## ABSTRACT

A new ecologically inspired paradigm in cancer treatment known as “adaptive therapy” capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment sensitive cells to survive. These, in turn, suppress proliferation of the less fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multi-drug adaptive therapies. First, frequency-dependent “cycles” of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary “search space” reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences.

Dobzhansky’s now-famous quote that “nothing in biology makes sense except in the light of evolution” succinctly explains a worldview that has been widely adopted by the cancer biology community^{1}. Taken one step further, others have claimed that “nothing in evolution makes sense except in the light of ecology” which provided the basis for designing adaptive cancer therapies centered on principles from evolution and ecology^{2-4}.

Cancer is an evolutionary and ecological process^{5,6} driven by random mutations^{7,8} responsible for the genetic diversity and heterogeneity that typically arises via waves of clonal and subclonal expansions^{9,10}. Clones and subclones compete and Darwinian selection favors highly proliferative cell phenotypes, which in turn drive rapid tumor growth^{5,6}.

Recent emphasis on personalized medicine has largely focused on the development of therapies that target specific mutations. These targeted therapies do extend patient lives but cancer cells tend to evolve resistance within months or years^{11,12}. Prior to therapy, pre-existing resistant cell types are suppressed and kept in check by competitively superior, therapy-sensitive cell types. With the targeted therapy suppressing the sensitive cell, these resistant cell types experience competitive release^{13}. If total eradication of all cancer cells is not accomplished, the tumor will relapse derived from resistant cells that survived initial therapy^{14,15}. Upon relase, a second drug may be administered. Yet continuous use of this subsequent targeted therapy may inevitably result in the emergence of the corresponding resistant clones (Fig. 1A). This approach ignores considerations of heterogeneity and therapy as a selection event in somatic evolution^{9,16,17}.

## Enlightenment via evolution

Eradicating most disseminated cancers may be impossible, undermining the typical treatment goal of killing as many tumor cells as possible^{18,19}. Previous schools of thought saw maximum cell-kill as either leading to a cure or, at worst, maximizing life extension. Attempting to kill as many cancer cells as quickly as possible may be evolutionarily unsound and facilitate resistance evolution and loss of therapy efficacy. Evolution matters. A recent (2012) systematic literature analysis of cancer relapse and therapeutic research showed that while evolutionary terms rarely appeared in papers studying therapeutic relapse before 1980 (< 1%), the use of evolutionary terms has steadily increased more recently, due to the potential benefits of studying therapeutic relapse from an evolutionary perspective^{20}.

A new paradigm in the war on cancer replaces the “treatment-for-cure” strategy with “treatment-for-contain” - receiving cues from agriculturists who have similarly abandoned the goal of complete eradication of pests in favor of more limited and strategic application of insecticides for control^{18,21}. This eco-evolutionary inspired paradigm for cancer treatment known as “adaptive therapy” capitalizes on subclonal competitive interactions. Resistance may confer some fitness costs due to increased rates of DNA repair or other costly activities required to pump toxic drugs across cell membrances. Cancer cell resistance mechanisms, whether mitigation, detoxification, or re-routing metabolic pathways, divert finite resources that would otherwise be available for cell proliferation or other avenues for cell survival^{13,19,}^{22}.

The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment sensitive cells to survive (see Fig. 1B, blue). These readily treatable sensitive cell serve to supress the proliferation of the less fit resistant populations (see Fig. 1B, red). Adaptive therapies have now been tested experimentally^{23},^{23,24} and are currently being applied across multiple clinical trials (NCT02415621; NCT03511196; NCT03543969; NCT03630120) at the Moffitt Cancer Center^{25}. These adaptive therapies capitalize on competition for space and resources between drug-sensitive and slow growing drug-resistant populations^{26-28}.

## Steering patient-specific evolution

This adaptive approach means that each patient’s treatment is truly personalized based on the tumor’s state and response rather than a one-size-fits-all fixed treatment regime^{29}. There remain several open challenges in designing adaptive therapies. First, treatments can aim to steer and control the eco-evolutionary dynamics to where the tumor finds itself in an evolutionary dead end^{30}, an evolutionary double-bind^{31-33}, or evolutionarily stable control^{18,27,34}. Yet, for clinical practice, how to design such therapies remains difficult. Second, it’s not yet clear how to extend these evolutionarily enlightened therapeutic concepts to multiple treatments. Two schematic examples are illustrated in Fig. 1C and 1D. Is it evolutionarily optimal to reproduce the single drug adaptive therapy in a sequential (Fig. 1C) setting or in combination (Fig. 1D)? Synergizing treatments such that evolving resistance to one drug makes cells more susceptible to another requires mathematical modeling as well as improved monitoring methods^{35,36}.

