Alpha blocking and 1/fβ spectral scaling in resting EEG can be accounted for by a sum of damped alpha band oscillatory processes

The dynamical and physiological basis of alpha band activity and 1/f^β noise in the EEG are the subject of continued speculation. Here we conjecture, on the basis of empirical data analysis, that both of these features may be economically accounted for through a single process if the resting EEG is conceived of being the sum of multiple stochastically perturbed alpha band damped linear oscillators with a distribution of dampings (relaxation rates). The modulation of alpha-band and 1/f^β noise activity by changes in damping is explored in eyes closed (EC) and eyes open (EO) resting state EEG. We aim to estimate the distribution of dampings by solving an inverse problem applied to EEG power spectra. The characteristics of the damping distribution are examined across subjects, sensors and recording condition (EC/EO). We find that there are robust changes in the damping distribution between EC and EO recording conditions across participants. The estimated damping distributions are found to be predominantly bimodal, with the number and position of the modes related to the sharpness of the alpha resonance and the scaling (β) of the power spectrum (1/f^β). The results suggest that there exists an intimate relationship between resting state alpha activity and 1/f^β noise with changes in both governed by changes to the damping of the underlying alpha oscillatory processes. In particular, alpha-blocking is observed to be the result of the most weakly damped distribution mode becoming more heavily damped. The results suggest a novel way of characterizing resting EEG power spectra and provides new insight into the central role that damped alpha-band activity may play in characterising the spatio-temporal features of resting state EEG.     

Singular behavior of slow dynamics of single excitable cells

In various kinds of cultured cells, it has been reported that the membrane potential exhibits fluctuations with long-term correlations, although the underlying mechanism remains to be elucidated. A cardiac muscle cell culture serves as an excellent experimental system to investigate this phenomenon because timings of excitations can be determined over an extended time period in a noninvasive manner through visualization of contractions, although the properties of beat-timing fluctuations of cardiac muscle cells at the single-cell level remains to be fully clarified. In this article, we report on our investigation of spontaneous contractions of cultured rat cardiac muscle cells at the single-cell level. It was found that single cells exhibit several typical temporal patterns of contractions and spontaneous transitions among them. Detrended fluctuation analysis on the time series of interbeat intervals revealed the presence of 1/f^β noise at sufficiently large timescales. Furthermore, multifractality was also found in the time series of interbeat intervals. These experimental trends were successfully explained using a simple mathematical model, incorporating correlated noise into ionic currents. From these findings, it was established that singular fluctuations accompanying 1/f^β noise and multifractality are intrinsic properties of single cardiac muscle cells.     

Power spectra of extinction in the fossil record

Recent Fourier analyses of fossil extinction data have indicated that the power spectrum of extinction during the Phanerozoic may take the form of 1/f noise, a result which, it has been suggested, could be indicative of the presence of `critical dynamics'' in the processes giving rise to extinction. In this paper we examine extinction power spectra in some detail, using family-level data from two widely available compilations. We find that although the average form of the power spectrum roughly obeys the 1/f law, the spectrum can be represented more accurately by dividing it into two regimes: a low-frequency one which is well fit by an exponential, and a high-frequency one in which it follows a power law with a 1/f² form. We give explanations for the occurrence of each of these behaviours and for the position of the crossover between them.     

Quantification of emotion by nonlinear analysis of the chaotic dynamics of electroencephalograms during perception of 1/f music

The goal of this study is to quantify and determine the way in which the emotional response to music is reflected in the electrical activities of the brain. When the power spectrum of sequences of musical notes is inversely proportional to the frequency on a log-log plot, we call it 1/f music. According to previous research, most listeners agree that 1/f music is much more pleasing than white (1/f ⁰) or brown (1/f ²) music. Based on these studies, we used nonlinear methods to investigate the chaotic dynamics of electroencephalograms (EEGs) elicited by computer-generated 1/f music, white music, and brown music. In this analysis, we used the correlation dimension and the largest Lyapunov exponent as measures of complexity and chaos. We developed a new method that is strikingly faster and more accurate than other algorithms for calculating the nonlinear invariant measures from limited noisy data. At the right temporal lobe, 1/f music elicited lower values of both the correlation dimension and the largest Lyapunov exponent than white or brown music. We observed that brains which feel more pleased show decreased chaotic electrophysiological behavior. By observing that the nonlinear invariant measures for the 1/f distribution of the rhythm with the melody kept constant are lower than those for the 1/f distribution of melody with the rhythm kept constant, we could conclude that the rhythm variations contribute much more to a pleasing response to music than the melody variations do. These results support the assumption that chaos plays an important role in brain function, especially emotion. Received: 30 December 1996 / Accepted in revised form: 18 December 1997     

