- Open Access
An integrated multidisciplinary model describing initiation of cancer and the Warburg hypothesis
© Rietman et al.; licensee BioMed Central Ltd. 2013
Received: 13 February 2013
Accepted: 29 May 2013
Published: 10 June 2013
In this paper we propose a chemical physics mechanism for the initiation of the glycolytic switch commonly known as the Warburg hypothesis, whereby glycolytic activity terminating in lactate continues even in well-oxygenated cells. We show that this may result in cancer via mitotic failure, recasting the current conception of the Warburg effect as a metabolic dysregulation consequent to cancer, to a biophysical defect that may contribute to cancer initiation.
Our model is based on analogs of thermodynamic concepts that tie non-equilibrium fluid dynamics ultimately to metabolic imbalance, disrupted microtubule dynamics, and finally, genomic instability, from which cancers can arise. Specifically, we discuss how an analog of non-equilibrium Rayleigh-Benard convection can result in glycolytic oscillations and cause a cell to become locked into a higher-entropy state characteristic of cancer.
A quantitative model is presented that attributes the well-known Warburg effect to a biophysical mechanism driven by a convective disturbance in the cell. Contrary to current understanding, this effect may precipitate cancer development, rather than follow from it, providing new insights into carcinogenesis, cancer treatment, and prevention.
The metabolic shift from aerobic to anaerobic glucose biochemical energy processing by cells is strongly correlated with the transition to cancer, or as some have come to characterize the process, a reversion to a more primitive and competitive level of cellular existence (Warburg , Szent-Gyorgyi ), which may still possess some rudimentary cooperative elements e.g. early metazoans (Davies and Lineweaver ). Our focus in this manuscript is to develop a molecular physics model based on non-equilibrium thermodynamics to quantitatively describe that process. By better understanding this transition we should be able to not only address cancer more effectively but also other metabolic diseases including mitochondrial diseases (e.g. ) and diseases of proton pumps (e.g. ). This modeling approach may also shed some light on the relationship between the Warburg effect for cancer and the so-called inverse-Warburg effect  for neurological diseases e.g. Alzheimer’s disease .
where the symbols E, S, ES, P represent the enzyme, substrate, enzyme-substrate complex, and reaction product, respectively. The coefficients labeled by k’s represent forward, reverse and enzyme-substrate decomposition rate constants as indicated by their subscripts. Obviously, if there is a huge abundance of S and limited amount of E, the reaction is rate limited by the concentration of E. But if the cell is malfunctioning and producing an excess of E when an abundance of S is present, then the cell will increase the P concentration by massively parallel reactions. This is governed by the well-known Michaelis-Menten reaction kinetics of saturable chemical reactions . This effect is also described by the Le Chatelier principle of reaction dynamics . It states that chemical reactions move forward or backward so as to reduce excesses in the quantity of reactants or products, respectively, introduced into in the reaction vicinity.
We argue that non-equilibrium thermodynamics is a driving force for the ultimate transition of a cell from the normal to the cancer state, and that the first step in the process is an increased operation of the cytoplasmic glucose processing machinery due to a non-equilibrium mechanism analogous to Rayleigh-Benard convection (Figure 1) [16, 17]. Our proposed scheme that describes the development of the cancer phenotype at a cellular level is essentially a biophysics model, which should clearly be considered in parallel with more biochemical schemes [18–22]. We begin by reviewing some relevant physics of nonlinear dynamics and thermodynamics.
Most of the remainder of the paper will be devoted to present arguments and analyses aimed at supporting the use of Equation (4) in the context of the Warburg effect.
Several in vitro and in vivo experiments have already demonstrated that an increase in extracellular glucose [30, 31] or lactic acid  concentration can lead to increased tumorigenesis. Further, hypoxia has been linked to causing the metabolic shift to glycolysis, and to cause malignant progression, with much experimental evidence [33–38].
Goldbeter  discusses at length glycolytic oscillations, and uses a series of differential equations to model the dynamics for some of the chemical species involved in the reactions. The observed oscillations come about as a result of the fact that there is a delay in manufacture of the intermediate nicotinamide adenine dinucleotide (NADH) and the fact that there is a finite number of molecular components available for the glycolytic processing. The cycle time has been observed in S. carsbegensis to be about 5 minutes using fluorescence of the glycolytic intermediate, NADH . More interestingly, Hess et al.  measured the oscillation frequency for different doses of fructose or glucose as input. As shown in Figure 3, as the concentration of the glucose (or fructose) increases, the period of oscillation decreases. This can only come about from increased concentration in the number of enzymes to participate in the reactions. As the number of enzymes and the number of molecular components increase, so does the entropy because the increase in numbers enables more ways to dissipate free energy, in this case represented as chemical potential of a glucose gradient . As the concentration increases the cycle time decreases indicating a more efficient processing of glucose per time unit.
More recently, Aromolaran et al.  describe, and show experimentally, glycolytically generated adenosine triphosphate (ATP) and Ca2+ waves propagating through a cell from application of glycolytic inhibitors focally injected from a glass pipette with a 1.5 micron diameter tip. The authors discover that glycolytically generated ATP is likely a key modulator of Ca2+ homeostasis. Of course, this has direct effect on the permeability of the mitochondrial wall, as shown by Yang et al.  who describe glycolytic oscillation depolarizing the mitochondrial membrane. The authors describe a model based on the logistic function showing there is a region where the oscillations are “too rapid for observation.” Though they do not use the term ‘chaos’, this is likely a chaotic state observed in the logistic functions and other “chaotic dynamical functions.”
