Extending the Kinetic-Bystander Model for Spatially Fractionated Radiotherapy with Intracellular Epigenetic Memory

1. Introduction

Spatially fractionated radiation therapy (SFRT), delivered through GRID and LATTICE arrangements, produces clinical responses in bulky and otherwise refractory tumours that are difficult to reconcile with the spatial-independence assumptions of conventional radiobiology (Mohiuddin et al., 1999; Penagaricano et al., 2010; Tubin et al., 2019; Griffin et al., 2020). The treated regions receive ablative dose; the intervening valleys receive little to none; yet the tumour as a whole frequently responds in ways that exceed what dose-volume calculations predict. Three families of mechanism have been proposed in the literature: kinetic bystander signalling, in which irradiated cells emit diffusible factors that produce hazard at unirradiated neighbours (McMahon et al., 2013; McMahon et al., 2017); vascular damage in high-dose peaks producing systemic effects (Mohiuddin et al., 1999); and immune activation, particularly under hypofractionated SFRT regimens that resemble in-situ vaccination (Tubin et al., 2019; Tubin et al., 2021; Jenkins et al., 2024). Despite years of effort, the field has not converged on a unified account.

Among formal mechanistic models, the kinetic-bystander framework of McMahon and colleagues is the most rigorous account of how irradiated cells signal to their neighbours. The model couples extracellular signal concentration to a threshold-activated hazard at the bystander cell, with signal production proportional to dose, first-order decay, and a piecewise structure capturing the production-versus-decay phases. The framework provides the kinetic foundation for many subsequent extensions in the SFRT-bystander literature.

Two related limitations of the kinetic-bystander framework, however, point at the same underlying gap. First, the framework is parametrised at the chemical-kinetic level (signal production, diffusion, decay, threshold) and at the population-and-hazard level (cells exposed to above-threshold signal accumulate hazard at rate $\mu$); it does not specify what occurs inside the recipient cell once the signal arrives. The hazard rate $\mu$aggregates the entire intracellular response — receptor binding, signal transduction, transcriptional and post-transcriptional consequences, accumulation of damage or stress, decisions about survival — into a single parameter.

Second, recent structural identifiability analysis (Vaitheeswaran, 2026a) has shown that this kinetic-bystander framework exhibits intrinsic non-identifiability under conventional surviving-fraction observation. The eight parameters of the McMahon model collapse to five independent functional combinations in the dose-response signature: three dimensions of structural non-identifiability persist regardless of how densely the surviving-fraction observable is sampled. In the asymptotic large-dose regime, the direct radiosensitivity $\alpha$and the bystander rate product $\mu \gamma$are linearly confounded; in the near-threshold regime, the signal-dynamics parameters ${\eta }_{eff}$, ${\rho }_{max}$, $\lambda$, and ${\rho }_T$become entangled. These are not failures of estimation under noise. They are failures of the model-observation pairing at the level of the input-output map.

These two limitations are not independent. A model that compresses the intracellular response into a single hazard parameter $\mu$has, by construction, no observables to offer other than surviving fraction; without such observables, identifiability fails. The intracellular black box and the identifiability gap are two presentations of the same problem.

The intervening decade has seen substantial extension of the kinetic-bystander framework, in two distinct directions. The first is biological-scope broadening: reviews and synthesis papers (Asur et al., 2015; Moghaddasi et al., 2022; Jenkins et al., 2024) have established that radiation-induced non-targeted effects in SFRT comprise three classes — bystander signalling between low-dose and high-dose regions, cohort effects within irradiated volumes, and abscopal effects at distant sites — with substantial weight given to immune-mediated mechanisms including vascular restructuring, immune infiltration, antigen presentation, and immunological memory. The second direction is phenomenological model extension: empirical dose-distance interaction terms (Arous et al., 2025) have been added to the linear-quadratic framework to better capture the spatial signature of SFRT cell survival data without committing to a mechanism. The kinetic-bystander framework itself has been applied to clinical SFRT plans (Balvasi et al., 2025) and tested in theoretical simulation studies (Mahmoudi et al., 2022), but its mathematical structure has not been substantially modified.

Neither extension direction addresses the residual gap. The biological-scope broadening has identified that organism-level immune memory matters in SFRT — T cells, antigen presentation, lymph node biology, immunological memory in the conventional immunological sense — but says nothing about what happens inside individual bystander cells at the molecular level. The phenomenological extensions improve fitting but do not provide a mechanism for the parameters they add. The residual gap is therefore narrower and more specific: a molecular, cell-intrinsic, durable mechanism for the intracellular consequence of bystander signalling at the single bystander cell, complementary to but distinct from the organism-level immune-memory mechanisms.

We propose, as a hypothesis, that recent advances in the cellular memory literature provide this missing intracellular substrate. Li, Ravindran, O'Farrell and colleagues (Li et al., 2026) have demonstrated that the transcription factor AP-1, downstream of stress-response pathways including reactive oxygen species, cytokine signalling, and the DNA damage response, mediates the formation of cellular memory in cancer cells acquiring therapy resistance. The mechanism is specific: stress-activated JNK drives AP-1 nuclear translocation; AP-1 recruits the CBP/p300 acetyltransferase complex; CBP/p300 deposits H3K27 acetylation at AP-1-occupied loci; the bromodomain of CBP/p300 reads and propagates these marks across cell divisions; the resulting cis-epigenetic memory persists for weeks to months and durably modifies the cell's response to subsequent therapy. The mechanism is demonstrated to depend on AP-1 (attenuated by JNK-IN-8 and T-5224), on CBP/p300 catalytic activity (attenuated by A-485), and on CBP/p300 bromodomain function (attenuated by SGC-CBP30). The paper notes that AP-1 sits downstream of many stress pathways and that similar mechanisms may operate in other contexts.

The bystander signals identified in the McMahon framework — reactive oxygen species, inflammatory cytokines, DNA damage response derivatives — are precisely the stress signals shown to activate the AP-1 / CBP-p300 axis in other contexts. We therefore propose:

• Claim 1 (mechanism). Bystander signals during SFRT activate AP-1 in recipient cells via stress pathways, leading to CBP/p300-mediated cis-epigenetic memory formation that durably modifies cell behaviour, and this constitutes the missing intracellular layer of the kinetic-bystander framework at the single-cell level.
• Claim 2 (SFRT relevance). Incorporating this mechanism into the kinetic-bystander framework produces an extended model that explains cross-fraction accumulating effects, time-ordering sensitivity, and AP-1/CBP-p300-dependent response — features the original framework and its existing phenomenological extensions do not produce.
• Claim 3 (identifiability). The mechanism augments the observable space with chromatin and pharmacological observables that couple specifically to the intracellular memory layer, addressing the identifiability gap that conventional surviving-fraction observation leaves open.
• Claim 4 (complementarity to immune memory). The proposed cell-intrinsic memory operates at a different scale (single cell vs. organism), through different machinery (chromatin marks vs. T-cell repertoire), and is complementary to the immune-mediated mechanisms emphasised in recent reviews. A complete account of cross-fraction SFRT effects probably needs both.

We support these claims through three analyses that require neither numerical simulation nor re-analysis of clinical data: a timescale-matching argument with explicit attention to the pulsed-versus-continuous-exposure distinction; three structural propositions establishing parameter-independent predictions; and a literature-derived order-of-magnitude reconciliation of the relevant parameters. We make the connection to existing phenomenological extensions explicit by predicting how the empirical interaction parameter of Arous et al. (2025) should depend on AP-1 / CBP-p300 axis status and on fraction number. We close with concrete experimental predictions and an honest enumeration of limitations.

The paper is positioned as a hypothesis paper. Each bridging step from established biology to SFRT mechanism is explicit and labelled. The proposal is not validated. The intent is to establish that the proposed mechanism is biologically and mathematically coherent, complementary to existing extensions of the framework, makes predictions distinguishable from current models, and warrants direct experimental test.

