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Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER.
Quantifying uncertainty, variability and likelihood for ordinary differential equation models
(2010)
Background: In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results: The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well- known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions: While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.
As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved.
We propose a novel strategy for global sensitivity analysis of ordinary differential equations. It is based on an error-controlled solution of the partial differential equation (PDE) that describes the evolution of the probability density function associated with the input uncertainty/variability. The density yields a more accurate estimate of the output uncertainty/variability, where not only some observables (such as mean and variance) but also structural properties (e.g., skewness, heavy tails, bi-modality) can be resolved up to a selected accuracy. For the adaptive solution of the PDE Cauchy problem we use the Rothe method with multiplicative error correction, which was originally developed for the solution of parabolic PDEs. We show that, unlike in parabolic problems, conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time. We provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy. The performance of the method is studied by means of low-dimensional case studies. The favorable properties of the spatial discretization technique suggest that this may be the starting point for an error-controlled sensitivity analysis in higher dimensions.
The drug concentrations targeted in meropenem and piperacillin/tazobactam therapy also depend on the susceptibility of the pathogen. Yet, the pathogen is often unknown, and antibiotic therapy is guided by empirical targets. To reliably achieve the targeted concentrations, dosing needs to be adjusted for renal function. We aimed to evaluate a meropenem and piperacillin/tazobactam monitoring program in intensive care unit (ICU) patients by assessing (i) the adequacy of locally selected empirical targets, (ii) if dosing is adequately adjusted for renal function and individual target, and (iii) if dosing is adjusted in target attainment (TA) failure. In a prospective, observational clinical trial of drug concentrations, relevant patient characteristics and microbiological data (pathogen, minimum inhibitory concentration (MIC)) for patients receiving meropenem or piperacillin/tazobactam treatment were collected. If the MIC value was available, a target range of 1-5 x MIC was selected for minimum drug concentrations of both drugs. If the MIC value was not available, 8-40 mg/L and 16-80 mg/L were selected as empirical target ranges for meropenem and piperacillin, respectively. A total of 356 meropenem and 216 piperacillin samples were collected from 108 and 96 ICU patients, respectively. The vast majority of observed MIC values was lower than the empirical target (meropenem: 90.0%, piperacillin: 93.9%), suggesting empirical target value reductions. TA was found to be low (meropenem: 35.7%, piperacillin 50.5%) with the lowest TA for severely impaired renal function (meropenem: 13.9%, piperacillin: 29.2%), and observed drug concentrations did not significantly differ between patients with different targets, indicating dosing was not adequately adjusted for renal function or target. Dosing adjustments were rare for both drugs (meropenem: 6.13%, piperacillin: 4.78%) and for meropenem irrespective of TA, revealing that concentration monitoring alone was insufficient to guide dosing adjustment. Empirical targets should regularly be assessed and adjusted based on local susceptibility data. To improve TA, scientific knowledge should be translated into easy-to-use dosing strategies guiding antibiotic dosing.
The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at & 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial.
Cell-level systems biology model to study inflammatory bowel diseases and their treatment options
(2023)
To help understand the complex and therapeutically challenging inflammatory bowel diseases (IBDs), we developed a systems biology model of the intestinal immune system that is able to describe main aspects of IBD and different treatment modalities thereof. The model, including key cell types and processes of the mucosal immune response, compiles a large amount of isolated experimental findings from literature into a larger context and allows for simulations of different inflammation scenarios based on the underlying data and assumptions. In the context of a large and diverse virtual IBD population, we characterized the patients based on their phenotype (in contrast to healthy individuals, they developed persistent inflammation after a trigger event) rather than on a priori assumptions on parameter differences to a healthy individual. This allowed to reproduce the enormous diversity of predispositions known to lead to IBD. Analyzing different treatment effects, the model provides insight into characteristics of individual drug therapy. We illustrate for anti-TNF-alpha therapy, how the model can be used (i) to decide for alternative treatments with best prospects in the case of nonresponse, and (ii) to identify promising combination therapies with other available treatment options.
Congenital adrenal hyperplasia (CAH) is the most common form of adrenal insufficiency in childhood; it requires cortisol replacement therapy with hydrocortisone (HC, synthetic cortisol) from birth and therapy monitoring for successful treatment. In children, the less invasive dried blood spot (DBS) sampling with whole blood including red blood cells (RBCs) provides an advantageous alternative to plasma sampling.