Tumor-initiating cells are not enriched in cisplatin-surviving BRCA1;p53-deficient mammary tumor cells in vivo

Although many breast cancers respond to chemotherapy or hormonal therapy, lack of tumor eradication is a central clinical problem preceding the development of drug resistant tumors. Using the K14cre;Brca1^F5-13/F5-13;p53^F2-10/F2-10mouse model for hereditary breast cancer, we have previously studied responses of mammary tumors generated in to clinically relevant anti-cancer drugs, including cisplatin. The BRCA1- and p53-deficient tumors generated in this model are hypersensitive to cisplatin and never become resistant to this agent due to the large, irreversible deletion in Brca1. We show here that even dose-dense treatment with a maximum tolerated dose of cisplatin does not result in complete tumor eradication. To explain this result we have addressed the hypothesis that the lack of eradication of drug-sensitive tumors is due to increased in vivo chemotherapy resistance of tumor-initiating cells (TICs). Using the CD24 and CD49f cell surface markers which detect normal mouse mammary stem cells, we have identified tumor-initiating cells in BRCA1- and p53-deficient tumors. In addition to the "OLE_LINK14">Lin^-/CD24⁺/CD49f⁺ subpopulation, we show that a larger population of Lin^-/CD24⁺/CD49f^- cells also has tumor-initiating capability in at least two serial orthotopic transplantations, suggesting that these are not more differentiated transit-amplifying cells. However, we did not find an enrichment of TICs in cisplatin-treated tumor remnants. We conclude that in this model the tolerance of the cisplatin-surviving cells cannot be attributed to special biochemical defense mechanisms of TICs.

     

Membrane potential fluctuations in <Emphasis Type="Italic">Chara australis</Emphasis>: a characteristic signature of high external sodium

We have studied fluctuations in membrane PD in Chara australis at frequencies between 1 and 500 mHz, by classical noise analysis and by inspection of the PD time-course. The former shows (1) a quasi-Lorentzian (1/f ²) rise of noise power as frequency falls, and (2) a marked increase in noise power when the cell is exposed to high salinity (Chara australis is a salt-sensitive species). The latter shows that, as well as initiating depolarization, exposure to 50 mM Na as either chloride or sulfate usually initiates a continuous but random series of small depolarizations which gives rise to the increase in noise and whose mechanism is discussed.     

Noise analysis and relaxation experiments of transport of hydrophobic anions across lipid membranes at equilibrium and nonequilibrium

Under equilibrium and nonequilibnum steady-stale conditions the spectral intensity of current noise S_J(f) generated by the transport of hydrophobic unions across lipid bilayer membranes was investigated. The experimental results were compared with different reaction models S_J(f) showed a characteristic increase proportional to f² between frequency-independent tails at low and high frequencies. This gradient was found to be independent of applied voltage which indicates the contribution of a single voltage-dependent reaction step of ion translocation across the membrane From the shape of S_J(f) at low frequencies the rate constant of ion desorption from the membrane into the aqueous phase could be estimated. Unambiguous evidence for the application of a general model, which includes the coupling of slow ion diffusion in the aqueous phase to ion adsorption/desorption at the membrane interface, could not be obtained from the low-frequency shape of S_J(f). The shot noise of this ion transport determines the amplitude of S_J(f) at high frequencies which decreases with increasing voltage applied. Analysis of voltage-jump current-relaxation experiments and of current noise carried cut on one membrane yielded significant differences of the derived ion partition coefficient. This deviation is qualitatively described on the basis of incomplete reaction steps.     

