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A biophysical basis of enhanced interstitial fluid pressure in tumors
Medical Hvypotheses (1999) 53(6), 526–529 © 1999 Harcourt Publishers Ltd Article No. mehy.1998.0805
A biophysical basis of enhanced interstitial fluid pressure in tumors H. P. Rutz Department of Radiation Oncology, Kantonsspital Winterthur, CH-8401 Winterthur, Switzerland
Summary It is widely accepted that enhanced interstitial fluid pressure (IFP) in tumors is a major obstacle against delivery of therapeutic agents. On the other hand, the origin of enhanced IFP remains controversial. Here, the Van’t Hoff equation is applied to examine how glucose breakdown to CO2 and lactate in tumor cells may affect intracellular osmotic pressure. According to the equation, it is found that production of CO2 from glucose lowers osmotic pressure inside cells, while glycolytic production of lactate generates significant increases. Crucial to a net enhancement of pressure in cells is the Warburg ratio, the ratio of the fraction of glucose transformed to lactate divided by the fraction of glucose metabolized to CO2: if (and only if) the ratio is higher than 1.0, there is a resulting increase in intracellular osmotic pressure. Under fully anaerobic glycolysis, the enhancement of intracellular pressure is maximal, namely 19.3 mmHg per mM of glucose metabolized to lactate (Van’t Hoff equation). Cells are then biological pressure pumps driven by glycolytic production of lactate, causing IFP to raise. It is proposed that a regulatory feedback loop prevents IFP to raise above microvascular pressure (MVP). Accordingly, enhanced IFP in tumors is the result of high rates of tumor glycolysis, and enhancement of IFP is limited by MVP. It is thus concluded that a high rate of glycolytic production of lactate in tumor cells ultimately prevents both access of therapeutic agents to the malignant cells and immunological surveillance, and that it indirectly drives outward currents of interstitial fluid, thereby propelling both the process of tumor infiltration of surrounding structures and metastatic spread, depending on deformability and proteolytic capacity of the malignant cells. © 1999 Harcourt Publishers Ltd
INTRODUCTION Resistance to current forms of therapy and the occurrence of metastatic spread are the two major causes underlying failure in the fight against cancer. In recent years, it has become clear that enhanced tumor interstitial fluid pressure (IFP) is a major barrier against the delivery of therapeutic agents to malignant cells (1–7) such as classical drugs, monoclonal antibodies, oligonucleotides, viruses and cells mediating antitumor immunity. The relevance of IFP with respect to propelling infiltration of healthy tissue and the metastatic process has not yet been fully recognized. However, it is well established that IFP is uniformly elevated throughout tumors, with pressure droping sharply outside (1,2) Received 15 April 1998 Accepted 25 August 1998 Correspondence to: Dr med. Hans Peter Rutz, Abteilung für RadioOnkologie, Kantonsspital Winterthur, Postfach, CH-8401 Winterthur, Switzerland. Phone: +41 52 266 26 46; Fax: +41 52 266 45 14; E-mail: [email protected] This research was supported by the Seymour Obermer Foundation.
