Harnessing Flex Point Symmetry to Estimate Logistic Tumor Population Growth.

The observed time evolution of a population is well approximated by a logistic growth function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential, then decelerates as the population approaches its limit size, i.e., the carrying capacity. In mathematical oncology, the tumor carrying capacity has been postulated to be dynamically evolving as the tumor overcomes several evolutionary bottlenecks and, thus, to be patient specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against published pan-cancer animal and human breast cancer data, achieving a 30% to 40% reduction in the time at which subsequent data collection is necessary to estimate the logistic growth rate and carrying capacity correctly. These results could improve tumor dynamics forecasting and augment the clinical decision-making process.

A new perspective on tumor progression: Evolution via selection for function.

Tumorigenesis is commonly attributed to Darwinian processes involving natural selection among cells and groups of cells. However, progressing tumors are those that also achieve an appropriate group phenotypic composition (GPC). Yet, the selective processes acting on tumor GPCs are distinct from that associated with classical Darwinian evolution (i.e. natural selection based on differential reproductive success) as tumors are not genuine evolutionary individuals and do not exhibit heritable variation in fitness. This complex evolutionary scenario is analogous to the recently proposed concept of 'selection for function' invoked for the evolution of both living and non-living systems. Therefore, we argue that it is inaccurate to assert that Darwinian processes alone account for all the aspects characterizing tumorigenesis and cancer progression; rather, by producing the genetic and phenotypic diversity required for creating novel GPCs, these processes fuel the evolutionary success of tumors that is dependent on selection for function at the tumor level.

Calibrating tumor growth and invasion parameters with spectral spatial analysis of cancer biopsy tissues.

The reaction-diffusion equation is widely used in mathematical models of cancer. The calibration of model parameters based on limited clinical data is critical to using reaction-diffusion equation simulations for reliable predictions on a per-patient basis. Here, we focus on cell-level data as routinely available from tissue biopsies used for clinical cancer diagnosis. We analyze the spatial architecture in biopsy tissues stained with multiplex immunofluorescence. We derive a two-point correlation function and the corresponding spatial power spectral distribution. We show that this data-deduced power spectral distribution can fit the power spectrum of the solution of reaction-diffusion equations that can then identify patient-specific tumor growth and invasion rates. This approach allows the measurement of patient-specific critical tumor dynamical properties from routinely available biopsy material at a single snapshot in time.

Nanoparticles use magnetoelectricity to target and eradicate cancer cells.

This study presents the first in vivo and in vitro evidence of an externally controlled, predictive, MRI-based nanotheranostic agent capable of cancer cell specific targeting and killing via irreversible electroporation (IRE) in solid tumors. The rectangular-prism-shaped magnetoelectric nanoparticle is a smart nanoparticle that produces a local electric field in response to an externally applied magnetic field. When externally activated, MENPs are preferentially attracted to the highly conductive cancer cell membranes, which occurs in cancer cells because of dysregulated ion flux across their membranes. In a pancreatic adenocarcinoma murine model, MENPs activated by external magnetic fields during magnetic resonance imaging (MRI) resulted in a mean three-fold tumor volume reduction (62.3% vs 188.7%; P < .001) from a single treatment. In a longitudinal confirmatory study, 35% of mice treated with activated MENPs achieved a durable complete response for 14 weeks after one treatment. The degree of tumor volume reduction correlated with a decrease in MRI T 2 * relaxation time ( r = .351; P = .039) which suggests that MENPs have a potential to serve as a predictive nanotheranostic agent at time of treatment. There were no discernable toxicities associated with MENPs at any timepoint or on histopathological analysis of major organs. MENPs are a noninvasive alternative modality for the treatment of cancer. Summary: We investigated the theranostic capabilities of magnetoelectric nanoparticles (MENPs) combined with MRI via a murine model of pancreatic adenocarcinoma. MENPs leverage the magnetoelectric effect to convert an applied magnetic field into local electric fields, which can induce irreversible electroporation of tumor cell membranes when activated by MRI. Additionally, MENPs modulate MRI relaxivity, which can be used to predict the degree of tumor ablation. Through a pilot study (n=21) and a confirmatory study (n=27), we demonstrated that, ≥300 µg of MRI-activated MENPs significantly reduced tumor volumes, averaging a three-fold decrease as compared to controls. Furthermore, there was a direct correlation between the reduction in tumor T 2 relaxation times and tumor volume reduction, highlighting the predictive prognostic value of MENPs. Six of 17 mice in the confirmatory study's experimental arms achieved a durable complete response, showcasing the potential for durable treatment outcomes. Importantly, the administration of MENPs was not associated with any evident toxicities. This study presents the first in vivo evidence of an externally controlled, MRI-based, theranostic agent that effectively targets and treats solid tumors via irreversible electroporation while sparing normal tissues, offering a new and promising approach to cancer therapy.