Fgfr1 Inactivation in the Mouse Telencephalon Results in Impaired Maturation of Interneurons Expressing Parvalbumin

Fibroblast growth factors (Fgfs) and their receptors (Fgfr) are expressed in the developing and adult CNS. Previous studies demonstrated a decrease in cortical interneurons and locomotor hyperactivity in mice with a conditional Fgfr1 deletion generated in radial glial cells during midneurogenesis (Fgfr1^f/f;hGfapCre+). Here, we report earlier and more extensive inactivation of Fgfr1 in neuroepithelial cells of the CNS (Fgfr1^f/f;NesCre+). Similar to findings in Fgfr1^f/f;hGfapCre+ mice, parvalbumin positive (PV+) cortical interneurons are also decreased in the neocortex of Fgfr1f/f;NesCre+ mice when compared to control littermates (Fgfr1f/f). Fgfr1f/f;NesCre+ embryos do not differ from controls in the initial specification of GABAergic cells in the ganglionic eminence (GE) as assessed by in situ hybridization for Dlx2, Mash1 and Nkx2. Equal numbers of GABAergic neuron precursors genetically labeled with green fluorescent protein (GFP) were observed at P0 in Fgfr1^f/f;hGfapCre+;Gad1-GFP mutant mice. However, fewer GFP+ and GFP+/PV+ interneurons were observed in these mutants at adulthood, indicating that a decrease in cortical interneuron markers is occurring postnatally. Fgfr1 is expressed in cortical astrocytes in the postnatal brain. To test whether the astrocytes of mice lacking Fgfr1 are less capable of supporting interneurons, we co-cultured wild type Gad1-GFP+ interneuron precursors isolated from the medial GE (MGE) with astrocytes from Fgfr1f/f control or Fgfr1^f/f;hGfapCre+ mice. Interneurons grown on Fgfr1 deficient astrocytes had small soma size and fewer neurites per cell, but no differences in cell survival. Decreased soma size of Gad67 immunopositive interneurons was also observed in the cortex of adult Fgfr1^f/f;NesCre+ mice. Our data indicate that astrocytes from Fgfr1 mutants are impaired in supporting the maturation of cortical GABAergic neurons in the postnatal period. This model may elucidate potential mechanisms of impaired PV interneuron maturation relevant to neuropsychiatric disorders that develop in childhood and adolescence.     

Simulated power spectral density (PSD) of background electrocorticogram (ECoG)

The ECoG background activity of cerebral cortex in states of rest and slow wave sleep resembles broadband noise. The power spectral density (PSD) then may often conform to a power-law distribution: a straight line in coordinates of log power vs. log frequency. The exponent, x, of the distribution, 1/f^x, ranges between 2 and 4. These findings are explained with a model of the neural source of the background activity in mutual excitation among pyramidal cells. The dendritic response of a population of interactive excitatory neurons to an impulse input is a rapid exponential rise and a slow exponential decay, which can be fitted with the sum of two exponential terms. When that function is convolved as the kernel with pulses from a Poisson process and summed, the resulting “brown” or “black noise conforms to the ECoG time series and the PSD in rest and sleep. The PSD slope is dependent on the rate of rise. The variation in the observed slope is attributed to variation in the level of the background activity that is homeostatically regulated by the refractory periods of the excitatory neurons. Departures in behavior from rest and sleep to action are accompanied by local peaks in the PSD, which manifest emergent nonrandom structure in the ECoG, and which prevent reliable estimation of the 1/f^x exponents in active states. We conclude that the resting ECoG truly is low-dimensional noise, and that the resting state is an optimal starting point for defining and measuring both artifactual and physiological structures emergent in the activated ECoG.     

Mammalian Fbh1 is important to restore normal mitotic progression following decatenation stress

We have addressed the role of the F-box helicase 1 (Fbh1) protein during genome maintenance in mammalian cells. For this, we generated two mouse embryonic stem cell lines deficient for Fbh1: one with a homozygous deletion of the N-terminal F-box domain (Fbh1^f/f), and the other with a homozygous disruption (Fbh1^?/?). Consistent with previous reports of Fbh1-deficiency in vertebrate cells, we found that Fbh1^?/? cells show a moderate increase in Rad51 localization to DNA damage, but no clear defect in chromosome break repair. In contrast, we found that Fbh1^f/f cells show a decrease in Rad51 localization to DNA damage and increased cytoplasmic localization of Rad51. However, these Fbh1^f/f cells show no clear defects in chromosome break repair. Since some Rad51 partners and F-box-associated proteins (Skp1-Cul1) have been implicated in progression through mitosis, we considered whether Fbh1 might play a role in this process. To test this hypothesis, we disrupted mitosis using catalytic topoisomerase II inhibitors (bisdioxopiperazines), which inhibit chromosome decatenation. We found that both Fbh1^f/f and Fbh1^?/? cells show hypersensitivity to topoisomerase II catalytic inhibitors, even though the degree of decatenation stress was not affected. Furthermore, following topoisomerase II catalytic inhibition, both Fbh1-deficient cell lines show substantial defects in anaphase separation of chromosomes. These results indicate that Fbh1 is important for restoration of normal mitotic progression following decatenation stress.     

