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Results for “systems biology”

Search indexed bioRxiv preprints in genomics, neuroscience, cell biology and bioinformatics. Read source abstracts and check manuscript versions; preprints are not peer reviewed.

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bioRxiv2023

Structural and practical identifiability of contrast transport models for DCE-MRI

Compartment models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

systems biology↗

bioRxiv2024

Incorporating temporal information during featureengineering bolsters emulation of spatio-temporalemergence

MotivationEmergent biological dynamics derive from the evolution of lower-level spatial and temporal processes. A long-standing challenge for scientists and engineers is identifying simple low-level rules that give rise to complex higher-level dynamics. High-resolution biological data acquisition enables this identification and has evolved at a rapid pace for both experimental and computational approaches. Simultaneously harnessing the resolution and managing the expense of emerging technologies--e.g. live cell imaging, scRNAseq, agent-based models--requires a deeper understanding of how spatial and temporal axes impact biological systems. Effective emulation is a promising solution to manage the expense of increasingly complex high-resolution computational models. In this research, we focus on the emulation of a tumor microenvironment agent-based model to examine the relationship between spatial and temporal environment features, and emergent tumor properties. ResultsDespite significant feature engineering, we find limited predictive capacity of tumor properties from initial system representations. However, incorporating temporal information derived from intermediate simulation states dramatically improves the predictive performance of machine learning models. We train a deep-learning emulator on intermediate simulation states and observe promising enhancements over emulators trained solely on initial conditions. Our results underscore the importance of incorporating temporal information in the evaluation of spatio-temporal emergent behavior. Nevertheless, the emulators exhibit inconsistent performance, suggesting that the underlying model characterizes unique cell populations dynamics that are not easily replaced. AvailabilityAll source codes for the agent-based model, emulation, and analyses are publicly available at github.com/bagherilab/ARCADE, github.com/bagherilab/emulation, and github.com/bagherilab/emulation_analysis, respectively. Contactnbagheri@uw.edu

systems biology↗

bioRxiv2024

Unraveling principles of thermodynamics for genome-scale metabolic networks using graph neural networks

The fundamental laws of thermodynamics determine the feasibility of all natural processes including metabolism. Although several algorithms have been developed to predict the most important thermodynamic parameter, the standard Gibbs free energy, for metabolic reactions and metabolites, their application to genome-scale metabolic networks (GEMs) with thousands of metabolites and reactions is still limited. Here, we develop a graph neural network (GNN)- based model dGbyG for predicting Gibbs energy for metabolites and metabolic reactions which outperforms all existing methods in accuracy, versatility, robustness, and generalization ability. By applying dGbyG to the human GEM, Recon3D, we identify a critical subset of reactions with substantial negative values of the standard Gibbs free energy change, which we name thermodynamic driver reactions. These reactions exhibit distinctive network topological characteristics akin to driver nodes defined in control theory and remarkable heterogeneity in enzyme abundance, implying evolutionary constraints on the selection of thermodynamic parameters of metabolic networks. We also develop a thermodynamics-based flux balance analysis (TFBA) approach to integrate reaction thermodynamics with GEMs to curate these models. Our work not only transcends the augmentation of accessible thermodynamic data to facilitate an enriched understanding of metabolism, but also enables refinement of metabolic reconstructions from a thermodynamic perspective, thereby underscoring the critical role of thermodynamics in the accurate modeling of biological systems.

systems biology↗

bioRxiv2024

MoCHI: neural networks to fit interpretable models and quantify energies, energetic couplings, epistasis and allostery from deep mutational scanning data

The massively parallel nature of deep mutational scanning (DMS) allows the quantification of the phenotypic effects of thousands of perturbations in a single experiment. We have developed MoCHI, a software tool that allows the parameterisation of arbitrarily complex models using DMS data. MoCHI simplifies the task of building custom models from measurements of mutant effects on any number of phenotypes. It allows the inference of free energy changes, as well as pairwise and higher-order interaction terms (energetic couplings) for specified biophysical models. When a suitable user-specified mechanistic model is not available, global nonlinearities (epistasis) can be estimated directly from the data. MoCHI also builds upon and leverages theory on ensemble (or background-averaged) epistasis to learn sparse predictive models that can incorporate higher-order epistatic terms and are informative of the genetic architecture of the underlying biological system. The combination of DMS and MoCHI allows biophysical measurements to be performed at scale, including the construction of complete allosteric maps of proteins. MoCHI is freely available (https://github.com/lehner-lab/MoCHI) and implemented as an easy-to-use python package relying on the PyTorch machine learning framework.

