Special Relativity William Pye

Tumour Dynamics

Ryan Li

A cancer tumour is a group of aberrant cells whose uncontrolled expansion harms the surrounding host tissue, often leading to patient death. It is also a population of genetically and phenotypically varied cells that compete, multiply, and contribute to the cellular society. Tools from population biology are therefore increasingly used to study cancer dynamics. Cancer’s genetic instability and high mutation rate, along with strict spatial limits, a lack of resources, and immune surveillance, result in fast selection for the fittest tumour cells’ survival.

SOMATIC EVOLUTION THEORY

The nature of life is the arrangement and management of genetic information recorded in DNA, powered by energy obtained from solar and chemical sources and polished via mutation, selection, sex, and recombination. To preserve previous evolutionary achievements, biological organisms spend extensively in a wide range of DNA repair systems that ensure correct DNA replication during cell division and the removal of DNA damage. However, random mutations nevertheless accumulate in genomes and contribute to diminished fitness with age. According to the somatic mutation hypothesis of ageing, the accumulation of mutations in the genetic material of somatic cells over time leads to a reduction in cellular function.

Cells (blue) are constantly exposed to DNA damaging events throughout normal organismal ageing, which eventually results in cells containing numerous mutations (red). Some mutations develop in genomic areas, resulting in uncontrolled cell growth. Adopting a mutator phenotype allows for faster somatic evolution, which constantly acts to select for cells capable of bypassing many defensive systems that prevent uncontrolled cell growth.

PROTO-ONCOGENES AND TSGs

Cancer progression involves multiple genetic events, which can activate oncogenes and disrupt the function of specific tumour suppressor genes. Proto-oncogenes are genes that ordinarily aid in the growth of cells. When a proto-oncogene mutates or has excessive copies, it can permanently activate. When this happens, the cell proliferates uncontrollably, resulting in cancer. This mutant gene is referred to as an oncogene. Tumour suppressor genes (TSGs) are normal genes that regulate cell division, correct DNA errors, or induce apoptosis. When TSGs fail to function properly, cells can multiply uncontrollably, leading to cancer. For example, tumour suppressor p53 mutates in almost half of all malignancies, and its expression and mutational status drastically influence cellular competitiveness. Oncogenes result from the activation of protooncogenes, but TSGs cause cancer when they are inactivated.

CLONAL COOPERATION INDUCES METASTASIS

Tumours are made up of numerous subclones with varied genetic and phenotypic traits as a result of genetic and epigenetic modifications, as well as variable tumour microenvironments. Intratumor heterogeneity promotes clonal collaboration through cell-cell contact or factor secretion, resulting in faster tumour development. Subpopulations originating from the same tumour might have varying metastatic potentials. Furthermore, there is a link between tumour heterogeneity and metastasis. Despite the apparent relevance of distinct inherent properties of different subpopulations, collaborative interactions across subpopulations can also help the metastatic cascade. Subpopulations may obtain a selective advantage throughout the metastatic phase if interclonal cooperation exists. Metastatic subclones can increase the metastatic potential of non-metastatic subclones. For example, the rat mammary cancer cell line has two stable subtypes: epithelioid cells (E-cells) and myoepithelioid cells (M-cells). Surprisingly,

collagenase, enzymes that break down the native collagen that holds animal tissues together, could only be secreted enough when both cellular types were present. In brief, a soluble component produced by M-cells stimulates collagenase production by E-cells, demonstrating that interclonal cooperation may increase at least local invasiveness. The presence of a metastatic subpopulation in the circulation can enhance the metastatic potential of non-metastatic subpopulations located in either subcutaneous sites or circulation.

CLONAL COOPERATION INDUCES TUMOR GROWTH

Human cancers have a high genetic and phenotypic variability, partly due to the chromosomal instability in cancer cells. Tumorigenesis, the gain of malignant properties in normal cells, are aided by complex signalling connections between cancer cells and their surroundings and collaboration or competition amongst diverse cancer clones.