Osmotic water permeability of plasma and vacuolar membranes in protoplasts II. Theoretical basis

Water permeability of the plasma membrane (PM) and the vacuolar membrane (VM) is important for intracellular and transcellular water movement in plants, because mature plant cells have large central vacuoles. We have developed a new method for measuring the osmotic water permeability of the PM and VM (P _f1 and P _f2, respectively) in individual plant cells. Here, the theoretical basis and procedure of the method are discussed. Protoplasts isolated from higher plant tissues are used to measure P _f1 and P _f2. Because of the semi-permeability (selective permeability) of cellular membranes, protoplasts swell or shrink under hypotonic or hypertonic conditions. A theoretical three-compartment model is presented for simulating time-dependent volume changes in the vacuolar and cytoplasmic spaces in a protoplast during osmotic excursions. The model describes the theoretical relationships between P _f1, P _f2 and the bulk osmotic water permeability of protoplasts (P _f(bulk)). The procedure for measuring the osmotic water permeability is: (1) P _f(bulk) is calculated from the time when half of the total change in protoplast volume is completed, by assuming that the protoplast has a single barrier to water movement across it (two-compartment model); (2) P _f2 of vacuoles isolated from protoplasts is obtained in the same manner; and (3) P _f1 is determined from P _f(bulk) and P _f2 according to the three-compartment model. The theoretical relationship between P _fl (m s⁻¹) and L _Pl (hydraulic conductivity, l=1, 2) (m s⁻¹ Pa⁻¹) is also discussed. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorised users. Tsuneo Kuwagata and Mari Murai-Hatano contributed equally to the paper.     

1/f noise in black lipid membranes induced by ionic channels formed by chemically dimerized gramicidin A

Summary The noise behavior of lipid bilayer membranes, doped with a chemically dimerized gramicidin A, was investigated. In contrast to normal gramicidin A, which generates a Lorentzian type power spectrum due to the formation and disappearance of conducting dimers, the current power spectrum densityS _m (f) obtained with this gramicidin A derivative showed over several orders of magnitude a clear 1/f behavior. The intensity of this 1/f component was analyzed as a function of the membrane-applied voltage, membrane resistance, electrolyte concentration, and composition. The relationship between the meansquare fluctuation in current and the membrane current mean value was found to follow Hooge's equation, i.e., I ²=I _m ² /N f whereN is the number of channels and is a constant equal to 1.0×10^–2. It is suggested that a 1/f type noise was observed because the chemically dimerized form of gramicidin A produces long lasting cation selective channels.     

A novel mouse model for liver metastasis of prostate cancer reveals dynamic tumour‐immune cell communication

ObjectivesIn contrast to extensive studies on bone metastasis in advanced prostate cancer (PCa), liver metastasis has been under‐researched so far. In order to decipher molecular and cellular mechanisms underpinning liver metastasis of advanced PCa, we develop a rapid and immune sufficient mouse model for liver metastasis of PCa via orthotopic injection of organoids from PbCre⁺; rb1^f/f;p53^f/f mice.Materials and MethodsPbCre⁺;rb1^f/f;p53^f/f and PbCre⁺;pten^f/f;p53^f/f mice were used to generate PCa organoid cultures in vitro. Immune sufficient liver metastasis models were established via orthotopic transplantation of organoids into the prostate of C57BL/6 mice. Immunofluorescent and immunohistochemical staining were performed to characterize the lineage profile in primary tumour and organoid‐derived tumour (ODT). The growth of niche‐labelling reporter infected ODT can be visualized by bioluminescent imaging system. Immune cells that communicated with tumour cells in the liver metastatic niche were determined by flow cytometry.ResultsA PCa liver metastasis model with full penetrance is established in immune‐intact mouse. This model reconstitutes the histological and lineage features of original tumours and reveals dynamic tumour‐immune cell communication in liver metastatic foci. Our results suggest that a lack of CD8⁺ T cell and an enrichment of CD163⁺ M2‐like macrophage as well as PD1⁺CD4⁺ T cell contribute to an immuno‐suppressive microenvironment of PCa liver metastasis.ConclusionsOur model can be served as a reliable tool for analysis of the molecular pathogenesis and tumour‐immune cell crosstalk in liver metastasis of PCa, and might be used as a valuable in vivo model for therapy development.     

