IFAC-PapersOnLine

There is a large variability between individuals in the response to anesthetic drugs, that seriously limits the achievable performance of closed-loop controlled drug dosing. Full individualization of patient models based on early clinical response data has been suggested as a means to improve performance with maintained robustness (safety). We use estimation theoretic analysis and realization theory to characterize practical identifiability of the standard pharmacological model structure from anesthetic induction phase data and conclude that such approaches are not practically feasible.

The paper addresses the critical challenge of accurately characterising steady states in biomolecular systems, which are often complex, nonlinear, multistable and subject to significant uncertainties. Traditional numerical methods often fail to provide complete or guaranteed solutions under these conditions. To overcome these limitations, the research proposes and evaluates the application of interval analysis methodologies. We provided algorithms for interval Newton and interval Krawczyk methods for rigorously bounding all possible steady states (both stable and unstable) in multistable, multidimensional nonlinear systems. This study involves a comparative analysis of these two methods in conjunction with interval bisection and interval constraint propagation. We addressed numerical examples for an array of biologically plausible models, involving both feedback and feedforward gene networks. The work recommends the choice of the most suitable method for various types of biomolecular systems, ultimately offering a robust computational framework to understand cellular functions and design synthetic biological circuits.

We present an automated model reduction algorithm that uses quasi-steady state approximation to minimize the error between the desired outputs. Additionally, the algorithm minimizes the sensitivity of the error with respect to parameters to ensure robust performance of the reduced model in the presence of parametric uncertainties. We develop the theory for this model reduction algorithm and present the implementation of the algorithm that can be used to perform model reduction of given SBML models. To demonstrate the utility of this algorithm, we consider the design of a synthetic biological circuit to control the population density and composition of a consortium consisting of two different cell strains. We show how the model reduction algorithm can be used to guide the design and analysis of this circuit.

In this study we develop a computational framework for the reconstruction of the phase dynamics of the somitogenesis clock oscillator. Our understanding of the somitogenesis clock, a developmental oscillator found in the vertebrate embryo, has been revolutionised by the development of real time reporters of clock gene expression. However, the signals obtained from the real time reporters are typically noisy, nonstationary and spatiotemporally dynamic and there are open questions with regard to how post-processing can be used to both improve the insight gained from a given experiment and to constrain theoretical models. In this study we present a methodology, which is a variant of empirical mode decomposition, that reconstructs the phase dynamics of the somitogenesis clock. After validating the methodology using synthetic datasets, we define a set of metrics that use the reconstructed phase profiles to infer biologically meaningful quantities. We perform experiments in which the signal from a real time reporter of the somitogenesis clock is recorded and reconstruct the phase dynamics. Application of the defined metrics yields results that are consistent with previous experimental observations. Moreover, we extend previous work by developing a gradient descent method for defining automated kymographs and showing that boundary conditions are non-homogeneous. By studying phase dynamics along phase gradient descent trajectories, we show that, consistent with a previous theoretical model, the oscillation frequency is inversely correlated with the phase gradient but that the coefficient is not constant in time. The proposed methodology provides a tool kit for that can be used in the analysis of future experiments and the quantitative observations can be used to guide the development of future mathematical models.

The field of synthetic biology focuses on creating modular components which can be used to generate complex and controllable synthetic biological systems. Unfortunately, the intrinsic noise of gene regulation can be large enough to break these systems. Noise is largely treated as a nuisance and much past effort has been spent to create robust components that are less influenced by noise. However, extensive analysis of noise combined with smart microscopy tools and optognenetic actuators can create control opportunities that would be difficult or impossible to achieve in the deterministic setting. In previous work, we proposed an Optogenetic Maxwells Demons (OMD) control problem and found that deep understanding and manipulation of noise could create controllers that break symmetry between cells, even when those cells share the same optogenetic input and identical gene regulation circuitry. In this paper, we extend those results to analyze (in silico) the robustness of the OMD control under changes in system volume, with time observation/actuation delays, and subject to parametric model uncertainties.

