Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks. We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth–death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy. Accompanying code in R is available at https://github.com/cbskust/DDE_BD. Supplementary data are available at Bioinformatics online.

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time. Here, we find that conventional approaches with this assumption cause serious bias in epidemiological parameter estimation. To address this bias, we developed a Bayesian inference method by adopting more realistic history-dependent disease dynamics. Our method more accurately and precisely estimates the reproduction number than the conventional approaches solely from confirmed cases data, which are easy to obtain through testing. It also revealed how the infectious period distribution changed throughout the COVID-19 pandemic during 2020 in South Korea. We also provide a user-friendly package, IONISE, that automates this method.

Freshwater harmful algal blooms (HABs) have become a global concern because blooms contain cyanotoxins that can cause liver damage and other negative health impacts. In South Korea, HABs have been frequently observed along the major rivers (Han, Geum, Nakdong, and Youngsan) in recent years. However, there are hardly any studies that report a linkage between HABs and human health, especially along the four major rivers where dams, weirs, and reservoirs were constructed, and sediments were dredged under the Four Major Rivers Project (FMRP) that ended in 2012. The goals of this study were to summarize spatial distribution patterns of HABs and investigate a potential association between HABs and liver diseases. Chlorophyll-a concentration was used to estimate bloom intensity since it was the only available bloom-related parameter that covers the entire rivers. Liver disease data (ICD-10 codes: K71–K77) were sorted by administrative districts. Generalized linear mixed model was used to analyze the bloom, liver diseases, and population data (2005–2016). The results show that chlorophyll-a levels significantly increased since 2013, except Han River region. There was a significant association between HAB intensity and incidence rate of liver diseases, except Han River area, and the extent of association significantly increased after the completion of the FMRP. For future studies, more in-depth epidemiological investigations are warranted in those areas to accurately determine more specific associations between HABs and liver diseases as well as other bloom-related diseases and symptoms. In addition, identification of major exposure pathways to cyanotoxins is needed to better protect public health in those bloom-affected areas.

Motivation: Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality.Results: We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components.Availability and implementation: Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.

Simultaneous recordings of gene network dynamics across large populations have revealed that cell characteristics vary considerably even in clonal lines. Inferring the variability of parameters that determine gene dynamics is key to understanding cellular behavior. However, this is complicated by the fact that the outcomes and effects of many reactions are not observable directly. Unobserved reactions can be replaced with time delays to reduce model dimensionality and simplify inference. However, the resulting models are non-Markovian, and require the development of new inference techniques. We propose a non-Markovian, hierarchical Bayesian inference framework for quantifying the variability of cellular processes within and across cells in a population. We illustrate our approach using a delayed birth–death process. In general, a distributed delay model, rather than a popular fixed delay model, is needed for inference, even if only mean reaction delays are of interest. Using in silico and experimental data we show that the proposed hierarchical framework is robust and leads to improved estimates compared to its non-hierarchical counterpart. We apply our method to data obtained using time-lapse microscopy and infer the parameters that describe the dynamics of protein production at the single cell and population level. The mean delays in protein production are larger than previously reported, have a coefficient of variation of around 0.2 across the population, and are not strongly correlated with protein production or growth rates. Accompanying code in Python is available at https://github.com/mvcortez/Bayesian-Inference. kresimir.josic@gmail.com or jaekkim@kaist.ac.kr or cbskust@korea.ac.kr Supplementary data are available at Bioinformatics online.

Hong H, et al. Immune Netw. 2022 May;22(3):e23. https://doi.org/10.4110/in.2022.22.e23