Search bioRxiv⌕ Search

bioRxiv · 10.1101/2022.08.08.503176

Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks

Abstract

Dynamical models in the form of systems of ordinary differential equations have become a standard tool in systems biology. Many parameters of such models are usually unknown and have to be inferred from experimental data. Gradient-based optimization has proven to be effective for parameter estimation. However, computing gradients becomes increasingly costly for larger models, which are required for capturing the complex interactions of multiple biochemical pathways. Adjoint sensitivity analysis has been pivotal for working with such large models, but methods tailored for steady-state data are currently not available. We propose a new adjoint method for computing gradients, which is applicable if the experimental data include steady-state measurements. The method is based on a reformulation of the backward integration problem to a system of linear algebraic equations. The evaluation of the proposed method using real-world problems shows a speedup of total simulation time by a factor of up to 4.4. Our results demonstrate that the proposed approach can achieve a substantial improvement in computation time, in particular for large-scale models, where computational efficiency is critical. Author summaryLarge-scale dynamical models are nowadays widely used for the analysis of complex processes and the integration of large-scale data sets. However, computational cost is often a bottleneck. Here, we propose a new gradient computation method that facilitates the parameterization of large-scale models based on steady-state measurements. The method can be combined with existing gradient computation methods for time-course measurements. Accordingly, it is an essential contribution to the environment of computationally efficient approaches for the study of large-scale screening and omics data, but not tailored to biological applications, and, therefore, also useful beyond the field of computational biology.

Source connections

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lakrisenko, P., Stapor, P., Grein, S., Paszkowski, Łukasz, Pathirana, D., Fröhlich, F., Lines, G. T., Weindl, D., Hasenauer, J.. 2022-08-11. Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks. https://doi.org/10.1101/2022.08.08.503176

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

Homogeneous network inference for subtype-stratified master regulator analysis in cancer

Master-regulator analysis of 34 TCGA tumour cohorts (cancer x molecular subtype; n between 27 and 562 tumours) requires one regulatory network per cohort. Mutual-information (MI) networks inferred with ARACNe3 are the usual choice, but they are not available for the smallest cohorts; filling the gap with correlation networks would mix two methods inside the very comparison between subtypes that the analysis is meant to make. We therefore infer every network with a single procedure, fixed-size Spearman regulons (FSR): rank correlation between regulator and target, a fixed effect-size threshold rho >= 0.2, the per-target data-processing-inequality (DPI) pruning implemented in corto, bootstrap support, and truncation to the 100 best-supported targets per regulator. We quantify what this choice concedes and what it provides, labelling each claim as a standard result, a heuristic, or an empirical result. Rank correlation is more powerful than the MI estimators we simulated for n < 200 but cannot see non-monotone dependence, which in a synthetic worst case costs at most about 0.05-0.10 of the master regulators recovered; the per-target DPI is a heuristic with a measurable disagreement rate with the MI-based one; and pairwise dependence is not direct interaction, for MI and correlation alike. Where both methods are feasible (n >= 95) they overlap in 0.7 of the top-20 regulators, the same as two filterings of the same ARACNe3 network, although the rank correlation of the full score vector shows a measurable method effect in the tail. Subsampling large real cohorts indicates that networks inferred from fewer than 60 tumours do not reliably reproduce their own cohort's master regulators, that 60-100 is a grey zone, and that a cancer-wide network does not rescue small subtypes. We present FSR as an adequate and uniform choice for multi-cohort analysis, not as a statistically superior one.

systems biology↗

Low-fidelity simulator selection for multi-fidelity inference of epithelial vertex models

Vertex models link cell division, neighbour exchange, and intercellular forces to epithelial tissue form through parameters such as junctional line tension and perimeter contractility. Bayesian inference of these parameters from data quantifies their uncertainty, but for stochastic models of proliferating tissues it requires many costly simulations. Multi-fidelity simulation-based inference reduces this cost by training on many runs of a cheaper, less accurate ('low-fidelity') simulator before refining with a few full ('high-fidelity') runs. Low-fidelity versions can be constructed in several ways, for example by stopping simulations early, coarsening the timestep, or averaging fewer replicates, but it is unclear which to choose before committing to costly training. To address this, we introduce PRISM (Paired Ranking Index for Simulator Matching), a screen that compares each candidate with the full simulator on paired runs, scoring agreement in cell-packing statistics against cost. For a vertex model of a proliferating tissue, PRISM flags stopping early as unreliable before training; once trained, this choice can produce confidently wrong parameter estimates. By contrast, a coarser timestep, within the range tested, is cheap and accurate; while fewer replicates are accurate but too costly. Using a screened low-fidelity simulator, multi-fidelity inference outperforms approximate Bayesian computation and neural-network inference trained on full simulations alone, at matched cost and with well-calibrated uncertainty. The same pattern recurs for a second vertex model fitted to published Drosophila pupal-wing imaging data, although there stopping halfway proves safe. Together, our findings suggest that which approximations are safe depends on the model, and that screening them before training makes multi-fidelity inference of tissue mechanics practical.

systems biology↗

Calibrating developmental dynamics from single-cell atlases: lineage paths outrun least-action routes

Single-cell atlases infer developmental dynamics from destructive snapshots, yet how far realized lineage paths depart from such inferred dynamics has never been measured with controls. We introduce LADD (Least-Action Developmental Dynamics), a measurement framework that learns a stochastic developmental vector field from time-series single-cell RNA-seq and computes minimum-action and minimum-time paths, together with a three-layer calibration protocol that separates genuine path deviation from the generic cost of centroid measurement, and we compare its forecasting component with optimal-transport and flow-matching methods. In the lineage-resolved Caenorhabditis elegans atlas, the raw action ratio of observed lineage-centroid trajectories to optimal paths is 3.79, yet forward-simulated ensembles of the learned model itself score 2.07, leaving a genuine excess of about two-fold. In zebrafish (Danio rerio), the observed ratio sits entirely at the model's floor. Three mechanisms that could explain the residual deviation (detours, flow-opposition, and fate-map complexity) are each excluded; what remains is speed, with lineages moving 30-43% faster along the learned flow. We report validity boundaries for temporal resolution, cross-species comparison, and energetic interpretation, delimiting where action-based trajectory comparisons are meaningful.

systems biology↗