In the case of Rayleigh-Benard convection rolls, as shown in Figure 2, the rolls can be modeled with a sine-circle map, for example, θi+1 = f(θ i ) where the function is periodic in the angle [44, 45]. There are some theoretical arguments for the glucose oscillators being embedded in the cell membrane. Demetrius et al.  argue that the enzymes’ concentration would oscillate due to periodicities in the redox potential and the result could be modeled as harmonic oscillators. Further, Tyner et al.  measure electrical gradients in the cell, and we show that a relevant protein, glyceraldehyde 3-phosphate dehydrogenase (GAPDH) associated with glucose processing in the cytoplasm accumulate at the membrane thus showing experimental support for our hypothesis that molecular oscillators accumulate at boundaries. Lastly, Pokorny  suggests Duffing oscillators  as a potential model of oscillatory states of a cell. In the following subsections we first provide some experimental validation for the differences in GAPDH localization. Then we follow that with some simplistic analytical modeling to show phase locking of oscillators potentially resulting chaos and disruptions of mitochondria.
Experimental validation for GAPDH distribution
These predictions of GAPDH distribution were tested by using antibodies against GAPDH in normal human mammary epithelial cells (HMECs) under normal culture conditions, purchased from Life technologies.
These clear experimental results support our conjecture that there is an increase in the glycolytic processing as a result of an external glucose gradient. We now describe some analytical models outlining the phase locking of the glucose oscillators and the implications.
Sine circle Map modeling
There has been research showing a quasi-periodic route to chaos in biochemical systems [21, 39, 50, 51]. The biochemical system, in these cases, glycolysis, starts at some given frequency and as external glucose is pulsed, starting at a frequency similar to the glycolysis value, the biochemical reactions begin to phase lock with the external pulses and first results in increased amplitude followed by period doubling as the external glucose pulse frequency increases. Finally, at a stochastic external glucose pulse frequency, the observed internal pulses are only about 3–4 X higher than the original glucose oscillations, but the actual sine wave appears as if there is a frequency and/or amplitude modulation. The oscillations observed in the cell extracts are not chaotic. Analytical models of these biochemical systems [52, 53], based on differential equations, support a periodic-doubling route to chaos, though in the real biochemical systems chaos is rarely observed. This is likely due to the fact that a cell is not just “a bag of chemicals” but really a hybrid between a chemical network and molecular nanomachines. The equations of dynamics also apply to mechanical systems, yet real machines are not capable of being driven into chaotic state, because of friction and physical constraints in the machine. Similarly, nanomachines are not likely able to be driven into chaotic states because of secondary bonding effects, e.g. van der Waals forces, and steric hindrance and potential energy surfaces .
In the above, cell-free extract, experiments, the investigators monitored NADH to observe the oscillations in the range of 0.002 to 0.005 Hz. Yang, et al.  did experiments on tissue models of rabbit ventricular myocytes and observed adenosine diphosphate (ADP) oscillations. Of course, when combining these experimental observations it must be remembered that there are 2 NADH molecules and 4 molecules of ADP per glucose molecule in the glycolysis reaction. Yang et al.  observed oscillation increases from about 0.02 to 0.067 Hz; but like the cell-free experiments, they did not observe chaos. Since chaos has been observed in real-world chemical systems , the lack of observed chaos in these biochemical and tissue experiments can be explained as follows.
In the case of tissue-based experiments, the oscillators are operating at a fixed frequency all driven by chemical kinetics and Le Chatelier’s principle. The observation of increase in frequency is likely the mean-field effect from an increase in the numbers of oscillators and this would also account for the observed effect on decrease of energy-density-rate as the concentration increases. This means the cell is adapting to the excess external glucose by producing more glycolysis oscillators. As will be shown shortly, these oscillators can phase lock with each other and produce oscillations at a frequency about 2 or 3 times higher.
In the case of the cell-free extract, it is not likely that more oscillator-components are being produced on demand, so Le Chatelier’s principle will not be modulating the overall molecular network. Instead, the existing molecular components for oscillator construction are fixed, and more in situ oscillators may form because of the excess glucose. Again these oscillators can phase lock and produce the observed frequencies.
Kaneko  discusses many options of coupling the oscillators. In all cases the phase diagram contains regions of fixed points, oscillations, and undefined or chaos. This is to be expected from the bifurcation of the function as shown in Figure 6. The hard boundary in our phase diagram at κ = 2 is to be expected as shown in Figure 7. The fact that the oscillations begin prior to 2.5 is due to the fact that the thresholding and signal transfer changes the dynamics. The regions in the phase diagram labeled n are for n-cycle, or strange attractor .
In mapping this phase diagram to glycolytic oscillations we would not expect all threshold values to be valid. If we set the threshold to 0.5 then the bifurcation parameter represents the glucose dosage and we have 2 cycles over a small range until the 4-cycles followed by continued increase in the glucose (bifurcation parameter) results in n-cycles. A 4-cycle in this phase space would look like a doubled 2-cycle, amplitude modulated glycolytic oscillator; and an n-cycle would look like an amplitude or frequency modulated 2-cycle or 4-cycle. These types of modulations have been observed by Hess et al.  and von Klitzing and Betz .