2. Background

2.1. The Kinetic-Bystander Framework

The McMahon et al. (2013) framework treats bystander signalling at the chemical-kinetic level. Cells receiving dose $D$produce a signalling factor — taken in the original work to represent a cytokine, reactive oxygen species, nitric oxide, or related diffusible mediator — for a dose-dependent duration $\gamma D$, at per-cell rate ${\eta }_{eff}$, approaching equilibrium concentration ${\rho }_{max}$. The factor undergoes first-order decay with rate $\lambda$. In the well-mixed limit, the signal concentration $\rho \left(t\right)$evolves as:

$$\begin{array}{cccc}& {\displaystyle \frac{d\rho }{dt}}={\eta }_{eff}\left(1−{\displaystyle \frac{\rho }{{\rho }_{max}}}\right)-\lambda \rho (\mathrm{production}\mathrm{phase},t\le \gamma D)& & \end{array}$$

(1)

$$\begin{array}{cccc}& {\displaystyle \frac{d\rho }{dt}}=-\lambda \rho (\mathrm{decay}\mathrm{phase},t>\gamma D)& & \end{array}$$

(2)

Bystander cells accumulate hazard while $\rho >{\rho }_T$at constant rate $\mu$. The total log-kill at dose $D$is

$$\begin{array}{cccc}& -\mathrm{l}\mathrm{n}S\left(D\right)=\alpha D+\beta D^2+H_{byst}\left(D\right),& & \end{array}$$

(3)

with bystander contribution

$$\begin{array}{cccc}& H_{byst}\left(D\right)=\mu \cdot t_{above}\left(D\right),& & \end{array}$$

(4)

where $t_{above}\left(D\right)$is the integrated time during which $\rho$exceeds ${\rho }_T$. The model has eight parameters: ${\eta }_{eff},{\rho }_{max},\lambda ,\mu ,{\rho }_T,\gamma ,\alpha ,\beta$.

The framework captures three biologically essential features: dose-dependent signal production, threshold-mediated bystander activation, and a piecewise transition between production and decay. It does not, however, specify the intracellular events that translate signal exposure into modified cell behaviour. The hazard rate $\mu$is an aggregated parameter representing the entire intracellular response.

As established by structural identifiability analysis (Vaitheeswaran, 2026a), the model collapses to five independent functional combinations under surviving-fraction observation. In the asymptotic large-$D$ regime where ${\rho }_{end}\to {\rho }_{ss}$, the bystander log-kill linearises and the linear coefficient becomes $\alpha +\mu \gamma$, confounding direct and bystander pathways. In the near-threshold regime, the dynamics-defining parameters ${\eta }_{eff},{\rho }_{max},\lambda ,{\rho }_T$are recoverable only through their joint contribution to the threshold-crossing geometry. Three dimensions of structural non-identifiability persist regardless of how densely the surviving-fraction observable is sampled.

2.2. Extensions and Elaborations of the Kinetic-Bystander Framework

The decade since McMahon (2013) has seen the framework extended along two distinct lines, neither of which addresses the intracellular black box at the molecular level.

Biological-scope broadening. Asur, Butterworth, Penagaricano, Prise & Griffin (2015) reviewed the experimental landscape of high-dose bystander effects in GRID and IMRT, and introduced the conceptually important three-class framework that the field now standardly uses: bystander effects (cell-to-cell signalling from irradiated to unirradiated cells), cohort effects (signalling within the irradiated volume itself, particularly relevant when the majority of cells receive non-trivial dose, which is the modal SFRT geometry), and abscopal effects (distant, immune-mediated tumour responses). The cohort-effect concept is an important addition because much of the bystander phenomenology in SFRT does not involve unirradiated cells — peaks and valleys are both irradiated, only at very different doses, and intra-volume signalling is at least as relevant as low-dose-to-high-dose signalling.

Moghaddasi, Reid, Bezak & Marcu (2022) provided a broader survey of radiobiological and treatment-related aspects of SFRT including GRID, LATTICE, SBRT-PATHY, and microbeam radiotherapy, discussing bystander, vascular, immune, and abscopal effects in the context of clinical implementation. Jenkins, Johnsrud, Dings & Griffin (2024) consolidated the field with substantially more weight on immune-mediated mechanisms: vascular restructuring in irradiated volumes, immune infiltration in tumour microenvironment, enhanced antigen presentation, activated T cells in non-irradiated tumour regions, and the development of immunological memory as a component of cohort-type and abscopal effects. The 2024 review explicitly invokes memory in the SFRT context.

The memory described in this immune-centred line of work is organism-level and immunological: T-cell repertoire, antigen-presentation history, lymph-node-mediated immune memory in the conventional immunological sense. It operates on timescales of days to weeks to months, mediated by professional immune-cell biology, and has nothing to do with cell-intrinsic chromatin state. This is real progress on the scope of what bystander-related biology covers in SFRT, and it is distinct from the cell-intrinsic mechanism we propose. We address the relationship between these two layers explicitly in Section 9.

Phenomenological model extension. Arous, Larsen Lie, Jeppesen Edin & Malinen (2025) proposed a Modified Linear-Quadratic (MLQ) model for in vitro SFRT cell survival, in which the LQ dose-response is augmented with a dose-distance interaction term:

$$\begin{array}{cccc}& -\mathrm{l}\mathrm{n}S(D,d)=\alpha D+\beta D^2+\delta \cdot D\cdot d,& & \end{array}$$

(5)

where $d$is the nearest distance to a high-dose peak region and $\delta$is an interaction coefficient. Fitting to A549 lung cancer cells irradiated through striped and dotted dose patterns, they obtained $\alpha =0.249$Gy⁻¹, $\beta =0.032$Gy⁻², and $\delta =-0.040$Gy⁻¹ cm⁻¹. The negative sign of $\delta$indicates that cells far from peaks survive less than the LQ baseline predicts; the magnitude captures the empirical SFRT cell-survival signature with one additional parameter.

The MLQ improves single-fraction fitting over pure LQ and provides a compact dose-response framework for SFRT planning. It is, however, phenomenological: $\delta$is a regression coefficient with no specified biological interpretation, and the model is fitted only to single-fraction data. It does not provide a mechanism for $\delta$, does not address cross-fraction dynamics, does not predict pharmacological modulation, and adds rather than reduces the parameter count relative to LQ.

Application of McMahon to clinical plans. Balvasi, Mahmoudi, Geraily et al. (2025) applied the McMahon kinetic-bystander framework directly to VMAT-based SFRT plans (VMAT-GRID and 3D-LRT) for lung cancer, computing modified survival ratios and dosimetric indices across 3D voxelised volumes. Mahmoudi et al. (2022) performed a theoretical simulation study of the implications of bystander effects for SFRT outcomes. Both apply the McMahon framework as given; neither modifies its mathematical structure.

Dosimetric and physical implementation. Lee, Seol, Kim et al. (2025) provided a planning-physics study of LATTICE delivery on a clinical LINAC with the Millennium 120 multi-leaf collimator, evaluating PVDR, modulation complexity, vertex diameter, and separation. This is implementation-side work essential for clinical translation but does not bear on the bystander mechanism question.

2.3. The Residual Gap

After this decade of extension, the residual gap is sharpened rather than reduced. The biological scope of "non-targeted effects" has broadened to include cohort effects and immune-mediated mechanisms. The phenomenological fitting has improved through interaction parameters. The McMahon framework has been validated in clinical-plan applications. None of these developments addresses the question of what occurs molecularly inside an individual bystander cell between signal arrival and modified behaviour.

The cohort and abscopal frameworks specify that signalling between cells occurs at multiple scales; they do not specify what happens within any cell receiving such signals. The immune-memory mechanism specifies that organism-level memory matters; it does not specify cell-intrinsic memory. The MLQ $\delta$specifies that there is a dose-distance correction; it does not specify what biological state determines $\delta$. The intracellular black box of McMahon's $\mu$is therefore still open after a decade of accumulated extensions, and the structural identifiability problem that follows from it remains.

The proposal of this paper targets this residual gap and only this residual gap. We do not propose to displace the cohort, abscopal, or immune-memory mechanisms; we propose to fill the cell-intrinsic layer that those mechanisms presuppose but do not specify. We do not propose to replace the MLQ; we propose a mechanism that should predict how its parameter $\delta$depends on pharmacology and fraction number.

2.4. The Li et al. (2026) Cis-Epigenetic Memory Mechanism

Li, Ravindran, O'Farrell and colleagues have recently demonstrated, in a melanoma model under MAPK inhibitor therapy, that cells exposed to stress can form durable cellular memory of their transcriptional state at the moment of perturbation. The mechanism is mediated by the AP-1 transcription factor, generally composed of FOS and JUN family heterodimers. Stress signals — including reactive oxygen species, cytokines (TNF-$\alpha$, IL-1), DNA damage response activation, mechanical stress, and heat shock — activate JNK, which phosphorylates JUN family proteins and drives AP-1 nuclear translocation. AP-1 then recruits the CBP/p300 acetyltransferase complex, which deposits H3K27 acetylation marks at AP-1-occupied loci. Recent structural studies establish that CBP/p300 operates by a read-write mechanism: the bromodomain reads existing H3K27 acetylation patterns, and the histone acetyltransferase (HAT) domain writes additional marks (Colino-Sanguino et al., 2019; Ibrahim et al., 2022; Kikuchi et al., 2023). This read-write architecture supports propagation of the acetylation pattern across cell divisions and is the proposed molecular substrate for cis-epigenetic memory.