Figure 2 provides a schematic of steering the tumor into “cycles” of tumor evolution. A cycle is defined as a treatment regimen that steers the tumor into periodic and repeatable temporal dynamics of tumor composition. As seen in figure 2, a weekly biopsy shows the frequencies (pie charts) of 4 phenotypes (blue, green, red, yellow) in the evolving tumor over time. At each time step, the state of the tumor is given by a vector, , indicating the frequency of each cell type composing the tumor. In this example, the fifth week produces a tumor composition, , which is approximately equivalent to the tumor composition at the start of therapy (). Theoretically, such cycles could be repeated ad infinitum to steer and trap tumor evolution in a repeatable (and controllable) cycle.

A trial may use sequences of *n* available drugs either alone or in combination (shown for *n =* 2 in figure 2). We employ the temiinology “treatment” to indicate the 2^{n} possible combinations: no drug, single drug, or combination therapy. These treatments can be administered in any arbitrary sequence with the goal of controlling *m* cell types. An adaptive trial for metastatic castrate resistant prostate cancer (NCT02415621) uses only two treatments: 1. Lupron and 2. Lupron & Abiraterone. Likewise, an adaptive trial for advanced BRAF mutant melanoma (NCT03543969) administers Vemurafenib and Cobimetinib in combination, followed by no treatment. Both trials use only two treatments out of the four (2^{2}) combinations possible with two drugs (no treatment; first drug only; second drug only; first and second drug in combination therapy). Opening up trial design to include the full range of complexity (i.e. 2^{n}) may allow for greater tumor control, but the treatment administered at each clinical decision time point must be chosen with care and forethought, to steer the tumor into a desirable evolutionary state.

Adaptive therapy has been attempted clinically using proxy measurements for tumor volume such as prostate-specific antigen marker (PSA) for prostate or lactate dehydrogenase (LDH) for melanoma. While these blood biomarkers are crude measurements of tumor burden, there have been many recent advances in reliable methods of monitoring tumor evolution using circulating tumor DNA as an informative, inherently specific, and highly sensitive biomarker of metastatic cancers (see^{37}). As monitoring methods mature, so must methods of prediction and quantification of evolution^{25},^{38},^{39}. To that end, the purpose of this paper is to introduce the following three concepts to consider in the pursuit of designing multi-drug adaptive therapies:

Frequency-dependent “cycles” of tumor evolution

Treatment-dependent evolutionary “search space”

Frequency-dependent evolutionary velocities

As seen in Fig. 1B,C, and D, the goal of an adaptive therapy is to maintain a stable tumor volume consisting of a substantive drug-sensitive population (blue) that is able to out-compete and suppress resistant populations (red, green, yellow). Adaptive therapy maintains a stable tumor volume in favor of controlling the tumor composition (i.e. mitigating the onset competitive release of resistance). Using this simplifying assumption of a (relatively) constant tumor volume allows us to focus on the frequency dynamics within the tumor, ignoring (for the moment) population dynamics and turning to a game theoretic modelling framework. Frequency-dependent models of tumor evolution are particularly suited for studying tumor control (i.e. “cycles” of tumor evolution), determining the set of possible evolutionary dynamics (i.e. evolutionary search space), and timing of evolution (i.e. evolutionary velocity). The next section uses a simplified extension of a previously published model of prostate cancer^{25,40}. This case study introduces and develops these generalizable concepts for designing multi-drug adaptive therapy treatment schedules for three cell types (m = 3 phenotypes; figure 2) under two drug treatments (n = 2 drugs; figure 2). In principle, the concepts applied to this particular case study can be extended to an arbitrary number of available treatment combinations for desired control of an arbitrary number of cell types.