Bioprocess development is commonly characterized by long development times, especially in the early screening phase. After promising candidates have been pre-selected in screening campaigns, an optimal operating strategy has to be found and verified under conditions similar to production. Cultivating cells with pulse-based feeding and thus exposing them to oscillating feast and famine phases has shown to be a powerful approach to study microorganisms closer to industrial bioreactor conditions. In view of the large number of strains and the process conditions to be tested, high-throughput cultivation systems provide an essential tool to sample the large design space in short time. We have recently presented a comprehensive platform, consisting of two liquid handling stations coupled with a model-based experimental design and operation framework to increase the efficiency in High Throughput bioprocess development. Using calibrated macro-kinetic growth models, the platform has been successfully used for the development of scale-down fed-batch cultivations in parallel mini-bioreactor systems. However, it has also been shown that parametric uncertainties in the models can significantly affect the prediction accuracy and thus the reliability of optimized cultivation strategies. To tackle this issue, we implemented a multi-stage Model Predictive Control (MPC) strategy to fulfill the experimental objectives under tight constraints despite the uncertainty in the parameters and the measurements. Dealing with uncertainties in the parameters is of major importance, since constraint violation would easily occur otherwise, which in turn could have adverse effects on the quality of the heterologous protein produced. Multi-stage approaches build up scenario tree, based on the uncertainty that can be encountered and computing optimal inputs that satisfy the constrains despite of such uncertainties. Using the feedback information gained through the evolution along the tree, the control approach is significantly more robust than standard MPC approaches without being overly conservative. We show in this study that the application of multi-stage MPC can increase the number of successful experiments, by applying this methodology to a mini-bioreactor cultivation operated in parallel.

Ensuring a stable and robust phenotype expression is a key challenge for the correct operation of synthetically engineered cells, and feedback has been highlighted as a key mechanism to achieve this goal. Biomolecular PID controllers have been extensively leveraged at a single cell level to regulate gene expression. However, single-cell architectures suffer from limited modularity and might pose a significant challenge for their in vivo implementation due to high metabolic load and possible incompatible reactions. To overcome these limitations, it has been proposed to distribute the control actions over different cell populations realizing a multicellular feedback control architecture. In this paper we provide design guidelines derived by means of the root contours method to tune the control gains of a multicellular PID controller. We then validate performance, robustness and modularity of the multicellular PID controller through in silico simulations in BSim.

Periodic behavior is a widespread biological phenomenon occurring across various spatiotemporal scales, where upstream stimuli are encoded into dynamic intracellular signals such as oscillations, varying in duration, amplitude, and frequency. Disruptions to this periodicity can lead to a range of pathologies, for which we propose an adaptive feedback controller with an Incoherent Feedforward Loop (IFFL)-like topology, based on chemical reactions, designed to restore sustained oscillations in systems that have lost their periodicity. By approximating the controllers dynamics, we defined the design requirements for the first implementation of a biomolecular adaptive controller and tested its applicability for destabilizing the steady-state behavior of a self-inhibiting gene. Numerical simulations illustrate the adaptive behavior of the controller and its ability to tune both the amplitude and the period of the resulting oscillations.

In pharmacometrics, developing and selecting models is crucial for quantitatively assessing drug-biological interactions, treatment planning, and gaining insights into underlying processes. These validated models are essential for predictive analytics and strategic decision-making in drug development and clinical practice. Unlike traditional methods, machine learning (ML) offers a data-driven alternative to conventional, first-principle approaches. This paper presents an automatic method to derive unknown or uncertain (sub)models using longitudinal, heterogeneous data. Initially, we employ deep nonlinear mixed effect (DeepNLME) to train a neural network as a universal approximator, which then generates a parameterized representation of the underlying process. Subsequently, we apply symbolic regression to identify a set of potential models expressed as equations. Within the study parameters, the proposed method outperforms the baseline models and demonstrates the validity of both the DeepNLME approach and the symbolic regression approach.

Efforts to model complex biological systems increasingly face challenges from ambiguous relationships within the model, such as through partially unknown mechanisms or unmodelled intermediate states. Hybrid neural differential equations are a recent modeling framework which has been previously shown to enable identification and prediction of complex phenomena, especially in the context of partially unknown mechanisms. We extend the application of hybrid neural differential equations to enable incorporation of theorized but unmodelled states within differential equation models. We find that beyond their capability to incorporate partially unknown mechanisms, hybrid neural differential equations provide an effective method to include knowledge of unmeasured states into differential equation models.