The Li et al. paper demonstrates the mechanism through three converging lines of evidence: dose-escalation experiments showing that cells exposed to low-dose therapy adapt to subsequently survive higher doses; passenger-gene experiments showing that transiently induced gene expression (dexamethasone-driven FKBP5, TGM2, LTBP1) is committed to durable memory when therapy is applied during the induction window; and a dual-colour AP-1 reporter system demonstrating that the memory is encoded in cis, dependent on the activity of the gene at the time of perturbation rather than on its sequence alone. Pharmacological intervention confirms the mechanism: AP-1 activity inhibition (JNK-IN-8, T-5224) prevents memory formation; CBP/p300 catalytic inhibition (A-485) prevents both resistant colony formation and memory; CBP/p300 bromodomain inhibition (SGC-CBP30) prevents memory persistence specifically. Memory persists for at least one month in continuous culture and shows no recovery after CBP/p300 inhibition, indicating cis encoding rather than trans regulatory milieu.

The paper notes explicitly that AP-1 sits downstream of many stress-response pathways and that similar memory mechanisms have been observed in wound healing, inflammatory responses, and aging contexts (Ge et al., 2017; Naik et al., 2017; Larsen et al., 2021; Patrick et al., 2024). The authors propose that the mechanism may operate generally in contexts where cells form memories of stress states. The hypothesis of the present paper extends this positioning to the radiation bystander context.

Although several stress-responsive transcriptional systems could, in principle, mediate persistent intracellular adaptation—including NFκB, STAT3, and YAP/TAZ—we focus on the AP-1 / CBP-p300 axis for four reasons. First, AP-1 occupies a uniquely proximal position downstream of the major classes of bystander-associated stress signals already implicated in radiation biology, including reactive oxygen species, inflammatory cytokines, and DNA-damage-response signalling (Karin, 1995; Christmann and Kaina, 2013; Hei et al., 2008). Second, unlike many stress-response pathways that primarily encode transient transcriptional activation, the mechanism demonstrated by Li et al. (2026) explicitly establishes durable cis-epigenetic memory through a molecular read–write architecture involving AP-1-guided recruitment and bromodomain-mediated propagation of CBP/p300 activity across cell divisions. Third, the pathway is unusually experimentally tractable: distinct pharmacological interventions separately target memory formation (JNK-IN-8, T-5224), catalytic mark deposition (A-485), and memory persistence (SGC-CBP30), enabling mechanistic separation of stages rather than pathway-wide suppression. Finally, AP-1 activity has already been repeatedly implicated in radiation response, stress adaptation, and genotoxic conditioning across multiple contexts (Amundson et al., 1998; Christmann and Kaina, 2013). This choice should therefore be interpreted not as an exclusion of NFκB-, STAT3-, or YAP-mediated persistence mechanisms, but as a deliberately conservative selection of a pathway that simultaneously satisfies the requirements of stress coupling, durable state retention, and experimental perturbability.

3. The Extended Bystander Model

3.1. The Coupled System

We extend the kinetic-bystander framework by appending a cell-intrinsic memory layer to the bystander response. The upstream signal kinetics, Equations (1)–(2), are preserved unchanged. The downstream hazard is reinterpreted: rather than $\mu$aggregating the entire intracellular response in a single hazard rate, the response is decomposed into AP-1 activation, memory formation, and effects of memory on subsequent radiosensitivity.

Let $\rho \left(t\right)$denote the bystander signal concentration as in McMahon. Let $A\left(t\right)$denote the AP-1 activity in the recipient cell, normalised to lie in $\left[0,1\right]$. Let $M_{cell}\left(t\right)$denote the cell's memory state, also normalised to $\left[0,1\right]$, representing the cumulative cis-epigenetic mark deposition at AP-1-occupied loci as a fraction of locus-finite capacity.

AP-1 dynamics. AP-1 activation requires bystander signal above threshold and is itself bounded and cooperative:

$$\begin{array}{cccc}& {\displaystyle \frac{dA}{dt}}=k_A\cdot \varphi \left(\rho \right)\cdot (1-A)-{\lambda }_{A}A,& & \end{array}$$

(6)

where $k_A$is the activation rate constant, ${\lambda }_A$is the AP-1 decay rate, and $\varphi$is a Hill-form activation function:

$$\begin{array}{cccc}& \varphi \left(\rho \right)=\left\{\begin{array}{cc}0,& \rho \le {\rho }_T\\ {\displaystyle \frac{\left(\rho −{\rho }_T{)}^{n_A}\right.}{K_{\varphi }^{n_A}+(\rho -{\rho }_T{)}^{n_A}}},& \rho >{\rho }_T\end{array}\right.& & \end{array}$$

(7)

with cooperativity $n_A$and half-maximal-response parameter $K_{\varphi }$. The form is chosen to reflect the threshold-and-cooperativity structure of kinase activation cascades upstream of AP-1 (Karin, 1995; Christmann and Kaina, 2013). The threshold ${\rho }_T$is inherited from McMahon; below it, no AP-1 activation occurs.

Memory dynamics. Memory accumulation requires above-threshold AP-1 activity (representing the CBP/p300 recruitment threshold), is bounded by chromatin capacity $M_{cap}$, and decays only on long timescales:

$$\begin{array}{cccc}& {\displaystyle \frac{d{M}_{cell}}{dt}}=k_M\cdot \psi \left(A\right)\cdot (1-M_{cell})-{\lambda }_M{M}_{cell},& & \end{array}$$

(8)

where $k_M$is the memory formation rate constant, ${\lambda }_M$is the memory decay rate, and $\psi$is a Hill-form CBP/p300 recruitment function:

$$\begin{array}{cccc}& \psi \left(A\right)={\displaystyle \frac{A^{n_M}}{K_{\psi }^{n_M}+A^{n_M}}}& & \end{array}$$

(9)

with cooperativity $n_M$and half-maximal-recruitment parameter $K_{\psi }$. The Li et al. (2026) data support ${\lambda }_M^{-1}\gg$inter-fraction interval (memory persistence on the order of weeks to months, see Section 4), so in the SFRT context ${\lambda }_M$is effectively zero on the treatment timescale and may be set to zero in single-course analyses.

Memory-modulated radiosensitivity. The cell's effective radiosensitivity at any given fraction depends on its current memory state:

$$\begin{array}{cccc}& {\alpha }_{eff}\left(M_{cell}\right)={\alpha }_0[1-{\delta }_{\alpha }\cdot g(M_{cell}\left)\right],& & \end{array}$$

(10)

$$\begin{array}{cccc}& {\beta }_{eff}\left(M_{cell}\right)={\beta }_0[1-{\delta }_{\beta }\cdot g(M_{cell}\left)\right],& & \end{array}$$

(11)

where ${\alpha }_0,{\beta }_0$are baseline (memory-free) radiosensitivity parameters, ${\delta }_{\alpha },{\delta }_{\beta }$are the maximal sensitivity modulations, and $g$is the memory-to-phenotype mapping. We adopt the simplest non-trivial form:

$$\begin{array}{cccc}& g\left(M_{cell}\right)=M_{cell},& & \end{array}$$

(12)

so that radiosensitivity modulation scales linearly with normalised memory state. The sign and magnitude of ${\delta }_{\alpha },{\delta }_{\beta }$depend on which loci carry the memory: AP-1-occupied loci involved in DNA damage response, apoptosis regulation, or stress tolerance can produce either protective ($\delta >0$) or sensitising ($\delta <0$) memory depending on the cell's pre-existing transcriptional state at the time of signal arrival. This is the mechanistic basis for the heterogeneity Li et al. observed across distinct cellular states.

Total log-kill across fractions. Let $M_{cell,n}^{-}$denote the memory state at the start of fraction $n$(immediately before that fraction's signal exposure). For a course of $N$fractions, the total log-kill is

$$\begin{array}{cccc}& -\mathrm{l}\mathrm{n}{S}_{total}={\displaystyle \sum _{n=1}^N}\left[{\alpha }_{eff}\left(M_{cell,n}^{-}\right)D_n+{\beta }_{eff}\left(M_{cell,n}^{-}\right)D_n^2+H_{byst,n}\left(D_n\right)\right],& & \end{array}$$

(13)

where $H_{byst,n}\left(D_n\right)$is the direct bystander hazard during fraction $n$, computed from McMahon kinetics (Equations 1–4) applied to that fraction's signal exposure, and where $M_{cell,n}^{-}$evolves between fractions according to Equation 8 integrated over the inter-fraction interval.