526
resulting in convective outflow of interstitial fluid at tumor periphery (8–10) so that enhanced IFP may push tumor cells to infiltrate and metastasize. The origin of enhanced IFP, however, is disputed among various authors. Some think that enhanced IFP is caused by enhanced microvascular pressure (MVP) in tumors (1–4,6,7) while others challenge this model (5). In this paper, the biophysical basis underlying generation of enhanced IFP in tumors is analyzed with respect to the role of glucose breakdown to either CO2 or to lactate in the process of cellular energy metabolism. THE PRODUCTION OF LACTATE IN TUMORS It has long been established that tumors may produce large amounts of lactate (11–13). Lactate is produced mainly from glucose but also from amino acids. However, as hypoxia and anoxia gradually develop along with tumor size, the formation of lactate from glucose becomes more and more important and ultimately – in anoxic tumor microregions – energy is generated exclusively from glucose degradation to lactate (13). In his
Pressure in tumors
original paper, Warburg referred to these metabolic states as ‘aerobic glycolysis’ and ‘anaerobic glycolysis’ (11,12). Anaerobic glycolysis obviously requires cells to tolerate hypoxia, and not to respond with induction of a p53dependent apoptotic response (14), nor to subside to development of necrosis. Hence, anaerobic glycolysis is not universial in tumors. In this manuscript, the Van’t Hoff equation equation is applied to assess changes in osmotic pressure that result from glucose breakdown in tumor energy metabolism. It is found that cells are pressure pumps driven by glycolytic production of lactate. GENERATION OF ENHANCED OSMOTIC PRESSURE FROM WITHIN TUMORS The laws of physical chemistry allow to describe how molecules like glucose or lactate dissolved in a solute cause osmotic pressure, provided that different concentrations are separated by a semipermeable membrane, or in more general terms, that there are concentration gradients among molecules with different rates of diffusion (15). If a solution is dilute (up to the mM range), osmotic pressure follows the Van’t Hoff equation P=c.R.T
(15)
P is pressure in atm, c is molar concentration, R is 8.2 3 1022 atmLK21mole21, and T is the absolute temperature. Accordingly, at 37 °C (310 K), a dissolved compound generates a pressure of 0.0254 atm, or 2.58 kPa, or 19.3 mmHg per mM. Since cellular metabolism is separated from the interstitial space by the cell membrane (not an ideal semipermeable membrane), the Van’t Hoff equation can be applied to approximately assess how pressures inside the cell change as a function of glucose breakdown in the intermediary metabolism. If glucose is fully metabolized to CO2, the number of molecules in solution will decrease from an initial number of seven (1 3 glucose and 6 3 O2) to only six (6 3 CO2) for each molecule of glucose metabolized. In this process, a mM of molecules is thus removed from the solution per mM of glucose metabolized, decreasing osmotic pressure by 19.3 mmHg per mM of glucose metabolized to CO2. If lactate is formed from glucose, two molecules of lactate are generated from just one (glucose). As a result, there is a net gain of one mM of molecules dissolved in the solute per mM of molecules (glucose) metabolized. According to the Van’t Hoff equation, this results in an enhancement in osmotic pressure by 19.3 mmHg for each mM of glucose metabolized to lactate. If on the other hand lactate is formed in tumors from an amino acid, © 1999 Harcourt Publishers Ltd
527
molecules are transformed (transamination) without changing the number of molecules in solution, and hence, no change in osmotic pressure will result. Finally, there may be other metabolic pathways in tumor cells generating pressure. Cells may thus behave like living hydraulic pumps, generating pressure by osmotic changes caused by intermediary metabolism, and transmitting it to the surrounding interstitial fluid, depending on the flux of glucose to lactate or CO2. Furthermore, as lactate reaches the interstitial space, its osmotic partial pressure will add to the osmotic pressure already in place, since rates of diffusion of the hydrated lactate molecules is below the rate for free water. The production of lactate in tumors thus drives malignant cells to behave like hydraulic pumps, and it adds osmotic pressure to the interstitial fluid surrounding the malignant cells. THE WARBURG RATIO In his original paper on glucose metabolism in malignant cells, Warburg introduced a ratio (the Warburg ratio), in which the amount of glucose fermented (to lactate) is set in relation to the amount of glucose oxidized (to CO2) (11,12). If the Warburg ratio is below 1.0, more glucose is metabolized to CO2 than to lactate. Hence, the number of molecules in solution is still decreasing, since more molecules of glucose are removed than molecules of lactate produced. If the Warburg ratio equals 1.0, then the number of molecules in the solute remains stable, since two mM of glucose metabolized are replaced by two mM of lactate produced. If, however, the Warburg ratio increases above 1.0, more glucose is metabolized