We now turn our attention to the mitochondria and explore the possible implications from glycolytic oscillations on mitochondrial stability. It is known that the glycolytic oscillations result in similar pH oscillations (e.g. Hess et al. ). But these oscillations are about π/2 out of phase. This has implications on the polarization of the mitochondrial membrane. The cell contains buffer mechanisms to minimize pH imbalance, but too much polarization of the mitochondrial membrane will cause the mitochondria to break down. The phase lag in pH can lead to a potential problem.
The ratio of V f /K m shows an actual phase transition at pH 7.5. The authors did not discuss the significance of this phase transition. Later work by Aromolaran et al.  showed waves of Ca2+ ions traversing the cell as a result of a localized ATP perturbation. These waves are able to traverse the entire cell within 30 seconds – far faster than diffusion. Other work by Ramanujand and Herman  show a nonlinear scaling of glucose metabolism in normal and cancer cells, where the scaling exponent is different for both types of cells. This is analogous to our observed Φ variation as a function of glucose. Lastly, Aon et al.  describe experiments on percolation and criticality  in mitochondrial networks of a cell. The authors used a local perturbation induced by a two-photon laser excitation. They observed a cell-wide transition to take place within 4 seconds resulting in depolarization of the majority of the mitochondria in the cell.
This depolarization of the mitochondria membrane also accompanies an ATP depletion. This can in turn effect the following reactions :
D-glucose + ATP → D-glucose-6-phosphate + ADP
D-fructose-6-phosphate + ATP → D-fructose-1,6-bisphosphate + ADP
1,3-bisphosphoglycerate + ADP → 3-phosphoglycerate + ATP
phosphoenolpyruvate + ADP → pyruvate + ATP
ATP is needed to maintain Ca2+. A lag in production of ATP, as the above reactions compete with other reactants and products in the overall molecular network, could induce changes in the cytoskeleton via pH effects on the growth dynamics of the microtubules.
amongst other reactions. Using Le Chatelier’s principle we can argue that forcing this reaction in the reverse direction by using 3-bromopyruvate will deplete the ATP and thus induce the cancer cell to enter into an apoptotic state. This type of behavior has in fact been reported by Ko et al.  and Mathupala et al. , who reported significant reduction in tumor volume in mice by treatment with 3-bromopyruvate.
The metabolic shift to glycolysis leads to acidosis, which subsequently results in an acidic extracellular pH . Gillies has documented an acidic extracellular environment in numerous tumors . Several studies link acidosis to genomic instability. Morita et al. show low pH leads to sister-chromatin exchanges and chromosomal aberrations [71, 72]. Brusick, Cifone, and Cipollaro report that low pH environments (~pH 6.5) caused genomic toxicity [73–75]. Several studies link the tumor environment, with hypoxia and low pH as inducing genomic instability by DNA repair activity being reduced , and enrichment for mismatch-repair deficient cells .
Thus, convincing evidence exists that a hypoxic and acidic environment will lead to genomic instability due to impairment of DNA repair processes.
In addition, Suresh  has reviewed the biomechanics of normal and cancer cells and shows that transformed cells routinely have altered deformability. This effect is likely due to the differences in the actin microfilaments – the major structural element of a cell [79, 80].
The cytoskeleton also consists of microtubules that have a bending stiffness 2.6 X 10-23 N m2 which is about 1000 times stiffer than actin filaments . Microtubules, unless stabilized by ligands or microtubule-associated protein, are in a constant dynamic instability process being polymerized and depolymerized with a half-life of about 2 minutes . This dynamic instability phenomenon has been mathematically modeled in detail by Sept et al. , and Bolterauer et al.  among others. The ends of actin filaments and microtubules are caped with ATP and guanosine triphosphate (GTP), respectively. GTP is created by the citric acid cycle in the mitochondria. Obviously, a mitochondria failure may reduce the concentration of ATP and GTP, if other systems do not compensate for the mitochondrial failure. A reduction in GTP results in a higher rate of depolymerization of microtubules  and a decrease in ATP concentration reduces the rate of growth of actin filaments . Too few microtubules and/or microtubules being too short to participate in proper spindle pole formation can lead to mitotic catastrophe and/or potentially lead to chromosome instability. Bakhoum et al.  and Thompson et al.  describe the mechanism for this instability. Persistent mis-oriented attachment of chromosomes to the spindle microtubules leads to severe chromosome segregation defects.
We have described an integrated system model for the progression of a healthy cell to a cancer state and some of the implications. The potentially aberrant state of the cell may start by an excess glucose or other nutrient external to the cell impacting the cell or by internal defects leading to metabolic enzyme redistribution processes. This excess nutrient is essentially a chemical potential difference between inside and outside of the cell creating stress. Through a process analogous to Rayleigh-Benard convection, stable molecular oscillators accumulate in the cytoplasm to exploit this chemical gradient. The continued activity of these oscillators results in mitochondrial destabilization, which may occur as a non-equilibrium phase transition. Once the mitochondria begin to perform aberrantly there will be a chemical imbalance in key components for microtubule assembly/disassembly. This imbalance is driven by Le Chatelier’s principle. The disruption in microtubule lengths and/or microtubule count will lead to chromosomal instability via kinetochore-microtubule dynamics finally leading to mitotic failure. In unlucky cases this will result in chromosome mis-segregation and cancer if mitotic catastrophe does not occur.