Equation (13) is the key equation distinguishing the extended model. The radiosensitivity terms ${\alpha }_{eff}$and ${\beta }_{eff}$at each fraction depend on the memory state at the start of that fraction, which in turn depends on the history of all previous fractions. Pure McMahon recovers Equation (13) in the limit ${\delta }_{\alpha },{\delta }_{\beta }\to 0$, where memory has no effect on radiosensitivity and the total log-kill reduces to a sum of identical per-fraction contributions ${\alpha }_0{D}_n+{\beta }_0{D}_n^2+H_{byst,n}\left(D_n\right)$.

3.2. Connection to the Arous MLQ

The MLQ model of Arous et al. (2025), Equation (5), captures the SFRT cell-survival signature as a dose-distance interaction term $\delta Dd$added to LQ. In the present extended model, this empirical interaction is reinterpreted mechanistically.

At a single fraction, the bystander signal field $\rho (\mathbf{x},t)$depends on the spatial distribution of irradiated cells, falling off with distance $d$from high-dose peaks. The hazard $H_{byst}(D,d)$at a cell at distance $d$from the nearest peak captures the McMahon bystander contribution in a spatially explicit form. For dose-response data fitted at single fractions, this contribution maps onto an empirical $\delta Dd$term, with $\delta$depending implicitly on signal kinetics, threshold, and the McMahon $\mu$parameter.

In the extended model, the same single-fraction fitted $\delta$should additionally depend on the cell's AP-1 / CBP-p300 axis state through its effect on the relationship between $\rho$exposure and the relevant cellular response. More importantly, in multi-fraction regimens, the cumulative cell-kill is no longer a simple sum of single-fraction MLQ contributions: it includes memory-modulated radiosensitivity terms (Equation 13) that the MLQ does not capture.

The extended model therefore predicts three specific things about MLQ-style fitted parameters:

(i) Fitted $\delta$should attenuate under JNK-IN-8 or SGC-CBP30 co-treatment (because the memory contribution to the empirical $\delta$vanishes when memory cannot form or persist).

(ii) Fitted $\delta$should vary across cell lines according to their baseline AP-1 axis state (cells with low baseline AP-1 activity should show smaller $\mid \delta \mid$).

(iii) Multi-fraction MLQ fits should show $\mid \delta \mid$growing with fraction number until saturation, in contrast to single-fraction $\delta$which is fixed. This third prediction is the most distinctive: a phenomenological model with fixed $\delta$cannot reproduce $\delta$that grows with $N$unless explicitly modified.

These are concrete bridges from a mechanistic hypothesis to an empirical parameter in a recently-published model.

3.3. The Intracellular Layer as a New Observable Space

The principal structural change introduced by the extension is that the intracellular response is no longer a single aggregated parameter $\mu$. It is a sequence of measurable states — AP-1 activation $A\left(t\right)$, memory accumulation $M_{cell}\left(t\right)$— each of which is directly accessible through established experimental methods. AP-1 activity can be measured through phospho-c-Jun staining, AP-1 reporter constructs, or transcriptomic signatures of AP-1 target genes. Memory accumulation can be measured through chromatin accessibility assays (ATAC-seq) at AP-1-binding sites, through histone modification profiling (CUT&RUN, ChIP-seq for H3K27ac), and through transcriptional persistence of induced genes.

These are not surviving-fraction observables. They are intracellular state observables, available throughout the irradiation course and across fractions. The implications for identifiability are taken up in Section 5.4.

4. Timescale Consistency Analysis

We rely on timescale matching as the primary plausibility check because the model has not been simulated and parameter values have not been fitted. The timescale argument must therefore bear unusual weight, and we work through it carefully — including the points where it does and does not hold cleanly.

4.1. The Four Timescales in Question

For the proposed mechanism to operate as a cross-fraction bystander memory layer in SFRT, four timescales must align:

(i) ${\tau }_{AP-1}$— AP-1 activation time from signal arrival. (ii) ${\tau }_{form}$— Time for one fraction's signal exposure to deposit a functionally significant memory increment. (iii) ${\lambda }_M^{-1}$— Memory persistence (inverse of memory decay rate). (iv) $\mathsf{\Delta }{t}_{inter}$— Inter-fraction interval.

For cross-fraction memory accumulation to occur, three conditions must hold: ${\tau }_{AP-1}$must be shorter than the within-fraction signal exposure window; ${\tau }_{form}$must be sufficiently short that one fraction produces a measurable memory increment; and ${\lambda }_M^{-1}$must be longer than $\mathsf{\Delta }{t}_{inter}$so memory persists between fractions.

4.2. Single-Fraction Signal Exposure Window

McMahon kinetics produce a signal field $\rho \left(t\right)$that rises during the production phase (duration $\gamma D$) and decays after. With typical parameter ranges from the bystander literature ($\gamma \sim 0.1$–$1$ h/Gy, $\lambda \sim 0.1$–$1$ h⁻¹), a single SFRT fraction at peak doses of 10–20 Gy produces above-threshold signal exposure of approximately 1–6 hours in valley regions. The exact duration depends on threshold proximity and signal kinetics; the order of magnitude is hours, not minutes or days.

4.3. AP-1 Activation Timescale

AP-1 activation through the JNK pathway is a well-characterised rapid kinase response. Phospho-c-Jun appears within minutes of stimulus arrival; AP-1 nuclear translocation and DNA binding occur within 15–60 minutes; sustained AP-1 transcriptional activity under continued stimulus persists for hours (Karin, 1995; Christmann and Kaina, 2013). Li et al. (2026) confirm rapid AP-1 reporter activation kinetics in their dual-colour reporter system.

Comparison: ${\tau }_{AP-1}\sim$minutes to one hour; single-fraction signal exposure $\sim$hours. AP-1 activation completes comfortably within the single-fraction window with substantial margin.

4.4. Memory Formation Under Pulsed Exposure: The Critical Timescale Question

This is the timescale most worth scrutinising honestly, because the Li et al. (2026) experimental design and the SFRT delivery pattern differ in an important way.

Li et al. consolidated phenotypic memory under continuous drug exposure of approximately 10–14 days. SFRT delivers pulsed bystander signal exposure: roughly hourly pulses, separated by inter-fraction gaps of 1–7 days, over a course of 2–6 weeks. The question is whether pulsed exposure can produce cross-fraction memory accumulation comparable to what continuous exposure produces.

Three considerations bear on this:

(i) Initial chromatin mark deposition is rapid. H3K27 acetylation by CBP/p300 at activated loci is detectable within hours of stimulus onset (Creyghton et al., 2010; Raisner et al., 2018). A single hour-scale AP-1 activation pulse during one SFRT fraction is therefore long enough for measurable chromatin mark deposition, even if not for full phenotypic consolidation.

(ii) Marks persist between pulses. The Li et al. data establish memory persistence of at least 28–35 days in continuous culture after the inducing stimulus is removed. This persistence operates between pulses too: marks deposited during fraction $n$remain present through the inter-fraction gap and are available at fraction $n+1$.

(iii) The CBP/p300 read-write mechanism predicts cumulative deposition under pulsed exposure. The bromodomain of CBP/p300 reads existing H3K27ac marks at AP-1-occupied loci and the HAT domain deposits additional marks (Colino-Sanguino et al., 2019; Ibrahim et al., 2022; Kikuchi et al., 2023). At fraction $n+1$, AP-1 reactivation occurs in a chromatin environment that already carries marks from fraction $n$; CBP/p300 reading those marks should accelerate further deposition. The mechanism therefore predicts that pulsed exposures should cumulatively build memory faster than the per-pulse deposition rate would suggest from naïve linear extrapolation.

(iv) The passenger-gene experiment in Li et al. directly demonstrates that brief signal exposure can seed memory. In Figure 3 of Li et al. (2026), three days of dexamethasone exposure followed by removal does not produce durable gene expression — but the same three-day pulse followed by trametinib produces durable memory of the dex-induced state. This is the experimental demonstration that a brief stimulus pulse, in combination with a subsequent or concurrent AP-1-activating stress, can produce committed memory. The mechanism's operation under pulsed exposure is therefore not an extrapolation from continuous-exposure data; it is directly demonstrated for the brief-pulse-plus-stress regime that is structurally analogous to SFRT.

