First Experimental Measurements of Biophotons from Astrocytes and Glioblastoma Cell Cultures

Abstract

Biophotons are non-thermal and non-bioluminescent ultraweak photon emissions, first hypothesised by Gurwitsch as a regulatory mechanism in cell division, and then experimentally observed in living organisms. Today, two main hypotheses explain their origin: stochastic decay of excited molecules and coherent electromagnetic fields produced in biochemical processes. Recent interest focuses on the role of biophotons in cellular communication and disease monitoring. This study presents the first campaign of biophoton emission measurements from cultured astrocytes and glioblastoma cells, conducted at Fondazione Pisana per la Scienza (FPS) using two ultra-sensitive setups developed in collaboration between the National Laboratories of Frascati (LNF-INFN) and the University of Rome II Tor Vergata. The statistical analyses of the collected data revealed a clear separation between cellular signals and dark noise, confirming the high sensitivity of the apparatus. The Diffusion Entropy Analysis (DEA) was applied to the data to uncover dynamic patterns, revealing anomalous diffusion and long-range memory effects that may be related to intercellular signaling and cellular communication. These findings support the hypothesis that biophoton emissions encode rich information beyond intensity, reflecting metabolic and pathological states. The differences revealed by applying the Diffusion Entropy Analysis to the biophotonic signals of Astrocytes and Glioblastoma are highlighted and discussed in the paper. This work lays the groundwork for future studies on neuronal cultures and proposes biophoton dynamics as a promising tool for non-invasive diagnostics and the study of cellular communication.

1. Introduction

Biophotons are ultraweak photon emissions observed in all living organisms. They were first hypothesized by Gurwitsch in 1924 [1]. While studying onion root development, he found that UV radiation from nearby roots enhanced mitosis without biochemical contact. A quartz (UV-transparent) barrier preserved the effect, but an opaque one suppressed it. This led to the idea of a photonic regulatory mechanism called the “morphogenetic field” [1,2]. In the following decades, emissions were detected in the UV [3,4,5,6] and visible [7,8] ranges from germinating seeds and other biological samples. In the 1980s, Popp coined the term biophoton to describe this “mitogenic radiation” and began to study its role [9]. Ultraweak photon emission (UPE), typically 1–1000 photons/s/cm², is now recognized as a universal phenomenon in living systems, distinct from bioluminescence and not thermal radiation in nature [9,10,11,12].

Two main hypotheses address biophoton origins [9,11]: (i) random radiative decay of metabolically excited molecules (e.g., oxidative reactions), and (ii) coherent EM fields generated by biochemical processes, possibly involving oxygen. Experimental data show that stress increases biophoton emission, supporting both models [13,14], which are not mutually exclusive.

Biophotons have recently attracted growing interest due to their potential role in cellular communication and regulation, with applications spanning toxicology, health monitoring, and cancer research [15,16,17].

Glioblastoma (GBM) is the most common and aggressive malignant primary brain tumour in adults. In the 2021 WHO classification, GBM is defined as an IDH-wildtype diffuse astrocytic tumour, CNS WHO grade 4, typically showing microvascular proliferation and/or necrosis [18]. The current standard of care is maximal safe resection followed by radiotherapy with concomitant and adjuvant temozolomide (the Stupp protocol), yet median overall survival is 14–16 months [19]. Light-based strategies are widely explored in GBM, for example, photodynamic therapy, while preclinical monitoring commonly relies on bioluminescence imaging of luciferase-tagged glioma cells [20,21,22]. However, to our knowledge, there are no prior studies directly measuring endogenous ultra-weak photon emission (biophotons) from GBM cells (or astrocytes) under label-free, dark conditions; existing optical read-outs in GBM either use exogenous reporters or deliver external light. However, evidence that brain tissue emits UPE in non-tumour contexts supports biological plausibility [23,24]. Establishing whether GBM and astrocytes emit detectable biophotons and quantifying their statistical structure would therefore fill a methodological gap and may offer new insight into redox dynamics and intercellular signalling in malignant glia.

In this paper, we present biophoton measurements from astrocyte and glioblastoma cell samples, conducted at the Fondazione Pisana per la Scienza (FPS) using two experimental setups developed by INFN–Frascati and the University of Tor Vergata [25,26,27]. These apparatuses, previously employed in plant germination studies [25,26,27], enable ultra-sensitive detection in dark conditions (2–3 counts/s) at room temperature (≈25 °C). For the first time in this context, Diffusion Entropy Analysis (DEA) was applied to cellular biophoton signals, allowing for the identification of crucial events potentially linked to intercellular communication. The adoption of DEA marks a significant step forward in the analysis and interpretation of biophotonic data.

2. Material and Methods

2.1. The Experimental Apparatuses

The collaboration developed two experimental setups dedicated to measuring biophotons emitted by living cell cultures. The first apparatus, developed at Tor Vergata University and referred to as the “TOV” setup, consists of a rectangular black PVC chamber with a cylindrical recess designed to hold the Petri dish and a rectangular lid with a photo-counting detector aligned with the center of the cylindrical recess. A small hole is located below the central circular elevation in the cylindrical recess, within the PVC chamber, slightly recessed from the lateral walls. This hole allows for air exchange while minimizing light infiltration as much as possible. The second apparatus, built at the INFN National Laboratories of Frascati (LNF) and referred to as the “LNF” setup, features a cylindrical black PVC chamber with a similar cylindrical recess and a cylindrical lid housing the photo-counting detector aligned with the center of the recess. In this case, air intake is controlled through valves located on the upper part of the structure. In both the apparatuses, the detector is a H12386-210 high-speed photo-counting head (Hamamatsu Photonic Italia S.r.l, Arese, Italy) [28] powered at +5 Vcc. The phototube has a circular active area with a 5 mm radius and is extremely sensitive in the wavelength range from 230 to 700 nm with a peak sensitivity at 400 nm [28,29].