Cell-cell interactions rely heavily on pathways that control cell growth and death. Normal cells in a tissue respond to irradiation by promoting cell proliferation to restore tissue homeostasis following cytotoxic insults. This adopts the mechanism of cell competition (CC). CC is a homeostatic process in which cells detect and remove less-fit cells by initiating apoptosis of the less-fit cells. This is followed by compensatory proliferation, in which surrounding normal cells revive proliferation and thereby restore tissue size in response to the less-fit cell’s death. The idea of “super-competition” is identified as another cell behaviour in which mutant cells proliferate much more aggressively as they actively induce apoptosis to their neighbour normal cells. In all of these interactions, apoptosis promotes the cell proliferation of surviving cells, and if these events are stopped, tissue homeostasis is compromised. Stabilisation of a cancer tumour’s heterogenic nature occurs because of evolution; tumour heterogeneity is desirable, as a positive growth effect on subclones can confer a fitness advantage to them, and because multiple subclones with high fitness will then interfere with each other, inhibiting expansion of individual subclones.

Tumour cells use cell competition to promote tumour development. For example, CC between wild-type (WT) and mutant (MT) p53 progenitor cells, where MT p53 progenitors have a competitive advantage over WT counterparts, eliminates WT p53 cells from the progenitor pool via differentiation. Because p53 mutations are important cancer drivers, WT and MT p53 cells often engage in CC. CC selects MT p53 cells with higher neoplastic potential at the expense of WT cells, allowing cancer to spread aggressively. On the same principle, radiation-induced apoptosis triggers similar compensatory type signalling interactions. The cells that die due to radiotherapy encourage the compensatory proliferation of the surviving, and thereby radiation-resistant, cancer cells. Furthermore, referring to the cancer stem cell (CSC) theory, dying non-CSCs may stimulate compensatory proliferation of CSCs, which contributes to the aggressiveness of recurrent tumours, at least in part. This demonstrates that CC is active in cancer cell selection and may potentially drive the progression of oncogenic events and consequently tumour growth.

HYPERTUMOURS

Despite the benefits of subpopulation cooperation, it can result in tumour collapse if the driving subclone, which induces other subclones to grow non-cell autonomously, is outcompeted by fast-growing exploitive subclones. This may result in tumour collapse because it promotes homogeneity within the tumour, rendering it incapable of reacting to unfavourable circumstances such as hypoxia if “incompetent communicators” become prevalent; tumour homogeneity is undesirable. Competition between different clones of a cancer line reduces the ability and effects of cancer metastasis. Even if metastatic subclones arise through mutation, interclonal competition may hinder its proliferation, providing a potential explanation for recent surprising findings that most metastases are derived from early mutants in primary tumours. A phenotypic feature that is nearly always favoured in nascent tumours is angiogenesis, or the formation of new blood vessels within the neoplasm, as this delivers nutrients needed for tumour proliferation. Tumour cells induce angiogenesis when exposed to hypoxia by secreting tumour angiogenic factors (TAF). Competing tumour cells differ in growth potential and sensitivity to changes in local oxygen pressure, which influences birth and death rates and their ability to release TAF. Under realistic conditions, tumours anticipate the emergence of “hypertumours,” which are aggressive cells that fail to release enough TAF to promote tumour growth. In essence, hypertumours are “cheaters” who take advantage of the vascular infrastructure that other tumour cells have developed. This cheater population grows parasitically on the tumour, potentially harming it to the point of unviability. Hypertumours represent the primary mechanism by which tumours develop ischemic necrosis, a loss of blood flow.

THERAPEUTIC IMPLICATIONS

Intratumor heterogeneity positively correlates with a shorter time to relapse and increased multidrug resistance in different types of cancers. Almost all cancer patients die of recurrent malignancies rather than newly-diagnosed, naive tumours. Some patients respond relatively well to first-line therapy regimens but do not survive subsequent recurrences due to the recurrent tumours’ lack of therapeutic response to medicines.

Patients returning to clinics frequently encounter cancer relapse during or immediately after treatment due to quickly regrowing therapy-refractory tumours. Treatment of heterogeneous tumours with targeted therapies leads to the elimination of therapy-sensitive subclones, leaving behind intrinsically drug-resistant as well as death-resistant subclones. The bulk of the tumour will thereafter be repopulated by drugresistant subclones. Therefore, recurrent tumour samples include more of said resistant cells than naive, making treatment challenging. Furthermore, numerous additional cooperative processes may play a role in therapeutic resistance. For example, subclones expressing large quantities of immune-inhibitory molecules may help other subclones avoid immunological treatments like chimeric antigen receptor T-cell therapy by generating an immune-suppressive TME. Thus, reducing intratumor heterogeneity or disrupting existing clonal cooperation may be critical to overcoming resistance and postponing relapse.