The honest summary is that the Li et al. data demonstrate the mechanism's operation under (a) continuous sustained exposure over 10–14 days and (b) brief seed-pulse followed by ongoing stress. SFRT corresponds to neither of these regimens exactly; it corresponds to (c) repeated brief pulses separated by gaps, without continuous stress. The mechanism predicts that case (c) should produce cumulative memory through the read-write mechanism, but Li et al. did not directly test this regime. The pulsed-cumulative prediction is therefore one of the testable predictions of the present proposal (Section 7, Prediction P1), not an established finding.

4.5. Memory Persistence Versus Inter-Fraction Interval

Li et al. demonstrate memory persistence of at least 28–35 days in continuous culture after stimulus removal, with no decay observed within the measurement window and the authors noting probable persistence well beyond. Clinical SFRT inter-fraction intervals range from 24 hours to 7 days; total course durations span 2–6 weeks.

Comparison: ${\lambda }_M^{-1}\ge 28$–$35$ days, likely longer; $\mathsf{\Delta }{t}_{inter}\sim 1$–$7$ days; total course $\sim 14$–$42$ days. The ratio ${\lambda }_M^{-1}/\mathsf{\Delta }{t}_{inter}\ge 4$–$35$, comfortably exceeding unity. Memory laid down at fraction $n$persists through the inter-fraction gap and is present at fraction $n+1$. For course durations of 2–6 weeks, memory persistence comfortably exceeds total course duration, supporting the simplifying assumption ${\lambda }_M\approx 0$during a single treatment course.

This is the cleanest part of the timescale argument. Memory persistence exceeds the timescales it needs to exceed by at least an order of magnitude.

4.6. Summary Timescale Assessment

Quantity	Required for cross-fraction memory	Measured / inferred from Li et al. (2026)	Status
AP-1 activation	$\lesssim$single-fraction signal duration (~hours)	Minutes to one hour	Clean fit
Single-pulse mark deposition	Detectable within one fraction's signal window	Hours-scale, demonstrated under continuous exposure	Plausible, awaits pulsed-exposure measurement
Cumulative memory under pulsed exposure	Memory grows across fractions	Read-write mechanism predicts this; passenger-gene experiment supports brief-pulse-plus-stress	Hypothesis, not directly demonstrated
Memory persistence	$\gg$inter-fraction interval	$\ge$28–35 days; likely months	Clean fit, with substantial margin

The argument is robust on three of four timescales. The fourth — cumulative memory accumulation under pulsed (rather than continuous) exposure — is mechanistically predicted but not directly demonstrated in Li et al. (2026). This is acknowledged honestly and converted to a testable prediction rather than glossed.

4.7. What the Timescale Analysis Does and Does Not Establish

The timescale analysis establishes that the proposed mechanism is plausible — its measured rate constants and persistence windows are compatible with the requirements of cross-fraction SFRT memory, with the caveat noted above. It does not establish that the mechanism actually operates in irradiated bystander cells (no radiation experiment is in evidence), nor that the predicted cumulative memory under pulsed exposure actually occurs (no pulsed-exposure experiment is in evidence). These are the targets of the predictions in Section 7.

The argument fails — and would be ruled out — if any of the following were the case: AP-1 activation required hours rather than minutes; chromatin mark deposition required days of continuous exposure rather than hours; memory persistence were comparable to or shorter than inter-fraction intervals. None of these failure modes is supported by the available data. The proposal survives the timescale check, with the honest caveat that pulsed-exposure dynamics specifically remain to be directly tested.

5. Structural Propositions

A simulation-based demonstration that the proposed mechanism produces specific behaviours would invite the objection that parameter values were chosen to produce them. We instead establish three structural properties of the coupled system that follow from the form of Equations (6)–(13) regardless of parameter values. Each is a property that pure McMahon dynamics, the MLQ extension of Arous (2025), and direct application of McMahon to clinical plans (Balvasi et al., 2025) all demonstrably lack.

Proposition 1 (cross-fraction memory accumulation)

*Let the cell state evolve under Equations (6)–(8) across $N$fractions delivered at intervals $\mathsf{\Delta }t$with $\mathsf{\Delta }t\ll {\lambda }_M^{-1}$. Then $M_{cell}$at the start of fraction $n+1$is a non-decreasing function of $n$for any history of fractions in which at least some fractions produce bystander signal exceeding ${\rho }_T$at the cell with sufficient duration for AP-1 activation to exceed the CBP/p300 recruitment threshold.*

*Proof.* Under the assumption $\mathsf{\Delta }t\ll {\lambda }_M^{-1}$, between-fraction memory decay is negligible: $M_{cell}\left(t_{n+1}^{-}\right)-M_{cell}\left(t_n^{+}\right)\approx -{\lambda }_M{M}_{cell}\cdot \mathsf{\Delta }t\approx 0$. Within fraction $n$, $M_{cell}$evolves under

$${\displaystyle \frac{d{M}_{cell}}{dt}}=k_M\psi \left(A\right)(1-M_{cell})-{\lambda }_M{M}_{cell},$$

which is non-negative whenever $\psi \left(A\right)(1-M_{cell})\ge {\lambda }_M{M}_{cell}/k_M$. For ${\lambda }_M$small (as established in Section 4) and $\psi \left(A\right)>0$over the AP-1 activation window of fraction $n$, the right-hand side is strictly positive over a finite duration, so $M_{cell}$increases monotonically during the fraction. Between fractions, $M_{cell}$is approximately conserved. The state at the start of fraction $n+1$is therefore at least as large as the state at the start of fraction $n$, and strictly larger whenever fraction $n$produces above-threshold AP-1 activation. $\square$*Comparison to existing models.* In pure McMahon dynamics, the bystander hazard $H_{byst}\left(D\right)$is a fixed function of single-fraction dose; the state of the bystander cell at the start of the next fraction is unchanged. The MLQ of Arous et al. (2025) is single-fraction by construction and contains no cross-fraction state. Application of McMahon to clinical plans (Balvasi et al., 2025) inherits the framework's memorylessness. None of these models contains a quantity that accumulates across fractions in the bystander cell.

Proposition 2 (time-ordering sensitivity)

*Consider two SFRT regimens delivering the same total dose, with the same cumulative dose to each spatial location $\mathbf{x}$, differing only in the temporal ordering of which spatial locations receive high dose at each fraction. The final memory state $M_{cell}(\mathbf{x},t_N)$depends on the temporal ordering of fractions for any non-zero ${\delta }_{\alpha }$or ${\delta }_{\beta }$.*

*Proof.* At fraction $n$, the local memory increment at location $\mathbf{x}$is

$$\mathsf{\Delta }{M}_{cell}(\mathbf{x},n)={\int }_{t_n}^{t_n+\tau }{k}_M\psi \left(A\right(\mathbf{x},t\left)\right)(1-M_{cell}(\mathbf{x},t\left)\right)dt-{\lambda }_M{M}_{cell}(\mathbf{x},t_n)\cdot \tau ,$$

where $\tau$is the per-fraction integration window. The integrand depends on the current $M_{cell}(\mathbf{x},t_n)$through the $\left(1−M_{cell}\right)$saturation factor. For two regimens that differ in fraction ordering, the cell at location $\mathbf{x}$at fraction $n$sees different prior history and therefore different $M_{cell}(\mathbf{x},t_n)$, so the same per-fraction signal exposure produces a different memory increment. Furthermore, ${\alpha }_{eff}\left(M_{cell}\right)$at fraction $n$depends on $M_{cell}(\mathbf{x},t_n)$, so the direct cell-kill at fraction $n$also depends on the order. The two regimens therefore produce different trajectories and different final outcomes whenever ${\delta }_{\alpha }\ne 0$or ${\delta }_{\beta }\ne 0$. $\square$*Comparison to existing models.* Pure McMahon, MLQ, and direct McMahon application are all memoryless across fractions. The bystander response at each fraction depends only on the dose delivered at that fraction. There is no order-dependence; reordering identical-cumulative-dose regimens produces identical predicted outcomes. The order-dependence in the proposed system follows from the saturation factor in the memory dynamics and from the dependence of ${\alpha }_{eff}$on $M_{cell}$.

