Computation and measurement of cell decision making errors using single cell data

Single-Cell Measurements and Modeling and Computation of Decision-Making Errors in a Molecular Signaling System with Two Output Molecules

A cell constantly receives signals and takes different fates accordingly. Given the uncertainty rendered by signal transduction noise, a cell may incorrectly perceive these signals. It may mistakenly behave as if there is a signal, although there is none, or may miss the presence of a signal that actually exists. In this paper, we consider a signaling system with two outputs, and introduce and develop methods to model and compute key cell decision-making parameters based on the two outputs and in response to the input signal. In the considered system, the tumor necrosis factor (TNF) regulates the two transcription factors, the nuclear factor κB (NFκB) and the activating transcription factor-2 (ATF-2). These two system outputs are involved in important physiological functions such as cell death and survival, viral replication, and pathological conditions, such as autoimmune diseases and different types of cancer. Using the introduced methods, we compute and show what the decision thresholds are, based on the single-cell measured concentration levels of NFκB and ATF-2. We also define and compute the decision error probabilities, i.e., false alarm and miss probabilities, based on the concentration levels of the two outputs. By considering the joint response of the two outputs of the signaling system, one can learn more about complex cellular decision-making processes, the corresponding decision error rates, and their possible involvement in the development of some pathological conditions.

There's Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-Scale Machines

The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic view. Such a view dissolves the contingent dichotomies driven by human cognitive biases (e.g., a tendency to oversimplify) and prior technological limitations in favor of a more continuous view, necessitated by the study of evolution, developmental biology, and intelligent machines. Form and function are tightly entwined in nature, and in some cases, in robotics as well. Thus, efforts to re-shape living systems for biomedical or bioengineering purposes require prediction and control of their function at multiple scales. This is challenging for many reasons, one of which is that living systems perform multiple functions in the same place at the same time. We refer to this as "polycomputing"-the ability of the same substrate to simultaneously compute different things, and make those computational results available to different observers. This ability is an important way in which living things are a kind of computer, but not the familiar, linear, deterministic kind; rather, living things are computers in the broad sense of their computational materials, as reported in the rapidly growing physical computing literature. We argue that an observer-centered framework for the computations performed by evolved and designed systems will improve the understanding of mesoscale events, as it has already done at quantum and relativistic scales. To develop our understanding of how life performs polycomputing, and how it can be convinced to alter one or more of those functions, we can first create technologies that polycompute and learn how to alter their functions. Here, we review examples of biological and technological polycomputing, and develop the idea that the overloading of different functions on the same hardware is an important design principle that helps to understand and build both evolved and designed systems. Learning to hack existing polycomputing substrates, as well as to evolve and design new ones, will have massive impacts on regenerative medicine, robotics, and computer engineering.

Genetic diseases: How the noise fits in

Many disease-causing mutations can have mild or no effects in some people. This incomplete phenotype penetrance phenomenon is still poorly understood, but model animal studies now show that it is stochastic, with the outcome akin to flipping a coin. These findings can affect how genetic diseases are understood and treated.

TNF controls a speed-accuracy tradeoff in the cell death decision to restrict viral spread

Rapid death of infected cells is an important antiviral strategy. However, fast decisions that are based on limited evidence can be erroneous and cause unnecessary cell death and subsequent tissue damage. How cells optimize their death decision making strategy to maximize both speed and accuracy is unclear. Here, we show that exposure to TNF, which is secreted by macrophages during viral infection, causes cells to change their decision strategy from "slow and accurate" to "fast and error-prone". Mathematical modeling combined with experiments in cell culture and whole organ culture show that the regulation of the cell death decision strategy is critical to prevent HSV-1 spread. These findings demonstrate that immune regulation of cellular cognitive processes dynamically changes a tissues' tolerance for self-damage, which is required to protect against viral spread.

Benefit and Risk Evaluation of Biased μ-Receptor Agonist Oliceridine versus Morphine

BACKGROUND

To improve understanding of the respiratory behavior of oliceridine, a μ-opioid receptor agonist that selectively engages the G-protein-coupled signaling pathway with reduced activation of the β-arrestin pathway, the authors compared its utility function with that of morphine. It was hypothesized that at equianalgesia, oliceridine will produce less respiratory depression than morphine and that this is reflected in a superior utility.

