Models of hybrid dynamical systems are widely used to answer questions about the causes and effects of dynamic events in time. Unfortunately, existing causal reasoning formalisms lack support for queries involving the dynamically triggered, discontinuous interventions that characterize hybrid dynamical systems. This mismatch can lead to ad-hoc and error-prone causal analysis workflows in practice. To bridge the gap between the needs of hybrid systems users and current causal inference capabilities, we develop a rigorous counterfactual semantics by formalizing interventions as transformations to the constraints of hybrid systems. Unlike interventions in a typical structural causal model, however, interventions in hybrid systems can easily render the model ill-posed. Thus, we identify mild conditions under which our interventions maintain solution existence, uniqueness, and measurability by making explicit connections to established hybrid systems theory. To illustrate the utility of our framework, we formalize a number of canonical causal estimands and explore a case study on the probabilities of causation with applications to fishery management. Our work simultaneously expands the modeling possibilities available to causal inference practitioners and begins to unlock decades of causality research for users of hybrid systems.

Drug discovery is a challenging process, requiring the optimization of compounds to become safe and effective. Predicting molecular properties is an indispensable step in the drug discovery pipeline. Traditionally, this process is costly, involving multiple rounds of experiments, rendering it impractical for every candidate compound. Deep learning techniques have emerged as a promising approach to drug discovery to reduce the cost during the process. However, prevalent research in deep learning models focused on predicting molecular properties has primarily fixated on single-modal models, neglecting the potential benefits of combining different data modalities. To overcome this limitation, we introduce MRL-Mol: a deep Multimodal Representation Learning framework for accurate Molecular properties prediction. MRL-Mol harnesses three data modalities: sequence, graph, and image, augmenting the depth of comprehension. Leveraging a large-scale unlabeled dataset ( 1M unique molecules), we pretrain MRL-Mol to extract inter- and intra-modal information. Our study demonstrates the superior performance of MRL-Mol in predicting molecular properties across six benchmark datasets. Notably, MRL-Mol outperforms other state-of-the-art molecular properties prediction models. These findings suggest that by combining information from multiple data modalities, MRL-Mol can comprehend molecules better than single-modal deep learning models and identify molecular properties with better accuracy.

SUMMARY: We introduce Eliater, a Python package for estimating the effect of perturbation of an upstream molecule on a downstream molecule in a biomolecular network. The estimation takes as input a biomolecular network, observational biomolecular data, and a perturbation of interest, and outputs an estimated quantitative effect of the perturbation. We showcase the functionalities of Eliater in a case study of Escherichia coli transcriptional regulatory network. AVAILABILITY AND IMPLEMENTATION: The code, the documentation, and several case studies are available open source at https://github.com/y0-causal-inference/eliater.

Causal query estimation in biomolecular networks commonly selects a 'valid adjustment set', i.e. a subset of network variables that eliminates the bias of the estimator. A same query may have multiple valid adjustment sets, each with a different variance. When networks are partially observed, current methods use graph-based criteria to find an adjustment set that minimizes asymptotic variance. Unfortunately, many models that share the same graph topology, and therefore same functional dependencies, may differ in the processes that generate the observational data. In these cases, the topology-based criteria fail to distinguish the variances of the adjustment sets. This deficiency can lead to sub-optimal adjustment sets, and to miss-characterization of the effect of the intervention. We propose an approach for deriving 'optimal adjustment sets' that takes into account the nature of the data, bias and finite-sample variance of the estimator, and cost. It empirically learns the data generating processes from historical experimental data, and characterizes the properties of the estimators by simulation. We demonstrate the utility of the proposed approach in four biomolecular Case studies with different topologies and different data generation processes. The implementation and reproducible Case studies are at https://github.com/srtaheri/OptimalAdjustmentSet.

MOTIVATION: Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components. However, in practice many pathway components are left unobserved (latent) because they are either unknown, or difficult to measure. Latent variable models (LVMs) are well-suited for such estimation. Unfortunately, LVM-based estimation of causal queries can be inaccurate when parameters of the latent variables are not uniquely identified, or when the number of latent variables is misspecified. This has limited the use of LVMs for causal inference in biomolecular pathways. RESULTS: In this article, we propose a general and practical approach for LVM-based estimation of causal queries. We prove that, despite the challenges above, LVM-based estimators of causal queries are accurate if the queries are identifiable according to Pearl's do-calculus and describe an algorithm for its estimation. We illustrate the breadth and the practical utility of this approach for estimating causal queries in four synthetic and two experimental case studies, where structures of biomolecular pathways challenge the existing methods for causal query estimation. AVAILABILITY AND IMPLEMENTATION: The code and the data documenting all the case studies are available at https://github.com/srtaheri/LVMwithDoCalculus. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Counterfactual inference is a useful tool for comparing outcomes of interventions on complex systems. It requires us to represent the system in form of a structural causal model, complete with a causal diagram, probabilistic assumptions on exogenous variables, and functional assignments. Specifying such models can be extremely difficult in practice. The process requires substantial domain expertise, and does not scale easily to large systems, multiple systems, or novel system modifications. At the same time, many application domains, such as molecular biology, are rich in structured causal knowledge that is qualitative in nature. This article proposes a general approach for querying a causal biological knowledge graph, and converting the qualitative result into a quantitative structural causal model that can learn from data to answer the question. We demonstrate the feasibility, accuracy and versatility of this approach using two case studies in systems biology. The first demonstrates the appropriateness of the underlying assumptions and the accuracy of the results. The second demonstrates the versatility of the approach by querying a knowledge base for the molecular determinants of a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-induced cytokine storm, and performing counterfactual inference to estimate the causal effect of medical countermeasures for severely ill patients.