Proposition 3 (threshold-mediated phase boundary)

*The proposed system exhibits a phase boundary in the space of SFRT regimens, separating regimes in which bystander signals at unirradiated cells produce durable memory effects from regimes in which they do not. The boundary is determined by the activation thresholds in $\varphi$and $\psi$(Equations 7 and 9) and by the spatial-temporal pattern of dose. Across the boundary, qualitative outcomes change discontinuously even as dose varies continuously.*

*Proof.* AP-1 activity $A\left(t\right)$given by Equation 6 saturates near zero for $\rho <{\rho }_T$(because $\varphi =0$) and approaches a substantial fraction of unity for $\rho \gg {\rho }_T$, with the transition sharpness controlled by the cooperativity $n_A$. Similarly, $\psi \left(A\right)$in Equation 9 is negligible for $A<K_{\psi }$and approaches unity for $A\gg K_{\psi }$. Therefore, for SFRT regimens in which the spatial-temporal signal field $\rho (\mathbf{x},t)$never exceeds ${\rho }_T$at a given location, that location accumulates no memory; for regimens in which $\rho$exceeds ${\rho }_T$at that location with sufficient duration for $A$to exceed $K_{\psi }$, the location accumulates memory at the rate determined by $\psi$. The transition between these regimes is the phase boundary; it depends on peak-valley dose ratio, peak spacing, fraction number, inter-fraction interval, and the values of ${\rho }_T,K_{\varphi },K_{\psi }$. $\square$*Comparison to existing models.* Pure McMahon has a single threshold structure (${\rho }_T$) which produces a single-fraction phase boundary (above-threshold cells accumulate hazard, below-threshold cells do not). MLQ has no explicit threshold; the dose-distance interaction term operates smoothly. The proposed system adds a second threshold structure (the CBP/p300 recruitment threshold in $\psi$) operating on a different state variable, and produces phase behaviour in the cross-fraction trajectory that depends on the joint geometry of ${\rho }_T$and $K_{\psi }$.

5.4. Implications for Identifiability

The three propositions also bear on the identifiability problem of the original kinetic-bystander framework. As established by Vaitheeswaran (2026a), McMahon under surviving-fraction observation collapses to five identifiable combinations from eight parameters. The non-identifiability is rooted in the aggregation of the entire intracellular response into the single parameter $\mu$.

The extended model replaces $\mu$with an explicit intracellular layer carrying its own state variables ($A$ and $M_{cell}$). This augments the observable space in three ways:

(i) Chromatin observables. Memory state $M_{cell}$is directly measurable through chromatin accessibility assays at AP-1-occupied loci (ATAC-seq, CUT&RUN for H3K27ac, ChIP-seq for AP-1 binding). These observables are independent of surviving-fraction measurements and respond directly to bystander signal exposure history.

(ii) Pharmacological observables. Perturbations of the AP-1 axis (JNK-IN-8, T-5224) and CBP/p300 axis (A-485, SGC-CBP30) provide functional handles that selectively modify $A$and $M_{cell}$. The change in surviving fraction under these perturbations, compared to baseline, isolates the bystander-memory contribution from the direct hazard. This is the most consequential identifiability improvement: it breaks the asymptotic $\alpha +\mu \gamma$confound that is the most severe failure mode in the original model.

(iii) Time-resolved observables across fractions. Cross-fraction effects manifest in dose-response measurements at different fraction numbers and orderings; these provide multiple snapshots of the surviving-fraction map that constrain memory-layer parameters. Propositions 1 and 2 imply distinguishable trajectories under different fraction numbers and orderings, providing a richer input-output map than single-fraction dose-response alone.

A full identifiability analysis of the extended system is beyond the scope of this hypothesis paper. The structural argument is that the additional observables couple specifically to parameters that pure McMahon cannot resolve. Chromatin observables constrain $k_M,K_{\psi },n_M$directly. Pharmacological observables under AP-1 inhibition isolate the bystander contribution to $-\mathrm{l}\mathrm{n}S$, breaking the $\alpha +\mu \gamma$degeneracy. Cross-fraction observables constrain the memory-to-phenotype mapping parameters ${\delta }_{\alpha },{\delta }_{\beta }$. The combined observable space substantially exceeds the surviving-fraction-only regime under which McMahon is non-identifiable, and a properly designed measurement programme should be able to recover the extended-model parameters.

The general lesson is that identifiability is a property of the model-observation pairing. The original kinetic-bystander framework is non-identifiable not because surviving fraction is a poor observable, but because the model compresses the intracellular response into a single parameter that surviving fraction cannot disentangle from the direct response. A model that explicitly represents the intracellular state can be paired with observables of that state.

6. Literature-Derived Parameter Ranges

The proposed mechanism's plausibility rests on whether the relevant parameters take values that allow the bridging steps from radiation bystander signalling to AP-1 activation to memory formation to operate in concert. We assemble order-of-magnitude estimates from the published literature without fitting any new data.

Bystander signal concentrations under SFRT-relevant dose regimes. Measurements in irradiated cell cultures and tissue models report bystander-associated reactive oxygen species concentrations in the range ${10}^{-7}$–${10}^{-5}$ M for cytoplasmic ROS following doses of $1$–$10$ Gy, with persistence of minutes to hours (Mothersill and Seymour, 2001; Azzam et al., 2002; Hei et al., 2008). Inflammatory cytokine release under irradiation (TNF-$\alpha$, IL-6, IL-1$\beta$) reaches picomolar to low-nanomolar concentrations in conditioned media, with kinetics of hours to days (Hei et al., 2008; Najafi et al., 2014).

**AP-1 activation thresholds.** Quantitative studies of JNK and AP-1 activation under oxidative and inflammatory stress report half-maximal activation at micromolar H₂O₂, nanomolar TNF-$\alpha$, and DNA-damage signal levels achieved at clinically relevant radiation doses (Adler et al., 1995; Karin, 1995; Christmann and Kaina, 2013). Activation kinetics are within minutes, consistent with the Li et al. (2026) reporter dynamics. These provide the empirical anchor for the parameters ${\rho }_T$and $K_{\varphi }$in Equation (7).

Memory formation kinetics. H3K27 acetylation by CBP/p300 at induced loci is detectable within hours (Creyghton et al., 2010; Raisner et al., 2018); stable phenotypic consequences of cis-memory require longer windows (Li et al. 2026: 10–14 days for full phenotypic consolidation under continuous exposure), and persistence has been documented across weeks in multiple stress contexts (Naik et al., 2017; Larsen et al., 2021; Patrick et al., 2024). These provide anchors for $k_M$(rate of mark deposition under sustained AP-1 activity) and ${\lambda }_M^{-1}$(mark persistence).

Spatial scales. Bystander signal propagation distances reported in microbeam, GRID, and conditioned-media studies range from ${10}^2$to ${10}^3\mu$m for diffusible mediators (Mothersill and Seymour, 1998; Belyakov et al., 2005), and several mm for circulating cytokine effects in vivo. These scales overlap clinically used SFRT peak-to-valley spacings of $1$–$10$ mm (Mohiuddin et al., 1999; Penagaricano et al., 2010; Lee et al., 2025) and the cell-to-peak distances over which the MLQ $\delta Dd$term operates (Arous et al., 2025).

Assembly. The available ranges are compatible with the proposed mechanism's operation. Bystander signal concentrations at SFRT-relevant doses plausibly exceed AP-1 activation thresholds at peak-valley distances consistent with clinical geometries. AP-1 activation kinetics fit within single-fraction signal-exposure windows. Memory formation timescales for initial mark deposition fit within single-fraction exposure (hours), and memory persistence exceeds the total course duration (weeks). No parameter is required to take a value at the edge of its biologically plausible range to make the mechanism work.

This is not a calibrated model. It is a check that the mechanism is not ruled out by readily available parameter ranges. The check would have failed had any of the relevant biological numbers been off by orders of magnitude from what the synthesis requires; the fact that they are not is informative even though it falls short of validation.

7. Testable Predictions

The proposed mechanism makes a set of distinguishable predictions, of which several are accessible with existing experimental tools.

**P1 (cross-fraction memory accumulation under pulsed exposure).** Bystander cells in valley regions of a multi-fraction SFRT regimen should exhibit cumulative chromatin accessibility changes at AP-1-binding loci across fractions, distinguishable from the transient response to a single fraction. *This is the prediction that addresses the pulsed-versus-continuous concern raised in Section 4.4.* Predicted measurement: ATAC-seq or CUT&RUN for H3K27ac at AP-1-occupied loci in valley regions, sampled across the SFRT course. Predicted pattern: progressive accumulation across fractions reaching a $M_{cap}$-mediated saturation, qualitatively distinct from the transient single-fraction response.

P2 (AP-1 inhibition attenuates cross-fraction effect). Co-treatment with JNK-IN-8 or T-5224 during a multi-fraction SFRT course should reduce the cross-fraction component of the SFRT effect while leaving single-fraction bystander effects largely intact. Predicted measurement: SFRT outcome under inhibitor vs vehicle, compared between single-fraction and multi-fraction regimens. Predicted pattern: inhibitor effect grows with fraction number, becoming significant only in multi-fraction regimens.