systems biology↗

bioRxiv2024

Inferring Metabolic Objectives and Tradeoffs in Single Cells During Embryogenesis

While proliferating cells optimize their metabolism to produce biomass, the metabolic objectives of cells that perform non-proliferative tasks are unclear. The opposing requirements for optimizing each objective results in a trade-off that forces single cells to prioritize their metabolic needs and optimally allocate limited resources. To define metabolic objectives and tradeoffs in biological systems mathematically, we integrated bulk and single-cell omics data with a novel framework to infer cell objectives using metabolic modeling and machine learning. We validated this framework by identifying essential genes from CRISPR-Cas9 screens in embryonic stem cells, and by inferring the metabolic objectives of quiescent cells and during different cell-cycle phases. Applying this to embryonic cell states, we observed a decrease in metabolic entropy upon development. We further uncovered a trade-off between glutathione and biosynthetic precursors in 1-cell zygote, 2-cell embryo, and blastocyst cells, potentially representing a trade-off between pluripotency and proliferation.

systems biology↗

bioRxiv2024

Understanding flux switching in metabolic networks through an analysis of synthetic lethals

Biological systems are extremely robust and exhibit high levels of redundancy for multiple cellular functions. Some of this redundancy manifests as alternative pathways in metabolism. Synthetic double lethals in metabolic networks comprise pairs of reactions, which, when deleted simultaneously, abrogate cell growth. However, when one reaction from such pairs is removed, the cell reroutes its metabolites through alternative pathways. Very little is known about the set of reactions through which fluxes are rerouted. Analysing this redistribution would help us to uncover the linkage between the reactions in a synthetic double lethal and also understand the complexity underlying the reroutings. Studying synthetic lethality in the context of pathogenic bacteria can offer valuable insights into therapeutic interventions. In this work, we propose a constraint-based approach to unravel these alternate pathways and complex interdependencies within and across metabolic modules. The approach involves a generic optimisation that minimises the extent of rerouting between two reaction deletions, corresponding to synthetic lethal pairs. We also include a systematic analysis of synthetic lethals by identifying the reaction classes that make up these synthetic lethals. We applied our computational workflow to several existing high-quality genome-scale models to show that these rerouted reactions span across metabolic modules, thereby illustrating the complexity and uniqueness of metabolism. Our results provide interesting insights into the organisation of metabolic networks and their redundancy. The algorithm is available at https://github.com/RamanLab/minRerouting. Contact: kraman@iitm.ac.in

systems biology↗

bioRxiv2024

Emergence of temporal noise hierarchy in co-regulated genes of multi-output feed-forward loop

Natural variations in gene expression, called noise, are fundamental to biological systems. The expression noise can be beneficial or detrimental to cellular functions. While the impact of noise on individual genes is well-established, our understanding of how noise behaves when multiple genes are co-expressed by shared regulatory elements within transcription networks remains elusive. This lack of understanding extends to how the architecture and regulatory features of these networks influence noise. To address this gap, we study the multi-output feed-forward loop motif. The motif is prevalent in bacteria and yeast and influences co-expression of multiple genes by shared transcription factors. Focusing on a two-output variant of the motif, the present study explores the interplay between its architecture, co-expression patterns of the two genes (including symmetric and asymmetric expressions), and the associated noise dynamics. We employ a stochastic modeling approach to investigate how the binding affinities of the transcription factors influence symmetric and asymmetric expression patterns and the resulting noise dynamics in the co-expressed genes. This knowledge could guide the development of strategies for manipulating gene expression patterns through targeted modulation of transcription factor binding affinities.

systems biology↗

bioRxiv2024

Multi-omics Analysis Reveals Important Role for Microbial-derived Metabolites from Botryllus schlosseri in Metal Interactions