Both apparatuses were already used for biophoton measurements on germinating plants, delivering excellent performance and reliable results [25,27]. More details and schematic drawing of the apparatus can be found in [25,27]. The setups were designed to be inserted in a dedicated incubator to preserve environmental conditions suitable for the survival and well-being of cells. Data were collected and processed using an ARDUINO board, controlled with a Node-Red-based DAQ system. The Petri dishes, with a 3 cm radius, were positioned inside the setups, exactly at the center of the detector, and at a vertical distance of 3 cm from it. This configuration was determined through a Monte Carlo simulation, which estimated the maximum geometric detection efficiency at this distance. In both setups, the center of the detector was perfectly aligned with the center of the Petri dish. The devices installed in the incubator of the FPS laboratory are shown in Figure 1. Despite the slight structural differences between the two devices, their measurement efficiency and suitability for biophoton detection are equivalent, as tested by the collaboration in the laboratory. Any residual variability in the acquired data is instead attributable to the intrinsic sensitivity of the photo-counting heads and to the natural, non-uniform evolution of the biological samples, which may differ in number, timing, and spatial distribution even when derived from the same cell population. It is also important to note that the two acquisitions are performed simultaneously but remain fully independent, as each apparatus relies on its own phototube and electronic chain.

2.2. Cell Lines and Sample Preparation

Commercial human glioblastoma cell lines U87-MG, T98G, U118-MG, and commercial human brain astrocytes (HBAs) were maintained at 37 °C and 5% CO₂ in a humidified incubator (ATCC, Manassas, VA, USA). Cells were grown in DMEM (high glucose) supplemented with 10% fetal bovine serum (Gibco) and 1% penicillin–streptomycin (Gibco) and passaged at 70–80% confluence using 0.05% trypsin–EDTA, following the vendor’s recommendations (Thermo Fisher Scientific, Waltham, MA, USA).

At baseline (T0), 150,000 HBA cells and 350,000 T98G cells were seeded, respectively. After cell attachment, cultures were exposed to different experimental conditions and collected either at baseline (T0) or after 48 h (T2). For HBA cells, one set of cultures (HBA-T0) was collected at seeding as a control. A second group (HBA-T2) was maintained inside the TOV machine for 48 h, while additional groups were placed outside the TOV machine. Among these, some cultures were kept in the same incubator as the TOV machine, which was shielded from external light exposure, whereas others were transferred to a separate incubator that was not shielded and therefore exposed to ambient light. Similarly, T98G cells were subdivided into different groups. The control group (T98G-T0) was collected at seeding. Subsequent cultures were maintained for 48 h (T98G-T2) either inside the TOV machine or inside the LNF machine. Additional cultures were kept outside both the TOV and LNF machines but within the same incubator, which was shielded from external light. Finally, a separate group of T98G cultures was maintained outside both machines in an unshielded incubator, directly exposed to ambient light.

2.3. Crystal Violet Staining

At T0 or T2, dishes were rinsed in PBS, fixed in 4% paraformaldehyde (PFA) for 10–15 min at room temperature, rinsed, and stained with Crystal Violet (CV) (0.1% w/v in 20% methanol). Excess dye was removed with water, and plates were air-dried prior to imaging and quantification. Cells were de-stained using a 10% acetic acid solution, and the absorbance of the solution was then measured at 590 nm.

2.4. The Data Taking Conditions

The entire campaign of measurements was carried out in the biological laboratories of Fondazione Pisana per la Scienza, where the research group at the laboratories, coordinated by Chiara Mazzanti, provided circular Petri dishes with cell cultures of astrocytes and glioblastoma. The DAQ time window was fixed at 1 s [29]. The measurements were performed with the two devices installed inside an incubator, where an external hole was drilled for the cables to exit, towards the readout chips (placed outside the incubator). The entire incubator, including the cable exit, was adequately shielded with black electrical tape, aluminium foil, and a green sheet, as shown in Figure 1. The temperature inside the incubator was 37 °C to sustain optimal conditions for the life and proliferation of cells in culture. Before the measurements on cell samples, preliminary data acquisition without a target inside the machines revealed dark counts of approximately 10–20 counts per second, consistent with the data sheets provided by Hamamatsu for the detector [29] at the incubator temperature (37 °C). This attests to the high light shielding efficiency the apparatus provides, ideal for measuring weak light signals, as expected for biophotons.

3. Collected Data and Preliminary Observations

3.1. The Data Taking Campaign

A one-week window in September 2024 was allocated for the collaboration to acquire data, encompassing installation, measurements, and final dismantling of the setup. In this period, one full measurement cycle with both devices was explicitly performed. Given the limited timeframe, the schedule was structured as follows:

(a)

About two days of measurements in complete darkness, with no samples present in either setup, aimed at assessing residual luminescence decay and background levels.

(b)

Two days of measurements with astrocyte cell cultures placed in both setups.

(c)

Two days of measurements with glioblastoma cell cultures placed in both setups.

The data collected are shown in Figure 2 and Figure 3.

Looking at the graphs in Figure 2 and Figure 3, a clear distinction between the dark condition and the cell-containing samples was observed for both glioblastoma and astrocyte cultures, attributable to the evident emission of biophotons. During the measurements, no significant increase in emission intensity was observed despite the growth in cell population. This is likely because cell proliferation does not occur uniformly, but rather locally and irregularly. Combined with the low geometrical efficiency of the setup (less than 1%), this makes any potential increase in signal hardly detectable. Moreover, biophoton emission is not necessarily isotropic: since the cells are essentially planar, the emission may preferentially occur towards adjacent cells. Consequently, an increase in the number of cells does not necessarily correspond to a higher signal in the direction of the photocounter. Moreover, slight discrepancies between the results can be attributed to both the intrinsic differences in sample behaviour—such as growth timing, cell count, and local aggregation—and the limited geometric efficiency of the detection setup.

Although the geometric efficiency is below 1%, this parameter does not affect the analysis of the statistical patterns; rather, it simply quantifies the remaining margin for improving the absolute detectability of the biophoton signal.

