Model-based evaluation of spatiotemporal data reduction methods with unknown ground truth through optimal visualization and interpretability metrics.

Optimizing and benchmarking data reduction methods for dynamic or spatial visualization and interpretation (DSVI) face challenges due to many factors, including data complexity, lack of ground truth, time-dependent metrics, dimensionality bias and different visual mappings of the same data. Current studies often focus on independent static visualization or interpretability metrics that require ground truth. To overcome this limitation, we propose the MIBCOVIS framework, a comprehensive and interpretable benchmarking and computational approach. MIBCOVIS enhances the visualization and interpretability of high-dimensional data without relying on ground truth by integrating five robust metrics, including a novel time-ordered Markov-based structural metric, into a semi-supervised hierarchical Bayesian model. The framework assesses method accuracy and considers interaction effects among metric features. We apply MIBCOVIS using linear and nonlinear dimensionality reduction methods to evaluate optimal DSVI for four distinct dynamic and spatial biological processes captured by three single-cell data modalities: CyTOF, scRNA-seq and CODEX. These data vary in complexity based on feature dimensionality, unknown cell types and dynamic or spatial differences. Unlike traditional single-summary score approaches, MIBCOVIS compares accuracy distributions across methods. Our findings underscore the joint evaluation of visualization and interpretability, rather than relying on separate metrics. We reveal that prioritizing average performance can obscure method feature performance. Additionally, we explore the impact of data complexity on visualization and interpretability. Specifically, we provide optimal parameters and features and recommend methods, like the optimized variational contractive autoencoder, for targeted DSVI for various data complexities. MIBCOVIS shows promise for evaluating dynamic single-cell atlases and spatiotemporal data reduction models.

DEGBOE: Discrete time Evolution modeling of Gene mutation through Bayesian inference using qualitative Observation of mutation Events.

An important aspect of cancer progression concerns the way in which gene mutations accumulate in cellular lineages. Comprehensive efforts into cataloging cancer genes have revealed that tumors demonstrate variability in genes that accumulate mutations which depend on the presence or absence of other mutations. However, understanding the stochastic process by which mutations arise across the genome is an important open problem of this nature in biology due to modeling discrete variate time-series is the most challenging, and, as yet, least well-developed of all areas of research in time-series. In this paper, a DEGBOE framework is proposed to model the mutation time-series given the sequence data of the gene mutations. The method relates the discrete-time, nonlinear and nonstationary series of gene mutations to the time-varying autoregressive moving average model. It presents the observation as a nonlinear function dependent on two variables: gene mutation, and gene-gene interactions characterizing the effects of the varying presence or absence of other gene mutations on a mutations' occurrence and evolution. DEGBOE is applied to model the dynamics of frequently mutated genes in lung cancer, includingEGFR,KRAS, and TP53. The results of the model are analyzed and compared to the original simulated data of theDNAwalk, and experimental lung cancer mutations data. It identifies the driver role of TP53 mutations in lung cancer progression.

Mathematical Modeling of Proliferative Immune Response Initiated by Interactions Between Classical Antigen-Presenting Cells Under Joint Antagonistic IL-2 and IL-4 Signaling.

During an adaptive immune response from pathogen invasion, multiple cytokines are produced by various immune cells interacting jointly at the cellular level to mediate several processes. For example, studies have shown that regulation of interleukin-4 (IL-4) correlates with interleukin-2 (IL-2) induced lymphocyte proliferation. This motivates the need to better understand and model the mechanisms driving the dynamic interplay of proliferation of lymphocytes with the complex interaction effects of cytokines during an immune response. To address this challenge, we adopt a hybrid computational approach comprising of continuous, discrete and stochastic non-linear model formulations to predict a system-level immune response as a function of multiple dependent signals and interacting agents including cytokines and targeted immune cells. We propose a hybrid ordinary differential equation-based (ODE) multicellular model system with a stochastic component of antigen microscopic states denoted as Multiscale Multicellular Quantitative Evaluator (MMQE) implemented using MATLAB. MMQE combines well-defined immune response network-based rules and ODE models to capture the complex dynamic interactions between the proliferation levels of different types of communicating lymphocyte agents mediated by joint regulation of IL-2 and IL-4 to predict the emergent global behavior of the system during an immune response. We model the activation of the immune system in terms of different activation protocols of helper T cells by the interplay of independent biological agents of classic antigen-presenting cells (APCs) and their joint activation which is confounded by the exposure time to external pathogens. MMQE quantifies the dynamics of lymphocyte proliferation during pathogen invasion as bivariate distributions of IL-2 and IL-4 concentration levels. Specifically, by varying activation agents such as dendritic cells (DC), B cells and their joint mechanism of activation, we quantify how lymphocyte activation and differentiation protocols boost the immune response against pathogen invasion mediated by a joint downregulation of IL-4 and upregulation of IL-2. We further compare our in-silico results to in-vivo and in-vitro experimental studies for validation. In general, MMQE combines intracellular and extracellular effects from multiple interacting systems into simpler dynamic behaviors for better interpretability. It can be used to aid engineering of anti-infection drugs or optimizing drug combination therapies against several diseases.

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks.

The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered-perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

Elucidating effects of reaction rates on dynamics of the lac circuit in Escherichia coli.

Gene expression is regulated by a complex transcriptional network. It is of interest to quantify uncertainty of not knowing accurately reaction rates of underlying biochemical reactions, and to understand how they affect gene expression. Assuming a kinetic model of the lac circuit in Escherichia coli, regardless of how many reactions are involved in transcription regulation, transcription rate is shown to be the most important parameter affecting steady state production of mRNA and protein in the cell. In particular, doubling the transcription rate approximately doubles the number of mRNA synthesized at steady state for any rates of transcription inhibition and activation. On the other hand, increasing the rate of transcription inhibition by 10% reduces the average steady state count of mRNA by about 7%, whereas changes in the rate of transcription activation appear to have no such effect. Furthermore, for wide range of reaction rates in the kinetic model of the lac genetic switch considered, protein production was observed to always reach a maximum before the degradation reduces its count to zero, and this maximum was found to be always at least 27 protein molecules. Such value appears to be a fundamental structural property of genetic circuits making it very robust against changes in the internal and external conditions.

Determining the Transcription Rates Yielding Steady-State Production of mRNA in the Lac Genetic Switch of Escherichia coli.

To elucidate the regulatory dynamics of the gene expression activation and inactivation, an in silico biochemical model of the lac circuit in Escherichia coli was used to evaluate the transcription rates that yield the steady-state mRNA production in active and inactive states of the lac circuit. This result can be used in synthetic biology applications to understand the limits of the genetic synthesis. Since most genetic networks involve many interconnected components with positive and negative feedback control, intuitive understanding of their dynamics is often difficult to obtain. Although the kinetic model of the lac circuit considered involves only a single positive feedback, the developed computational framework can be used to evaluate supported ranges of other reaction rates in genetic circuits with more complex regulatory networks. More specifically, the inducible lac gene switch in E. coli is regulated by unbinding and binding of the inducer-repressor complexes to or from the DNA operator to switch the gene expression on and off. The dependency of mRNA production at steady state on different transcription rates and the repressor complexes has been studied by computer simulations in the Lattice Microbe software. Provided that the lac circuit is in active state, the transcription rate is independent of the inducer-repressor complexes present in the cell. In inactive state, the transcription rate is dependent on the specific inducer-repressor complex bound to the operator that inactivates the gene expression. We found that the repressor complex with the largest affinity to the operator yields the smallest range of the feasible transcription rates to yield the steady state while the lac circuit is in inactive state. In contrast, the steady state in active state can be obtained for any value of the transcription rate.