P3 (CBP/p300 bromodomain inhibition attenuates persistence). SGC-CBP30 applied between fractions should reduce the cross-fraction effect of SFRT specifically by disrupting memory persistence, distinguishable from JNK-IN-8 which disrupts memory formation. Predicted pattern: differential timing dependence of the two inhibitor classes — JNK-IN-8 most effective when present during fractions, SGC-CBP30 most effective when present between fractions.

P4 (time-ordering effect). Two SFRT regimens delivering identical cumulative dose to each region, differing only in the temporal ordering of which regions receive high dose, should produce different outcomes. Predicted measurement: matched-dose alternating-pattern SFRT regimens with reversed fraction sequences, with outcome assessed in preclinical models. Predicted pattern: order-dependent outcome, as required by Proposition 2.

P5 (tumour-context dependence). Tumours with high baseline AP-1 activity and intact CBP/p300 function should show stronger SFRT cross-fraction effects than tumours with diminished AP-1 / CBP-p300 axis. Predicted measurement: SFRT response stratified by pre-treatment AP-1 / CBP-p300 status (immunohistochemistry, transcriptomic signature). Predicted pattern: stratification of response by AP-1 axis status.

P6 (single-cell heterogeneity in memory formation). Within a population of bystander cells exposed to the same signal, the cells that ultimately exhibit memory should be those with higher AP-1 activity at the time of signal arrival, paralleling the Li et al. (2026) finding that initial AP-1 activity is encoded into the durable state. Predicted measurement: single-cell tracking with AP-1 reporters in bystander populations under SFRT conditions.

P7 (signal-class specificity). Bystander signals capable of activating AP-1 (ROS, cytokines, DDR-derived signals) should seed memory; signals that do not engage the AP-1 axis should not. Predicted measurement: selective inhibition of individual signal pathways (ROS scavengers, cytokine-receptor blockade) with assessment of resulting memory formation. Predicted pattern: only AP-1-engaging signal pathways contribute to cross-fraction effects.

**P8 (predictions on the Arous MLQ $\delta$parameter).** The empirical dose-distance interaction parameter $\delta$fitted by Arous et al. (2025) should satisfy three specific properties that follow from Section 3.2: (a) $\mid \delta \mid$should attenuate under JNK-IN-8 or SGC-CBP30 co-treatment; (b) $\mid \delta \mid$should vary across cell lines according to baseline AP-1 axis state; (c) $\mid \delta \mid$fitted to multi-fraction SFRT data should grow with fraction number until $M_{cap}$-mediated saturation, in contrast to single-fraction $\mid \delta \mid$which is fixed. *This prediction provides a concrete bridge from the present mechanistic hypothesis to a recently-published empirical model in the field.*

Predictions P1–P3 are directly accessible with established assays and pharmacological tools. P4 requires preclinical SFRT models with regimen flexibility. P5 requires correlative pre-treatment biomarker work, which existing SFRT cohorts may already support. P6 requires single-cell reporter systems. P7 requires coordinated pathway dissection in bystander models. P8 requires extending the Arous 2D dosimetry approach with pharmacological co-treatments and multi-fraction regimens — a tractable extension of an already-published protocol.

8. Limitations and Scope

The proposal is positioned as a hypothesis. Each step of the bridging argument is a hypothesis to be tested.

Mechanism is hypothesised, not demonstrated. Li et al. (2026) establish the AP-1 / CBP-p300 cis-memory mechanism in melanoma cells under MAPK inhibitor stress. The extension to radiation bystander signals is plausible — AP-1 sits downstream of multiple stress-response pathways, and ROS, cytokine, and DDR signals are all known AP-1 activators (Christmann and Kaina, 2013; Naik et al., 2017; Larsen et al., 2021) — but it is not demonstrated in the radiation context. Whether bystander signals from irradiated cells produce sufficient AP-1 activation in unirradiated neighbours to drive the cis-memory mechanism, and whether the resulting memory has functional consequences for subsequent radiation response, are open questions.

Pulsed-exposure dynamics not directly tested. Section 4.4 documents this explicitly: Li et al. (2026) demonstrated the mechanism under continuous exposure over 10–14 days and under brief-pulse-plus-stress regimens, but did not test repeated brief pulses with multi-day gaps — the regime structurally analogous to SFRT. The mechanism predicts cumulative memory under pulsed exposure through the CBP/p300 read-write mechanism, but this prediction (Prediction P1) is itself one of the testable items rather than an established finding.

Scope of explanation. The proposed mechanism addresses one layer of SFRT response: the cell-intrinsic intracellular consequence of bystander signalling at single bystander cells. It does not address vascular damage in peaks, organism-level immune memory (Jenkins et al., 2024), the cohort-effect signalling within irradiated volumes (Asur et al., 2015), the empirical dose-distance interaction captured by MLQ (Arous et al., 2025), or the broader treatment-microenvironment dynamics discussed in Moghaddasi et al. (2022). A complete account of SFRT will integrate the proposed mechanism with these other layers. The present proposal contributes a specific upgrade to one mechanistic component.

Parameters are plausible, not measured. The order-of-magnitude reconciliation of Section 6 establishes that the relevant biological numbers are compatible with the proposed mechanism. None of the numbers has been measured for SFRT specifically. A calibrated model requires direct measurement of bystander-signal-driven AP-1 activation, memory formation rates, and memory effects on radiosensitivity in radiation contexts.

Spatial structure is stylised. The treatment in Section 3 abstracts from the detailed spatial geometry of clinical SFRT (GRID hole spacing, LATTICE vertex arrangement, MR-guided dose painting). A spatially explicit treatment, with realistic dose distributions and tissue geometry, would be needed for clinical application.

Identifiability claim is structural, not formal. Section 5.4 argues that the augmented observable space addresses the non-identifiability of the original model, but this is a structural argument rather than a formal identifiability proof of the extended model. A complete generating-series analysis of the extended system, in the style of Vaitheeswaran (2026a), is the natural next theoretical step.

9. Discussion

9.1. Bystander Signalling as a Memory-Laden Process

The proposal recasts bystander signalling from a kinetic phenomenon into a memory-laden one. Under the original framework, the bystander effect at fraction $n$is a fixed function of the dose delivered at fraction $n$. Under the proposal, the bystander effect at fraction $n$depends on the cumulative bystander signal exposure across fractions $1$through $n-1$, integrated by the intracellular AP-1 / CBP-p300 axis into a durable memory state that modulates the cell's radiosensitivity.

This reframing has implications beyond SFRT. Bystander effects in microbeam experiments, in multi-fraction conventional radiotherapy, in re-irradiation scenarios, and in radiation-immunotherapy combinations all involve signal propagation between irradiated and non-irradiated cells. Wherever signal exposure is repeated or sustained, the proposed memory layer predicts that recipient cells should not respond identically to each signal pulse — they should respond according to a state that the past pulses have shaped.

9.2. Relationship to Immune-Mediated Memory in SFRT

The most important neighbouring framework is the immune-mediated memory mechanism emphasised in Jenkins et al. (2024) and elaborated in Moghaddasi et al. (2022). Both that framework and the present proposal invoke memory in the SFRT context, but at different scales and through different machinery.

The immune-memory mechanism operates at the organism level: T-cell repertoire, antigen-presenting cells, lymph-node biology, systemic immune surveillance. Memory in this sense is the conventional immunological notion — antigen-specific T cells circulating after initial priming, capable of recognising and responding to recurrent or distant antigen presentation. The mechanism's relevant timescales are days to weeks for priming and weeks to years for memory persistence. Its observables are immune-cell infiltration, lymph-node activation, peripheral T-cell expansion, and clinical evidence of abscopal responses.

The proposed mechanism operates at the single-cell level: chromatin marks at AP-1-occupied loci in individual bystander cells, durable transcriptional state changes encoded in cis. Memory in this sense is cell-intrinsic and operates whether the cell is part of an immune compartment or not. Its relevant timescales are hours for formation and weeks to months for persistence. Its observables are chromatin accessibility, AP-1 activity, H3K27ac mark distribution.

These mechanisms are complementary, not competing, and probably interact. Immune-derived cytokines (TNF-$\alpha$, IL-1, IFN-$\gamma$, IL-6) are well-established AP-1 activators (Karin, 1995; Christmann and Kaina, 2013), so the immune system can drive cis-memory formation in bystander cells via cytokine release. Conversely, AP-1-driven gene expression includes modulators of antigen presentation (MHC class I and II regulation), so cis-memory in tumour cells can affect immune recognition of those cells at subsequent fractions. A full account of SFRT response across multi-fraction regimens will likely involve both layers operating in tandem.