3.2. Statistical Analyses of the Experimental Data

The signal-to-noise ratio (SNR) was estimated by calculating the signal and noise power from the recorded time series. The power of a signal, normalised to the length N of the time series, was defined as follows:

$$P(N)={\displaystyle \frac{1}{N}}\sum _{t=1}^{N}x{\left(t\right)}^2$$

(1)

The SNR was then obtained as follows:

$$SNR={\displaystyle \frac{P_{signal}\left(N\right)-P_{noise}\left(N\right)}{P_{noise}\left(N\right)}}$$

(2)

where $P_{signal}\left(N\right)$ and $P_{noise}\left(N\right)$ represent, respectively, the power of signals produced during the astrocytes and glioblastoma measurements, and the power of the noise signal collected with each apparatus empty, in dark conditions, and inside the incubator.

We also estimated the mean value of each set of data collected

$$<n>={\displaystyle \frac{1}{N}}\sum _{t=1}^{N}x\left(t\right)$$

(3)

and the variance:

$${\sigma }^2={\displaystyle \frac{1}{N}}\sum _{t=1}^N{[x\left(t\right)-<n>]}^2$$

(4)

The power of the signal is connected with the $\sigma$ and $<n>$ by $P\left(N\right)={\sigma }^2+<n{>}^2$. The variance will be fundamental for the data analysis with the Diffusion Entropy Analysis (DEA), described in the next subsections.

Table 1. Table of the mean values $<n>$, standard deviations ($\sigma$), skewness, and estimated Signal-to-Noise Ratios (SNRs) extracted by the analysis on dark (background), astrocytes, and glioblastoma data acquired with LNF and TOV machines. The dark data were acquired with the empty setups inside the incubators.

Setup	Data	$<\mathit{n}>$	$\mathit{\sigma }$	Skewness	SNR
LNF	Background (Dark)	13.76	4.19	0.41
	Astrocytes	22.82	5.51	0.33	1.68
	Glioblastoma	20.27	5.06	0.32	1.09
TOV	Background (Dark)	16.27	4.38	0.34
	Astrocytes	20.34	4.81	0.31	0.54
	Glioblastoma	19.54	4.73	0.35	0.43

summarizes the mean values $<n>$, standard deviations ($\sigma$), skewness, and estimated SNRs for the datasets acquired using both LNF and TOV setups.

In both setups, the dark (background) measurements show lower mean signals, as expected, since they correspond to acquisitions without biological samples. The noise levels (expressed by $\sigma$) are comparable across the different conditions and setups, with slightly higher values in the LNF configuration. When comparing astrocytes and glioblastoma samples, we observe a progressive increase in the mean signal $<n>$ from dark to astrocytes and glioblastoma, reflecting the higher biological activity or scattering contribution of the samples. In both experimental setups, the mean values of the counts obtained with the presence of cellular samples are significantly higher than the values obtained without them. To verify whether this result has a robust degree of statistical significance, we performed a one-sided permutation test on the difference of means [30]. Suppose we have two independent series of observations: one corresponding to the noise $x_{n_1},\dots ,x_{n_{noise}}$, and one corresponding to the signal $y_{n_1},\dots ,y_{n_{signal}}$. We focus our attention on the observed difference of sample means $D_{obs}=\overline{y}-\overline{x}$. The basic idea behind this test is to assume that the signal data are not different from the noise data, and therefore the observed differences are just random fluctuations, the so-called null hypothesis H0. If so, the assignment of each observation to the “noise” or “signal” group is arbitrary, and one can pool all data into a single combined dataset:

$$\mathbb{Z}=\left\{x_{n_1},\dots ,x_{n_{noise}},y_{n_1},\dots ,y_{n_{signal}}\right\}$$

(5)

containing $n=n_{noise}+n_{signal}$ values. From this pooled dataset, we generate surrogate datasets by randomly permuting the labels: at each iteration, we draw (without replacement) $n_{signal}$ values to form a “pseudo-signal” set and assign the remaining $n_{noise}$ values to a “pseudo-noise” set. For each such permutation, we compute the mean difference:

$$D^{*}={\overline{y}}^{*}-{\overline{x}}^{*}$$

(6)

Repeating this procedure many times yields the empirical null distribution of $D^{*}$ under the assumption of no real difference between groups. The p-value is then estimated as the proportion of permutations where $D^{*}\ge D_{obs}$, with a plus-one correction to avoid zero values:

$$p={\displaystyle \frac{\#\{D^{*}\ge D_{obs}\}+1}{M+1}}$$

(7)

where M (in our case M = 20,000) is the number of performed permutations. If the null hypothesis is true, the p-value tells us how often, by shuffling the data, we get a difference as large as the one we observed. The smaller the p-value, the less likely it is that the signal series is due to a random fluctuation in the noise. In both experimental setups, we obtain p-values of the order of ${10}^{-5}$, a very small value which indicates that the probability that the signal originates from a noise fluctuation is practically negligible. For instance, if the signal were purely noise, we would have $p\approx 0.5$.

From Table 1, the SNR values reveal a clear difference between the two setups. These results may suggest a better sensitivity of the LNF setup, leading to more reliable detection of biological signals, especially for the glioblastoma samples. However, as already discussed in the previous section, the non-uniform distribution and proliferation of cells, varying from sample to sample, and the potentially anisotropic nature of biophoton emission are likely contributing factors to the observed discrepancies. Table 1 also includes the skewness values of the count distributions within the selected time windows. Skewness quantifies the asymmetry of a distribution relative to its mean. For reference, a Gaussian distribution has a skewness of zero (${\gamma }_1=0$), indicating perfect symmetry, while the skewness of a Poisson distribution is given by ${\gamma }_1=\frac{1}{\sqrt{\mu }}$, where $\mu$ is the parameter of the Poisson distribution. For a $\lambda =13.76$, a Poisson distribution would exhibit a skewness of approximately ${\gamma }_1=0.269$. However, the observed values of standard deviation and skewness for the six experimental count distributions strongly deviate from these theoretical expectations. This implies that the distributions cannot be adequately described by either Gaussian or Poisson statistics, pointing to more complex underlying dynamics in the biophotonic emission processes.

