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Cancer risk across species

Abstract
Introduction
Materials
Methods
Proof
Graph
Results
Discussion

Abstract

Preparedness against cancer in humans, mammals and birds reflects the potency of the autonomic nervous system (ANS) and mental characteristics.

Hypothesis
It is established that transformed cells lose the anchorage to adjacent cells and express an excess of adrenergic receptors. Afferent autonomic nerves respond to this and trigger a cascade in the brain causing intensive discharge of noradrenalin from efferent sympathetic nerves near the receptive cell, which ceases.

Methods
The statistics leads to experiments with a system of nonhomogeneous differential equations that confirm an inverse relationship between cancer and ANS.

Conclusion
The ratio of ANS in the brain to the whole brain determines the prevalence of cancer across species. This ratio is larger in birds and big mammals.
Psychological factors that counteract carcinogenesis are important within species, e.g. schizophrenia and the obscure establishment of a mental cancer preparedness in infancy.


Introduction

Keep in mind that the probability of malignant transformation of a cell is millions of times greater in whales than in mice, because of the enormous difference in the number of cells. Paradoxically, Beluga whales have a cancer prevalence of 1/367 of mice (table), which necessarily disqualifies the substantially immutable suppressor-genes, e.g. DNA repair, as significant anticancer factors in mammals and birds. The failure of wild-type p53 gene therapy in human cancer cells, expressing a mutant p53 protein and other cases, contributes to this contention.

Deductively, it seems evident that a species-specific fraction of spontaneous and induced malignant transformations, probably myriads during a lifespan, becomes eradicated before tumorigenesis. ANS might be the effector, since it through the action of noradrenalin is capable of inducing apoptosis in lymphoproliferative diseases such as leukaemia, lymphomas and myelomas. It also explains the reciprocal relationship between body weight and cancer, and opens further up for the significance of the psyche by cancer.

Tumors may be innervated by autonomic nerves, and since 'nerves always have a function' it is conceivable that autonomic afferent fibres, presumably parasympathetic, are able to sense freely disseminating cancer cells who lost the anchoring to adjacent cells. A subsequent release of a hierarchical cascade in the brain may regulate the selective discharge of high levels of noradrenalin from sympathetic efferent nerves into that location in a pinprick fashion, where the cancer cell will be the obvious target due to its over-expression of adrenoceptors. The discharge may take place in a pulse-like manner, probably with an enhanced uptake and reuptake of catecholamines from the surrounding interstitium to the nerve terminals. This will increase the synthesis of cAMP in the cancer cell, whereby cellular processes are accelerated and lead to depletion of substrates and energy resources. The lethal effect may appear within short time, perhaps even minutes.
It is a discrete system, which departs from the haematogenous flow of catecholamines produced in the adrenal medulla, and it is localized to the brain, as proved by the following: Catecholamines in the brain become liberated by amphetamine, whose therapeutic field of activity predominantly is the central nervous system (CNS). The use of amphetamine reduces the incidence of spontaneous tumors in mice and rats, however, not exclusively within the therapeutic CNS-field, but throughout the entire body.

The low cancer risk in birds may be attributed to a superior function of specifically ANS since the corpus striatum, a basic part of the cerebral hemispheres, is proportionally larger in birds and better developed, which favours instinctive behaviour and autonomous processes.

Individual susceptibility
ANS operates, at least in humans, as a mentally-based cancer preparedness formed early in life by conditioning. This explains why a particular carcinogen does not necessarily cause cancer in all exposed, which is parallel to the limited penetrance in some hereditary cancers. Stress, ascribed to 'fight or flight', differs from the high sympathetic activity and sense of own body observed in schizophrenia and is also distinct from the low sympathetic activity in the elderly. Not unexpectedly is the cancer incidence in both groups inversely proportional to their sympathetic activity.
All things considered, there is hardly a common denominator for a mental condition that predisposes to cancer. But nevertheless, it is striking that Denmark has one of the highest cancer-incidences in the world in spite of huge investments in the cancer research and comprehensive restrictions against suspected carcinogens. Is it a matter of competence or can it be related to the abandonment of the individual because of an overprotective and controlling society?


Materials and methods

The 'materials' comprise eleven species, shown in the table below, where the frequency of malignant tumors is either given in advance or was determined using the tables in the references for rats and mice.
The elephant’s cancer mortality rate is 4.81% against 11% in humans. Hence, 4.81/11 multiplied by 320/105 (the tumor frequency in humans) = 139.9/105, which equals the tumor frequency in elephants.
It has been suggested that the elephant's low cancer risk is due to multiple copies of the p53 gene. However, the weight and cancer frequency of the elephant fits persuasively with the tendency of species in the table below.
The 'methods' are divided into two stages: The relationship between body weight and cancer, brain/body and cancer as well as the proportionality between these entities, became analyzed by power regression and linear regression. This was followed by a system of differential equations where the resulting graph displays the species-specific activity of the sympathetic nervous system compared with the frequency of cancer.