Physics Extension

Dr Marc Scott

The Sun is not the first star to sit in our portion of the Milky Way. You weigh a fraction less travelling west in the northern hemisphere than you do travelling east. There are just as many numbers on the number line between 0 and 1 as there are in total. Science and the mathematics which supports its many theories is a marvellous and wonderful subject, enabling us to detail, predict and change the world around us, as well as astound us with bizarre and beautiful claims.

Over the last two years, Physics Extension has been an opportunity for any keen Sixth Formers to embark on getting to grips with the rules of the Universe from an undergraduate perspective. Open to all, not only our physicists, the weekly sessions have delved into topics such as classical mechanics (avalanche theory, rocket motion, gyroscopic motion), cosmology (FRW metric, shape and expansion of the Universe), thermodynamics (heat engines, the laws of thermodynamics, the derivation of the Boltzmann factor, microstates and macrostates) and the beginnings quantum mechanics (UV catastrophe, Planck distribution, Bohr model, Schrodinger’s equation). An outlet for those eager to push beyond the confines of the A Level specification, the class allows our future physicists and engineers to grapple with the mathematically abstract ideas which underpin the structure of bridges or the interactions between atoms. With Extension Physics there is no endgame, no exam to pass, no concrete syllabus to rigidly adhere to; our only stipulation is curiosity and a willingness to questions everything (especially the typos and frequent minus sign errors!). It is 90 minutes in the week, where people get together to discuss and learn about physics, what could be more fantastic than that?!

SIXTH FORM BIOLOGY & CHEMISTRY ENRICHMENT

The Radcliffe Punt

Mr Richard Evans & Dr Suzana Zizek

On a Wednesday evening in September 2020, seven aspirational Upper Sixth science students headed up to the biology lab B1. They subsequently participated in the first session of our Radcliffe Punt enrichment programme, designed to encourage Caterham’s Sixth Form science community to broaden their reading, presentation, and problemsolving skills beyond the limits of our A-Level syllabi. Originally envisioned as an Oxbridge preparation programme, and originally named Trinity Merton (after two Oxbridge colleges), the Radcliffe Punt settled into its new name and form in February 2021, when that year’s Lower Sixth picked up the gauntlet. Despite the Oxbridge-inspired current name, Radcliffe Punt has a much wider scope than just preparing attendees – the Punters – with interview skills. Our doors are open to all keen scientists. We launched our 2021 programme by handing out a couple of prestigious journal articles (past and present) from chemistry and biology, and the challenge for the Punters was simply to read them and prepare for an open-ended discussion at the next session. From the versatility of oxygen in biology to the sophistication of organic chemistry lab work, we went off on many tangents, all of which allowed the Punters to demonstrate the breadth of their reading and on-the-spot thinking. Since then, our biology and chemistry challenges have taken many enriching forms. We have debated the merits of mandatory COVID vaccinations and “designer babies” (albeit not at the same time). We have displayed various graphs and images on the screen and asked the Punters to “say what they see” and “explain what they see.” We have tested the Punters’ public speaking skills through presentations on grisly diseases and by playing the Radio 4 favourite Just a Minute (with topics ranging from “peer review” to “the chemistry of the amino acids”). We have, from a supposedly innocuous opening question, dived into a half-hour discussion about the insidious impact of Andrew Wakefield’s fraudulent claims about MMR vaccinations. In all of these, our focus has been on developing the Punters as all-round scientists. The world-leading scientist of the 21st century is not just capable of conducting high-quality experimental work; we must also be able to sell a compelling, evidence-based written or spoken argument, without resorting to the uncivil ad hominem attacks that have sadly become so common in today’s political world. The health of our planet and the organisms that inhabit it will continue to depend on our ability to be “the very model of a modern world-leading scientist.” Join us at the Radcliffe Punt to evolve into the best thinker that you can be.