Marine microbial communities govern many of the biological and chemical processes in the ocean, including element cycles, ecosystem health, and disease. Marine organisms are surrounded by microbes and complex molecular interactions occur between bacterial symbionts, eukaryotic hosts, and their pathogens or prey. Trace metals in the ocean can be either beneficial or detrimental to marine life depending on their concentrations and bioavailability. Multiple marine tunicate species are known to bioaccumulate trace metals in their mantel, and research suggests tunicate microbiota plays an important role in this process. Botryllus schlosseri, a marine colonial tunicate, has become a model organism for cellular and developmental studies, yet its ecological interactions are still not well understood. Using an integrated multidisciplinary approach, we established a comprehensive baseline and explored correlations between members of the B. schlosseri microbiome, metabolome, and metallome to elucidate the ecological effects of trace metals in host-microbe-pathogen interactions. We identified significant correlations between metals, including manganese, nickel, cerium, zinc, and cobalt, with various metabolites and bacterial taxa. These findings offer insights into B. schlosseri biological and chemical interactions with their symbionts and their environment, contributing to bridging the knowledge gap of host-microbiome-environment interactions and establishing a foundation for continuing research on the ecological effects of trace metals in these biological systems. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=83 SRC="FIGDIR/small/622856v2_ufig1.gif" ALT="Figure 1"> View larger version (29K): org.highwire.dtl.DTLVardef@190204org.highwire.dtl.DTLVardef@1d36c40org.highwire.dtl.DTLVardef@168150eorg.highwire.dtl.DTLVardef@3e4ce7_HPS_FORMAT_FIGEXP M_FIG C_FIG HighlightsO_LIBotryllus schlosseri tissue was highly enriched in metals compared to seawater C_LIO_LIB. schlosseri microbiome {beta}-diversity significantly different from seawater C_LIO_LIPan-metabolome indicated microbial metabolites in core and flexible metabolome C_LIO_LIMulti-omics revealed interactions between metals, metabolites, and microbes C_LI

systems biology↗

bioRxiv2024

Spotiphy enables single-cell spatial whole transcriptomics across the entire section

Spatial transcriptomics (ST) has advanced our understanding of tissue regionalization by enabling the visualization of gene expression within whole tissue sections1, but the approach remains dogged by the challenge of achieving single-cell resolution without sacrificing whole genome coverage2,3. Here we present Spotiphy (Spot imager with pseudo single-cell resolution histology), a novel computational toolkit that transforms sequencing-based ST data into single-cell-resolved whole-transcriptome images. In evaluations with Alzheimers disease (AD) and normal mouse brains, Spotiphy delivers the most precise cellular compositions. For the first time, Spotiphy reveals novel astrocyte regional specification in mouse brains. It distinguishes sub-populations of DAM (Disease-Associated Microglia) located in different AD mouse brain regions. Spotiphy also identifies multiple spatial domains as well as changes in the patterns of tumor-tumor microenvironment interactions using human breast ST data. Spotiphy enables visualization of cell localization and gene expression in tissue sections, offering key insights into the function of complex biological systems.

systems biology↗

bioRxiv2024

Integrating qualitative and quantitative data across multiple labs for model calibration

The integration of computational models with experimental data is a cornerstone for gaining insight into biomedical applications. However, parameter fitting procedures often require a vast availability and frequency of data that are challenging to obtain from a single source. Here, we present a novel methodology "CrossLabFit" designed to integrate qualitative data from multiple laboratories, overcoming the constraints of single-lab data collection. Our approach harmonizes disparate qualitative assessments--ranging from different experimental labs to categorical observations--into a unified framework for parameter estimation. By using machine learning algorithms, these qualitative constraints are represented as dynamic "qualitative windows" that capture significant trends to which models must adhere. For numerical implementation, we developed a GPU-accelerated version of differential evolution to navigate in the cost function that integrated quantitative and qualitative data. We validate our approach across a series of case studies, demonstrating significant improvements in model accuracy and parameter identifiability. This work opens a new paradigm for collaborative science, enabling a methodological road to combine and compare findings between studies to improve our understanding of biological systems and beyond.

systems biology↗

bioRxiv2024

Cytosolic fructose - an underestimated player in the regulation of the sucrose biosynthesis?