to lactate than to CO2, so that more molecules are added to the solute than removed. Under complete hypoxia/anoxia, one mM of glucose is replaced by two mM of lactate, resulting in an increase of osmotic pressure by 19.3 mm Hg per mM of glucose metabolized. Glycolytic activity of tumor tissue (the Warburg ratio) and glucose availability thus determine the amount of pressure generated within cells. THEORETICAL PREDICTIONS VS. PRESSURES REPORTED Postbrandial plasma glucose levels of 7.8 mM are the upper limit of normal physiological glucose concentrations (4.2–6.4 mM); higher values are found in diabetic patients or, in diabetic patients with cancer (16). Thus (e.g. calculations for a closed volume), if 4.2 mM of glucose were converted to lactate under complete anaerobic glycolysis, this would enhance osmotic pressure by 80 mmHg; if 7.8 mM of glucose were metabolized to lactate, by as much as 150 mmHg. Medical Hypotheses (1999) 53(6), 526–529
528
Rutz
In normal tissue, IFP is in the range of 2 5 to (+) 5 mmHg (17–20). Tumor IFP was first noted to be elevated in experimental animal tumors by Young and colleges (21). Only recently have human studies of tumor IFP been published. These studies report that pressure in tumors may vary considerably, namely, from 5 mmHg (untreated lymphomas) to 15 mmHg (carcinomas of the head and neck, breast, cervix, colon) to 30 mmHg and higher (melanoma, renal cell carcinoma, recurrent lymphomas) (5,18–20,22,23). The single highest measurement of tumor IFP reported to date was 107 mmHg in a melanoma (23). Hence, pressure does not build up to its full theoretical potential predicted on the basis of the Van’t Hoff equation. Several reasons may account for this observation: First, tumors are not a closed volume; pressure is released at tumor periphery by convection of interstitial fluid (8–10). Second, it is expected that not all glucose is metabolized to lactate (the Warburg ratio). Third, malignant cells may lack glycolytic capacity to survive under hypoxia, for example, certain cells enter apoptosis under such conditions (14). Fourth, glucose supply to hypoxic and anoxic tumor cells may be limited. Fifth, IFP can not raise above MVP, due to the following regulatory feedback mechanism: as IFP increases above MVP, microvascular circulation and convection of interstitial fluid will collapse, so that convection of fluid to the malignant cells will collapse, leading to progressively increasing diffusion distances for nutrient supply. As result, glycolysis will decrease and stop, and pressure drop. Pressure is then released by convective outflow of interstitial fluid at tumor periphery (8–10), with tumor behaving like a poroelastic solid (4). As IFP subsequently falls below MVP, microcirculation will reestablish, restoring glucose supply, and thereby, permitting resumption of glycolysis and a new raise in IFP. In this model, IFP and MVP are strictly interdependent, as found experimentally (4): if MVP is raised, IFP may raise to a higher level, since convection collapse and subsequent stop of glucose supply will occur at a higher level. If MVP is low, IFP is at lower levels. IFP is thus closely linked to MVP, either below or equal to MVP. LEVELS OF LACTATE AND METASTATIC SPREAD: FIRST CLUE TO CAUSE AND EFFECT There is an intriguing association between production of lactate in tumors and the probability of metastatic spread: tumor hypoxia predicts the likelyhood of distant metastasis in human soft tissue sarcoma (24), and high levels of lactate in human cervical and head and neck cancers correlate with the incidence of distant metastasis (25,26). Hence, the risk of developing metastatic disease in cancer is traced back to degrees of tumor hypoxia, glycolytic Medical Hypotheses (1999) 53(6), 526–529
activity of malignant cells, and resulting amounts of lactate generated. This biophysical and evidence-based model finally helps to explain why cell deformability is such an important attribute for selection in the metastatic process: as in the experimental model used in vitro for selection of malignant cells (27), tumor cells are pressed through a filter in vivo, namely, a filter formed by the extracellular matrix in the interstitial space. Through this filtration process in vivo, the cells with best deformability are naturally selected for infiltration and metastatic spread. Along similar lines of reasoning, a mechanistic model becomes evident which allowes to explain why proteolytic capacity of malignant cells is so important, too, in the selection process for metastatic spread (28): those cells detaching most easily from extracellular matrix are the ones most likely to be carried away along the currents of interstitial fluid leaving tumor bulk. Pressure gradients at tumor periphery and resulting flow of interstitial fluid and hydraulic propulsion of tumor cells thus underly the infiltrative pattern from which cancer has been given its name, as well as subsequent detachment of malignant cells from primary tumors. Infiltration of surrounding tissue and metastatic spread into blood and lymphatic vessels thus depend on glycolytic activity, deformability and proteolytic capacity.
