Multiple cryoprotectant toxicity model for vitrification solution optimization.

Vitrification is a promising cryopreservation technique for complex specimens such as tissues and organs. However, it is challenging to identify mixtures of cryoprotectants (CPAs) that prevent ice formation without exerting excessive toxicity. In this work, we developed a multi-CPA toxicity model that predicts the toxicity kinetics of mixtures containing five of the most common CPAs used in the field (glycerol, dimethyl sulfoxide (DMSO), propylene glycol, ethylene glycol, and formamide). The model accounts for specific toxicity, non-specific toxicity, and interactions between CPAs. The proposed model shows reasonable agreement with training data for single and binary CPA solutions, as well as ternary CPA solution validation data. Sloppy model analysis was used to examine the model parameters that were most important for predictions, providing clues about mechanisms of toxicity. This analysis revealed that the model terms for non-specific toxicity were particularly important, especially the non-specific toxicity of propylene glycol, as well as model terms for specific toxicity of formamide and interactions between formamide and glycerol. To demonstrate the potential for model-based design of vitrification methods, we paired the multi-CPA toxicity model with a published vitrification/devitrification model to identify vitrifiable CPA mixtures that are predicted to have minimal toxicity. The resulting optimized vitrification solution composition was a mixture of 7.4 molal glycerol, 1.4 molal DMSO, and 2.4 molal formamide. This demonstrates the potential for mathematical optimization of vitrification solution composition and sets the stage for future studies to optimize the complete vitrification process, including CPA mixture composition and CPA addition and removal methods.

Causal Geometry.

Information geometry has offered a way to formally study the efficacy of scientific models by quantifying the impact of model parameters on the predicted effects. However, there has been little formal investigation of causation in this framework, despite causal models being a fundamental part of science and explanation. Here, we introduce causal geometry, which formalizes not only how outcomes are impacted by parameters, but also how the parameters of a model can be intervened upon. Therefore, we introduce a geometric version of "effective information"-a known measure of the informativeness of a causal relationship. We show that it is given by the matching between the space of effects and the space of interventions, in the form of their geometric congruence. Therefore, given a fixed intervention capability, an effective causal model is one that is well matched to those interventions. This is a consequence of "causal emergence," wherein macroscopic causal relationships may carry more information than "fundamental" microscopic ones. We thus argue that a coarse-grained model may, paradoxically, be more informative than the microscopic one, especially when it better matches the scale of accessible interventions-as we illustrate on toy examples.

Inverse Problems in Systems Biology: A Critical Review.

Systems Biology may be assimilated to a symbiotic cyclic interplaying between the forward and inverse problems. Computational models need to be continuously refined through experiments and in turn they help us to make limited experimental resources more efficient. Every time one does an experiment we know that there will be some noise that can disrupt our measurements. Despite the noise certainly is a problem, the inverse problems already involve the inference of missing information, even if the data is entirely reliable. So the addition of a certain limited noise does not fundamentally change the situation but can be used to solve the so-called ill-posed problem, as defined by Hadamard. It can be seen as an extra source of information. Recent studies have shown that complex systems, among others the systems biology, are poorly constrained and ill-conditioned because it is difficult to use experimental data to fully estimate their parameters. For these reasons was born the concept of sloppy models, a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. Furthermore the concept of sloppy models contains also the concept of un-identifiability, because the models are characterized by many parameters that are poorly constrained by experimental data. Then a strategy needs to be designed to infer, analyze, and understand biological systems. The aim of this work is to provide a critical review to the inverse problems in systems biology defining a strategy to determine the minimal set of information needed to overcome the problems arising from dynamic biological models that generally may have many unknown, non-measurable parameters.

Relative sensitivity analysis of the predictive properties of sloppy models.

Commonly among the model parameters characterizing complex biological systems are those that do not significantly influence the quality of the fit to experimental data, so-called "sloppy" parameters. The sloppiness can be mathematically expressed through saturating response functions (Hill's, sigmoid) thereby embodying biological mechanisms responsible for the system robustness to external perturbations. However, if a sloppy model is used for the prediction of the system behavior at the altered input (e.g. knock out mutations, natural expression variability), it may demonstrate the poor predictive power due to the ambiguity in the parameter estimates. We introduce a method of the predictive power evaluation under the parameter estimation uncertainty, Relative Sensitivity Analysis. The prediction problem is addressed in the context of gene circuit models describing the dynamics of segmentation gene expression in Drosophila embryo. Gene regulation in these models is introduced by a saturating sigmoid function of the concentrations of the regulatory gene products. We show how our approach can be applied to characterize the essential difference between the sensitivity properties of robust and non-robust solutions and select among the existing solutions those providing the correct system behavior at any reasonable input. In general, the method allows to uncover the sources of incorrect predictions and proposes the way to overcome the estimation uncertainties.