METHODS

Data from a previous trial that compared the respiratory and analgesic effects of oliceridine and morphine in healthy male volunteers (n = 30) were reanalyzed. A population pharmacokinetic-pharmacodynamic analysis was performed and served as basis for construction of utility functions, which are objective functions of probability of analgesia, P(analgesia), and probability of respiratory depression, P(respiratory depression). The utility function = P(analgesia ≥ 0.5) - P(respiratory depression ≥ 0.25), where analgesia ≥ 0.5 is the increase in hand withdrawal latency in the cold pressor test by at least 50%, and respiratory depression ≥ 0.25 is the decrease of the hypercapnic ventilatory response by at least 25%. Values are median ± standard error of the estimate.

RESULTS

The two drugs were equianalgesic with similar potency values (oliceridine: 27.9 ± 4.9 ng/ml; morphine 34.3 ± 9.7 ng/ml; potency ratio, 0.81; 95% CI, 0.39 to 1.56). A 50% reduction of the hypercapnic ventilatory response by morphine occurred at an effect-site concentration of 33.7 ± 4.8 ng/ml, while a 25% reduction by oliceridine occurred at 27.4 ± 3.5 ng/ml (potency ratio, 2.48; 95% CI, 1.65 to 3.72; P < 0.01). Over the clinically relevant concentration range of 0 to 35 ng/ml, the oliceridine utility function was positive, indicating that the probability of analgesia exceeds the probability of respiratory depression. In contrast, the morphine function was negative, indicative of a greater probability of respiratory depression than analgesia.

CONCLUSIONS

These data indicate a favorable oliceridine safety profile over morphine when considering analgesia and respiratory depression over the clinical concentration range.

Information transmission from NFkB signaling dynamics to gene expression

The dynamic signal encoding paradigm suggests that information flows from the extracellular environment into specific signaling patterns (encoding) that are then read by downstream effectors to control cellular behavior. Previous work empirically quantified the information content of dynamic signaling patterns. However, whether this information can be faithfully transmitted to the gene expression level is unclear. Here we used NFkB signaling as a model to understand the accuracy of information transmission from signaling dynamics into gene expression. Using a detailed mathematical model, we simulated realistic NFkB signaling patterns with different degrees of variability. The NFkB patterns were used as an input to a simple gene expression model. Analysis of information transmission between ligand and NFkB and ligand and gene expression allows us to determine information loss in transmission between receptors to dynamic signaling patterns and between signaling dynamics to gene expression. Information loss could occur due to biochemical noise or due to a lack of specificity. We found that noise-free gene expression has very little information loss suggesting that gene expression can preserve specificity in NFkB patterns. As expected, the addition of noise to the gene expression model results in information loss. Interestingly, this effect can be mitigated by a specific choice of parameters that can substantially reduce information loss due to biochemical noise during gene expression. Overall our results show that the cellular capacity for information transmission from dynamic signaling patterns to gene expression can be high enough to preserve ligand specificity and thereby the accuracy of cellular response to environmental cues.

Modeling and measurement of signaling outcomes affecting decision making in noisy intracellular networks using machine learning methods

Characterization of decision-making in cells in response to received signals is of importance for understanding how cell fate is determined. The problem becomes multi-faceted and complex when we consider cellular heterogeneity and dynamics of biochemical processes. In this paper, we present a unified set of decision-theoretic, machine learning and statistical signal processing methods and metrics to model the precision of signaling decisions, in the presence of uncertainty, using single cell data. First, we introduce erroneous decisions that may result from signaling processes and identify false alarms and miss events associated with such decisions. Then, we present an optimal decision strategy which minimizes the total decision error probability. Additionally, we demonstrate how graphing receiver operating characteristic curves conveniently reveals the trade-off between false alarm and miss probabilities associated with different cell responses. Furthermore, we extend the introduced framework to incorporate the dynamics of biochemical processes and reactions in a cell, using multi-time point measurements and multi-dimensional outcome analysis and decision-making algorithms. The introduced multivariate signaling outcome modeling framework can be used to analyze several molecular species measured at the same or different time instants. We also show how the developed binary outcome analysis and decision-making approach can be extended to more than two possible outcomes. As an example and to show how the introduced methods can be used in practice, we apply them to single cell data of PTEN, an important intracellular regulatory molecule in a p53 system, in wild-type and abnormal cells. The unified signaling outcome modeling framework presented here can be applied to various organisms ranging from viruses, bacteria, yeast and lower metazoans to more complex organisms such as mammalian cells. Ultimately, this signaling outcome modeling approach can be utilized to better understand the transition from physiological to pathological conditions such as inflammation, various cancers and autoimmune diseases.

