a reflection of the allosteric cooperativity . in contrast , the average structural order of the binding loops is similar to the weighted average of the open and closed state flexibility . the exception is the @xmath79-sheet in the c - terminal end of loop iv which takes on the open state structure at higher ligand concentrations . this `` late '' transition is in harmony with its lower binding affinity . in this paper , we introduce a method to simulate binding curves involving a protein that undergoes a conformational change upon binding . this approach allows us to identify the structural origins of binding affinity and to quantify allosteric cooperativity within a simple coarse - grained description of the protein dynamics . in this implicit ligand model , the protein conformation modulates the protein - ligand interactions through effective ligand - mediated contacts among residues in the binding site . the influence of ligand concentration on the effective binding strength is described through its uniform chemical potential . applying this approach to cam , we find that this model can distinguish the binding properties of the two domains of cam : binding loops i and ii of ncam have similar affinities , while in ccam , binding loop iii has significantly greater affinity than loop iv . the broader range of binding affinities in ccam accounts for its greater cooperativity . simulated populations of the ligation states as a function of concentration are accurately described by the mwc model with appropriate binding free energies for the individual loops . these binding free energies are average properties of the simulated ensemble and are not obvious solely from the open and closed structures . while the simulated binding thermodynamics is well - described by the mwc model , this simple analysis can obscure complexities in the free energy landscape . in separate publication , we describe how subtle differences in the topology and stability of the two domains lead to distinct simulated mechanisms for ca@xmath0-free domain opening for ncam and ccam ( submitted ) . in particular , we find that ccam unfolds more readily than ncam during the domain opening transition under similar conditions , a result consistent with the lower thermal stability of the c - terminal domain in the intact protein.@xcite although the unfolded conformations play a minor role in the binding thermodynamics described in this paper ( aside from modifying the binding free energies to the open and closed states ) , global folding and unfolding in the domain opening transition likely has a significant qualitative influence on the binding kinetics . this is a problem we plan to address in future work . we would like to thank daniel gavazzi for help in figure preparation . financial support from the national science foundation grant no . mcb-0951039 is gratefully acknowledged . 47ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1016/j.sbi.2004.01.005 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1038/nchembio.232 [ * * , ( ) ] link:\doibase 10.1038/nature06522 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1002/prot.340210302 [ * * , ( ) ] link:\doibase 10.1110/ps.9.1.10 [ * * , ( ) ] link:\doibase 10.1126/science.1169377 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1073/pnas.0802524105 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1110/ps.03259908 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1110/ps.9.8.1519 [ * * , ( ) ] link:\doibase 10.1073/pnas.0804672105 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1006/jmbi.1999.2770 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1016/s0006 - 3495(01)76182 - 6 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1016/j.jmb.2013.03.013 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1006/jmbi.1999.3188 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1021/ja067791a [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1073/pnas.0806872106 [ * * , ( ) ] * supporting information : coarse - grained molecular simulations of allosteric cooperativity * and the y - axis represents simulated free energy in units of @xmath80 . ] simulated free energy in terms of one - dimensional progress coordinate , @xmath81 , as shown in fig.s1 , illustrates that for both domains , the closed state is more stable in the unligated ensemble . binding of first ligand stabilizes both the closed and open states but the high affinity open state is stabilized to a greater extent due to its structural compatibility with the ligand . in the fully saturated ensemble , the open state has greater stability . for the results presented in the paper , we made specific choices for the ligand - mediated contact strength , @xmath82 , and interaction range , @xmath83 , respectively . as shown in fig.s2 , with the increase of @xmath84 and @xmath33 , the value of @xmath53 for individual loops decreases . however , the slope of the binding transition curve at a concentration for which @xmath85 remains the same . here , we only show results for binding loop i as an illustration .

structural origins of binding affinity and lmodulin ( cam ) through ensembles are simulated explicitly and ligand binding and unbinding is within the grand canonical ensemble . nod - wyman - changeux with appropriate binding free energ the open and closed ensembles a the two domains of cam s structural compatibility with the ligand

ion of the p in this paper , structural origins of binding affinity and of binding two ca@xmath0ions lmodulin ( cam ) through simple coarse - grained open and closed conformational ensembles are simulated explicitly and ligand binding and unbinding is within the grand canonical ensemble . nod - wyman - changeux with appropriate binding free energ the open and closed ensembles a ccurately describes the simulated the two domains of cam c - terminal domain n - terminal domain s structural compatibility with the ligand as well as the

interactions between a protein and a ligand are often accompanied by a redistribution of the population of thermally accessible conformations . this dynamic response of the protein s functional energy landscape enables a protein to modulate binding affinities and control binding sensitivity to ligand concentration . in this paper , we investigate the structural origins of binding affinity and allosteric cooperativity of binding two ca@xmath0ions to each domain of calmodulin ( cam ) through simulations of a simple coarse - grained model . in this model , the protein s conformational transitions between open and closed conformational ensembles are simulated explicitly and ligand binding and unbinding is treated implicitly within the grand canonical ensemble . ligand binding is cooperative because the binding sites are coupled through a shift in the dominant conformational ensemble upon binding . the classic monod - wyman - changeux model of allostery with appropriate binding free energy to the open and closed ensembles accurately describes the simulated binding thermodynamics . the simulations predict that the two domains of cam have distinct binding affinity and cooperativity . in particular , c - terminal domain binds ca@xmath0with higher affinity and greater cooperativity than the n - terminal domain . from a structural point of view , the affinity of an individual binding loop depends sensitively on the loop s structural compatibility with the ligand in the bound ensemble , as well as the conformational flexibility of the binding site in the unbound ensemble .

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