## Results

### Case study: metastatic castrate resistant prostate cancer

In progressive prostate cancer, continuous or intermittent androgen deprivation (IAD) are common treatments that generally leads to a substantial decline in tumor burden. Eventually, tumor burden rebounds as a result of the rise of castrate-resistant cells^{41}. Upon castrate-resistance, adaptive therapy using abiraterone has shown considerable treatment success. Previously, this disease was described by a population dynamics model with three cell types: those that require testosterone for growth, *T*^{+}, cells that require testosterone but produce their own, *T*^{P}, or cells that are independent of testosterone, *T*^{-25}. This model served to motivate a clinical trial (NCT02415621) which administers continuous Lupron (limiting systemic testosterone production) and cycles of adaptive Abiraterone (anti-androgen). This model suggests that even with adaptive therapy, disease progression can be greatly delayed but remains inevitable.

In order to track the state vector of the tumor, , we set the variables *x*_{1}, *x*_{2}, *x*_{3} to the corresponding frequency of dependent (*T*^{+}), producers (*T*^{P}) and independent (*T*^{-}) cells, respectively, such that ∑_{i}*x*_{i},· = 1. The temporal dynamics of these different populations under treatment can be characterized inside a trilinear coordinates simplex (Fig. 3A) which gives a representation of every possible value of x, on a triangle. The corners represent a tumor consisting of 100% of either *T* ^{+} (top corner), *T*^{P} (left corner), and *T*^{-} (right corner). Figure 3 shows the temporal dynamics under each treatment.

Every treatment scenario has an associated long-time equilibrium state: the tumor composition where all temporal dynamics eventually converge. For example, continuous treatment of Lupron leads to roughly equal fraction of *T* ^{+} and *T*^{P} (blue circle Fig. 3B). Continuous treatment of Lupron & Abiraterone leads to full saturation of *T*^{-} (blue circle Fig. 3C). Similarly, administering no treatment leads to an equilibrium of mostly *T* ^{+} and roughly equal (but small) proportions of *T*^{-} and *T*^{P} (purple circle Fig. 3D). The goal of adaptive therapy in prostate cancer is to delay the onset of the resistant *T*^{-} population by well-timed *switching* between each treatment. This is equivalent to switching between each triangular phase portrait in figure 3 before reaching the resistant equilibrium state of any given treatment. In theory, a periodic (closed) cycle can be constructed by switching between treatments at carefully chosen times in order to design schedules that are superior to continuous maximum tolerated dose^{42}, ^{43}.

### Searching for cycles

For example, figure 4A shows a patient with an initial condition of roughly equal fractions of each cell type (blue circle). Lupron might be administered for some time (blue line) before switching to no treatment (purple line), followed by a switch to both Lupron & Abiraterone (red line). This sequence of treatments arrives back at the same initial condition: an evolutionary cycle. This treatment sequence can be repeated, controlling the tumor. The dashed lines on figure 4A show dynamics under continuous treatment which lead to respective equilibrium states, spiralling out of the evolutionary cycle.

The identical evolutionary cycle paradigm is shown with cell fraction, over time in figure 4B. By appropriate treatment switching, the three cell types remain in competition with each other, and no cell type is able to dominate but instead are balanced indefinitely in closed periodic cycles thereby avoiding the emergence of resistance. The tumor undergoes 3 such evolutionary cycles, where the tumor “resets” back the initial state before treatment (pie charts, figure 4).

From this perspective, adaptive therapy benefits from treatment holidays precisely because these holidays help the tumor composition be pushed into an approximate cycle. Yet, when slightly off, resistance still *eventually* occurs in adaptive therapy regimes when not on an exact cycle (Fig. 1B, red). By observation, many such cycles exist in the state space shown in Fig. 3D: for example, traveling down any Lupron trajectory (blue), switching to a no treatment trajectory (purple) and so on, repeated ad infinitum. Where do such cycles exist? Which cycles are preferable? To answer these questions, the next section introduces concepts of evolutionary search space and evolutionary velocity.

### Evolutionary search space

These same phase portraits can be drawn for each pairwise treatment combination (Fig. 5). Each treatment has an associated equilibrium (solid circles), which can be connected by a single evolutionary trajectory. These two connecting trajectories represent a bounding region of state space where a periodic cycle resulting from sequential combination of the two treatments is guaranteed on the outer rim of this region (directionality shown with black arrows). As can be seen in Fig. 5, all external trajectories tend toward either treatment’s equilibrium, or towards the inside of the bounding domain. The implications are clear: sequential treatment between any two drugs for a sufficiently long time results in limiting the “evolutionary search space” of the tumor composition.