Insights about collective decision-making at the genetic level

By living in a collective, individuals can share and aggregate information to base their decisions on the many rather than on the one, thereby increasing accuracy. But a collective can also be defined at the molecular level. In the following, we reason that genes, by working collectively, share fundamental features with social organisms, which ends, without invoking cognition, in wiser responses. For that, we compile into a single picture the terms redundancy, stochastic resonance, intrinsic and extrinsic noise, and cross-regulation.

Multisite phosphorylation provides a reliable mechanism for making decisions in noisy environments

The ability to make decisions at the cellular level is absolutely critical for the survival of organisms. Eukaryotic cells are constantly making binary decisions in response to internal and environmental signals. Among the most notable transducers of information are protein kinases. The regulation of these signaling proteins often relies on the activity of other protein kinases located upstream in the signaling cascade. However, these signaling systems are by their own nature an important source of molecular noise. Herein, we have assessed the role of multisite phosphorylation in detecting signals in the face of molecular noise. To address this issue, we have conceptually envisioned the biochemical transduction machinery as a classifier model that can lead to four possible outputs: true positives and negatives, and false positives and negatives. In this probabilistic framework, we show that multisite phosphorylation represents a mechanism to filter noise during the decision-making process. We present results showing that nonessential phosphorylation sites contribute to increase the rate of true positives while, at the same time, they can lessen the rate of false positives. This simultaneous increase in sensitivity and specificity, makes multisite phosphorylation a valuable and easily implemented mechanism to reliably transduce information in noisy contexts.

Robustness, Accuracy, and Cell State Heterogeneity in Biological Systems

The robustness of biological systems is often depicted as a key system-level emergent property that allows uniform phenotypes in fluctuating environments. Yet, analysis of single-cell signaling responses identified multiple examples of cellular responses with high degrees of heterogeneity. Here we discuss the implications of the observed lack of response accuracy in the context of new observations coming from single-cell approaches. Single-cell approaches provide a new way to measure the abundance of thousands of molecular species in a single-cell. Repeatedly, analysis of cell distributions identifies clusters within these distributions where cells can be grouped into specific cell states. If cells in a population occupy distinct cell states, the observed variable response could in fact be accurate for each cell conditioned on its own internal state. In this view, the observed lack of accuracy, i.e. response heterogeneity, could in fact be beneficial and a potentially regulated feature of cell state variability. Therefore, to truly determine whether the observed response heterogeneity is a desired property or a physical limitation, future analysis of signaling heterogeneity must take into account the internal states of cells in the population.

Information processing in the NF-κB pathway

The NF-κB pathway is known to transmit merely 1 bit of information about stimulus level. We combined experimentation with mathematical modeling to elucidate how information about TNF concentration is turned into a binary decision. Using Kolmogorov-Smirnov distance, we quantified the cell’s ability to discern 8 TNF concentrations at each step of the NF-κB pathway, to find that input discernibility decreases as signal propagates along the pathway. Discernibility of low TNF concentrations is restricted by noise at the TNF receptor level, whereas discernibility of high TNF concentrations it is restricted by saturation/depletion of downstream signaling components. Consequently, signal discernibility is highest between 0.03 and 1 ng/ml TNF. Simultaneous exposure to TNF or LPS and a translation inhibitor, cycloheximide, leads to prolonged NF-κB activation and a marked increase of transcript levels of NF-κB inhibitors, IκBα and A20. The impact of cycloheximide becomes apparent after the first peak of nuclear NF-κB translocation, meaning that the NF-κB network not only relays 1 bit of information to coordinate the all-or-nothing expression of early genes, but also over a longer time course integrates information about other stimuli. The NF-κB system should be thus perceived as a feedback-controlled decision-making module rather than a simple information transmission channel.