Plants must continuously adapt to environmental fluctuations, which significantly influence their photosynthetic performance and overall metabolism. The sucrose cycling system within plant cells plays a critical regulatory role during stress conditions. This study employed a systems biology approach to analyze system stabilities mathematically under various regulatory conditions impacting sucrose cycling dynamics. We investigated the effects of mutations within this cycle, specifically HEXOKINASE1 (Arabidopsis thaliana gin2-1), alongside high-light exposure. Finally, we confirmed the modelling output in vitro by enzyme assays. The implementation of experimental subcellular metabolite data into a Structural Kinetic Model (SKM) enabled exploration of regulatory responses and system stabilities within a three-compartment model. Within system instabilities, gin2-1 was more instable than its wild type. The gin2-1 mutation particularly was destabilized when fructokinase function was impaired by phosphorylated sugars. Additionally, we confirmed that phosphorylated sugars serve as stronger activators of sucrose-phosphate synthase (SPS) than glucose does. Interestingly, models with fructose SPS activation exhibited a similar stability pattern. Consequently, we proposed and confirmed in silico a triple activation of SPS by highly activating phosphorylated sugars and lower activating nonphosphorylated hexoses. Additionally, we biochemically confirmed the previously unknown, but now predicted, activation of SPS by fructose in vitro. In summary, our study highlights the essential role of sucrose cycling in plant cells under stress conditions. The in silico findings reveal that phosphorylated sugars are stronger activators of SPS than glucose and introduce a previously unknown activation mechanism by fructose. These potential activation capacities were confirmed in vitro through SPS enzyme activity assays, underscoring the efficiency of our systems biology approach. Overall, this research provides valuable insights into carbohydrate metabolism regulation and paves the way for future investigations to deepen our understanding of the complexities involved in sucrose cycling and biosynthesis in plants.

plant biology↗

bioRxiv2024

Mechanistic origins of temperature scaling in the early embryonic cell cycle

Temperature profoundly impacts organismal physiology and ecological dynamics, particularly affecting ectothermic species and making them especially vulnerable to climate changes. Although complex physiological processes usually involve dozens of enzymes, empirically it is found that the rates of these processes often obey the Arrhenius equation, which was originally proposed for individual chemical reactions. Here we have examined the temperature scaling of the early embryonic cell cycle, with the goal of understanding why the Arrhenius equation approximately holds and why it breaks down at temperature extremes. Using experimental data from Xenopus laevis, Xenopus tropicalis, and Danio rerio, plus published data from Caenorhabditis elegans, Caenorhabditis briggsae, and Drosophila melanogaster, we find that the apparent activation energies (Ea values) for the early embryonic cell cycle for diverse ectotherms are all similar, 75 {+/-} 7 kJ/mol (mean {+/-} std.dev., n = 6), which corresponds to a Q10 value at 20{degrees}C of 2.8 {+/-} 0.2 (mean {+/-} std.dev., n = 6). Using computational models, we find that the approximate Arrhenius scaling and the deviations from it at high and low temperatures can be accounted for by biphasic temperature scaling in critical individual components of the cell cycle oscillator circuit, by imbalances in the Ea values for different partially rate-determining enzymes, or by a combination of both. Experimental studies of cycling Xenopus extracts indicate that both of these mechanisms contribute to the general scaling of temperature, and in vitro studies of individual cell cycle regulators confirm that there is in fact a substantial imbalance in their Ea values. These findings provide mechanistic insights into the dynamic interplay between temperature and complex biochemical processes, and into why biological systems fail at extreme temperatures.

systems biology↗

bioRxiv2025

Evaluating Transcriptomic Integration for Cyanobacterial Constraint-based Metabolic Modelling