The above synthesis of ideas surrounding the subject of Warburg initiation, or the transition from aerobic glycolysis to anaerobic suggests not only an avenue for treatment but also an avenue for prevention of cancer.
We hypothesize that excess of glucose and sugar-like energy sources or metabolic enzyme abnormalities, through a non-equilibrium phase transition (a symmetry breaking phenomenon) analogous to the Rayleigh-Benard convection, may cause a cell to prefer to process this energy source using substrate glycolysis. Continued excess substrate glycolysis will cause further phase transitions to disrupt the mitochondria via depolarization and also disrupt microtubule dynamics. When a cell then passes through mitosis, the chance of mitotic failure is increased. When a cell enters mitotic failure, it may undergo an aneuploidy event [88, 89]. All this suggests that a low glycemic diet would lower the incidence of cancer, and may suggest a mechanism why metformin, which lowers blood glucose levels, is associated with improved outcomes in diabetic cancer patients [90, 91] and reduced risk of pancreatic cancer .
The above synthesis of ideas also supports targeting cells that have made the glycolytic switch. For instance, the work of Pedersen  and his colleagues (Ko et al. [69, 94]; Mathupala et al. ) have used 3-bromopyruvate to inhibit glyceraldehyde 3-phosphate dehydrogenase (GAPDH), which effectively inhibits glycolysis . In addition, 3-bromopyruvate may force, via Le Chatelier’s principle, some reverse reactions to essentially deprive the cancer cell of substrate-created ATP. This leaves the cell little choice except to enter apoptosis. We further hypothesize that a Br derivative of 3-phosphoglycerate would similarly, though perhaps not as energetically, and perhaps not as toxically, facilitate via Le Chatelier’s principle, a reverse reaction to deprive a cancer cell of ATP.
Further, since microtubule dynamics are dysregulated by glucose oscillations and its associated pH oscillations, we speculate that metronomic dosing of microtubule poisons (e.g. nocodazol, taxol, vinblastine) would be an effective treatment strategy for cancers.
In our list of “prescriptions” above many of these are already known or in use. These current practices are essentially “prediction” of our theory and were strictly based on biophysics with little detailed biochemical or cellular biochemistry being considered.
We thank Heiko Enderling for helpful discussions. We thank Eric J. Chaisson for discussion on the Phi parameter. DEF acknowledges funding from Alberta Innovates Health Solutions and the Alberta Cancer Foundation. JAT acknowledges funding from NSERC, the Allard Foundation, Alberta Advanced Education and Technology, the Canadian Breast Cancer Foundation and the Alberta Cancer Foundation. EAR, PH, and LH acknowledge grant number U54CA149233 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute. We thank Philip Winter for computer and software support.
- Warburg O: On the origin of cancer cells. Science. 1956, 123: 309-314. 10.1126/science.123.3191.309.View ArticlePubMedGoogle Scholar
- Szent-Györgyi A: The living state and cancer. Proc Nat Acad Sci USA. 1977, 74: 2844-2847. 10.1073/pnas.74.7.2844.PubMed CentralView ArticlePubMedGoogle Scholar
- Davies PCW, Lineweaver CH: Cancer tumors as Metazoa 1.0: tapping genes of ancient ancestors. Phys Biol. 2011, 8: 015001-10.1088/1478-3975/8/1/015001.PubMed CentralView ArticlePubMedGoogle Scholar
- Miceli MV, Jazwinski SM: Common and cell type-specific responses of human cells to mitochondrial dysfunction. Exp Cell Res. 2005, 302: 270-280. 10.1016/j.yexcr.2004.09.006.View ArticlePubMedGoogle Scholar
- Marino ML, Fais S, Djavaheri-Mergny M, Villa A, Meschini S, Lozupone F, Venturi G, Della Mina P, Pattingre S, Rivoltini L, et al: Proton pump inhibition induces autophagy as a survival mechanism following oxidative stress in human melanoma cells. Cell death & disease. 2010, 1: e87-10.1038/cddis.2010.67.View ArticleGoogle Scholar
- Demetrius LA, Simon DK: An inverse-Warburg effect and the origin of Alzheimer’s disease. Biogerontology. 2012, 13: 583-594. 10.1007/s10522-012-9403-6.View ArticlePubMedGoogle Scholar
- Bennett DA: Is there a link between cancer and Alzheimer disease?. Neurology. 2010, 75: 1216-1217.PubMedGoogle Scholar
- Kacser H, Burns JA: The control of flux. Symp Soc Exp Biol. 1973, 27: 65-104.PubMedGoogle Scholar