The Functional Transcriptomic Landscape Informs Therapeutic Strategies in Multiple Myeloma.

Several therapeutic agents have been approved for treating multiple myeloma (MM), a cancer of bone marrow resident plasma cells. Predictive biomarkers for drug response could help guide clinical strategies to optimize outcomes. Here, we present an integrated functional genomic analysis of tumor samples from MM patients that were assessed for their ex vivo drug sensitivity to 37 drugs, clinical variables, cytogenetics, mutational profiles, and transcriptomes. This analysis revealed a MM transcriptomic topology that generates "footprints" in association with ex vivo drug sensitivity that have both predictive and mechanistic applications. Validation of the transcriptomic footprints for the anti-CD38 monoclonal antibody daratumumab and the nuclear export inhibitor selinexor demonstrated that these footprints can accurately classify clinical responses. The analysis further revealed that daratumumab and selinexor have anti-correlated mechanisms of resistance, and treatment with a selinexor-based regimen immediately after a daratumumab-containing regimen was associated with improved survival in three independent clinical trials, supporting an evolutionary-based strategy involving sequential therapy. These findings suggest that this unique repository and computational framework can be leveraged to inform underlying biology and to identify therapeutic strategies to improve treatment of MM.

Extracellular microvesicle microRNAs, along with imaging metrics, improve detection of aggressive prostate cancer.

Prostate cancer is the most commonly diagnosed cancer in men worldwide. Early diagnosis of the disease provides better treatment options for these patients. Magnetic resonance imaging (MRI) provides an overall assessment of prostate disease. Quantitative metrics (radiomics) from the MRI provide a better evaluation of the tumor and have been shown to improve disease detection. Recent studies have demonstrated that plasma extracellular vesicle microRNAs (miRNAs) are functionally linked to cancer progression, metastasis, and aggressiveness. In our study, we analyzed a matched cohort with baseline blood plasma and MRI to access tumor morphology using imaging-based radiomics and cellular characteristics using miRNAs-based transcriptomics. Our findings indicate that the univariate feature-based model with the highest Youden's index achieved average areas under the receiver operating characteristic curve (AUC) of 0.76, 0.82, and 0.84 for miRNA, MR-T2W, and MR-ADC features, respectively, in identifying clinically aggressive (Gleason grade) disease. The multivariable feature-based model demonstrated an average AUC of 0.88 and 0.95 using combinations of miRNA markers with imaging features in MR-ADC and MR-T2W, respectively. Our study demonstrates combining miRNA markers with MRI-based radiomics improves predictability of clinically aggressive prostate cancer.

A gene for all seasons: The evolutionary consequences of HIF-1 in carcinogenesis, tumor growth and metastasis.

Oxygen played a pivotal role in the evolution of multicellularity during the Cambrian Explosion. Not surprisingly, responses to fluctuating oxygen concentrations are integral to the evolution of cancer-a disease characterized by the breakdown of multicellularity. Poorly organized tumor vasculature results in chaotic patterns of blood flow characterized by large spatial and temporal variations in intra-tumoral oxygen concentrations. Hypoxia-inducible growth factor (HIF-1) plays a pivotal role in enabling cells to adapt, metabolize, and proliferate in low oxygen conditions. HIF-1 is often constitutively activated in cancers, underscoring its importance in cancer progression. Here, we argue that the phenotypic changes mediated by HIF-1, in addition to adapting the cancer cells to their local environment, also "pre-adapt" them for proliferation at distant, metastatic sites. HIF-1-mediated adaptations include a metabolic shift towards anaerobic respiration or glycolysis, activation of cell survival mechanisms like phenotypic plasticity and epigenetic reprogramming, and formation of tumor vasculature through angiogenesis. Hypoxia induced epigenetic reprogramming can trigger epithelial to mesenchymal transition in cancer cells-the first step in the metastatic cascade. Highly glycolytic cells facilitate local invasion by acidifying the tumor microenvironment. New blood vessels, formed due to angiogenesis, provide cancer cells a conduit to the circulatory system. Moreover, survival mechanisms acquired by cancer cells in the primary site allow them to remodel tissue at the metastatic site generating tumor promoting microenvironment. Thus, hypoxia in the primary tumor promoted adaptations conducive to all stages of the metastatic cascade from the initial escape entry into a blood vessel, intravascular survival, extravasation into distant tissues, and establishment of secondary tumors.