CONCLUSIONS These considerations link biochemical reactions in maligant tumors to the physico-chemical buildup of pressure in tumor cells and the surrounding interstitial space, limited only by glycolytic capacity of the malignant cells, glucose and oxygen supply which determine the Warburg ratio and MVP. According to this hypothesis, glycolytic production of lactate in tumor cells represents a biophysical engine generating enhanced IFP. Tumor metabolism thus represents the origin of a major barrier against delivery of diagnostic and therapeutic agents to malignant cells, such as classical drugs, hormones and antihormones, cytokines, monoclonal antibodies, oligonucleotides, viruses and cells mediating antitumor immunity, including natural host tumor surveillance. Tumor glucose metabolism, however, also underlies and determines propulsion of interstitial fluid currents – driving both the process of tumor infiltration and the resulting process of metastatic spread.
ACKNOWLEDGEMENTS The author thanks G. Imanidis for explaining colligative properties of molecules (Van’t Hoff equation), H. Müller and J.B. Little for encouragement, R.K. Jain for critical scepticism, and
© 1999 Harcourt Publishers Ltd
Pressure in tumors
A. Nogawa, W. Mueller-Klieser, C. De Wit, S. Walenta, O. Thews, P. Vaupel and C.N. Coleman for critically raising specific questions and constructive comments that have helped to improve this model. This work was kindly supported by a grant of the Seymour Obermer Foundation.
REFERENCES 1. Jain R. K., Baxter L. T. Mechanism of heterogenous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure. Cancer Res 1988; 48: 7022–7032. 2. Boucher Y., Baxter T. L., Jain R. K. Interstitial pressure gradients in tissue-isolated and subcutaneous tumors: implications for therapy. Cancer Res 1990; 50: 4478–4484. 3. Boucher Y., Jain R. K. Microvascular pressure is the principal driving force for interstitial hypertension in solid tumors: implications for vascular collapse. Cancer Res 1992; 52: 5110–5114. 4. Netti P. A., Baxter L. T., Boucher Y., Skalak R., Jain R. K. Timedependent behavior of interstitial fluid pressure in solid tumor: implications for drug delivery. Cancer Res 1995; 55: 5451–5458. 5. Curti B. D. Physical barriers to drug delivery in tumors. In: Chabner B. A., Longo D. L., eds. Cancer Chemotherapy and Biotherapy, 2nd edn Philadelphia: Lippincott-Raven, 1996: 709–719. 6. Jain R. K. How can we deliver molecular medicine to solid tumors? Science 1996; 271: 1079–1080. 7. Zhu H., Baxter L., Jain R. K. Potential limitations of radioimmunodetection and radioimmunotherapy with monoclonal antibodies: evaluation using a physiologicallybased pharmacokinetic model. J Nuc Med 1997; in press. 8. Gullino P., Grantham F. Studies on the exchange of fluids between host and tumor. I. A method for growing ‘tissueisolated’ tumors in laboratory animals. J Natl Cancer Inst 1961; 27: 679–693. 9. Butler T. P., Grantham F. A., Gullino P. M. Bulk transfer of fluid in the interstitial compartment of mammary tumors. Cancer Res 1975; 35: 3084–3088. 10. DiResta G. R., Lee J., Larson S. M., Arbit E. Growth, interstitial fluid pressure, and interstitial fluid velocity distribution profile. Microvasc Res 1993; 46: 158–177. 11. Warburg O., Posener K., Negelein E. Ueber den Stoffwechsel der Carcinomzelle. Biochem Z 1924; 152: 309–324. 12. Warburg O. On the origin of cancer cells. Science 1956; 123: 309–314. 13. Vaupel P., Kallinowski F., Okunieff P. Blood flow, oxygen and nutrient supply, and metabolic microenvironment of human tumors: a review. Cancer Res 1989; 49: 6449–6465.