- Atkins PW: Physical Chemistry. 1986, New York: W. H. Freeman and CompanyGoogle Scholar
- Davies PC, Demetrius L, Tuszynski JA: Cancer as a dynamical phase transition. Theor Biol Med Model. 2011, 8: 30-10.1186/1742-4682-8-30.PubMed CentralView ArticlePubMedGoogle Scholar
- Regula CS, Pfeiffer JR, Berlin RD: Microtubule assembly and disassembly at alkaline pH. J Cell Biol. 1981, 89: 45-53. 10.1083/jcb.89.1.45.PubMed CentralView ArticlePubMedGoogle Scholar
- Gillies RJ, Raghunand N, Karczmar GS, Bhujwalla ZM: MRI of the tumor microenvironment. J Magn Reson Imaging. 2002, 16: 430-450. 10.1002/jmri.10181.View ArticlePubMedGoogle Scholar
- Reshkin SJ, Bellizzi A, Caldeira S, Albarani V, Malanchi I, Poignee M, Alunni-Fabbroni M, Casavola V, Tommasino M: Na+/H+ exchanger-dependent intracellular alkalinization is an early event in malignant transformation and plays an essential role in the development of subsequent transformation-associated phenotypes. FASEB journal : official publication of the Federation of American Societies for Experimental Biology. 2000, 14: 2185-2197. 10.1096/fj.00-0029com.View ArticleGoogle Scholar
- Stock C, Schwab A: Protons make tumor cells move like clockwork. Pflugers Archiv : European journal of physiology. 2009, 458: 981-992. 10.1007/s00424-009-0677-8.View ArticlePubMedGoogle Scholar
- Harguindey S, Arranz JL, Wahl ML, Orive G, Reshkin SJ: Proton transport inhibitors as potentially selective anticancer drugs. Anticancer Res. 2009, 29: 2127-2136.PubMedGoogle Scholar
- Bergé P, Pomeau Y, Vidal C: Order within chaos: towards a deterministic approach to turbulence. 1986, New York: WileyGoogle Scholar
- Tritton DJ: Physical Fluid Dynamics. 1977, New York: Van Nostrand ReinholdView ArticleGoogle Scholar
- Vander Heiden MG, Locasale JW, Swanson KD, Sharfi H: Evidence for an Alternative Glycolytic Pathway in Rapidly Proliferating Cells. Science. 2010, 329: 1492-1499. 10.1126/science.1188015.View ArticlePubMedGoogle Scholar
- Yakovlev G, Hirst J: Transhydrogenation reactions catalyzed by mitochondrial NADH-ubiquinone oxidoreductase (Complex I). Biochemistry. 2007, 46: 14250-14258. 10.1021/bi7017915.View ArticlePubMedGoogle Scholar
- Galante YM, Lee Y, Hatefi Y: Effect of pH on the mitochondrial energy-linked and non-energy-linked transhydrogenation reactions. J Biol Chem. 1980, 255: 9641-9646.PubMedGoogle Scholar
- Termonia Y, Ross J: Oscillations and control features in glycolysis: numerical analysis of a comprehensive model. Proc Nat Acad Sci USA. 1981, 78: 2952-2956. 10.1073/pnas.78.5.2952.PubMed CentralView ArticlePubMedGoogle Scholar
- Hanahan D, Weinberg RA: Hallmarks of cancer: the next generation. Cell. 2011, 144: 646-674. 10.1016/j.cell.2011.02.013.View ArticlePubMedGoogle Scholar
- Anderson PW: Basic Notions Of Condensed Matter Physics. 1997, Boulder: Westview PressGoogle Scholar
- Parmigiani A, Huber C, Chopard B, Latt J, Bachmann O: Application of the multi distribution function lattice Boltzmann approach to thermal flows. The European Physical Journal Special Topics. 2009, 171: 37-43. 10.1140/epjst/e2009-01009-7.View ArticleGoogle Scholar
- Kalwarczyk T, Ziȩbacz N, Bielejewska A, Zaboklicka E, Koynov K, Szymański J, Wilk A, Patkowski A, Gapiński J, Butt H-J, Hołyst R:Comparative Analysis of Viscosity of Complex Liquids and Cytoplasm of Mammalian Cells at the Nanoscale. Nano Letters. 2011, 11: 2157-2163. 10.1021/nl2008218.View ArticlePubMedGoogle Scholar
- Chaisson EJ: Cosmic Evolution: The Rise of Complexity in Nature. 2001, Cambridge: Harvard University PressGoogle Scholar
- Demetrius L, Tuszynski JA: Quantum metabolism explains the allometric scaling of metabolic rates. Journal of the Royal Society Interface. 2010, 7: 507-514. 10.1098/rsif.2009.0310.PubMed CentralView ArticleGoogle Scholar
- Makarieva AM, Gorshkov VG, Li B-L, Chown SL, Reich PB, Gavrilov VM: Mean mass-specific metabolic rates are strikingly similar across life’s major domains: Evidence for life’s metabolic optimum. Proc Nat Acad Sci USA. 2008, 105: 16994-16999. 10.1073/pnas.0802148105.PubMed CentralView ArticlePubMedGoogle Scholar
- Hess B, Boiteux A, Krüger J: Cooperation of glycolytic enzymes. Adv Enzyme Regul. 1969, 7: 149-167.View ArticlePubMedGoogle Scholar
- Ingram DM, Castleden WM: Glucose increases experimentally induced colorectal cancer: A preliminary report. Nutr Cancer. 1981, 2: 150-152. 10.1080/01635588109513676.View ArticlePubMedGoogle Scholar
