Spread of human cancer cells occurs with probabilities indicative of a nongenetic mechanism

Abstract

There has been much uncertainty as to whether metastasis requires mutation at the time of spread. Here, we use clinical data to calculate the probability of the spread of melanoma and breast cancer cells. These calculations reveal that the probability of the spread of cancer cells is relatively high for small tumours (B1 event of spread for every 500 cells for melanomas of 0.1 mm) and declines as tumours increase in size (B1 event of spread for every 10 8 cells for melanomas of 12 mm). The probability of spread of breast cancer cells from the lymph nodes to the periphery is B1 event of spread for every 10 8 cells in the nodal masses, which have a mean diameter of 5 mm, while the probability of spread of cancer cells from the breast to the periphery when the primary masses are 5 mm is also B1 event of spread for every 10 8 cells. Thus, the occurrence of an event of spread from the breast to the lymph nodes appears not to increase the propensity of the progeny of those cells to spread from the lymph nodes to the periphery. These values indicate that the spread of human breast cancer and melanoma cells is unlikely to occur by a mechanism requiring mutation at the time of spread. There has been much uncertainty as to whether metastasis requires mutation at the time of spread (Cifone and Fidler, 1981;Fidler, 1983;Sobel, 1990;Welch et al, 2000;Yokota, 2000;Bernards and Weinberg, 2002;Couzin, 2003;Bernards, 2003;Van't Veer and Weigelt, 2003;Yang et al, 2004). Mutations have a number of characteristic features, in terms of the rates of their occurrence and other qualities, which are diagnostic: mutations are rare, a phenotype conferred on a cell by mutation is inherited by the progeny of the cell, and the rates of the appearance of phenotypes caused by mutations either remains constant over time for those phenotypes requiring only a single mutation, or increase in frequency for those phenotypes requiring the accumulation of multiple mutations. We have recently shown that from clinical data it is possible to measure the rates of metastatic spread, expressed in terms of the probability of spread per cell (Michaelson, 1999;Michaelson et al, 2002Michaelson et al, , 2003. Here we use this methology to measure the probability of spread per cell for human breast cancer and melanoma. The values of these probabilities are inconsistent with metastasis occurring by a process of mutation.

Why cancer at the primary site and in the lymph nodes contributes to the risk of cancer death

“…We have observed that, when information is available only on tumor size, a simple expression, the SizeOnly equation, accurately captures the relation between primary tumor size and lethality, as observed from our data on patients with breast carcinoma, renal cell carcinoma, and melanoma [1][2][3][4] (for the SizeOnly equation, see Equation 1 from the accompanying article 4 ). We also have observed that the relation between tumor size and the risk of cancer in the lymph nodes is captured well by a variant of the SizeOnly equation, the NodalSizeOnly equation (see Equation 1n in the accompanying article 4 ), as indicated by data from patients with breast carcinoma and patients with melanoma.…”

“…Apparently, the probability of an event of lethal spread, per cell, is the same regardless of the site from which the cancer cells originate. It often has been wondered whether mutation at the time of spread is a requirement for metastasis [8][9][10][11][12][13][14][15][16][17] ; however, following the reasoning outlined previously, 3 the values for the probabilities of metastatic spread of breast carcinoma, renal cell carcinoma, and melanoma cells presented here are difficult to reconcile with such genetic change: First, the value of the probability of lethal spread for the smallest melanomas (0.1 mm), at approximately 1 event of spread for every 500 cells, is many orders of magnitude greater than that expected for a genetic change. Second, the probability of metastatic spread per cell from the primary site declines as the tumor increases in size.…”

“…Indeed, we have demonstrated mathematically 3 that just such a process should be expected to result in a reduction in the per-cell probability of spread, such that the relation between p and N is well fit to…”

“…2 and 3) reveal the remarkable finding that, as tumors increase in size, the per-cell probability of the spread of cancer leaving a mass does not remain constant but declines in value. 1,3 Furthermore, this decline occurs in a very characteristic fashion, such that the relation between the probability of the spread of cancer cells and the size of the mass from which the cells emerge, N, is well fit by a power function:…”

“…3 Of course, the analogy would be closer if the bricks increased in number by mitosis, if the bricks had a chance for nonlethal spread to a local site (a fender?) from which a second event of lethal spread could occur, and if the pile was approximately spherical mass.…”