Whole-cell models that explicitly represent all cellular components at the molecular level have the potential to predict phenotype from genotype. However, even for simple bacteria, whole-cell models will contain thousands of parameters, many of which are poorly characterized or unknown. New algorithms are needed to estimate these parameters and enable researchers to build increasingly comprehensive models. We organized the Dialogue for Reverse Engineering Assessments and Methods (DREAM) 8 Whole-Cell Parameter Estimation Challenge to develop new parameter estimation algorithms for whole-cell models. We asked participants to identify a subset of parameters of a whole-cell model given the model's structure and in silico "experimental" data. Here we describe the challenge, the best performing methods, and new insights into the identifiability of whole-cell models. We also describe several valuable lessons we learned toward improving future challenges. Going forward, we believe that collaborative efforts supported by inexpensive cloud computing have the potential to solve whole-cell model parameter estimation.

The filamentous fungus Neurospora crassa played a central role in the development of twentieth-century genetics, biochemistry and molecular biology, and continues to serve as a model organism for eukaryotic biology. Here, we have reconstructed a genome-scale model of its metabolism. This model consists of 836 metabolic genes, 257 pathways, 6 cellular compartments, and is supported by extensive manual curation of 491 literature citations. To aid our reconstruction, we developed three optimization-based algorithms, which together comprise Fast Automated Reconstruction of Metabolism (FARM). These algorithms are: LInear MEtabolite Dilution Flux Balance Analysis (limed-FBA), which predicts flux while linearly accounting for metabolite dilution; One-step functional Pruning (OnePrune), which removes blocked reactions with a single compact linear program; and Consistent Reproduction Of growth/no-growth Phenotype (CROP), which reconciles differences between in silico and experimental gene essentiality faster than previous approaches. Against an independent test set of more than 300 essential/non-essential genes that were not used to train the model, the model displays 93% sensitivity and specificity. We also used the model to simulate the biochemical genetics experiments originally performed on Neurospora by comprehensively predicting nutrient rescue of essential genes and synthetic lethal interactions, and we provide detailed pathway-based mechanistic explanations of our predictions. Our model provides a reliable computational framework for the integration and interpretation of ongoing experimental efforts in Neurospora, and we anticipate that our methods will substantially reduce the manual effort required to develop high-quality genome-scale metabolic models for other organisms.

Microbial communities carry out the majority of the biochemical activity on the planet, and they play integral roles in processes including metabolism and immune homeostasis in the human microbiome. Shotgun sequencing of such communities' metagenomes provides information complementary to organismal abundances from taxonomic markers, but the resulting data typically comprise short reads from hundreds of different organisms and are at best challenging to assemble comparably to single-organism genomes. Here, we describe an alternative approach to infer the functional and metabolic potential of a microbial community metagenome. We determined the gene families and pathways present or absent within a community, as well as their relative abundances, directly from short sequence reads. We validated this methodology using a collection of synthetic metagenomes, recovering the presence and abundance both of large pathways and of small functional modules with high accuracy. We subsequently applied this method, HUMAnN, to the microbial communities of 649 metagenomes drawn from seven primary body sites on 102 individuals as part of the Human Microbiome Project (HMP). This provided a means to compare functional diversity and organismal ecology in the human microbiome, and we determined a core of 24 ubiquitously present modules. Core pathways were often implemented by different enzyme families within different body sites, and 168 functional modules and 196 metabolic pathways varied in metagenomic abundance specifically to one or more niches within the microbiome. These included glycosaminoglycan degradation in the gut, as well as phosphate and amino acid transport linked to host phenotype (vaginal pH) in the posterior fornix. An implementation of our methodology is available at http://huttenhower.sph.harvard.edu/humann. This provides a means to accurately and efficiently characterize microbial metabolic pathways and functional modules directly from high-throughput sequencing reads, enabling the determination of community roles in the HMP cohort and in future metagenomic studies.

Metabolism is central to cell physiology, and metabolic disturbances play a role in numerous disease states. Despite its importance, the ability to study metabolism at a global scale using genomic technologies is limited. In principle, complete genome sequences describe the range of metabolic reactions that are possible for an organism, but cannot quantitatively describe the behaviour of these reactions. We present a novel method for modeling metabolic states using whole cell measurements of gene expression. Our method, which we call E-Flux (as a combination of flux and expression), extends the technique of Flux Balance Analysis by modeling maximum flux constraints as a function of measured gene expression. In contrast to previous methods for metabolically interpreting gene expression data, E-Flux utilizes a model of the underlying metabolic network to directly predict changes in metabolic flux capacity. We applied E-Flux to Mycobacterium tuberculosis, the bacterium that causes tuberculosis (TB). Key components of mycobacterial cell walls are mycolic acids which are targets for several first-line TB drugs. We used E-Flux to predict the impact of 75 different drugs, drug combinations, and nutrient conditions on mycolic acid biosynthesis capacity in M. tuberculosis, using a public compendium of over 400 expression arrays. We tested our method using a model of mycolic acid biosynthesis as well as on a genome-scale model of M. tuberculosis metabolism. Our method correctly predicts seven of the eight known fatty acid inhibitors in this compendium and makes accurate predictions regarding the specificity of these compounds for fatty acid biosynthesis. Our method also predicts a number of additional potential modulators of TB mycolic acid biosynthesis. E-Flux thus provides a promising new approach for algorithmically predicting metabolic state from gene expression data.