To go deeper into this topic, we performed an analysis of the experimental data coming from both setups in terms of the count distribution function (CDF). For example, we show in Figure 4 the comparison between the CDF for astrocyte emission in the LNF setup and the best fit based on a Poisson function. Similar figures are obtained for all experimental data obtained in the two setups used.

From a visual comparison between the experimental CDFs and the corresponding fits in terms of Poisson functions, the presence of a significant tail compared to that typical of Poisson CDFs is clear. To quantify this visual observation, we used the following method: For each experimental CDF $p_{exp}\left(j\right)$, we construct the quantity $F_{exp}\left(k\right)={\sum }_{j\le k}{p}_{exp}\left(j\right)$, and for a given quantile q (in our case $q=0.9$), we define a threshold $th{r}_q=min\{k:F_{exp}\left(k\right)\ge q\}$; with this, we calculate the following tail indicators, in this case, the right tail:

$$M_{exp}\left(q\right)=\sum _{k\ge th{r}_q}{p}_{exp}\left(k\right)$$

(8)

$$E{S}_{exp}\left(q\right)=\frac{{\sum }_{k\ge th{r}_q}k·p_{exp}\left(k\right)}{M_{exp}\left(q\right)}$$

(9)

The quantity $M_{exp}\left(q\right)$ represents the probability of having counts $\ge th{r}_q$ found with the chosen quantile, while the quantity $E{S}_{exp}\left(q\right)$ represents the conditional average value of the counts that exceed the threshold, i.e., how large the count is in the tail defined by the quantile.

Table 2. The $M_{exp}\left(q\right)$ and $E{S}_{exp}\left(q\right)$ extracted by the analysis on background (dark), astrocytes, and glioblastoma data obtained with the LNF and TOV experimental setup.

	${\mathit{M}}_{\mathit{exp}}\left(\mathit{q}\right)\left(\mathit{LNF}\right)$	${\mathit{ES}}_{\mathit{exp}}\left(\mathit{q}\right)\left(\mathit{LNF}\right)$	${\mathit{M}}_{\mathit{exp}}\left(\mathit{q}\right)\left(\mathit{TOV}\right)$	${\mathit{ES}}_{\mathit{exp}}\left(\mathit{q}\right)\left(\mathit{TOV}\right)$
Astr	0.13	32.29	0.13	27.86
Dark	0.10	21.59	0.14	23.66
Glio	0.17	28.18	0.18	26.03

shows the values obtained for the two quantities defined above relating to the experimental data collected by the two measurement systems.

The two experimental configurations (LNF and TOV) differ slightly in geometry and in the photomultiplier, which, although it is formally of the same type, may exhibit marginally different characteristics. The comparison between the two setups shows that the probability of exceeding the threshold defined by the quantile is substantially consistent between the configurations. In particular, the tail probability is slightly higher in the glioblastoma samples (∼0.17–0.18) compared with astrocytes (∼0.13) and background (∼0.10–0.14), indicating that glioblastoma cells are more frequently associated with extreme count events. More striking differences emerge in the conditional mean values. While the background measurements display the lowest average counts in the tail (≈21–23), both cellular samples exhibit markedly larger values. Astrocytes in particular show the highest tail means (≈28–32), clearly exceeding those of glioblastoma (≈26–28) as well as the background. This suggests that although extreme events are more frequent in glioblastoma, those occurring in astrocytes tend to be more intense on average. Overall, these findings indicate that the presence of cells enhances both the probability and the magnitude of extreme counting events compared with the background. Moreover, astrocyte data are characterized by rarer but stronger tails, whereas glioblastoma by more frequent but slightly less intense tails. The small differences observed between LNF and TOV further indicate that the effects are intrinsic to the biological samples rather than to the measurement setup. Although the measurements were performed simultaneously on samples derived from equivalent cell lines, each culture naturally follows its own biological evolution, with variations in timing, dynamics, and spatial development. Despite these inherent divergences, the recorded signals and the subsequent analysis display a consistently similar trend across the two acquisitions, thereby strengthening the overall robustness and reliability of the measurement. More information and details about statistical data analyses applied to biophoton signals can be found in this recent work [31].

4. Data Analysis and Results

4.1. The Diffusion Entropy Analysis (DEA)

To characterise the complexity of the biophotonic signals, we applied the Diffusion Entropy Analysis (DEA) method [31,32]. This approach is particularly suitable for studying biological systems, which often deviate from the assumptions of equilibrium statistical mechanics—such as lack of memory, short-range interactions, and non-cooperative behaviour [33,34]. DEA belongs to a broader class of techniques designed to quantify temporal complexity in time series data. Unlike methods based on signal compression or spectral analysis, DEA transforms the original signal into a diffusion process and measures its complexity through the growth of the Shannon entropy associated with the corresponding probability distribution. In the case of ordinary Brownian motion, this entropy grows linearly with the logarithm of time, and any deviation from this expected scaling reflects the presence of correlations or structural complexity. In our analysis, DEA revealed such deviations in the biophoton emission time series, indicating the presence of non-trivial, possibly self-organised dynamics underlying the biological activity. A more comprehensive description of the method is available in [25,26,31], and a forthcoming dedicated publication will present a revised formulation of DEA specifically adapted for biophotonic signal analysis.

