Consider an example related to an excellent review of short timescale or acute hypoxia dynamics [1]. The authors in this paper present details for the very important observation of cyclical hypoxia, which has a dominant component of a few cycles per hour (see "kinetics" section on page 429). Such a timescale might correspond to biochemical transients in general, instead of just perfusion dynamics, and in particular to glycolytic oscillations [2]. Physics can play a large role in the understanding of such phenomena.

Glycolysis is a metabolism pathway that cells can use instead of the more typical process of aerobic respiration. With glycolysis, glucose is metabolized with a smaller net energy gain for the cell, bypassing the typical and more energy-efficient and oxygen-intensive process of aerobic respiration. As described below, glycolysis has been famously observed at abnormally high levels in cancer cells for a variety of reasons. Yeast cells rely completely on glycolysis for their energy, and the fields of biophysics and molecular dynamics have described striking oscillations in yeast glycolysis, and used nonlinear mechanics to successfully explain these dynamics.

I suggest that these oscillations could also play a major role in radiotherapy resistance and dynamics. Consider all of the following together:

Cancers exhibit glycolysis Many years ago, Otto Warburg observed that cancer cells exhibit a partial reliance on glycolysis even when there was an ample supply of oxygen [3]. Over the past decade, a larger role for this so-called aerobic glycolysis in many aspects of cancer has been confirmed [4]. Aerobic glycolysis is simply a term that describes the behaviour of cells that partially or totally rely on glycolysis even when they do not need to, such as during wound healing, for example, when the signalling and the glucose biomass from glycolysis is needed more than the energy, which is in the form of ATP (adenosine triphosphate) molecules.

Glycolysis exhibits oscillations There is another aspect of glycolysis that's less widely known outside of biophysics circles. It was observed in the 1960s that there is a ubiquitous phenomenon in glycolysis – the entire key reaction of the phosphofructokinase (PFK) enzyme is subject to spontaneous self-oscillations [5]. The PFK molecule is one of the most important regulatory enzymes in glycolysis – it comprises a central step in the process that affects the rest of the reactions chain. Such self-oscillations were explained by Evgeni Sel'kov in 1968 [6] and expanded upon many times.

ATP reacts with PFK to form adenosine diphosphate (ADP). PFK becomes more active by combining with the product itself, and so is autocatalytic. The more it reacts, the more it is further able to react, until it temporarily runs out of substrate. The process then repeats to become a nonlinear oscillation or a "limit cycle" under the right conditions, resulting in the oscillation of all intermediate metabolites. Large collections of yeast cells and beef heart extracts [7] can be synchronized and entrained to a pulsing substrate [5] (for proof of nonlinearity, see figure 2 of Boiteux et al [8]). A stochastic substrate input rate does not disrupt the oscillation, but the oscillations are still driven by the average substrate input rate.

Cancers exhibit oscillations As early as the 1970s, researchers noticed that hypoxia was changing on short timescales [9], and it is still being observed [10]. In fact, it was seen by many researchers – including recently in my lab using diffuse optics techniques – that the hypoxia oscillated in vivo, and that it is a common and well-established phenomenon [1]. Vascular flow modulates in phase with the cyclical hypoxia, leading researchers towards perfusion dynamics as the cause of cyclical hypoxia [11].

Therefore, one might conclude that the cause of cyclical hypoxia is modulating perfusion [1], and that vascular constriction or dilation is certainly likely to be part of the explanation. However, any mechanism that tightly couples the vascular dynamics to the metabolic dynamics could also produce this correlation, since all metabolites originating from PFK would experience oscillations. For example, signalling associated with vasoconstriction, like Ca2+, could also experience such transients [12]. The main point is that the vascular dynamics could respond to the metabolism dynamics and then subsequently affect the metabolic dynamics again. In effect, the vasoconstriction and vasodilation signalling may be just another coupled differential equation originating downstream from PFK and subsequently affecting the input to the PFK reaction.

There is evidence that radiotherapy can quickly alter tumour metabolism by tilting the balance towards more glycolysis [13]. The oxygen dynamics could then be very hard to generalize and test for predicted responses if nonlinearities are dominant. In other words, unless we know about the complex and nonlinear nature of these reactions ahead of time, our hypothesis testing could completely miss the cause-and-effect relationships that go into the assumptions.

An appropriate test, for example, may be whether a treatment moves from a stationary state to a non-stationary state, instead of simply an associated increase or decrease in oxygenation. For emerging treatments that deviate from typical fractionated dose schedules, there is a need to sense dynamic oxygen behaviour with sufficient time resolution and duration for adaptive treatments [14]. Hypoxia is likely to be the most important factor for emerging severely hypofractionated treatments [15].

If we apply the broad base of our physics knowledge to the biology itself, such as the above example of glycolysis and oscillations, there is much to be gained.