Tgfbr2 is required for development of the skull vault

Transforming growth factor β (TGFβ) is known to play important roles in multiple developmental processes. One of the main functions is in skeletal development. Our previous studies demonstrated that loss of Tgfbr2 in Prx1Cre-expressing limb mesenchyme results in defects in the long bones and joints of mice. Here we show that loss of Tgfbr2 also results in defects in the development of the skull vault indicating Tgfbr2 has a critical role in intramembranous bone formation as well as endochondral bone formation. Mutant mice did not survive after birth and demonstrated an open skull. The first signs of skull defects were observed at E14.5 day. Prx1Cre⁺/Tgfbr2^f/f embryos showed significantly reduced cell proliferation in the developing mesenchyme of the skull by E14.5 day without any detectable alteration in apoptosis suggesting that reduced cell proliferation in Prx1Cre⁺/Tgfbr2^f/f embryos was at least partially responsible for the defects observed. Immunofluorescent staining showed a significant reduction in the expression of Runx2/Cbfa1 and Osterix/Sp7 in Prx1Cre⁺/Tgfbr2^f/f embryos suggesting that osteoblast differentiation was also altered in Prx1Cre⁺/Tgfbr2^f/f embryos. To distinguish between the effects of losing Tgfbr2 on mesenchymal proliferation versus osteoblast differentiation, osteoprogenitor cells from the skulls of Tgfbr2^f/f embryos were cultured under conditions of high cell density and Tgfbr2 was deleted from the cells using Adeno-Cre virus. RT-PCR analysis showed that the mRNA level of Runx2 and Osterix as well as Dlx5 and Msx2 were down-regulated in Tgfbr2-deleted cultures compared to control cultures indicating that Tgfbr2 regulates osteoblast differentiation independent of regulating proliferation. Together, these results suggest that Tgfbr2 is required for normal development of the skull.     

Energy Detection Based on Undecimated Discrete Wavelet Transform and Its Application in Magnetic Anomaly Detection

Magnetic anomaly detection (MAD) is a passive approach for detection of a ferromagnetic target, and its performance is often limited by external noises. In consideration of one major noise source is the fractal noise (or called 1/f noise) with a power spectral density of 1/f^a (0<a<2), which is non-stationary, self-similarity and long-range correlation. Meanwhile the orthonormal wavelet decomposition can play the role of a Karhunen-Loève-type expansion to the 1/f-type signal by its decorrelation abilities, an effective energy detection method based on undecimated discrete wavelet transform (UDWT) is proposed in this paper. Firstly, the foundations of magnetic anomaly detection and UDWT are introduced in brief, while a possible detection system based on giant magneto-impedance (GMI) magnetic sensor is also given out. Then our proposed energy detection based on UDWT is described in detail, and the probabilities of false alarm and detection for given the detection threshold in theory are presented. It is noticeable that no a priori assumptions regarding the ferromagnetic target or the magnetic noise probability are necessary for our method, and different from the discrete wavelet transform (DWT), the UDWT is shift invariant. Finally, some simulations are performed and the results show that the detection performance of our proposed detector is better than that of the conventional energy detector even utilized in the Gaussian white noise, especially when the spectral parameter α is less than 1.0. In addition, a real-world experiment was done to demonstrate the advantages of the proposed method.     