We present a Python-based software package to automatically obtain phenomenological models of input-controlled synthetic biological circuits from descriptive models. From the parts and mechanism description of a synthetic biological circuit, it is easy to obtain a chemical reaction model of the circuit under the assumptions of mass-action kinetics using various existing tools. However, using these models to guide design decisions during an experiment is difficult due to a large number of reaction rate parameters and species in the model. Hence, phenomenological models are often developed that describe the effective relationships among the circuit inputs, outputs, and only the key states and parameters. In this paper, we present an algorithm to obtain these phenomenological models in an automated manner using a Python package for circuits with inputs that control the desired outputs. This model reduction approach combines the common assumptions of time-scale separation, conservation laws, and species abundance to obtain the reduced models that can be used for design of synthetic biological circuits. We consider an example of a simple gene expression circuit and another example of a layered genetic feedback control circuit to demonstrate the use of the model reduction procedure.

This paper presents the first implementation of a Proportional-Integral-Derivative (PID) biomolecular controller within a consortium of different cell populations, aimed at robust regulation of biological processes. By leveraging the modularity and cooperative dynamics of multiple engineered cell populations, we develop a comprehensive in silico analysis of the performance and robustness of P, PD, PI, and PID control architectures. Our theoretical findings, validated through in silico experiments using the BSim agent-based simulation platform, demonstrate the robustness and effectiveness of our multicellular PID control strategy. This innovative approach addresses critical limitations in current control methods, offering significant potential for applications in metabolic engineering, therapeutic contexts, and industrial biotechnology. Future work will focus on experimental validation in vivo and further refinement of the control models.

Temporal gradient estimation is a pervasive phenomenon in natural biological systems and holds great promise for synthetic counterparts with broad-reaching applications. Here, we advance the concept of BioSD (Biomolecular Signal Differentiators) by introducing a novel biomolecular topology, termed Autocatalytic-BioSD or AC-BioSD. Its structure allows for insensitivity to input signal changes and high precision in terms of signal differentiation, even when operating far from nominal conditions. Concurrently, disruptive high-frequency signal components are effectively attenuated. In addition, the usefulness of our topology in biological regulation is highlighted via a PID (Proportional-Integral-Derivative) bio-control scheme with set point weighting and filtered derivative action in both the deterministic and stochastic domains.

Modeling dynamical biological systems is key for understanding, predicting, and controlling complex biological behaviors. Traditional methods for identifying governing equations, such as ordinary differential equations (ODEs), typically require extensive quantitative data, which is often scarce in biological systems due to experimental limitations. To address this challenge, we introduce an approach that determines biomolecular models from qualitative system behaviors expressed as Signal Temporal Logic (STL) statements, which are naturally suited to translate expert knowledge into computationally tractable specifications. Our method represents the biological network as a graph, where edges represent interactions between species, and uses a genetic algorithm to identify the graph. To infer the parameters of the ODEs modeling the interactions, we propose a gradient-based algorithm. On a numerical example, we evaluate two loss functions using STL robustness and analyze different initialization techniques to improve the convergence of the approach.

The Izhikevich artificial spiking neuron model is among the most employed models in neuromorphic engineering and computational neuroscience, due to the affordable computational effort to discretize it and its biological plausibility. It has been adopted also for applications with limited computational resources in embedded systems. It is important therefore to realize a compromise between error and computational expense to solve numerically the models equations. Here we investigate the effects of discretization and we study the solver that realizes the best compromise between accuracy and computational cost, given an available amount of Floating Point Operations per Second (FLOPS). We considered three fixed-step solvers for Ordinary Differential Equations (ODE), commonly used in computational neuroscience: Euler method, the Runge-Kutta 2 method and the Runge-Kutta 4 method. To quantify the error produced by the solvers, we used the Victor Purpura spike train Distance from an ideal solution of the ODE. Counterintuitively, we found that simple methods such as Euler and Runge Kutta 2 can outperform more complex ones (i.e. Runge Kutta 4) in the numerical solution of the Izhikevich model if the same FLOPS are allocated in the comparison. Moreover, we quantified the neuron rest time (with input under threshold resulting in no output spikes) necessary for the numerical solution to converge to the ideal solution and therefore to cancel the error accumulated during the spike train; in this analysis we found that the required rest time is independent from the firing rate and the spike train duration. Our results can generalize in a straightforward manner to other spiking neuron models and provide a systematic analysis of fixed step neural ODE solvers towards an accuracy-computational cost tradeoff.