- Boubriak OA, Urban JPG, Cui Z: Monitoring of metabolite gradients in tissue-engineered constructs. Journal of the Royal Society Interface. 2006, 3: 637-648. 10.1098/rsif.2006.0118.PubMed CentralView ArticleGoogle Scholar
- Murphy JB, Hawkins JA: Comparative studies on the metabolism of normal and malignant cells. J Gen Physiol. 1925, 8: 115-130. 10.1085/jgp.8.2.115.PubMed CentralView ArticlePubMedGoogle Scholar
- Vaupel P, Mayer A: Hypoxia in cancer: significance and impact on clinical outcome. Cancer Metastasis Rev. 2007, 26: 225-239. 10.1007/s10555-007-9055-1.View ArticlePubMedGoogle Scholar
- Ruan K, Song G, Ouyang G: Role of hypoxia in the hallmarks of human cancer. J Cell Biochem. 2009, 107: 1053-1062. 10.1002/jcb.22214.View ArticlePubMedGoogle Scholar
- Brahimi-Horn MC, Chiche J, Pouyssegur J: Hypoxia and cancer. J Mol Med. 2007, 85: 1301-1307. 10.1007/s00109-007-0281-3.View ArticlePubMedGoogle Scholar
- Russo CA, Weber TK, Volpe CM, Stoler DL, Petrelli NJ, Rodriguez-Bigas M, Burhans WC, Anderson GR: An anoxia inducible endonuclease and enhanced DNA breakage as contributors to genomic instability in cancer. Cancer Res. 1995, 55: 1122-1128.PubMedGoogle Scholar
- Meng AX, Jalali F, Cuddihy A, Chan N, Bindra RS, Glazer PM, Bristow RG: Hypoxia down-regulates DNA double strand break repair gene expression in prostate cancer cells. Radiotherapy and Oncology. 2005, 76: 168-176. 10.1016/j.radonc.2005.06.025.View ArticlePubMedGoogle Scholar
- Rodriguez-Jimenez FJ, Moreno-Manzano V, Lucas-Dominguez R, Sanchez-Puelles JM: Hypoxia causes downregulation of mismatch repair system and genomic instability in stem cells. Stem Cells. 2008, 26: 2052-2062. 10.1634/stemcells.2007-1016.View ArticlePubMedGoogle Scholar
- Goldbeter A, Berridge J: Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. 1997, Cambridge: Cambridge University PressGoogle Scholar
- Pye EK: Periodicities in the intermediary metabolism. Biochronometry. Edited by: Menaker M. 1971, Washington, D.C: National Academy of Sciences, 623-636.Google Scholar
- Sharma V, Annila A: Natural process–natural selection. Biophys Chem. 2007, 127: 123-128. 10.1016/j.bpc.2007.01.005.View ArticlePubMedGoogle Scholar
- Aromolaran AS, Zima AV, Blatter LA: Role of glycolytically generated ATP for CaMKII-mediated regulation of intracellular Ca2+ signaling in bovine vascular endothelial cells. American Journal of Physiology Cell. 2007, 293: C106-C118. 10.1152/ajpcell.00543.2006.View ArticleGoogle Scholar
- Yang J-H, Yang L, Qu Z, Weiss JN: Glycolytic oscillations in isolated rabbit ventricular myocytes. J Biol Chem. 2008, 283: 36321-36327. 10.1074/jbc.M804794200.PubMed CentralView ArticlePubMedGoogle Scholar
- Hilborn R: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. 2001, New York: Oxford University PressGoogle Scholar
- Badii R, Politi A: Complexity: Hierarchical Structures and Scaling in Physics. 1999, Cambridge: Cambridge University PressGoogle Scholar
- Tyner KM, Kopelman R, Philbert MA: “Nanosized voltmeter” enables cellular-wide electric field mapping. Biophys J. 2007, 93: 1163-1174. 10.1529/biophysj.106.092452.PubMed CentralView ArticlePubMedGoogle Scholar
- Pokorny J: Biophysical cancer transformation pathway. Electromagn Biol Med. 2009, 28: 105-123. 10.1080/15368370802711615.View ArticlePubMedGoogle Scholar
- Thompson JMT, Stewart HB: Nonlinear Dynamics and Chaos. 2002, New York: John Wiley & SonsGoogle Scholar
- May RM: Simple mathematical models with very complicated dynamics. Nature. 1976, 261: 459-467. 10.1038/261459a0.View ArticlePubMedGoogle Scholar
- Boiteux A, Goldbeter A, Hess B: Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate: a model and experimental study. Proc Nat Acad Sci USA. 1975, 72: 3829-3833. 10.1073/pnas.72.10.3829.PubMed CentralView ArticlePubMedGoogle Scholar
- Markus M, Kuschmitz D, Hess B: Chaotic dynamics in yeast glycolysis under periodic substrate input flux. FEBS Lett. 1984, 172: 235-238. 10.1016/0014-5793(84)81132-1.View ArticlePubMedGoogle Scholar
- Martinez de la Fuente I, Martinez L, Veguillas J: Dynamic behavior in glycolytic oscillations with phase shifts. Biosystems. 1995, 35: 1-13. 10.1016/0303-2647(94)01473-K.View ArticlePubMedGoogle Scholar
- Martinez de la Fuente I, Martinez L, Veguillas J, Aguirregabiria JM: Quasiperiodicity route to chaos in a biochemical system. Biophys J. 1996, 71: 2375-2379. 10.1016/S0006-3495(96)79431-6.PubMed CentralView ArticlePubMedGoogle Scholar
- Rietman EA: Molecular Engineering of Nanosystems. 2001, New York: SpringerView ArticleGoogle Scholar