To modulate or to skip: De-escalating PARP inhibitor maintenance therapy in ovarian cancer using adaptive therapy.

Toxicity and emerging drug resistance pose important challenges in poly-adenosine ribose polymerase inhibitor (PARPi) maintenance therapy of ovarian cancer. We propose that adaptive therapy, which dynamically reduces treatment based on the tumor dynamics, might alleviate both issues. Utilizing in vitro time-lapse microscopy and stepwise model selection, we calibrate and validate a differential equation mathematical model, which we leverage to test different plausible adaptive treatment schedules. Our model indicates that adjusting the dosage, rather than skipping treatments, is more effective at reducing drug use while maintaining efficacy due to a delay in cell kill and a diminishing dose-response relationship. In vivo pilot experiments confirm this conclusion. Although our focus is toxicity mitigation, reducing drug use may also delay resistance. This study enhances our understanding of PARPi treatment scheduling and illustrates the first steps in developing adaptive therapies for new treatment settings. A record of this paper's transparent peer review process is included in the supplemental information.

Lung adenocarcinomas without driver genes converge to common adaptive strategies through diverse genetic, epigenetic, and niche construction evolutionary pathways.

Somatic evolution selects cancer cell phenotypes that maximize survival and proliferation in dynamic environments. Although cancer cells are molecularly heterogeneous, we hypothesized convergent adaptive strategies to common host selection forces can be inferred from patterns of epigenetic and genetic evolutionary selection in similar tumors. We systematically investigated gene mutations and expression changes in lung adenocarcinomas with no common driver genes (n = 313). Although 13,461 genes were mutated in at least one sample, only 376 non-synonymous mutations evidenced positive evolutionary selection with conservation of 224 genes, while 1736 and 2430 genes exhibited ≥ two-fold increased and ≥ 50% decreased expression, respectively. Mutations under positive selection are more frequent in genes with significantly altered expression suggesting they often "hardwire" pre-existing epigenetically driven adaptations. Conserved genes averaged 16-fold higher expression in normal lung tissue compared to those with selected mutations demonstrating pathways necessary for both normal cell function and optimal cancer cell fitness. The convergent LUAD phenotype exhibits loss of differentiated functions and cell-cell interactions governing tissue organization. Conservation with increased expression is found in genes associated with cell cycle, DNA repair, p53 pathway, epigenetic modifiers, and glucose metabolism. No canonical driver gene pathways exhibit strong positive selection, but extensive down-regulation of membrane ion channels suggests decreased transmembrane potential may generate persistent proliferative signals. NCD LUADs perform niche construction generating a stiff, immunosuppressive microenvironment through selection of specific collagens and proteases. NCD LUADs evolve to a convergent phenotype through a network of interconnected genetic, epigenetic, and ecological pathways.

Modeling non-genetic information dynamics in cells using reservoir computing.

Virtually all cells use energy-driven, ion-specific membrane pumps to maintain large transmembrane gradients of Na+, K+, Cl-, Mg++, and Ca++, but the corresponding evolutionary benefit remains unclear. We propose that these gradients enable a dynamic and versatile biological system that acquires, analyzes, and responds to environmental information. We hypothesize that environmental signals are transmitted into the cell by ion fluxes along pre-existing gradients through gated ion-specific membrane channels. The consequent changes in cytoplasmic ion concentration can generate a local response or orchestrate global/regional cellular dynamics through wire-like ion fluxes along pre-existing and self-assembling cytoskeleton to engage the endoplasmic reticulum, mitochondria, and nucleus.