At least one cycle exists for each pairwise treatment scenario: the outer rim of the absorbing state. There may be other cycles, existing only in the interior of the region. For some pairwise combinations, the bounding region is quite large (see Fig. 5A: Lupron ↔ Lupron & Abiraterone); for others quite small (see Fig. 5B: no treatment ↔ Lupron or C: no treatment ↔ Lupron & Abiraterone). Once treatment drives the tumor composition into one of these bounding regions, it’s impossible to traverse outside without the addition of a third treatment.

Considering the three treatment scenarios together (see Fig. 5D: no treatment ↔ Lupron ↔ Lupron & Abiraterone) expands the evolutionary search space. Arbitary cycles can be constructed by clever sequences of treatment inside this expanded evolutionary search space. To illustrate which regions in which cycles may be preferable, the next section will describe evolutionary velocity.

### Evolutionary velocity

The evolutionary “velocity” (and each of its velocity components) of each treatment scenario can be viewed on the same trilinear simplex, seen in Fig. 6 for no treatment (6, left column), Lupron (6, middle column), and Lupron & Abiraterone (5, right column). A low velocity indicates a slow change to the tumor composition (calculated as the magnitude of the resultant vector of all components in eqn. 1: see Supporting Information). Several recent studies have indicated the importance of studying temporal effects of drug administration. Using human breast cancer explants, in vitro cells, mouse in vivo studies combined with mathematical modeling, one study showed that a temporary exposure to a taxane induces phenotypic cell state transition towards a favored transient chemotherapy-tolerant state which disappears when the drugs are administered in combination^{44}. A separate study noted the appearance of weakly proliferative, resistant cells under high dose therapy is transient and controllable by non-genetic, stem-like (reversible) characteristics that depend on timing and length of drug administration^{45}.

In short: timing matters. Introduction of combination therapy or altering the timing of sequential therapy changes the evolutionary velocity of the underlying tumor composition. One can imagine scenarios where a fast or slow evolutionary velocity is desired. A tumor with a high composition of resistant cells may need to navigate to a fast dynamics region to rapidly decrease the resistant subpopulation. Alternatively, an adaptive regime may capitalize on slow velocities regions that ensure slow evolutionary dynamics on treatment holidays.

Frequency dynamics models allow for monitoring and control of the velocity of a single cell type (see Fig. 6 D - L). For example, under continuous Lupron & Abiraterone treatment, the velocity of the *T*^{-} population is positive for most of the state space (see Fig. 6L). In order to control the *T*^{-} population, it’s necessary to switch to a new treatment: Fig. 6J or Fig. 6K. Depending on the current tumor composition, no treatment or Lupron may be desirable for negative *T*^{-} velocity (blue).

### Discussion

In the design of multi-drug adaptive therapy, the optimal method of combining therapies in an additive or sequential manner is unclear. A key observation is that the goal of adaptive therapy is to maintain a stable tumor volume in favor of designing therapies that alter tumor composition. We advocate for the use of frequency-dependent competition models (and in particular evolutionary game theory) to design novel multi-drug adaptive therapy regimens. This is a promising modeling approach, and more work must be done combining population models of changing tumor volume with frequency dependent models of changing tumor fraction in order to eliminate clinically unfeasible treatment schedules from consideration.

While it’s clear that tumors evolve in response to treatment, it’s proved difficult to exploit evolutionary principles to steer tumor evolution in an ideal direction. One limitation of current adaptive therapy clinical trials is the limited selection of drugs and limited monitoring methods. Even despite the lack of monitoring the exact state of the tumor composition, the technique of maintaining a substantial drug-sensitive population for extended tumor control has shown promise in mathematical models as well as preclinical and clinical trials. However, each of the on-going or planned adaptive therapy clinical trial utilizes less than the full range of treatment options available. For example, prostate cancer adaptive therapy sequentially administers Lupron and combination Lupron & Abiraterone, while ignoring no treatment or Abiraterone monotherapy. Similarly, the planned melanoma trial administers no treatment alternating with combination Vemurafenib and Cobimetinib. The conceptual paradigms introduced here (cycles of tumor evolution, evolutionary search space, and evolutionary velocity) provide a path forward to reducing the complexity of selecting between 2^{n} treatment choices at every clinical decision point.