- Gurel O, Gurel D: Oscillations in Chemical Reactions. 1983, New York: Springer-VerlagGoogle Scholar
- Kaneko K: Theory and applications of coupled map lattices. 1993, New York: John Wiley & SonsGoogle Scholar
- Fischer KH, Hertz JA: Spin Glasses. 1993, Cambridge: Cambridge University PressGoogle Scholar
- Sinha S, Ditto WL: Computing with distributed chaos. Physical review E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. 1999, 60: 363-377. 10.1103/PhysRevE.60.363.PubMedGoogle Scholar
- von Klitzing L, Betz A: Metabolic control in flow systems. I. Sustained glycolytic oscillations in yeast suspension under continual substrate infusion. Arch Mikrobiol. 1970, 71: 220-225. 10.1007/BF00410155.View ArticlePubMedGoogle Scholar
- Ramanujan VK, Herman BA: Nonlinear scaling analysis of glucose metabolism in normal and cancer cells. J Biomed Opt. 2008, 13: 031219-10.1117/1.2928154.View ArticlePubMedGoogle Scholar
- Aon MA, Cortassa S, O’Rourke B: Percolation and criticality in a mitochondrial network. Proc Nat Acad Sci USA. 2004, 101: 4447-4452. 10.1073/pnas.0307156101.PubMed CentralView ArticlePubMedGoogle Scholar
- Pikovsky A, Rosenblum M, Kurths J: Synchronization: A Universal Concept in Nonlinear Sciences. 2003, Cambridge: Cambridge University PressGoogle Scholar
- Tinoco I, Sauer K, Wang JC: Physical chemistry: principles and applications in biological sciences. 1985, Englewood Cliffs, NJ: Prentice-HallGoogle Scholar
- Palsson BO: Systems Biology: Properties of Reconstructed Networks. 2006, Cambridge: Cambridge University PressView ArticleGoogle Scholar
- Hynne F, Danø S, Sørensen PG: Full-scale model of glycolysis in Saccharomyces cerevisiae. Biophys Chem. 2001, 94: 121-163. 10.1016/S0301-4622(01)00229-0.View ArticlePubMedGoogle Scholar
- Steuer R, Gross T, Selbig J, Blasius B: Structural kinetic modeling of metabolic networks. Proc Nat Acad Sci USA. 2006, 103: 11868-11873. 10.1073/pnas.0600013103.PubMed CentralView ArticlePubMedGoogle Scholar
- Wolf J, Passarge J, Somsen OJ, Snoep JL, Heinrich R, Westerhoff HV: Transduction of intracellular and intercellular dynamics in yeast glycolytic oscillations. Biophys J. 2000, 78: 1145-1153. 10.1016/S0006-3495(00)76672-0.PubMed CentralView ArticlePubMedGoogle Scholar
- Gehrmann E, Glasser C, Jin Y, Sendhoff B, Drossel B, Hamacher K: Robustness of glycolysis in yeast to internal and external noise. Phys Rev E Stat Nonlinear Soft Matter Phys. 2011, 84: 021913-View ArticleGoogle Scholar
- Ko YH, Smith BL, Wang Y, Pomper MG, Rini DA, Torbenson MS, Hullihen J, Pedersen PL: Advanced cancers: eradication in all cases using 3-bromopyruvate therapy to deplete ATP. Biochem Biophys Res Commun. 2004, 324: 269-275. 10.1016/j.bbrc.2004.09.047.View ArticlePubMedGoogle Scholar
- Mathupala SP, Ko YH, Pedersen PL: The pivotal roles of mitochondria in cancer: Warburg and beyond and encouraging prospects for effective therapies. Biochim Biophys Acta. 2010, 1797: 1225-1230. 10.1016/j.bbabio.2010.03.025.PubMed CentralView ArticlePubMedGoogle Scholar
- Morita T, Watanabe Y, Takeda K, Okumura K: Effects of pH in the in vitro chromosomal aberration test. Mutat Res. 1989, 225: 55-60. 10.1016/0165-7992(89)90033-X.View ArticlePubMedGoogle Scholar
- Morita T, Nagaki T, Fukuda I, Okumura K: Clastogenicity of low pH to various cultured mammalian cells. Mutat Res. 1992, 268: 297-305. 10.1016/0027-5107(92)90235-T.View ArticlePubMedGoogle Scholar
- Cifone MA, Myhr B, Eiche A, Bolcsfoldi G: Effect of pH shifts on the mutant frequency at the thymidine kinase locus in mouse lymphoma L5178Y TK+/− cells. Mutat Res. 1987, 189: 39-46. 10.1016/0165-1218(87)90031-0.View ArticlePubMedGoogle Scholar
- Brusick D: Genotoxic effects in cultured mammalian cells produced by low pH treatment conditions and increased ion concentrations. Environ Mutagen. 1986, 8: 879-886. 10.1002/em.2860080611.View ArticlePubMedGoogle Scholar
- Cipollaro M, Corsale G, Esposito A, Ragucci E, Staiano N, Giordano GG, Pagano G: Sublethal pH decrease may cause genetic damage to eukaryotic cell: a study on sea urchins and Salmonella typhimurium. Teratog Carcinog Mutagen. 1986, 6: 275-287. 10.1002/tcm.1770060404.View ArticlePubMedGoogle Scholar
- Yuan J, Narayanan L, Rockwell S, Glazer PM: Diminished DNA repair and elevated mutagenesis in mammalian cells exposed to hypoxia and low pH. Cancer Res. 2000, 60: 4372-4376.PubMedGoogle Scholar