Mathematical Model-Driven Deep Learning Enables Personalized Adaptive Therapy.

Standard-of-care treatment regimens have long been designed for maximal cell killing, yet these strategies often fail when applied to metastatic cancers due to the emergence of drug resistance. Adaptive treatment strategies have been developed as an alternative approach, dynamically adjusting treatment to suppress the growth of treatment-resistant populations and thereby delay, or even prevent, tumor progression. Promising clinical results in prostate cancer indicate the potential to optimize adaptive treatment protocols. Here, we applied deep reinforcement learning (DRL) to guide adaptive drug scheduling and demonstrated that these treatment schedules can outperform the current adaptive protocols in a mathematical model calibrated to prostate cancer dynamics, more than doubling the time to progression. The DRL strategies were robust to patient variability, including both tumor dynamics and clinical monitoring schedules. The DRL framework could produce interpretable, adaptive strategies based on a single tumor burden threshold, replicating and informing optimal treatment strategies. The DRL framework had no knowledge of the underlying mathematical tumor model, demonstrating the capability of DRL to help develop treatment strategies in novel or complex settings. Finally, a proposed five-step pathway, which combined mechanistic modeling with the DRL framework and integrated conventional tools to improve interpretability compared with traditional "black-box" DRL models, could allow translation of this approach to the clinic. Overall, the proposed framework generated personalized treatment schedules that consistently outperformed clinical standard-of-care protocols. SIGNIFICANCE: Generation of interpretable and personalized adaptive treatment schedules using a deep reinforcement framework that interacts with a virtual patient model overcomes the limitations of standardized strategies caused by heterogeneous treatment responses.

Deep reinforcement learning identifies personalized intermittent androgen deprivation therapy for prostate cancer.

The evolution of drug resistance leads to treatment failure and tumor progression. Intermittent androgen deprivation therapy (IADT) helps responsive cancer cells compete with resistant cancer cells in intratumoral competition. However, conventional IADT is population-based, ignoring the heterogeneity of patients and cancer. Additionally, existing IADT relies on pre-determined thresholds of prostate-specific antigen to pause and resume treatment, which is not optimized for individual patients. To address these challenges, we framed a data-driven method in two steps. First, we developed a time-varied, mixed-effect and generative Lotka-Volterra (tM-GLV) model to account for the heterogeneity of the evolution mechanism and the pharmacokinetics of two ADT drugs Cyproterone acetate and Leuprolide acetate for individual patients. Then, we proposed a reinforcement-learning-enabled individualized IADT framework, namely, I$^{2}$ADT, to learn the patient-specific tumor dynamics and derive the optimal drug administration policy. Experiments with clinical trial data demonstrated that the proposed I$^{2}$ADT can significantly prolong the time to progression of prostate cancer patients with reduced cumulative drug dosage. We further validated the efficacy of the proposed methods with a recent pilot clinical trial data. Moreover, the adaptability of I$^{2}$ADT makes it a promising tool for other cancers with the availability of clinical data, where treatment regimens might need to be individualized based on patient characteristics and disease dynamics. Our research elucidates the application of deep reinforcement learning to identify personalized adaptive cancer therapy.

Small extracellular vesicles from surviving cancer cells as multiparametric monitoring tools of measurable residual disease and therapeutic efficiency.

Although conventional anti-cancer therapies remove most cells of the tumor mass, small surviving populations may evolve adaptive resistance strategies, which lead to treatment failure. The size of the resistant population initially may not reach the threshold of clinical detection (designated as measurable residual disease/MRD) thus, its investigation requires highly sensitive and specific methods. Here, we discuss that the specific molecular fingerprint of tumor-derived small extracellular vesicles (sEVs) is suitable for longitudinal monitoring of MRD. Furthermore, we present a concept that exploiting the multiparametric nature of sEVs may help early detection of recurrence and the design of dynamic, evolution-adjusted treatments.

Testing Adaptive Therapy Protocols Using Gemcitabine and Capecitabine in a Preclinical Model of Endocrine-Resistant Breast Cancer.