m: male
f: female
Average bodyweight in kg     Malignant tumors/                  samplesize              Quota Weight ratio
(brain/body)
  Elephants    African and Asian; m. and f.   = 4800 139.9/105 14 0.00054
  Whales    1000   Beluga      = 1000 163/105 16 0.001
  Cattle    (500 + 600)/2       = 550 177.2/105 18 0.001
  Horses    (480 + 540)/2       = 510 256.3/105 26 0.0013
  Humans    (50 + 90)/2           = 70 320/105 32 0.02
  Dogs    (7 + 59)/2             = 33 828/105 83 0.0035
  Cats    (4 + 5)/2 = 4.5 257.4/105 26 0.0066
  Rabbits    271 m. of  2.7;                 
   328 f. of  3.0        =
2.86 16/599 ≈ 0.027 267 0.008
  Rats    Sprague-Dawley: 179 m of
   0.485; 181 f of  0.275           =
0.380 79/360 ≈ 0.22 2200 0.0163
  Mice    B6C3F1: 1471 m of 0.0291;           1452 f of 0.0302                   = 0.03 900/2885 ≈ 0.3 3000 0.026
  Birds    Melopsittacus undulatus (Budgerigar)
   (0.03 + 0.04)/2      = 0.035 0.158   (p.130) 1581 0.0833

Besides the links above about the weight ratio brain/body, allometric formulas have been used to calculate brain weight. All weights are calculated in grams:
log (brain weight) = log 0.809096 + 0.525·log (body weight).
Rabbits, rats and mice: log (brain weight) = log 0.0626 + 0.7739·log (body weight).


Proof

Statistics

Body weight versus cancer
The configuration of the eleven body weights against their respective cancer rates creates virtually a hyperbola due to the potentiated increase of cancer when the species get smaller, thus eliminating a linear regression.
However, the Power regression, y = b⋅xa, equal to y = 0.0391⋅x−0.4709, is able to deal with this particular configuration that exhibits very strong bonds between body weight and the corresponding frequency of cancer.
The raw data of the eleven species provide the correlation coefficient, r = 0.923147. Significance: t = r⋅[(10−2)/(1−r2)]1/2 = 7.203688. The degrees of freedom, 11−2 = 9, which according to statistic tables provide: P <0.001.

Weight-ratio brain/body versus cancer
The Power regression, y = b⋅xa = 2.5448⋅x1.0451, from the raw data of the weight-ratio brain/body against the frequency of cancer in the eleven species, provides: r = 0.800187,
t = 4.002603, leading to 0.001< P <0.01.

Modeling
Body weight, w, is equivalent to the number of cells, and the law of probability states that cell number and the likelihood of the occurrence of a malignant cell, C, will increase concomitantly. But strangely, a reduction in the cancer frequency is seen when w increases and the weight ratio brain/body (b/w) decreases, which requires insertion of a compensatory factor because of the immutable nature of the suppressor genes.
This paradox can be explained by the features of the autonomic nervous system, whose trophic centers in the brain evolutionally are adapted to the size and physiology of the species. Thus, the ratio of brain's ANS to the whole brain will increase by body size, because the ratio brain/body successively becomes smaller.
Therefore, in achieving an anticancer factor, the body weight, not the brain, should be multiplied by an arbitrary 'sympathetic coefficient', s, which gives sw. This term is subtracted from the above theoretical cancer incidence and provides the observed cancer incidence: C−sw = c, or C = sw + c, where c qualifies for the independent variable.

Proportionality between w + b/w and sw + c
The function of w is the ratio brain/body, f(w) = b/w. Their sum, w + b/w, is, as the following shows, highly correlated with the observed frequency of cancer:
The raw data of budgerigars and the ten mammals are inserted into w + b/w against sw + c and assessed at linear regression, y = a + b⋅x, or y = 0.0765 + 0.2⋅x. The coefficient, s, is currently set to 1/5 in mammals and 1/3 in birds, but additionally, experimentally, from 1/50 until 0.9, whereby the resulting, r2 = 1, yields a convincing correlation.

Hence, the following expression is verified as a proportionality of the above findings:

w + b/w ∝ sw + c

This is transformed into a default equation without affecting the final outcome:

x1 + x2 = x3 + c

Subsequently, it is arranged in order to set up the differential equations in MAPLE:

diff (x(c), c) − c = −x1 −x2 + x3


Differential equations
Some strains of rats and mice exhibit more or less malignancies than the common and well described Sprague-Dawley and B6C3F1, whose risk of cancer is consistent with the fact that the number of spontaneous tumors occurring in the rat significantly is smaller than those observed in the mouse.
The data of budgerigars are uniquely defined, but they have an extremely high incidence of spontaneous malignant tumors compared to other birds. However, the frequency is only about one half of the cancer found in mice.
The colors refer to the colors in the graph.