Mathematical Formulation of DEA

The Diffusion Entropy Analysis (DEA) approach begins by transforming a time series $\xi \left(t\right)$ representing, for example, the number of photons detected per second into a diffusion trajectory $x\left(t\right)$ through time integration. This trajectory reflects the cumulative behaviour of the signal and enables the investigation of its scaling properties. To study the complexity of the underlying process, we examine the probability distribution function (PDF) $p(x,l)$ of displacements over a moving window of size l. Then, the Shannon entropy is computed:

$$S(l)=-\int p(x,l)lnp(x,l)dx$$

(10)

If the process is characterized by a scaling law $p(x,l)\sim {\displaystyle \frac{1}{l^{\delta }}}F\left({\displaystyle \frac{x}{l^{\delta }}}\right)$, the entropy grows as $S\left(l\right)\propto \delta lnl$, where $\delta$ is the entropy scaling exponent and quantifies the type of diffusion: $\delta =0.5$ for normal diffusion, while $\delta \ne 0.5$ signals anomalous diffusion. However, not all anomalous scaling originates from stationary correlations. In systems with renewal events uncorrelated, memory-resetting events are separated by random waiting times $\tau$, distributed as $\Phi \left(\tau \right)\sim {\tau }^{-\mu }$: the source of complexity is non-stationary. These crucial events dominate the long-time behaviour when $1<\mu <3$, and standard correlation-based approaches fail to detect them. In the specific, we have three cases:

• $1<\mu <2$: corresponds to a strongly non-stationary regime, where the waiting-time distribution has a divergent mean and variance. In this case, the processes lack a characteristic time scale, and long waiting times dominate the dynamics.
• $2<\mu <3$: defines a weakly non-stationary regime in which the mean waiting time is finite while the variance diverges. The system exhibits subdiffusive behaviour with persistent temporal correlations and non-ergodic properties. This regime is of particular interest in the context of biophotonic signals, as it may indicate the presence of underlying temporal organization or self-structured dynamics rather than purely random activity.
• $\mu >3$: indicates a stationary regime, with both finite mean and variance of the waiting-time distribution. In this case, the process becomes ergodic and effectively Markovian in the long-time limit, leading to standard (Gaussian) diffusion. This pattern is typically associated with purely random dynamics, consistent with unstructured noise that lacks long-range temporal correlations.

In the conventional Diffusion Entropy Analysis (DEA) without any modification, the original time series $x\left(t\right)$ is directly integrated to generate diffusion trajectories. The scaling of the resulting entropy provides information about the overall complexity and correlations in the signal. However, this approach is primarily sensitive to Gaussian-like fluctuations and may not effectively capture rare and intermittent events, which are responsible for long-range memory effects. To overcome this limitation, DEA is modified using the so-called “stripes” method, which aims explicitly to highlight these crucial events. In this approach, the signal is converted into a binary sequence $z\left(t\right)$, which marks the times when the original signal crosses predefined thresholds (stripes). The “stripes” were defined with a width equal to $3\sigma$, where $\sigma$ is the standard deviation of the original signal (see Table 1). This binarization allows the isolation and emphasis of large excursions or significant transitions in the data. A new diffusion trajectory is then constructed from the binary sequence, from which a more robust and reliable estimation of the scaling exponent $\delta$ is extracted. In fact, this modified analysis enables the detection of memory and anomalous dynamics that are otherwise hidden in the standard DEA, providing a more sensitive characterisation of non-trivial temporal structures.

The relation between $\delta$ and the power-law index $\mu$ of the waiting-time distribution differs depending on whether stripes are used or not. Using the stripes is $\mu =1+{\displaystyle \frac{1}{\delta }}$. Without using the stripes, $\mu$ is determined as: $\mu =4-2\delta$ [26,27].

The “stripes” approach allows distinguishing between stationary and non-stationary sources of anomalous scaling, which is crucial for understanding the complexity of the system under study. In the context of biophoton emission, the identification of weakly non-stationary dynamics, associated with $2<\mu <3$ and scaling exponents $\delta \ne 0.5$, suggests the presence of crucial events that punctuate the activity of the biological system. These events are not merely stochastic fluctuations, but rather reflect self-organised temporal structures that govern the dynamics over long timescales. This interpretation supports the view that living cells are complex, far-from-equilibrium systems whose activity cannot be fully described by classical statistical mechanics. Instead, it involves hierarchical, memory-resetting processes essential for biological function and adaptation, and may be capable of communication mechanisms among cellular groups based on biophoton emission/reception.

As shown previously, the Shannon entropy is expected to follow the equation $S\left(l\right)=A+\delta lnl$, where the scaling exponent $\delta$ is experimentally estimated through a linear fit of $S\left(l\right)$ as a function of the logarithm of l (see Figure 5). One of the practical challenges of DEA is the choice of the fitting interval, as statistical fluctuations strongly influence the entropy values at the boundaries. To robustly characterise the scaling behaviour of the DEA curve, we implemented a sliding window fit procedure over the range between $ln\left(l\right)=2$ and $ln\left(l\right)=6$, where linearity is sufficiently preserved. This approach enables the local estimation of the scaling exponent $\delta$, revealing potential variations or instabilities in the scaling regime. The sliding window procedure involves the following steps:

• Select a global interval $[log\left(l_{min}\right),log\left(l_{max}\right)]$ along the horizontal axis.
• Define a moving window of width w, containing n evenly spaced data points.
• Perform a local linear fit within each window, estimating ${\delta }_i$ and its uncertainty ${\Delta }_{{\delta }_i}$.

The window is shifted by a step size of l, generating a sequence of local slope estimates:

$$\{{\delta }_1,{\delta }_2,{\delta }_3,\dots ,{\delta }_k\}.$$

For each contiguous block of slopes of defined length (in our case, we fixed this value at 5 windows), the standard deviation $\left({\Delta }_{\delta }\right)$ of the slopes within that block is computed. A block is classified as stable if

$${\Delta }_{\delta }<ϵ.$$

(11)

In our case, $ϵ=0.02$. If such a plateau is found, we compute

$${\delta }_{plateau}=\frac{{\sum }_{i\in plateau}{\delta }_i/{\Delta }_{{\delta }_i}^2}{{\sum }_{i\in plateau}1/{\Delta }_{{\delta }_i}^2},$$

(12)

$${\Delta }_{plateau}={\left(\sum _{i\in plateau}{\displaystyle \frac{1}{{\Delta }_{{\delta }_i}^2}}\right)}^{-1/2},$$

(13)

i.e., the weighted mean and associated standard deviation. If no block satisfies the stability criterion, the algorithm concludes that no statistically stable plateau is present in the selected interval. The value ${\delta }_{plateau}$ is then used to perform a constrained global fit of $S\left(l\right)$, fixing the slope to the plateau estimate. This allows for a direct comparison between local and global scaling behaviour, and highlights potential transitions or instabilities in the entropy dynamics. At the end, the final value of the scaling exponent $\delta$ is obtained by averaging over a restricted plateau region, where the variation of the scaling exponent is minimal.