Adaptive therapy, an ecologically inspired approach to cancer treatment, aims to overcome resistance and reduce toxicity by leveraging competitive interactions between drug-sensitive and drug-resistant subclones, prioritizing patient survival and quality of life instead of killing the maximum number of cancer cells. In preparation for a clinical trial, we used endocrine-resistant MCF7 breast cancer to stimulate second-line therapy and tested adaptive therapy using capecitabine, gemcitabine, or their combination in a mouse xenograft model. Dose modulation adaptive therapy with capecitabine alone increased survival time relative to MTD but not statistically significantly (HR = 0.22, 95% CI = 0.043-1.1, p = 0.065). However, when we alternated the drugs in both dose modulation (HR = 0.11, 95% CI = 0.024-0.55, p = 0.007) and intermittent adaptive therapies, the survival time was significantly increased compared to high-dose combination therapy (HR = 0.07, 95% CI = 0.013-0.42, p = 0.003). Overall, the survival time increased with reduced dose for both single drugs (p < 0.01) and combined drugs (p < 0.001), resulting in tumors with fewer proliferation cells (p = 0.0026) and more apoptotic cells (p = 0.045) compared to high-dose therapy. Adaptive therapy favors slower-growing tumors and shows promise in two-drug alternating regimens instead of being combined.

Experimental and phylogenetic evidence for correlated gene expression evolution in endometrial and skin fibroblasts.

Gene expression change is a dominant mode of evolution. Mutations, however, can affect gene expression in multiple cell types. Therefore, gene expression evolution in one cell type can lead to similar gene expression changes in another cell type. Here, we test this hypothesis by investigating dermal skin fibroblasts (SFs) and uterine endometrial stromal fibroblasts (ESFs). The comparative dataset consists of transcriptomes from cultured SF and ESF of nine mammalian species. We find that evolutionary changes in gene expression in SF and ESF are highly correlated. The experimental dataset derives from a SCID mouse strain selected for slow cancer growth leading to substantial gene expression changes in SFs. We compared the gene expression profiles of SF with that of ESF and found a significant correlation between them. We discuss the implications of these findings for the evolutionary correlation between placental invasiveness and vulnerability to metastatic cancer.

Immunomodulatory and pro-oncologic effects of ketamine and isoflurane anesthetics in a murine model.

INTRODUCTION: Volatile and intravenous anesthetics may worsen oncologic outcomes in basic science animal models. These effects may be related to suppressed innate and adaptive immunity, decreased immunosurveillance, and disrupted cellular signaling. We hypothesized that anesthetics would promote lung tumor growth via altered immune function in a murine model and tested this using an immunological control group of immunodeficient mice. METHODS: Lewis lung carcinoma cells were injected via tail vein into C57BL/6 immunocompetent and NSG immunodeficient mice during exposure to isoflurane and ketamine versus controls without anesthesia. Mice were imaged on days 0, 3, 10, and 14 post-tumor cell injection. On day 14, mice were euthanized and organs fixed for metastasis quantification and immunohistochemistry staining. We compared growth of tumors measured from bioluminescent imaging and tumor metastasis in ex vivo bioluminescent imaging of lung and liver. RESULTS: Metastases were significantly greater for immunocompromised NSG mice than immunocompetent C57BL/6 mice over the 14-day experiment (partial η2 = 0.67, 95% CI = 0.54, 0.76). Among immunocompetent mice, metastases were greatest for mice receiving ketamine, intermediate for those receiving isoflurane, and least for control mice (partial η2 = 0.88, 95% CI = 0.82, 0.91). In immunocompetent mice, significantly decreased T lymphocyte (partial η2 = 0.83, 95% CI = 0.29, 0.93) and monocyte (partial η2 = 0.90, 95% CI = 0.52, 0.96) infiltration was observed in anesthetic-treated mice versus controls. CONCLUSIONS: The immune system appears central to the pro-metastatic effects of isoflurane and ketamine in a murine model, with decreased T lymphocytes and monocytes likely playing a role.

Testing Adaptive Therapy Protocols using Gemcitabine and Capecitabine on a Mouse Model of Endocrine-Resistant Breast Cancer.