Body weight brain / body Sympathicus Cancer
Sprague-Dawley Rats - 0.380x1 - 0.0163x2 (s) 0.380x3 0.22c
B6C3F1 Mice - 0.030x1 - (1/40)x2 (s) 0.030x3 0.3c
Budgerigars - 0.035x1 - (1/12)x2 (s1) 0.035x3 0.158c

All values of the table above are multiplied by 1000 and inserted into the matrices below. The sympathetic coefficient, s, of rats and mice is set to 1/5 body weight.
The coefficient, s1, of the bird is put at 1/3 body weight in accordance with an advanced sympathetic activity.

- 380x1 - 16x2 76x3 220c
x′ = - 30x1 - 25x2 6x3 + 300c
- 35x1 - 83x2 12x3 158c


Solutions
The lines of the graph with the sympathetic coefficients, s = [1/5 1/5 1/3]T :

x1 (c) =
+ 5.19583 + 33.39707 c
+ C1 exp(−24.81245 c)
+ C2 exp(−373.05978 c)
+ C3 exp((135.87224−10−7 i) c −131 c)

x2 (c) =
−0.39054 + 11.90687 c
+ 1.82118⋅C1 exp(−24.81245 c) + 0.08431⋅C2 exp(−373.05979 c)
+ (−0.31778 + 1.12913⋅10−8 i)⋅C3 exp((4.87224−1.70892⋅10−7 i) c)
+ 0.33123⋅C3 exp((4.87224−1.70892⋅10−7 i) c)

x3 (c) =
+ 26.33635 + 166.59734 c
+ 5.05693⋅C1 exp(−24.81245 c) + 0.10907⋅C2 exp(−373.05979 c)
+ (−0.00279 + 1.28541⋅10−10 i)⋅C3 exp((4.87224−1.70892⋅10−7 i) c)
+ 5.06973⋅C3 exp((4.87224−1.70892⋅10−7 i) c)


By setting the independent variable c equal to zero, the symbolically solved parameters,
C1, C2 and C3, can be evaluated by aid of ordinary equations:
{C1 = 0.2546299436, C2 = 0.001384276583, C3 = −5.451840860}


Graph


The lines correspond to the above equations, x′, where the body weight of rats and mice is multiplied by 1/5 and budgerigars by 1/3 to form sw.

Results

The graph shows that increasing cancer risk and weight ratio brain/body correspond to a decrease in both body weight and sympathetic activity, which serves as a proof for the role of ANS in cancer. This order is also seen when s = [1/50 1/50 1/50]T, but here is the line for the body weight only slightly declining, indicating that such small coefficients do not reflect the real strength of ANS.
The constellation of the other probands was partly calculated and showed a similar pattern, but the large 'gaps' between their values rendered the calculations enormous, which resulted in a very restricted range of the lines.

It has been contested that increasing body weight generally can be correlated to a decreasing rate of cancer, but as stated, the choice of the statistical method is crucial. Unfortunately, statistics becomes largely customized the assumption that genes are the factor constituting the cancer defence.
Yet, the present sample is composed of species whose body weight and tumor incidence are adequately documented and deliver a high statistical significance, despite the use of raw data. This legitimizes the next step to a system of non-homogeneous differential equations whose result can not be manipulated - a method that is superior to the conventional statistical evaluation of research results.


Discussion

Cancer cells are not strictly autonomous, for instance require their excess of surface adrenoceptors an adequate supply of noradrenalin from sources outside the cell to allow proliferation and migration.
Trophic areas of ANS are subject to interference and inhibition from surrounding areas in CNS, resulting in inferior sympathetic functionality. This may particularly be true in small animals with correspondingly large brains because ratio sympathicus to the whole brain decreases faster than the body weight - as demonstrated in the graph. This may explain the potentiated increase of cancer in for instance mice and rats and perhaps in budgerigars too, since this family has large brains.

It is appropriate to emphasize that well known neurophysiological conditions, for instance the function of the genitals, are regulated by sympathicus and parasympathicus at approximately the same manner as may be the case with cancer. These regions, at least in humans, are subject to supervision from cortex cerebri, but in the infancy the pathways become conditioned and will manifest as various facets of sexuality in later life.
Furthermore, it is well established that psychological traumas might create sexual and hormonal dysfunction.

Citation
Mountcastle V.B. In: Medical Physiology, 14th Edn. St. Louis: Mosby, 1980: pp. 899, 903:
– 'The autonomic unification of this system would lead one to predict a generalized discharge. This seems to be less of a mystery than the channelling of activity through this system, which permits rather discrete reflex actions and the occurrence of tonic activity in only certain of the sympathetic fibers. The centers that control this system can, to a great degree, determine whether it discharges selectively or totally. Under basal conditions, selective tonic and reflex activities occur, but under stress or in anger the system discharges as a whole'. –


© Copyright Ebbe Lundsgaard, June 2018.