Optogenetic actuator - ERK biosensor circuits identify MAPK network nodes that shape ERK dynamics.

Combining single-cell measurements of ERK activity dynamics with perturbations provides insights into the MAPK network topology. We built circuits consisting of an optogenetic actuator to activate MAPK signaling and an ERK biosensor to measure single-cell ERK dynamics. This allowed us to conduct RNAi screens to investigate the role of 50 MAPK proteins in ERK dynamics. We found that the MAPK network is robust against most node perturbations. We observed that the ERK-RAF and the ERK-RSK2-SOS negative feedback operate simultaneously to regulate ERK dynamics. Bypassing the RSK2-mediated feedback, either by direct optogenetic activation of RAS, or by RSK2 perturbation, sensitized ERK dynamics to further perturbations. Similarly, targeting this feedback in a human ErbB2-dependent oncogenic signaling model increased the efficiency of a MEK inhibitor. The RSK2-mediated feedback is thus important for the ability of the MAPK network to produce consistent ERK outputs, and its perturbation can enhance the efficiency of MAPK inhibitors.

Likelihood-free nested sampling for parameter inference of biochemical reaction networks.

The development of mechanistic models of biological systems is a central part of Systems Biology. One major challenge in developing these models is the accurate inference of model parameters. In recent years, nested sampling methods have gained increased attention in the Systems Biology community due to the fact that they are parallelizable and provide error estimates with no additional computations. One drawback that severely limits the usability of these methods, however, is that they require the likelihood function to be available, and thus cannot be applied to systems with intractable likelihoods, such as stochastic models. Here we present a likelihood-free nested sampling method for parameter inference which overcomes these drawbacks. This method gives an unbiased estimator of the Bayesian evidence as well as samples from the posterior. We derive a lower bound on the estimators variance which we use to formulate a novel termination criterion for nested sampling. The presented method enables not only the reliable inference of the posterior of parameters for stochastic systems of a size and complexity that is challenging for traditional methods, but it also provides an estimate of the obtained variance. We illustrate our approach by applying it to several realistically sized models with simulated data as well as recently published biological data. We also compare our developed method with the two most popular other likeliood-free approaches: pMCMC and ABC-SMC. The C++ code of the proposed methods, together with test data, is available at the github web page https://github.com/Mijan/LFNS_paper.

Temporal perturbation of ERK dynamics reveals network architecture of FGF2/MAPK signaling.

Stimulation of PC-12 cells with epidermal (EGF) versus nerve (NGF) growth factors (GFs) biases the distribution between transient and sustained single-cell ERK activity states, and between proliferation and differentiation fates within a cell population. We report that fibroblast GF (FGF2) evokes a distinct behavior that consists of a gradually changing population distribution of transient/sustained ERK signaling states in response to increasing inputs in a dose response. Temporally controlled GF perturbations of MAPK signaling dynamics applied using microfluidics reveal that this wider mix of ERK states emerges through the combination of an intracellular feedback, and competition of FGF2 binding to FGF receptors (FGFRs) and heparan sulfate proteoglycan (HSPG) co-receptors. We show that the latter experimental modality is instructive for model selection using a Bayesian parameter inference. Our results provide novel insights into how different receptor tyrosine kinase (RTK) systems differentially wire the MAPK network to fine-tune fate decisions at the cell population level.

A finite state projection algorithm for the stationary solution of the chemical master equation.

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J. Chem. Phys. 124(4), 044104 (2006)], to provide approximate solutions to the CME by truncating the state-space. The FSP works well for finite time-periods but it cannot be used for estimating the stationary solutions of CMEs, which are often of interest in systems biology. The aim of this paper is to develop a version of FSP which we refer to as the stationary FSP (sFSP) that allows one to obtain accurate approximations of the stationary solutions of a CME by solving a finite linear-algebraic system that yields the stationary distribution of a continuous-time Markov chain over the truncated state-space. We derive bounds for the approximation error incurred by sFSP and we establish that under certain stability conditions, these errors can be made arbitrarily small by appropriately expanding the truncated state-space. We provide several examples to illustrate our sFSP method and demonstrate its efficiency in estimating the stationary distributions. In particular, we show that using a quantized tensor-train implementation of our sFSP method, problems admitting more than 100 × 106 states can be efficiently solved.

Cost-effectiveness of pembrolizumab for previously treated MSI-H/dMMR solid tumours in the UK.

OBJECTIVES: Patients with previously treated microsatellite instability-high (MSI-H)/mismatch repair deficient (dMMR) tumours have limited chemotherapeutic treatment options. Pembrolizumab received approval from the EMA in 2022 for the treatment of colorectal, endometrial, gastric, small intestine, and biliary MSI-H/dMMR tumour types. This approval was supported by data from the KEYNOTE-164 and KEYNOTE-158 clinical trials. This study evaluated the cost-effectiveness of pembrolizumab compared with standard of care (SoC) for previously treated MSI-H/dMMR solid tumours in line with the approved EMA label from a UK healthcare payer perspective. METHODS: A multi-tumour partitioned survival model was built consisting of pre-progression, progressed disease, and dead health states. Pembrolizumab survival outcomes were extrapolated using Bayesian hierarchical models (BHMs) fitted to pooled data from KEYNOTE-164 and KEYNOTE-158. Comparator outcomes were informed by published sources. Tumour sites were modelled independently and then combined, weighted by tumour site distribution. A SoC comparator was used to formulate the overall cost-effectiveness result with pembrolizumab as the intervention. SoC comprised a weighted average of the comparators by tumour site based on market share. Drug acquisition, administration, adverse events, monitoring, subsequent treatment, end-of-life costs, and testing costs were included. Sensitivity and scenario analyses were performed, including modelling pembrolizumab efficacy using standard parametric survival models. RESULTS: Pembrolizumab, at list price, was associated with £129,469 in total costs, 8.30 LYs, and 3.88 QALYs across the pooled tumour sites. SoC was associated with £28,222 in total costs, 1.14 LYs, and 0.72 QALYs across the pooled tumour sites. This yields an incremental cost-effectiveness ratio (ICER) of £32,085 per QALY. Results were robust to sensitivity and scenario analyses. CONCLUSIONS: This model demonstrates pembrolizumab provides a valuable new alternative therapy for UK patients with MSH-H/dMMR cancer at the cost of £32,085 per QALY, with confidential discounts anticipated to improve cost-effectiveness further.

Parameter inference for stochastic single-cell dynamics from lineage tree data.

BACKGROUND: With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference with this type of data. Most of currently available methods treat single-cell trajectories independently, ignoring the mother-daughter relationships and the information provided by the population structure. However, this information is essential if a process of interest happens at cell division, or if it evolves slowly compared to the duration of the cell cycle. RESULTS: In this work, we propose a Bayesian framework for parameter inference on single-cell time-lapse data from lineage trees. Our method relies on a combination of Sequential Monte Carlo for approximating the parameter likelihood function and Markov Chain Monte Carlo for parameter exploration. We demonstrate our inference framework on two simple examples in which the lineage tree information is crucial: one in which the cell phenotype can only switch at cell division and another where the cell state fluctuates slowly over timescales that extend well beyond the cell-cycle duration. CONCLUSION: There exist several examples of biological processes, such as stem cell fate decisions or epigenetically controlled phase variation in bacteria, where the cell ancestry is expected to contain important information about the underlying system dynamics. Parameter inference methods that discard this information are expected to perform poorly for such type of processes. Our method provides a simple and computationally efficient way to take into account single-cell lineage tree data for the purpose of parameter inference and serves as a starting point for the development of more sophisticated and powerful approaches in the future.