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14. Graeber T. G., Osmanian C., Jacks T. et al. Hypoxia-mediated selection of cells with diminished apoptotic potential in solid tumours. Nature 1996; 379: 88–91. 15. Atkins P. W. Physical Chemistry, 3rd edn. Boston: W. H. Freeman, 1986. 16. Braunwald E., Isselbacher K. J., Petersdorf R. G., Wilson J. D., Martin J. B., Fauci A. S., eds. Harrison’s Principles of Internal Medicine, 11th edn. 1988. 17. Guyton A. C. A concept of negative interstitial pressure based on pressures in implanted perforated capsules. Circ Res 1963; 12: 399–414. 18. Gutmann R., Leunig M., Feyh J. et al. Interstitial hypertension in head and neck tumors in patients: correlation with tumor size. Cancer Res 1992; 52: 1993–1995. 19. Roh H. D., Kalnicki S., Buchsbaum R., Bloomer W. D., Jain R. K. Interstistial hypertension in carcinoma of uterine cervix in patients: possible correlation with tumor oxygenation and radiation response. Cancer Res 1991; 51: 6695–6698. 20. Less J. R., Posner M. C., Boucher Y., Borochovitz D., Wolmark N., Jain R. K. Interstitial hypertension in human breast and colorectal tumors. Cancer Res 1992; 52: 6371–6374. 21. Young J. S., Lumsden C. E., Stalker A. L. The significance of the ‘tissue pressure’ of normal testicular and neoplastic (BrownPearce carcinoma) tissue in the rabbit. J Path Bacteriol 1950; 62: 313–333. 22. Boucher Y., Kirkwood J. M., Opacic D., Desantis M., Jain R. K. Interstitial hypertension in superficial metastatic melanomas in humans. Cancer Res 1991; 51: 6691–6694. 23. Curti B. D., Urba W. J., Alvord W. G. et al. Interstitial pressure of subcutaneous nodules in melanoma and lymphoma patients: changes during treatment. Cancer Res 1993; 53: 2204–2207. 24. Brizel D. M., Scully S. P., Harrelson J. M. et al. Tumor oxygenation predicts the likelyhood of distant metastasis in human soft tissue sarcoma. Cancer Res 1996; 56: 941–943. 25. Schwickert G., Walenta S., Sundfor K., Rofstad E. K., MuellerKlieser W. Correlation of high lactate levels in human cervical cancer with incidence of metastasis. Cancer Res 1995; 55: 4757–4759. 26. Walenta S., Salameh A., Lyng H. et al. Correlation of high lactate levels in head and neck tumors with incidence of metastasis. Am J Pathol 1997; 150(2): 409–415. 27. Ochalek T., Nordt F. J., Tullberg K., Burger M. M. Correlation between cell deformability and metastatic potential in B16-F1 melanoma cell variants. Cancer Res 1988; 48: 5124–5128. 28. Mignatti P., Rifkin D. B. Biology and biochemistry of proteinases in tumor invasion. Physiol Rev 1993; 73(1): 161–195.
Medical Hypotheses (1999) 53(6), 526–529
A biophysical basis of enhanced interstitial fluid pressure in tumors H. P. Rutz Department of Radiation Oncology, Kantonsspital Winterthur, CH-8401 Winterthur, Switzerland
Summary It is widely accepted that enhanced interstitial fluid pressure (IFP) in tumors is a major obstacle against delivery of therapeutic agents. On the other hand, the origin of enhanced IFP remains controversial. Here, the Van’t Hoff equation is applied to examine how glucose breakdown to CO2 and lactate in tumor cells may affect intracellular osmotic pressure. According to the equation, it is found that production of CO2 from glucose lowers osmotic pressure inside cells, while glycolytic production of lactate generates significant increases. Crucial to a net enhancement of pressure in cells is the Warburg ratio, the ratio of the fraction of glucose transformed to lactate divided by the fraction of glucose metabolized to CO2: if (and only if) the ratio is higher than 1.0, there is a resulting increase in intracellular osmotic pressure. Under fully anaerobic glycolysis, the enhancement of intracellular pressure is maximal, namely 19.3 mmHg per mM of glucose metabolized to lactate (Van’t Hoff equation). Cells are then biological pressure pumps driven by glycolytic production of lactate, causing IFP to raise. It is proposed that a regulatory feedback loop prevents IFP to raise above microvascular pressure (MVP). Accordingly, enhanced IFP in tumors is the result of high rates of tumor glycolysis, and enhancement of IFP is limited by MVP. It is thus concluded that a high rate of glycolytic production of lactate in tumor cells ultimately prevents both access of therapeutic agents to the malignant cells and immunological surveillance, and that it indirectly drives outward currents of interstitial fluid, thereby propelling both the process of tumor infiltration of surrounding structures and metastatic spread, depending on deformability and proteolytic capacity of the malignant cells. © 1999 Harcourt Publishers Ltd