Especially when developed in collaboration with clinicians, evolutionary models of cellular competition can provide clarity and power despite their simplicity. As a first step, we have illustrated these three adaptive paradigms in a specific case study (prostate cancer) for *n* = 2 drugs controlling *m* = 3 phenotypes (testosterone producers, testosterone dependent, testosterone independent cells). These techniques can be extended to any multi-drug adaptive therapy setting. The first step is to carefully choose competition parameters (i.e. the payoff matrix) of each cell phenotype under consideration and draw the dynamical phase portraits of possible evolutionary trajectories implies by the set of competition parameters. The power of evolutionary game theory is that the *relative* fitness of each phenotype is often easy to determine, allowing for straightforward construction and analysis of the model.

Each treatment will eventually fail due to resistance. The resistant state is the absorbing stable state of tumor phenotypic composition associated with continuous treatment. Example trajectories for a given treatment can be plotted, predicting the timing to reach this absorbing resistant state. When adding a second treatment in sequence, an absorbing bounded region of phenotype space (Fig. 5) can be drawn, which we term the evolutionary “search space” reachable with two or more treatments. This absorbing state space is bounded by a evolutionary cycle that connects the stable state points from each treatment. The search space may be be a small region (i.e. Fig. 5B) or large (i.e. Fig. 5A). Upon combining ail treatments, the state space is expanded, also leading to more options for cycles in new regions of the state space. Intuition would indicate that new drugs should be introduced that have “orthogonal” stable states - stable equilibria far from the equilibria of existing drugs. These orthogonal drugs open up the treatment space, allowing for more options in choosing cycles (Fig. 5D). The closeness of two stable states from two distinct treatments will give an idea of the “orthogonality” of two treatments, aiding treatment selection, the sequential ordering of treatments, and the timing of switching between treatments.

It is also important to note that not treating still allows the tumor to evolve. This no treatment case is often associated with slow evolution due to low selection. During treatment holidays used to avoid resistance to a first treatment, it may be wise to choose a faster (high selection) second treatment that gives a similar resultant tumor composition over the slow evolution of no treatment. Adaptive therapy is a promising step towards ecologically-inspired personalized medicine. Optimizing multi-drug adaptive therapy is not a straightforward task, but mathematical models are a powerful abstraction of clinical intuition, enabling the generation of new treatment schedules and comparisons to standard of care.

## Methods

Evolutionary game theory (EGT) is a mathematical framework that models frequency-dependent selection for strategies (phenotypes) among competing individuals. Competition between individuals is typically characterized by a “payoff matrix” which defines the fitness of an individual based upon interactions with another individual or the population at large^{46-48}. As a game, the payoff to an individual depends both on its strategy and the strategies of others in the population. As an *evolutionary* game, the payoffs to individuals possessing a particular strategy influences the changes in that strategy’s frequency. A strategy that receives a higher than population-wide average payoff will increase in frequency at the expense of strategies with lower than average payoffs. Such frequency-dependent mathematical models have shown success in modeling competitive release in cancer treatment^{13}, designing optimal cancer treatment^{49-51}, evolutionary double binds^{32}, glioblastoma progression^{52}, tumor-stroma interactions^{53}, the emergence of invasiveness in cancer^{54} as well as in co-cultures of alectinib-sensitive and alectinib-resistant non-small cell lung cancer^{55}.

In principle, there exist many frequency-dependent models of cell-cell competition which could adequately characterize this system: replicator dynamics models, stochastic Moran process models, spatially-explicit game theoretic representations, even normalized population dynamics models. Here, we simply require a model which analyzes trajectories of *relative* population sizes rather than *absolute* population sizes of *m* cell types under treatment from combinations of *n* drugs. For details on the specific implementation and parameterization of the model used in figures 3, 5, and 6, we refer the reader to Supplemental Information and to refs.^{25,40}.