FLEXURAL STIFFNESS AND MODULUS OF ELASTICITY OF FLOWER STALKS FROM ALLIUM SATIVUM AS MEASURED BY MULTIPLE RESONANCE FREQUENCY SPECTRA

Multiple resonance frequency spectra (MRFS) provide a rapid and repeatable method for determining the flexural stiffness and modulus of elasticity, E, of segments of plant stems and leaves. Each resonance frequency in a spectrum can be used to compute E, and removal of the distal portion of an organ produces characteristic shifts in spectra dependent upon the geometry of an organ. Hence, MRFS can be used to quantitatively determine the extent to which a particular leaf or stem morphology can be modelled according to beam theory. MRFS of flower stalks of Allium sativum L. are presented to illustrate the technique. The fundamental, f_1, and higher resonance frequencies, f₂ … f_n, of stems and the ratios of f₂/f₁ f₃/f_1, and f₃/f₂ increase as stalk length is reduced by clipping. The magnitudes of these shifts conform to those predicted from the MRFS of a linearly tapered beam. Morphometric data confirm this geometry in 21 flower stalks. Based on this model, the average modulus equals 3.71 × 10⁸ ± 0.32 × 10⁸ N/m², which compares favorably with values of E determined by static loading (3.55 × 10⁸ ± 0.22 × 10⁸ N/m²) and is in general agreement with ultrasonic measurements (3.8 × 10⁸ to 4.4 × 10⁸ N/m²). Data indicate that determinations of E from a single resonance frequency are suspect, since each resonance frequency yields slightly different values for E. Statistical evaluations from all the frequencies within a MRFS are more reliable for determining E and testing the appropriateness of beam theory to evaluate the biomechanical properties of plants.     

Noise analysis of the K+ current through the apical membrane ofNecturus gallbladder

Summary Current noise power spectra of the voltage-clamped (V=0)Necturus gallbladder, exposed to NaCl-Ringer's on both sides contained a relaxation noise component, which overlapped with a 1/f noise component, with being about 2. Substitution of all Na⁺ by K⁺ on either the serosal or mucosal side increased the relaxation as well as the 1/f noise component considerably. InNecturus gallbladder both noise components are reduced by addition of 10mm 2,4,6-triaminopyrimidine (TAP) or 5mm of tetraethylammonium (TEA⁺) added to ification of the mucosal solution to pH 5 and lower. Fivemm of tetraethylammonium (TEA⁺) added to the mucosal solution, abolished K⁺ relaxation noise and decreased the 1/f noise component. Applying a Cs⁺ concentration gradient across the epithelium did not yield relaxation noise. However, if Rb⁺ was substituted for all Na⁺ on one side, a Lorentzian noise component appeared in the spectrum. Its plateau was smaller than with KCl-Ringer's on the respective side. These data confirm the existence of fluctuating K⁺ channels in the apical membrane of theNecturus gallbladder. Furthermore it can be concluded that these channels have the permeability sequence K⁺>Rb⁺>Sc⁺. The inhibition of the fluctuations by mucosal acidification indicates the existence of acidic sites in the channel. The single-channel conductance was estimated to be between 6.5 and 40 pS.     

Tumor-initiating cells are not enriched in cisplatin-surviving BRCA1;p53-deficient mammary tumor cells in vivo

Although many breast cancers respond to chemotherapy or hormonal therapy, lack of tumor eradication is a central clinical problem preceding the development of drug-resistant tumors. Using the K14cre;Brca1^{F5–13/F5–13};p53^{F2–10/F2–10} mouse model for hereditary breast cancer, we have previously studied responses of mammary tumors to clinically relevant anti-cancer drugs, including cisplatin. The BRCA1- and p53-deficient tumors generated in this model are hypersensitive to cisplatin and never become resistant to this agent due to the large, irreversible deletion in Brca1. We show here that even dose-dense treatment with a maximum tolerated dose of cisplatin does not result in complete tumor eradication. To explain this result we have addressed the hypothesis that the lack of eradication of drug-sensitive tumors is due to increased in vivo chemotherapy resistance of tumor-initiating cells (TICs). Using the CD24 and CD49f cell surface markers that detect normal mouse mammary stem cells, we have identified tumor-initiating cells in BRCA1- and p53-deficient tumors. In addition to the Lin⁻/CD24⁺/CD49f⁺ subpopulation, we show that a larger population of Lin⁻/CD24⁺/CD49f cells also has tumor-initiating capability in at least two serial orthotopic transplantations, suggesting that these are not more differentiated transit-amplifying cells. However, we did not find an enrichment of TICs in cisplatin-treated tumor remnants. We conclude that in this model the tolerance of the cisplatin-surviving cells cannot be attributed to special biochemical defense mechanisms of TICs.Key words: tumor-initiating cells, cisplatin, genetically-engineered mouse model, BRCA1, breast cancer