INTRODUCTION Resistance to current forms of therapy and the occurrence of metastatic spread are the two major causes underlying failure in the fight against cancer. In recent years, it has become clear that enhanced tumor interstitial fluid pressure (IFP) is a major barrier against the delivery of therapeutic agents to malignant cells (1–7) such as classical drugs, monoclonal antibodies, oligonucleotides, viruses and cells mediating antitumor immunity. The relevance of IFP with respect to propelling infiltration of healthy tissue and the metastatic process has not yet been fully recognized. However, it is well established that IFP is uniformly elevated throughout tumors, with pressure droping sharply outside (1,2) Received 15 April 1998 Accepted 25 August 1998 Correspondence to: Dr med. Hans Peter Rutz, Abteilung für RadioOnkologie, Kantonsspital Winterthur, Postfach, CH-8401 Winterthur, Switzerland. Phone: +41 52 266 26 46; Fax: +41 52 266 45 14; E-mail: [email protected] This research was supported by the Seymour Obermer Foundation.
526
resulting in convective outflow of interstitial fluid at tumor periphery (8–10) so that enhanced IFP may push tumor cells to infiltrate and metastasize. The origin of enhanced IFP, however, is disputed among various authors. Some think that enhanced IFP is caused by enhanced microvascular pressure (MVP) in tumors (1–4,6,7) while others challenge this model (5). In this paper, the biophysical basis underlying generation of enhanced IFP in tumors is analyzed with respect to the role of glucose breakdown to either CO2 or to lactate in the process of cellular energy metabolism. THE PRODUCTION OF LACTATE IN TUMORS It has long been established that tumors may produce large amounts of lactate (11–13). Lactate is produced mainly from glucose but also from amino acids. However, as hypoxia and anoxia gradually develop along with tumor size, the formation of lactate from glucose becomes more and more important and ultimately – in anoxic tumor microregions – energy is generated exclusively from glucose degradation to lactate (13). In his
Pressure in tumors
original paper, Warburg referred to these metabolic states as ‘aerobic glycolysis’ and ‘anaerobic glycolysis’ (11,12). Anaerobic glycolysis obviously requires cells to tolerate hypoxia, and not to respond with induction of a p53dependent apoptotic response (14), nor to subside to development of necrosis. Hence, anaerobic glycolysis is not universial in tumors. In this manuscript, the Van’t Hoff equation equation is applied to assess changes in osmotic pressure that result from glucose breakdown in tumor energy metabolism. It is found that cells are pressure pumps driven by glycolytic production of lactate. GENERATION OF ENHANCED OSMOTIC PRESSURE FROM WITHIN TUMORS The laws of physical chemistry allow to describe how molecules like glucose or lactate dissolved in a solute cause osmotic pressure, provided that different concentrations are separated by a semipermeable membrane, or in more general terms, that there are concentration gradients among molecules with different rates of diffusion (15). If a solution is dilute (up to the mM range), osmotic pressure follows the Van’t Hoff equation P=c.R.T
(15)
P is pressure in atm, c is molar concentration, R is 8.2 3 1022 atmLK21mole21, and T is the absolute temperature. Accordingly, at 37 °C (310 K), a dissolved compound generates a pressure of 0.0254 atm, or 2.58 kPa, or 19.3 mmHg per mM. Since cellular metabolism is separated from the interstitial space by the cell membrane (not an ideal semipermeable membrane), the Van’t Hoff equation can be applied to approximately assess how pressures inside the cell change as a function of glucose breakdown in the intermediary metabolism. If glucose is fully metabolized to CO2, the number of molecules in solution will decrease from an initial number of seven (1 3 glucose and 6 3 O2) to only six (6 3 CO2) for each molecule of glucose metabolized. In this process, a mM of molecules is thus removed from the solution per mM of glucose metabolized, decreasing osmotic pressure by 19.3 mmHg per mM of glucose metabolized to CO2. If lactate is formed from glucose, two molecules of lactate are generated from just one (glucose). As a result, there is a net gain of one mM of molecules dissolved in the solute per mM of molecules (glucose) metabolized. According to the Van’t Hoff equation, this results in an enhancement in osmotic pressure by 19.3 mmHg for each mM of glucose metabolized to lactate. If on the other hand lactate is formed in tumors from an amino acid, © 1999 Harcourt Publishers Ltd