- Kondo A, Safaei R, Mishima M, Niedner H, Lin X, Howell SB: Hypoxia-induced enrichment and mutagenesis of cells that have lost DNA mismatch repair. Cancer Res. 2001, 61: 7603-7607.PubMedGoogle Scholar
- Suresh S: Biomechanics and biophysics of cancer cells. Acta Biomater. 2007, 3: 413-438. 10.1016/j.actbio.2007.04.002.PubMed CentralView ArticlePubMedGoogle Scholar
- Ketene AN: The AFM study of ovarian cell structural mechanics in the progression of cancer. Masters thesis. 2011, : Blacksburg, Virginia Virginia Tech, Mechanical EngineeringGoogle Scholar
- Creekmore AL, Silkworth WT, Cimini D, Jensen RV, Roberts PC, Schmelz EM: Changes in gene expression and cellular architecture in an ovarian cancer progression model. PLoS One. 2011, 6: e17676-10.1371/journal.pone.0017676.PubMed CentralView ArticlePubMedGoogle Scholar
- Fygenson D, Braun E, Libchaber A: Phase diagram of microtubules. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994, 50: 1579-1588. 10.1103/PhysRevE.50.1579.PubMedGoogle Scholar
- Sept D, Xu J, Pollard TD, McCammon JA: Annealing accounts for the length of actin filaments formed by spontaneous polymerization. Biophys J. 1999, 77: 2911-2919. 10.1016/S0006-3495(99)77124-9.PubMed CentralView ArticlePubMedGoogle Scholar
- Bolterauer H, Limbach HJ, Tuszyński JA: Models of assembly and disassembly of individual microtubules: stochastic and averaged equations. Journal of Biological Physics. 1999, 25: 1-22. 10.1023/A:1005159215657.PubMed CentralView ArticlePubMedGoogle Scholar
- Desai A, Mitchison TJ: Microtubule polymerization dynamics. Annu Rev Cell Dev Biol. 1997, 13: 83-117. 10.1146/annurev.cellbio.13.1.83.View ArticlePubMedGoogle Scholar
- Pollard TD: Rate constants for the reactions of ATP- and ADP-actin with the ends of actin filaments. J Cell Biol. 1986, 103: 2747-2754. 10.1083/jcb.103.6.2747.View ArticlePubMedGoogle Scholar
- Bakhoum SF, Thompson SL, Manning AL, Compton DA: Genome stability is ensured by temporal control of kinetochore-microtubule dynamics. Nat Cell Biol. 2009, 11: 27-35. 10.1038/ncb1809.PubMed CentralView ArticlePubMedGoogle Scholar
- Thompson SL, Bakhoum SF, Compton DA: Mechanisms of chromosomal instability. Current biology. 2010, 20: R285-R295. 10.1016/j.cub.2010.01.034.PubMed CentralView ArticlePubMedGoogle Scholar
- Vitale I, Galluzzi L, Castedo M, Kroemer G: Mitotic catastrophe: a mechanism for avoiding genomic instability. Nat Rev Mol Cell Biol. 2011, 12: 385-392.View ArticlePubMedGoogle Scholar
- Crasta K, Ganem NJ, Dagher R, Lantermann AB, Ivanova EV, Pan Y, Nezi L, Protopopov A, Chowdhury D, Pellman D: DNA breaks and chromosome pulverization from errors in mitosis. Nature. 2012, 482: 53-58. 10.1038/nature10802.PubMed CentralView ArticlePubMedGoogle Scholar
- Zhang P, Li H, Tan X, Chen L, Wang S: Association of metformin use with cancer incidence and mortality: A meta-analysis. Cancer Epidemiol. 2013, 37: 207-218. 10.1016/j.canep.2012.12.009.View ArticlePubMedGoogle Scholar
- Landman GWD, Kleefstra N, van Hateren KJJ, Groenier KH, Gans ROB, Bilo HJG: Metformin associated with lower cancer mortality in type 2 diabetes: ZODIAC-16. Diabetes Care. 2010, 33: 322-326. 10.2337/dc09-1380.PubMed CentralView ArticlePubMedGoogle Scholar
- Li D, Yeung S-CJ, Hassan MM, Konopleva M, Abbruzzese JL: Antidiabetic therapies affect risk of pancreatic cancer. Gastroenterology. 2009, 137: 482-488. 10.1053/j.gastro.2009.04.013.PubMed CentralView ArticlePubMedGoogle Scholar
- Pedersen PL: Warburg, me and Hexokinase 2: Multiple discoveries of key molecular events underlying one of cancers’ most common phenotypes, the “Warburg Effect”, i.e., elevated glycolysis in the presence of oxygen. J Bioenerg Biomembr. 2007, 39: 211-222. 10.1007/s10863-007-9094-x.View ArticlePubMedGoogle Scholar
- Ko YH, Verhoeven HA, Lee MJ, Corbin DJ, Vogl TJ, Pedersen PL: A translational study “case report” on the small molecule “energy blocker” 3-bromopyruvate (3BP) as a potent anticancer agent: from bench side to bedside. J Bioenerg Biomembr. 2012, 44: 163-170. 10.1007/s10863-012-9417-4.View ArticlePubMedGoogle Scholar
- Ganapathy-Kanniappan S, Geschwind J-FH, Kunjithapatham R, Buijs M, Vossen JA, Tchernyshyov I, Cole RN, Syed LH, Rao PP, Ota S, Vali M: Glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is pyruvylated during 3-bromopyruvate mediated cancer cell death. Anticancer Res. 2009, 29: 4909-4918.PubMed CentralPubMedGoogle Scholar
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