For a more detailed discussion of the analysis procedures, the reader is referred to [25,26]. In addition, a technical paper is currently in preparation, presenting an updated formulation of the analysis method. This revised approach has been specifically developed to meet the demands of real-world experimental conditions and is tailored for investigating biological signals, such as biophoton emissions.

A more detailed description of the DEA analysis performed can be found in the recent publication [31].

Figure 5. Graph of $S\left(l\right)$ vs. $lnl$ obtained with the Diffusion Entropy Analysis (DEA) with stripes on the data collected with the LNF machine measuring biophotons emitted by astrocyte culture. As predicted by the theory, $S\left(l\right)\propto \delta lnl$, and the linear fit in the region between $l=2$ and $l=6$ allows the extraction of the scaling factor $\delta$. For the calculation, we used a scaling window method, described in Section 4.1. The same method was applied to all data sets. Final results are reported in Table 3.

Figure 5. Graph of $S\left(l\right)$ vs. $lnl$ obtained with the Diffusion Entropy Analysis (DEA) with stripes on the data collected with the LNF machine measuring biophotons emitted by astrocyte culture. As predicted by the theory, $S\left(l\right)\propto \delta lnl$, and the linear fit in the region between $l=2$ and $l=6$ allows the extraction of the scaling factor $\delta$. For the calculation, we used a scaling window method, described in Section 4.1. The same method was applied to all data sets. Final results are reported in Table 3.

Table 3. Values of the scaling exponent $\mu$ obtained from the Diffusion Entropy Analysis (DEA), with and without the application of the stripes method, applied to the biophoton emission signals detected from cultured astrocytes and glioblastoma cells. For the DEA with stripes, a threshold-crossing window of 3$\sigma$ counts was used to generate the binary sequence (reference to Table 1).

Setup	Measurement	DEA Without Stripes	DEA with Stripes
LNF	Background (Dark)	$\mu$ = 2.76 ± 0.04 $\delta$ = 0.62 ± 0.02	$\mu$ = 3.04 ± 0.04 $\delta$ = 0.49 ± 0.01
	Astrocytes	$\mu$ = 2.42 ± 0.02 $\delta$ = 0.79 ± 0.01	$\mu$ = 2.75 ± 0.06 $\delta$ = 0.57 ± 0.02
	Glioblastoma	$\mu$ = 2.60 ± 0.04 $\delta$ = 0.70 ± 0.02	$\mu$ = 2.85 ± 0.07 $\delta$ = 0.54 ± 0.02
TOV	Background (Dark)	$\mu$ = 2.90 ± 0.04 $\delta$ = 0.55 ± 0.02	$\mu$ = 2.89 ± 0.07 $\delta$ = 0.53 ± 0.02
	Astrocytes	$\mu$ = 2.54 ± 0.04 $\delta$ = 0.73 ± 0.02	$\mu$ = 2.64 ± 0.03 $\delta$ = 0.61 ± 0.01
	Glioblastoma	$\mu$ = 2.70 ± 0.02 $\delta$ = 0.65 ± 0.01	$\mu$ = 2.79 ± 0.06 $\delta$ = 0.56 ± 0.02

Table 3. Values of the scaling exponent $\mu$ obtained from the Diffusion Entropy Analysis (DEA), with and without the application of the stripes method, applied to the biophoton emission signals detected from cultured astrocytes and glioblastoma cells. For the DEA with stripes, a threshold-crossing window of 3$\sigma$ counts was used to generate the binary sequence (reference to Table 1).

Setup	Measurement	DEA Without Stripes	DEA with Stripes
LNF	Background (Dark)	$\mu$ = 2.76 ± 0.04 $\delta$ = 0.62 ± 0.02	$\mu$ = 3.04 ± 0.04 $\delta$ = 0.49 ± 0.01
	Astrocytes	$\mu$ = 2.42 ± 0.02 $\delta$ = 0.79 ± 0.01	$\mu$ = 2.75 ± 0.06 $\delta$ = 0.57 ± 0.02
	Glioblastoma	$\mu$ = 2.60 ± 0.04 $\delta$ = 0.70 ± 0.02	$\mu$ = 2.85 ± 0.07 $\delta$ = 0.54 ± 0.02
TOV	Background (Dark)	$\mu$ = 2.90 ± 0.04 $\delta$ = 0.55 ± 0.02	$\mu$ = 2.89 ± 0.07 $\delta$ = 0.53 ± 0.02
	Astrocytes	$\mu$ = 2.54 ± 0.04 $\delta$ = 0.73 ± 0.02	$\mu$ = 2.64 ± 0.03 $\delta$ = 0.61 ± 0.01
	Glioblastoma	$\mu$ = 2.70 ± 0.02 $\delta$ = 0.65 ± 0.01	$\mu$ = 2.79 ± 0.06 $\delta$ = 0.56 ± 0.02

4.2. Results

4.2.1. GBM Cell Viability

Figure 6 shows the results of the crystal violet assay used to assess cell viability after 48 h under the different experimental conditions. After 48 h, HBA cells showed a modest increase in viability across all conditions. Cells cultured outside the TOV machine but within the shielded incubator reached 116.9 ± 3.1%, whereas those inside the TOV machine displayed 111.9 ± 6.6%. HBA cells maintained in the unshielded incubator exposed to ambient light exhibited a lower increase (107.6 ± 2.6%) compared with shielded conditions.