527
molecules are transformed (transamination) without changing the number of molecules in solution, and hence, no change in osmotic pressure will result. Finally, there may be other metabolic pathways in tumor cells generating pressure. Cells may thus behave like living hydraulic pumps, generating pressure by osmotic changes caused by intermediary metabolism, and transmitting it to the surrounding interstitial fluid, depending on the flux of glucose to lactate or CO2. Furthermore, as lactate reaches the interstitial space, its osmotic partial pressure will add to the osmotic pressure already in place, since rates of diffusion of the hydrated lactate molecules is below the rate for free water. The production of lactate in tumors thus drives malignant cells to behave like hydraulic pumps, and it adds osmotic pressure to the interstitial fluid surrounding the malignant cells. THE WARBURG RATIO In his original paper on glucose metabolism in malignant cells, Warburg introduced a ratio (the Warburg ratio), in which the amount of glucose fermented (to lactate) is set in relation to the amount of glucose oxidized (to CO2) (11,12). If the Warburg ratio is below 1.0, more glucose is metabolized to CO2 than to lactate. Hence, the number of molecules in solution is still decreasing, since more molecules of glucose are removed than molecules of lactate produced. If the Warburg ratio equals 1.0, then the number of molecules in the solute remains stable, since two mM of glucose metabolized are replaced by two mM of lactate produced. If, however, the Warburg ratio increases above 1.0, more glucose is metabolized to lactate than to CO2, so that more molecules are added to the solute than removed. Under complete hypoxia/anoxia, one mM of glucose is replaced by two mM of lactate, resulting in an increase of osmotic pressure by 19.3 mm Hg per mM of glucose metabolized. Glycolytic activity of tumor tissue (the Warburg ratio) and glucose availability thus determine the amount of pressure generated within cells. THEORETICAL PREDICTIONS VS. PRESSURES REPORTED Postbrandial plasma glucose levels of 7.8 mM are the upper limit of normal physiological glucose concentrations (4.2–6.4 mM); higher values are found in diabetic patients or, in diabetic patients with cancer (16). Thus (e.g. calculations for a closed volume), if 4.2 mM of glucose were converted to lactate under complete anaerobic glycolysis, this would enhance osmotic pressure by 80 mmHg; if 7.8 mM of glucose were metabolized to lactate, by as much as 150 mmHg. Medical Hypotheses (1999) 53(6), 526–529
528
Rutz
In normal tissue, IFP is in the range of 2 5 to (+) 5 mmHg (17–20). Tumor IFP was first noted to be elevated in experimental animal tumors by Young and colleges (21). Only recently have human studies of tumor IFP been published. These studies report that pressure in tumors may vary considerably, namely, from 5 mmHg (untreated lymphomas) to 15 mmHg (carcinomas of the head and neck, breast, cervix, colon) to 30 mmHg and higher (melanoma, renal cell carcinoma, recurrent lymphomas) (5,18–20,22,23). The single highest measurement of tumor IFP reported to date was 107 mmHg in a melanoma (23). Hence, pressure does not build up to its full theoretical potential predicted on the basis of the Van’t Hoff equation. Several reasons may account for this observation: First, tumors are not a closed volume; pressure is released at tumor periphery by convection of interstitial fluid (8–10). Second, it is expected that not all glucose is metabolized to lactate (the Warburg ratio). Third, malignant cells may lack glycolytic capacity to survive under hypoxia, for example, certain cells enter apoptosis under such conditions (14). Fourth, glucose supply to hypoxic and anoxic tumor cells may be limited. Fifth, IFP can not raise above MVP, due to the following regulatory feedback mechanism: as IFP increases above MVP, microvascular circulation and convection of interstitial