1Metabolic modelling has wide-ranging applications, including for the production of high-value compounds, understanding complex disease and analysing community interactions. Integrating transcriptomic data with genome-scale metabolic models is crucial for deepening our understanding of complex biological systems, as it enables the development of models tailored to specific conditions, such as particular tissues, environments, or experimental setups. Relatively little attention has been given to the assessment of such integration methods in predicting intracellular fluxes. While a few validation studies offer some insights, their scope remains limited, particularly for organisms like cyanobacteria, for which little metabolic flux data are available. Cyanobacteria hold significant biotechnological potential due to their ability to synthesize a wide range of high-value compounds with minimal resource inputs [21]. The impact of specific methodological decisions on integration, however, has scarcely been assessed beyond human models, with no thorough exploration of parameter choices in valve-based integration methods. By implementing a novel analysis pipeline, we evaluated these methodological decisions using the genome-scale model for Synechocystis sp. PCC 6803 (iSynCJ816 [17]) with existing transcriptomic data in biomass-optimised scenarios. Our analyses indicate that selecting an appropriate integration method may not always be straightforward and depends on the initial model configuration - a factor which is often overlooked during integration. By evaluating sets of methods, we identified a trade-off between the buffering of light into the system and maintenance of flux near system boundaries. We suggest that the use of the lazy-step mapping function with importance-based scaling results in the best predictions, particularly when these can be validated with experimental data. When using one-size-fits-all scaling with the lazy-step mapping function, it appears preferable to use light buffering to avoid inappropriate bound changes near the photosystems, a factor which importance-based scaling may help to compensate for. In cases where no experimental data can be used for validation, the novel thresholding approach could be adopted as this showed some improvements upon the standard Lazy method.

systems biology↗

bioRxiv2025

Artificial Neural Network Reveals the Role of Transport Proteins in Rhodopseudomonas palustris CGA009 During Lignin Breakdown Product Catabolism

Rhodopseudomonas palustris, a versatile bacterium with diverse biotechnological applications, can effectively breakdown lignin, a complex and abundant polymer in plant biomass. This study investigates the metabolic response of R. palustris when catabolizing various lignin breakdown products (LBPs), including the monolignols p-coumaryl alcohol, coniferyl alcohol, sinapyl alcohol, p-coumarate, sodium ferulate, and kraft lignin. Transcriptomics and proteomics data were generated for those specific LBP breakdown conditions and used as features to train machine learning models, with growth rates as the target. Three models--Artificial Neural Networks (ANN), Random Forest (RF), and Support Vector Machine (SV)--were compared, with ANN achieving the highest predictive accuracy for both transcriptomics (94%) and proteomics (96%) datasets. Permutation feature importance analysis of the ANN models identified the top twenty genes and proteins influencing growth rates. Combining results from both transcriptomics and proteomics, eight key transport proteins were found to significantly influence the growth of R. palustris on LBPs. Re-training the ANN using only these eight transport proteins achieved predictive accuracies of 86% and 76% for proteomics and transcriptomics, respectively. This work highlights the potential of ANN-based models to predict growth-associated genes and proteins, shedding light on the metabolic behavior of R. palustris in lignin degradation under aerobic and anaerobic conditions. ImportanceThis study is significant as it addresses the biotechnological potential of Rhodopseudomonas palustris in lignin degradation, a key challenge in converting plant biomass into commercially important products. By training machine learning models with transcriptomics and proteomics data, particularly Artificial Neural Networks (ANN), the work achieves high predictive accuracy for growth rates on various lignin breakdown products (LBPs). Identifying top genes and proteins influencing growth, especially eight key transport proteins, offers insights into the metabolic niche of R. palustris. The ability to predict growth rates using just these few proteins highlights the efficiency of ANN models in distilling complex biological systems into manageable predictive frameworks. This approach not only enhances our understanding of lignin derivative catabolism but also paves the way for optimizing R. palustris for sustainable bioprocessing applications, such as bioplastic production, under varying environmental conditions.

systems biology↗

bioRxiv2025

HUMESS: Integrating Quantitative Transcriptomic Analysis and Metabolic Modeling to Unveil Condition-Specific Gene Signatures

Transcriptomic analysis is a key tool for exploring gene expression, but the complexity of biological systems often limits its insights. In particular, the lack of intermodal or multi-layered analysis hinders the ability to fully capture key cellular functions such as metabolism from transcriptomic data alone. Here, we introduce a novel approach that integrates transcriptomic data with metabolic network modeling to address this. Unlike traditional methods, HUMESS prioritizes genes based on their metabolic significance, offering a deeper understanding of condition-specific gene expression. Our computational pipeline, supported by a user-friendly Rshiny application, enhances gene expression analysis by uncovering metabolic phenotypic signatures.