Highly effective cancer therapies often face limitations due to acquired resistance and toxicity. Adaptive therapy, an ecologically inspired approach, seeks to control therapeutic resistance and minimize toxicity by leveraging competitive interactions between drug-sensitive and drug-resistant subclones, prioritizing patient survival and quality of life over maximum cell kill. In preparation for a clinical trial in breast cancer, we used large populations of MCF7 cells to rapidly generate endocrine-resistance breast cancer cell line. We then mimicked second line therapy in ER+ breast cancers by treating the endocrine-resistant MCF7 cells in a mouse xenograft model to test adaptive therapy with capecitabine, gemcitabine, or the combination of those two drugs. Dose-modulation adaptive therapy with capecitabine alone increased survival time relative to MTD, but not statistically significant (HR: 0.22, 95% CI 0.043- 1.1 P = 0.065). However, when we alternated the drugs in both dose modulation (HR = 0.11, 95% CI: 0.024 - 0.55, P = 0.007) and intermittent adaptive therapies significantly increased survival time compared to high dose combination therapy (HR = 0.07, 95% CI: 0.013 - 0.42; P = 0.003). Overall, survival time increased with reduced dose for both single drugs (P < 0.01) and combined drugs (P < 0.001). Adaptive therapy protocols resulted in tumors with lower proportions of proliferating cells (P = 0.0026) and more apoptotic cells (P = 0.045). The results show that Adaptive therapy outperforms high-dose therapy in controlling endocrine-resistant breast cancer, favoring slower-growing tumors, and showing promise in two-drug alternating regimens.

Logistic tumor-population growth and ghost-points symmetry.

The observed time evolution of a population is well approximated by a logistic function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential at a constant rate and capped at a limit size, i.e., the carrying capacity. In mathematical oncology, the carrying capacity has been postulated to be co-evolving and thus patient-specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against a classic oncology database of logistic tumor growth, achieving a 30% to 40% reduction in the time necessary to correctly estimate the logistic growth rate and carrying capacity. Our results will improve tumor dynamics forecasting and augment the clinical decision-making process.

Converting genetic information to non-equilibrium cellular thermodynamics in enzyme-catalyzed reactions.

Living systems use genomic information to maintain a stable highly ordered state far from thermodynamic equilibrium but the specific mechanisms and general principles governing the interface of genetics and thermodynamics has not been extensively investigated. Genetic information is quantified in unitless bits termed "Shannon entropy", which does not directly relate to thermodynamic entropy or energy. Thus, it is unclear how the Shannon entropy of genetic information is converted into thermodynamic work necessary to maintain the non-equilibrium state of living systems. Here we investigate the interface of genetic information and cellular thermodynamics in enzymatic acceleration of a chemical reaction S+E→ES→E+P, where S and E are substrate and enzyme, ES is the enzyme substrate complex and P product. The rate of any intracellular chemical reaction is determined by probability functions at macroscopic (Boltzmann distribution of the reactant kinetic energies governed by temperature) or microscopic (overlap of reactant quantum wave functions) scales - described, respectively, by the Arrhenius and Knudsen equations. That is, the reaction rate, in the absence of a catalyst, is governed by temperature which determines the kinetic energy of the interacting molecules. Genetic information can act upon a when the encoded string of amino acids folds into a 3-deminsional structure that permits a lock/key spatial matching with the reactants. By optimally superposing the reactants' wave functions, the information in the enzyme increases the reaction rate by up to15 orders of magnitude under isothermal conditions. In turn, the accelerated reaction rate alters the intracellular thermodynamics environment as the products are at lower Gibbs free energy which permits thermodynamic work Wmax=-ΔG. Mathematically and biologically, the critical event that allows genetic information to produce thermodynamic work is the folding of the amino acid string specified by the gene into a 3-dimensional shape determined by its lowest energy state. Biologically, this allows the amino acid string to bind substrate and place them in an optimal spatial orientation. These key-lock are mathematically characterized by Kullback-Leibler Divergence and the interactions with the reaction channel now represent Fisher Information (the second derivative Kullback-Leibler divergence), which can take on the units of the process to which it is applied. Interestingly, Shannon is typically derived by "coarse graining" Shannon information. Thus, living system, by acting at a quantum level, "fine grain" Shannon information.