Accurate estimation of growth and metabolic rates is essential for understanding and optimizing bioprocesses, yet traditional methods often fail when faced with sparse or noisy concentration data. We present a probabilistic framework based on Bayesian inference and Nested Sampling that addresses these challenges by integrating biological knowledge directly into the model structure. The approach transforms raw concentration measurements into pseudo-concentrations that account for distortions caused by bioreactor volume changes (e.g., feed additions, sample withdrawals), and models metabolic rates as linear combinations of basis functions to yield continuous rate profiles from discrete data. Using in-silico simulations, we evaluated the framework under a range of experimental conditions and compared its performance with a conventional rate calculation method. We further analyzed the influence of key experimental design parameters - sampling frequency, sample volume, and measurement noise - on both rate estimation accuracy and concentration reconstruction quality. Results demonstrate that the proposed framework delivers accurate, robust metabolic rate estimates even under severe data sparsity and noise, offering a powerful tool for improving bioprocess characterization and optimization.

Achieving complex multi-species control objectives is essential for engineering advanced autoregulated biomolecular devices. This paper addresses the problem of robust steady-state tracking for outputs defined as multiplicative combinations of biomolecular species concentrations. We first introduce a control architecture realized via chemical reaction networks that steers the product of two target species concentrations in the controlled network to a prescribed value. A robust stability analysis is provided for closed-loop system families with distinct structural characteristics. The proposed framework is also extended to a more general formulation capable of regulating arbitrary monomial outputs involving multiple species. Numerical simulations of representative examples corroborate the theoretical results and illustrate the effectiveness of our approach.

Hybrid models that couple mechanistic ordinary differential equations (ODEs) with neural networks are increasingly used in bioprocess engineering, yet most published approaches assume either substantial prior knowledge or relatively large datasets. This work proposes a hybrid modeling framework for early-stage bioprocess development, where only a few batch experiments are available and standard artificial intelligence (AI) techniques are difficult to apply. The mechanistic structure is constructed using only qualitative, widely accepted biological constraints (e.g., non-negativity, zero-invariance, and biomass-mediated interactions), while unknown functional dependencies are learned by a feedforward neural network embedded in the ODE right-hand side. To exploit the natural organization of batch data, we introduce a minibatch training strategy in which each minibatch corresponds to one entire batch experiment, combined with regularization to mitigate overfitting. We demonstrate the approach on (i) synthetic Escherichia coli growth with overflow metabolism and (ii) experimental astaxanthin production by Xanthophyllomyces dendrorhous. In both cases, models trained from as few as three batch experiments accurately predict an unseen validation batch and the learned neural components recover biologically consistent patterns. Thus, the framework contributes to AI by enabling constrained neural differential models that learn interpretable dynamics from limited, structured data, with applications to early-stage bioprocess engineering.

Alcohol use disorder (AUD) also called alcohol dependence is a major public health problem, which affects almost 10% of the worlds population. Baclofen as a selective GABAB receptor agonist has emerged as a promising drug for the treatment of AUD, however, its optimal dosage varies according to individuals, and its exposure-response relationship has not been well established yet. In this study, we use a principled Bayesian workflow to estimate the parameters of a pharmacokinetic (PK) population model from Baclofen administration to patients with AUD. By monitoring various convergence diagnostics, the probabilistic methodology is first validated on synthetic longitudinal datasets and then, applied to infer the PK model parameters based on the clinical data that were retrospectively collected from outpatients treated with oral Baclofen. We show that state-of-the-art advances in automatic Bayesian inference using self-tuning Hamiltonian Monte Carlo (HMC) algorithms with a leveraged level of information in priors provide accurate predictions on Baclofen plasma concentration in individuals. This approach may pave the way to render non-parametric HMC sampling methods sufficiently easy and reliable to use in clinical schedules for personalized treatment of AUD.

Process models are increasingly used to support upstream process development in the biopharmaceutical industry for process optimization, scale-up and to reduce experimental effort. Parametric unstructured models based biological mechanisms are highly promising, since they do not require large amounts of data. The critical part in the application is the certainty of the parameter estimates, since uncertainty of the parameter estimates propagates to model predictions and can increase the risk associated with those predictions. Currently Fisher-Information-Matrix based approximations or Monte-Carlo approaches are used to estimate parameter confidence intervals and regularization approaches to decrease parameter uncertainty. Here we apply profile likelihood to determine parameter identifiability of a recent upstream process model. We have investigated the effect of data amount on identifiability and found out that addition of data reduces non-identifiability. The likelihood profiles of non-identifiable parameters were then used to uncover structural model changes. These changes effectively alleviate the remaining non-identifiabilities except for a single parameter out of 21 total parameters. We present the first application of profile likelihood to a complete upstream process model. Profile likelihood is a highly suitable method to determine parameter confidence intervals in upstream process models and provides reliable estimates even with non-linear models and limited data.