In contrast, T98G glioblastoma cells exhibited a marked proliferation under all experimental conditions. After 48 h, cells outside the machines but within the shielded incubator reached 309.6 ± 20.9%, while those inside the TOV machine grew to 293.7 ± 11.8%. Cultures maintained inside the LNF machine showed similar results (325.5 ± 30.7%), with the highest values observed in the unshielded incubator (324.7 ± 20.6%). These results indicate that, while astrocytes exhibited only a modest increase in cell number, glioblastoma cells proliferated robustly under all conditions, with a tendency toward higher growth in unshielded environments.

4.2.2. DEA Results

The data collected during the experimental acquisition are summarised in Figure 2 and Figure 3. Table 3 reports the values of the scaling exponent $\mu$ obtained from DEA analyses, both without and with the application of the stripes method. As explained in the previous paragraph, the comparison allows us to highlight the presence of memory effects and rare, crucial events in the biophoton emission signals.

In the background (dark) measurements, both setups (LNF and TOV) show $\mu$ values closer to 3, indicating a behaviour compatible with ordinary Gaussian diffusion and absence of long-range correlations. The application of the stripes method further confirms this observation, with $\mu$ values converging exactly or even closer to 3, as expected for purely stochastic background noise. The astrocyte and glioblastoma signals exhibit distinct scaling properties, both of which differ significantly from the scaling behaviour observed in the dark signals for both systems. In all cases, the power-law exponent $\mu$ associated with the astrocyte signals is lower than that of the glioblastoma signals. Notably, both fall consistently within the range $2<\mu <3$, indicating that the time series of photocounts from the two cell types follow non-trivial statistics. This range is compatible with the presence of crucial events and fractional Brownian motion (FBM), suggesting underlying temporal correlations and complex dynamics in the biophoton emission process.

The scaling exponent of dark measurements obtained by applying DEA without stripes correction is slightly lower than $\mu =3$. This fact was already noted in the measurement with seeds performed by the collaboration [25,27]. In our view, this deviation may be attributed to the presence of nonlinear components within the phototube–electronics system. By contrast, when stripes are used in the DEA analysis, the dark scaling exponent consistently approaches $\mu \approx 3$, which is the expected value for thermal-type noise.

The two experimental systems yield slightly different $\mu$ scaling values, with a discrepancy of about 10% in the analysis without stripe correction, which reduces to approximately 7% when stripes are applied. This difference may stem from intrinsic variations between the two experimental setups (LNF and TOV), such as differences in electronic response, phototube behaviour, or other instrumental factors. Additionally, slight observed variations likely stem from the distinct developmental profiles of the samples, combined with the inherently low geometric efficiency of the apparatus, which may amplify subtle differences in growth dynamics and spatial clustering. Despite this, the overall trend remains consistent: the scaling exponent associated with astrocyte signals is always higher than that of glioblastoma signals. In addition, differences in scaling factors were also observed even when comparing samples of the same type (astrocytes or glioblastoma) measured using different apparatuses (LNF and TOV). This variability is likely due to the non-standardised evolution of the cellular samples and the short time frame of data collection (two days). Despite starting from the same initial number of cells, the system exhibits non-deterministic behaviour, leading to differences in both cell numbers and aggregation patterns.

Overall, these results demonstrate that the combination of DEA with the stripes method provides a powerful tool for revealing and quantifying non-trivial dynamical features and memory effects in biophoton emissions, supporting the potential of this approach to discriminate between different cell types and conditions. Furthermore, the DEA values with stripes reveal the occurrence of statistically significant crucial events, which point to coordinated, non-random activity among astrocyte and glioblastoma cells. This pattern aligns with critically induced collective intelligence in astrocyte and glioblastoma populations, as reported in recent studies [35].

5. Conclusions and Future Perspectives

A first measurement campaign of biophoton emissions by cellular samples of astrocytes and glioblastoma was performed at the laboratories of Fondazione Pisana per la Scienza (FPS) in Pisa. The exposures lasted 2 days for each sample, and the measurements were performed with two similar setups designed and built at the National Laboratories of Frascati (LNF) and the University of Tor Vergata (TOV), in collaboration. Two days of background (dark) data were acquired for each setup installed in the incubator, with the chamber left empty of any biological target. The data collected, shown in Figure 2 and Figure 3, clearly highlight a separation between the background (dark counts) and the signals recorded from astrocyte and glioblastoma samples, due to cell-derived biophoton emission. The result is supported by the signal-to-noise ratio analysis (shown in Table 1) and confirms the high sensitivity achieved by both experimental setups in measuring the weak biophoton emissions in the visible range. As mentioned in Section 3.1, TOV and LNF devices have only a minor difference: very small intrinsic sensitivity variations of the photo-counting heads. This effect does not substantially impact the analysis nor the conclusions drawn from the data. Although the measurements were performed simultaneously on samples derived from equivalent cell lines, each culture naturally follows its own biological evolution. Despite these inherent differences, the recorded signals and the subsequent analysis display a consistently similar trend across the two acquisitions, confirming the robustness of the measurement. Interestingly, the overall intensity of emission did not show a marked increase over time, despite the progressive growth of the cell population. This may be because cell proliferation tends to occur in localised and non-uniform regions, rather than evenly across the entire culture. Additionally, the low geometrical efficiency of the detection setup (less than 1%) further reduces the likelihood of capturing any moderate increases in the emitted signal. Finally, it is also worth noting that biophoton emission is unlikely to be isotropic: given the planar morphology of the cell cultures, emissions may be directionally biased toward neighbouring cells. As a result, a higher number of cells does not necessarily lead to a proportional increase in the signal reaching the detector, which may be an indication of the communicative nature of the emission.