fluid will collapse, so that convection of fluid to the malignant cells will collapse, leading to progressively increasing diffusion distances for nutrient supply. As result, glycolysis will decrease and stop, and pressure drop. Pressure is then released by convective outflow of interstitial fluid at tumor periphery (8–10), with tumor behaving like a poroelastic solid (4). As IFP subsequently falls below MVP, microcirculation will reestablish, restoring glucose supply, and thereby, permitting resumption of glycolysis and a new raise in IFP. In this model, IFP and MVP are strictly interdependent, as found experimentally (4): if MVP is raised, IFP may raise to a higher level, since convection collapse and subsequent stop of glucose supply will occur at a higher level. If MVP is low, IFP is at lower levels. IFP is thus closely linked to MVP, either below or equal to MVP. LEVELS OF LACTATE AND METASTATIC SPREAD: FIRST CLUE TO CAUSE AND EFFECT There is an intriguing association between production of lactate in tumors and the probability of metastatic spread: tumor hypoxia predicts the likelyhood of distant metastasis in human soft tissue sarcoma (24), and high levels of lactate in human cervical and head and neck cancers correlate with the incidence of distant metastasis (25,26). Hence, the risk of developing metastatic disease in cancer is traced back to degrees of tumor hypoxia, glycolytic Medical Hypotheses (1999) 53(6), 526–529
activity of malignant cells, and resulting amounts of lactate generated. This biophysical and evidence-based model finally helps to explain why cell deformability is such an important attribute for selection in the metastatic process: as in the experimental model used in vitro for selection of malignant cells (27), tumor cells are pressed through a filter in vivo, namely, a filter formed by the extracellular matrix in the interstitial space. Through this filtration process in vivo, the cells with best deformability are naturally selected for infiltration and metastatic spread. Along similar lines of reasoning, a mechanistic model becomes evident which allowes to explain why proteolytic capacity of malignant cells is so important, too, in the selection process for metastatic spread (28): those cells detaching most easily from extracellular matrix are the ones most likely to be carried away along the currents of interstitial fluid leaving tumor bulk. Pressure gradients at tumor periphery and resulting flow of interstitial fluid and hydraulic propulsion of tumor cells thus underly the infiltrative pattern from which cancer has been given its name, as well as subsequent detachment of malignant cells from primary tumors. Infiltration of surrounding tissue and metastatic spread into blood and lymphatic vessels thus depend on glycolytic activity, deformability and proteolytic capacity.
CONCLUSIONS These considerations link biochemical reactions in maligant tumors to the physico-chemical buildup of pressure in tumor cells and the surrounding interstitial space, limited only by glycolytic capacity of the malignant cells, glucose and oxygen supply which determine the Warburg ratio and MVP. According to this hypothesis, glycolytic production of lactate in tumor cells represents a biophysical engine generating enhanced IFP. Tumor metabolism thus represents the origin of a major barrier against delivery of diagnostic and therapeutic agents to malignant cells, such as classical drugs, hormones and antihormones, cytokines, monoclonal antibodies, oligonucleotides, viruses and cells mediating antitumor immunity, including natural host tumor surveillance. Tumor glucose metabolism, however, also underlies and determines propulsion of interstitial fluid currents – driving both the process of tumor infiltration and the resulting process of metastatic spread.
ACKNOWLEDGEMENTS The author thanks G. Imanidis for explaining colligative properties of molecules (Van’t Hoff equation), H. Müller and J.B. Little for encouragement, R.K. Jain for critical scepticism, and
© 1999 Harcourt Publishers Ltd
Pressure in tumors
A. Nogawa, W. Mueller-Klieser, C. De Wit, S. Walenta, O. Thews, P. Vaupel and C.N. Coleman for critically raising specific questions and constructive comments that have helped to improve this model. This work was kindly supported by a grant of the Seymour Obermer Foundation.
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