The proposal does not claim that the cell-intrinsic mechanism explains the SFRT immune-mediated effects that Jenkins et al. (2024) and others have documented. It claims that there is an additional, cell-intrinsic memory layer at the single-cell level that current models do not capture and that the AP-1 / CBP-p300 axis provides a candidate substrate for.

9.3. Implications for Combined-Modality Strategies

If the mechanism holds, several clinical strategies become available. The most direct is pharmacological modulation of the AP-1 / CBP-p300 axis during fractionated SFRT. JNK inhibitors, FOS/JUN DNA-binding inhibitors, and CBP/p300 inhibitors (HAT and bromodomain) are all available as research tools, with several in clinical development. The Li et al. data suggest that timing matters: agents that block formation must be present during signal exposure, while agents that block persistence are effective if applied between fractions. The two inhibitor classes are therefore complementary rather than redundant.

A second strategy is regimen design that exploits the time-ordering sensitivity predicted by Proposition 2. If the order in which regions receive high dose modifies the final memory state, then optimised SFRT regimens may differ from current GRID and LATTICE arrangements by the temporal sequencing of spatial dose patterns. This is testable in preclinical models without requiring new pharmacological agents.

A third strategy is stratification: tumours with high baseline AP-1 activity may be especially responsive to SFRT and especially vulnerable to combined-modality interruption of that axis. Conversely, tumours with diminished AP-1 / CBP-p300 function may respond less well to SFRT, and the choice of modality could be informed by pre-treatment AP-1 axis characterisation.

A fourth strategy involves the immune-memory layer: combining AP-1 / CBP-p300 axis modulation with immune checkpoint inhibition — the latter already discussed in Jenkins et al. (2024) — exploits the complementarity between the two memory layers described in Section 9.2.

9.4. Relationship to Other Bystander Signalling Mechanisms

The proposed mechanism does not displace other bystander signalling mechanisms. Gap-junctional intercellular communication via connexins (Azzam et al., 2001), exosome-mediated signal transfer (Mutschelknaus et al., 2016), and microvesicle-borne RNA cargo (Jelonek et al., 2016) all contribute to bystander phenomenology. The proposal here addresses a different layer: not the delivery of bystander signals but their intracellular consequence. Multiple signal-delivery routes converge on a common stress-response axis (JNK-AP-1) that drives the proposed memory mechanism, and this axis is largely independent of which specific signal molecule arrived.

This compatibility is a feature. It means that the proposed memory layer can operate downstream of multiple bystander signalling routes, providing a unifying intracellular endpoint where the kinetic-bystander framework currently has only an aggregated hazard rate.

9.5. Relationship to the Phenomenological MLQ

The MLQ of Arous et al. (2025) and the present proposal address different aspects of the same problem. The MLQ provides a compact, fittable, phenomenological description of single-fraction SFRT cell survival; the present proposal provides a mechanism that should predict how the MLQ parameter $\delta$depends on biological state and on multi-fraction regimens. The two are not in conflict and could be combined productively: the MLQ provides empirical estimation infrastructure, the proposed mechanism provides interpretive structure for what the parameter means and predictions for how it should respond to perturbations.

9.6. Relation to Latent-State and State-Dependent Radiobiological Frameworks

Although the present work is formulated as a mechanistic extension of the McMahon kinetic-bystander model, its structure connects naturally to a broader systems-level view of radiobiological response under partial observability. In separate work, I argued that several representative radiobiological models across FLASH, SFRT, SBRT, and adaptive resistance exhibit structural or observation-dependent non-identifiability under clinically realistic observation regimes, implying that distinct internal configurations may generate indistinguishable observable outcomes (Vaitheeswaran, 2026a; Vaitheeswaran, 2026b). Under such conditions, the objective shifts from exact parameter recovery toward maintaining informative estimates of an evolving latent organizational state (Vaitheeswaran, 2026a; Vaitheeswaran, 2026b).

Viewed in that light, the present model may be interpreted as a local mechanistic instantiation of that broader idea. The additional intracellular layer introduced here does not eliminate observability constraints and is not claimed to render the system identifiable. Indeed, introducing hidden states generally increases representational flexibility while reducing direct parameter recoverability. Instead, the present formulation decomposes aggregated recipient-cell response into intermediate organizational variables that may expose additional experimentally accessible observables. In this interpretation, markers such as AP-1 activation, chromatin state, or persistence signatures are not themselves the latent state but candidate measurements informative about it.

This interpretation also aligns with recent state-dependent formulations proposed in other radiobiological contexts. In the M-ROD framework for FLASH radiotherapy, radiolytic oxygen depletion is extended through the introduction of a bounded internal state that evolves through activation, feedback, and decay and thereby encodes irradiation history (Vaitheeswaran, 2026c). Rather than treating radiosensitivity as an instantaneous function of oxygen concentration alone, M-ROD interprets biological response as a transition between dynamical regimes whose expression depends on prior exposure and temporal delivery structure. Importantly, the present work and M-ROD do not propose the same biological substrate and address different empirical regimes. However, they share a common architectural principle: introducing an internal state variable as a compact representation of hidden biological organization that mediates between physical exposure and observable response.

Seen together, these frameworks suggest a possible hierarchy of interpretation. The broader latent-state framework motivates why compressed observables repeatedly fail across radiobiology (Vaitheeswaran, 2026b); the present work proposes one candidate intracellular realization of hidden-state organization in bystander signaling; and M-ROD illustrates that similar state-dependent structure may emerge independently in ultra-high-dose-rate radiobiology (Vaitheeswaran, 2026c). The convergence across these otherwise distinct domains does not establish a unified mechanism, but it supports the broader hypothesis that history-dependent internal organization may represent a useful modeling primitive across radiobiological systems.

9.7. Relation to Predictive Observability and the Tumor Coupling Index Framework

The present formulation also connects naturally to recent predictive approaches that attempt to infer hidden organizational structure without recovering explicit mechanistic parameters. In separate work, I introduced the Tumor Coupling Index (TCI), a trajectory-based framework in which interaction is not estimated directly but detected operationally through predictive gain obtained from longitudinal spatial data (Vaitheeswaran, 2026d). That work showed that tumors with different internal coupling structures can exhibit nearly identical scalar trajectories while remaining distinguishable through differences in predictability, suggesting that observability may sometimes be improved not by richer mechanistic equations but by richer observables.

The present model and TCI approach operate at different levels but address related limitations. The current framework proposes an internal state variable mediating how recipient cells interpret and retain bystander exposure. TCI, by contrast, does not assume any specific mechanism and asks whether hidden coordination leaves measurable consequences in longitudinal data. One may therefore view them as complementary responses to the same compression problem: the mechanistic model proposes candidate internal variables, whereas the predictive framework proposes observables that may reveal their consequences.

This distinction is important. The present model remains explanatory and mechanistic; TCI remains operational and model-agnostic. Yet both move away from static endpoint measurements and toward trajectory-based characterization of tumor response. If organizational state influences response, its signature need not appear primarily as altered survival magnitude, but as altered coordination, persistence, and predictability of tumor evolution across time. In that sense, predictive observability may provide a practical experimental route for evaluating whether the kinds of hidden-state dynamics proposed here leave detectable consequences in clinical longitudinal imaging.

10. Conclusion

We proposed that the AP-1 / CBP-p300 cis-epigenetic memory mechanism demonstrated by Li et al. (2026) provides one candidate intracellular implementation for persistent recipient-cell state within the kinetic-bystander framework of McMahon et al. (2013), addressing a residual gap left open by subsequent extensions focused on immune coupling, phenomenological fitting, and treatment-planning applications.

Through timescale reconciliation, structural analysis, and literature-derived order-of-magnitude arguments, we showed that introducing a persistent intracellular layer naturally gives rise to cross-fraction accumulation, temporal ordering effects, and experimentally testable state dependence. The framework does not eliminate observability limitations or establish identifiability, but proposes additional observables—such as AP-1 activation, chromatin state, and pharmacological perturbation—that may expose aspects of previously compressed intracellular dynamics.

The proposal remains explicitly hypothetical and does not claim validation. Its value lies in generating falsifiable predictions: JNK and CBP/p300 perturbation should differentially affect memory formation and persistence, and multi-fraction SFRT should exhibit measurable dependence on delivery history. If supported experimentally, the kinetic-bystander framework gains a tractable intracellular memory layer; if not, the constraints established here narrow the search space for alternative substrates of persistent bystander response.