Recent studies have increasingly supported the hypothesis that biophoton emission may be involved in intercellular communication, particularly in the neural and oncological contexts. It has been demonstrated that neurons and glial cells, including astrocytes, emit spontaneous ultra-weak photon emissions that appear to be modulated by cellular activity and may propagate along neural pathways, suggesting a possible role in signal transmission within the brain [36]. This aligns with the hypothesis that biophoton emission is not isotropic and may be directionally biased. The planar morphology of the cultures and the lack of proportional increase in signal with cell number indicate that biophoton emission is not solely a metabolic byproduct, but may reflect structured or spatially organised cellular activity.

The Diffusion Entropy Analysis (DEA) was applied to the data, both with and without the stripes method, to achieve a comprehensive characterisation of ultra-weak biophoton emission from cultured astrocytes and glioblastoma cells. This approach enabled the identification of crucial events and the estimation of scaling exponents, providing insights into the underlying mechanisms governing biophoton signal generation and meaning. The DEA with no stripes results highlight the presence of anomalous diffusion dynamics and long-range memory effects in cellular biophoton emission, particularly evident in glioblastoma and astrocyte samples. The introduction of the stripes method further strengthens the evidence for the occurrence of rare and crucial events, allowing for a markedly clearer distinction of the non-trivial statistical features associated with living systems compared to background noise. The results obtained from both experimental setups (LNF and TOV) are quantitatively comparable, as shown in Table 3, supporting the consistency and robustness of the analysis method. Moreover, the DEA reveals a clear distinction between astrocytes and glioblastoma samples, with the latter exhibiting a lower scaling exponent. A lower scaling exponent is typically associated with a shift toward more pathological or degenerative states, possibly indicating a reduced capacity for complex, self-organised activity as the system approaches cellular dysfunction or death. These analyses suggest that biophoton emission signals contain rich dynamical information beyond simple intensity measurements.

In the dark condition without applying the stripes method, the estimated $\delta$ value is significantly greater than 0.5 ($\mu <3$). This deviation likely arises from nonlinear effects associated with the measurement apparatus, as well as thermal contributions due to the system operating at 3 °C. Such artefacts are effectively suppressed when using the stripes method, which acts as a filter, enhancing the detection of genuine dynamical features by reducing instrumental and thermal noise. Differences in scaling factors were also observed even when comparing samples of the same type (astrocytes or glioblastoma) measured using different instruments (LNF and TOV). This variability is likely due to the non-standardized evolution of the cellular samples and the short time frame of data collection (two days). Despite starting from the same initial number of cells, the system exhibits non-deterministic behaviour, leading to differences in both cell numbers and aggregation patterns. The distinct dynamical patterns revealed by DEA—particularly the presence of rare, crucial events and lower scaling exponents in glioblastoma samples—robustly demonstrate that the recorded signals possess a complex, non-trivial statistical structure. Such features are compatible with the idea that biophoton signals may carry biologically relevant information in a manner complementary to classical electrochemical signalling [37].

Recent molecular studies have also highlighted the role of membrane-associated proteins in glioblastoma progression and intercellular signalling. Ref. [38] demonstrated that TRAF4 regulates the deubiquitination of Caveolin-1, a key component of membrane signalling domains, thereby promoting glioblastoma malignancy. Caveolin-1 is known to participate in signal transduction and vesicular trafficking, processes that may intersect with biophoton-mediated communication. Although not directly linked to photon emission, the involvement of Caveolin-1 in cellular signalling dynamics supports the broader hypothesis that glioblastoma cells exhibit altered intercellular communication mechanisms, which could manifest in the distinct biophoton emission patterns observed in our DEA analysis.

The investigation of biophotons emitted by living organisms through state-of-art machines able to be highly sensitive to the signals and with the use of DEA analysis still representing, today, a new frontier for biological research, aiming to provide new insights into cellular metabolic states, reveal possible mechanisms of communication among cells through a self-organized biological signal, and potentially serve as a non-invasive diagnostic tool to differentiate between normal and tumour cells. Future studies will focus on further optimising the detection setups through the application of a Winston cone for a better integration of the signal and of a water cooling system to maximise the performance of the counter. The main goal is to increase the geometrical efficiency and, consequently, the overall sensitivity of the apparatuses, thereby improving the signal-to-noise ratio of the measurements. An additional optimisation and deepening of the data analysis method is being performed, which will be finalised into a dedicated paper about the DEA method applied to biophoton signal detection and, more generally, to the analysis of biological signals. As future perspectives, the collaboration is working to repeat this measurement with the updated apparatus and perform new measurements on neurons and other cellular cultures relevant to the central nervous systems and beyond. Our results are consistent with a growing body of evidence indicating that biophoton emission reflects the metabolic and pathological states of cells. In vitro studies have shown that tumour cells emit significantly more biophotons compared to non-malignant cells, suggesting that such emissions could potentially serve as non-invasive diagnostic markers for malignancies [39]. Moreover, the spectral characteristics of biophoton emission, such as ratios between infrared and ultraviolet photon emissions, have been shown to effectively differentiate cancerous versus non-cancerous cell types [40].

In the context of glioblastoma and astrocytes, although direct measurements of biophoton emission in these specific cell types are still sparse, the marked differences observed in our crystal violet viability assay, where glioblastoma (T98G) cells exhibited much higher proliferation compared to normal astrocytes (HBAs), align with the expectation that increased metabolic activity in tumour cells would correspond to elevated biophoton emission.

Furthermore, our application of DEA, particularly with the stripes method, has revealed distinct dynamical patterns: glioblastoma samples showed lower scaling exponents and more prominent rare, “crucial” events compared to astrocytes. These features indicate that biophoton emission signals carry rich dynamical information beyond mere intensity levels, possibly reflecting pathological alterations in self-organised cellular behaviour. The literature supports the presence of non-trivial statistical features in biophoton emission from living systems, often linked to complex metabolic or signalling processes [41]. Together, our findings and the existing literature suggest that biophoton emissions may serve not only as indicators of elevated metabolic or proliferative states in tumour cells, but also as potential encoders of underlying dynamic complexity. In glioblastoma, this may open new perspectives for non-invasive diagnostics, while interpretations involving cellular communication mechanisms mediated through biophoton dynamics should be considered exploratory.