The model presented below is a simplified frequency-dependent dynamics mathematical model (a qualitative extension of the model behind the first adaptive therapy clinical trial in metastatic prostate cancer^{25}). Using the simplifying assumption assumption of a (relatively) constant tumor volume allows us to focus on the frequency dynamics within the tumor, ignoring population dynamics. Tracking frequency dynamics that are themselves frequency-dependent allows us to use a game theoretic modeling framework.

We can use the 3 by 3 payoff matrix that describes the outcomes of interactions between the different cell types. The expected payoff to an individual of a given cell type is influenced by the frequency of cell types in the population (equation 1). This can be thought of as the “inner game“^{56}. The replicator equation from game theory, then translates these strategy-specific payoffs into the evolutionary dynamics described by changes in the frequencies of each cell type within the tumor (equation 2). This is the “outer game” where payoffs become translated into fitness.

The variables *x*_{1}, *x*_{2}, *x*_{3} are the corresponding frequency of dependent (*T*^{+}), producers (*T*^{P}) and independent (*T*^{-}) cells, respectively, such that ∑_{i}*x*_{i}. The prevalence of each cell type changes over time according to the changing payoffs, *f*_{i}, compared to the average payoff of all three populations 〈f〉 = ∑_{i}*f*_{i}*x*_{i}. Competitive interactions between these three cell types are summarized in the payoff matrix, *A*, below.

The expected payoff to a cell type is calculated as the product of the payoff entries and prevalence of each population (eqn. 2). Treatments are assumed to alter the carrying capacity for each cell type. Under Lupron, each producer cell is assumed to support 1.5 dependent cells, limiting the *T* ^{+} to rely on producers in the absence of systemic testosterone. During Lupron & Abiraterone combination treatment, each producer is capable of supporting 0.5 *T* ^{+} cells and the carrying capacity of *T*^{P} cells significantly drops due to local anti-androgen effects.

In order to simulate therapy, we introduced a weighting term, w,. The weighting term adjusts payoffs to a cell type by its carrying capacity (capacity of the tumor environment to support a given cell type). each cell type’s weighting term equals a given cell type’s carrying capacity, *K*_{i}, normalized by a maximum carrying capacity (*w*_{i} = *K*_{i}*/K*_{max} where *K*_{max} = 1.5 · 10^{4} cells). Under Lupron treatment only, the carrying capacities are given by: *K*_{1} = 1.5 · *K*_{2}; *K*_{2} = 10^{4}; *K*_{3} = 10^{4}. Combination Lupron & Abiraterone carrying capacities are given by: *K*_{1} = 0.5 · *K*_{2}; *K*_{2} = 10^{2}; *K*_{3} = 10^{425}. Carrying capacities for dynamics under no treatment are given by: *K*_{1} = 1.5 · 10^{4}, *K*_{2} = 10^{4}, *K*_{3} = 10^{4}.

The competition coefficients represented in the payoff matrix have been noted and described previously, and we summarize them in Supplemental Materials for convenience: Table 1 (under treatment) and Table 2 (no treatment)^{25,40,57}. Since there is cell-cell competition and niche partitioning with respect to association with surrounding vasculature, we assume that all coefficients are positive and bounded between 0 and 1. Consistent with ref.^{25}, two general rules are used to determine the relative values of inter-cell type interactions: 1) *T* ^{+} cells with no exogenous testosterone are the least competitive cell type and 2) the competitive effect of *T* cells is stronger on TP cells than on *T*^{+} cells. Unless otherwise noted parameters for untreated dynamics are: *a =* 0.2; *b =* 0.6; *c =* 0.3; *d =* 0.5; *e =* 0.4; *f =* 0.1, for Lupron only are: *a =* 0.4; *b =* 0.3; *c =* 0.6; *d =* 0.5; *e =* 0.2; *f =* 0.1, and for Lupron & Abirateron are: *a =* 0.5; *b =* 0.1; *c =* 0.6; *d =* 0.2; *e =* 0.4; *f =* 0.3.

## Acknowledgments

The authors gratefully acknowledge funding from the Physical Sciences Oncology Network (PSON) at the National Cancer Institute, U54CA193489 (supporting J. West, J. Brown and A. Anderson) and European Union’s Horizon 2020 research and innovation program, under the Marie Sklodowska-Curie grant agreement No. 690817 (L. You).