systems biology↗

bioRxiv2025

BooLEVARD: Boolean Logical Evaluation of Activation and Repression in Directed pathways

Boolean models are widely used for studying dynamic processes of biological systems. However, their inherent discrete nature limits their ability to capture continuous aspects of signal transduction, such as signal strength or protein activation levels. Although existing tools provide some path exploration capabilities that can be used to explore signal transduction circuits, the computational workload often requires simplifying assumptions that compromise the accuracy of the analysis. Here, we introduce BooLEVARD, a Python package designed to efficiently quantify the number of paths leading either to node activation or repression in Boolean models, which offers a more detailed and quantitative perspective on how molecular signals propagate through signaling networks. By focusing on the collection of non-redundant paths directly influencing Boolean outcomes, BooLEVARD enhances the precision of signal strength representation. We showcase the application of BooLEVARD in studying cell-fate decisions using a Boolean model of cancer metastasis, demonstrating its ability to identify critical signaling events. Furthermore, BooLEVARD provides a refined understanding of signaling dynamics, which can increase our understanding of disease development and drug responses. BooLEVARD is freely available at https://github.com/farinasm/boolevard.

systems biology↗

bioRxiv2025

Generative Approaches to Kinetic Parameter Inference in Metabolic Networks via Latent Space Exploration

Generative machine learning methods that utilize neural networks to parameterize large-scale and near-genome-scale kinetic models have yielded significant efficiency gains in model construction, paving the way for high-throughput dynamic metabolism studies in biomedical and biotechnological applications. Nevertheless, challenges remain in interpreting the outputs of generative neural networks and developing strategies to quickly adapt these networks to different organisms and physiological contexts without having to restart the modeling process from scratch. Here, we present a systematic framework for repurposing generative neural networks trained under one physiological context to build large-scale kinetic models tailored to another. We showcase the effectiveness of this framework through three case studies in Escherichia coli: (i) adjusting the speed of the dynamic response of aerobic metabolism, (ii) improving interpretability by identifying key enzymatic steps that limit the dynamic response speed of the metabolic models, and (iii) adapting a trained generator to capture the distinct dynamic behavior of anaerobic metabolism. To assess robustness and generalizability beyond E. coli, we extend our approach to large-scale kinetic models of Saccharomyces cerevisiae, systematically exploring latent-space-driven control of network dynamics across generators at different training stages and across multiple representative regions of the latent input space. Together, these results demonstrate that latent space exploration provides a transferable and computationally efficient strategy for controlling the dynamic behavior in large-scale kinetic models across species and physiological regimes. Given the growing adoption of generative neural networks in biological systems modeling, our approach has the potential to facilitate applications in personalized medicine and accelerate the high-throughput design of cell factories by streamlining model construction across diverse living organisms.

systems biology↗

bioRxiv2025

High-performance proteomics at any chromatographic flow rate

Current applications of mass spectrometry-based proteomics range from single cell to body fluid analysis that come with very different demands regarding sensitivity or sample throughput. Additionally, the vast molecular complexity of proteomes and the massive dynamic range of protein concentrations in these biological systems require very high-performance chromatographic separations in tandem with the high speed and sensitivity afforded by mass spectrometer. In this study, we focussed on the chromatographic angle and, more specifically, systematically evaluated proteome analysis performance across a wide range of chromatographic flow rates (0.3 - 50 L/min) and associated column diameters using a Vanquish Neo UHPLC coupled online to a Q Exactive HF-X mass spectrometer. Serial dilutions of HeLa cell line digests were used for benchmarking and total analysis time from injection-to-injection was intentionally fixed at 60 minutes (24 samples per day). The three key messages of the study are that i) all chromatographic flow rates are suitable for high-quality proteome analysis, ii) capLC (1.5 L/min) is a very robust, sensitive and quantitative alternative to nanoLC for many applications and iii) showcased proteome, phosphoproteome and drug proteome data provide sound empirical guidance for laboratories in selecting appropriate chromatographic flow rates and column diameters for their specific application.

systems biology↗