Potential differences in binding/association processes between plasma and DBS however need to be considered to correctly interpret DBS measurements for therapy monitoring. While capillary DBS samples would be used in clinical practice, venous cortisol DBS samples from children with adrenal insufficiency were analyzed due to data availability and to directly compare and thus understand potential differences between venous DBS and plasma. A previously published HC plasma pharmacokinetic (PK) model was extended by leveraging these DBS concentrations.
In addition to previously characterized binding of cortisol to albumin (linear process) and corticosteroid-binding globulin (CBG; saturable process), DBS data enabled the characterization of a linear cortisol association with RBCs, and thereby providing a quantitative link between DBS and plasma cortisol concentrations. The ratio between the observed cortisol plasma and DBS concentrations varies highly from 2 to 8. Deterministic simulations of the different cortisol binding/association fractions demonstrated that with higher blood cortisol concentrations, saturation of cortisol binding to CBG was observed, leading to an increase in all other cortisol binding fractions.
In conclusion, a mathematical PK model was developed which links DBS measurements to plasma exposure and thus allows for quantitative interpretation of measurements of DBS samples.
Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows
(2021)
Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach. <br /> Author summary Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum.
During preclinical development of a gestagenic drug, a significant increase of the total plasma concentration was observed after multiple dosing in pregnant rabbits, but not in (non-pregnant) rats or monkeys. We used a PBPK modeling approach in combination with in vitro and in vivo data to address the question to what extent the pharmacologically active free drug concentration is affected by pregnancy induced processes. In human, a significant increase in sex hormone binding globulin (SHBG), and an induction of hepatic CYP3A4 as well as plasma esterases is observed during pregnancy. We find that the observed increase in total plasma trough levels in rabbits can be explained as a combined result of (i) drug accumulation due to multiple dosing, (ii) increase of the binding protein SHBG, and (iii) clearance induction. For human, we predict that free drug concentrations in plasma would not increase during pregnancy above the steady state trough level for non-pregnant women.
Background
Cytochrome P450 (CYP) 3A contributes to the metabolism of many approved drugs. CYP3A perpetrator drugs can profoundly alter the exposure of CYP3A substrates. However, effects of such drug-drug interactions are usually reported as maximum effects rather than studied as time-dependent processes. Identification of the time course of CYP3A modulation can provide insight into when significant changes to CYP3A activity occurs, help better design drug-drug interaction studies, and manage drug-drug interactions in clinical practice.
Objective
We aimed to quantify the time course and extent of the in vivo modulation of different CYP3A perpetrator drugs on hepatic CYP3A activity and distinguish different modulatory mechanisms by their time of onset, using pharmacologically inactive intravenous microgram doses of the CYP3A-specific substrate midazolam, as a marker of CYP3A activity.
Methods
Twenty-four healthy individuals received an intravenous midazolam bolus followed by a continuous infusion for 10 or 36 h. Individuals were randomized into four arms: within each arm, two individuals served as a placebo control and, 2 h after start of the midazolam infusion, four individuals received the CYP3A perpetrator drug: voriconazole (inhibitor, orally or intravenously), rifampicin (inducer, orally), or efavirenz (activator, orally). After midazolam bolus administration, blood samples were taken every hour (rifampicin arm) or every 15 min (remaining study arms) until the end of midazolam infusion. A total of 1858 concentrations were equally divided between midazolam and its metabolite, 1'-hydroxymidazolam. A nonlinear mixed-effects population pharmacokinetic model of both compounds was developed using NONMEM (R). CYP3A activity modulation was quantified over time, as the relative change of midazolam clearance encountered by the perpetrator drug, compared to the corresponding clearance value in the placebo arm.
Results
Time course of CYP3A modulation and magnitude of maximum effect were identified for each perpetrator drug. While efavirenz CYP3A activation was relatively fast and short, reaching a maximum after approximately 2-3 h, the induction effect of rifampicin could only be observed after 22 h, with a maximum after approximately 28-30 h followed by a steep drop to almost baseline within 1-2 h. In contrast, the inhibitory impact of both oral and intravenous voriconazole was prolonged with a steady inhibition of CYP3A activity followed by a gradual increase in the inhibitory effect until the end of sampling at 8 h. Relative maximum clearance changes were +59.1%, +46.7%, -70.6%, and -61.1% for efavirenz, rifampicin, oral voriconazole, and intravenous voriconazole, respectively.
Conclusions
We could distinguish between different mechanisms of CYP3A modulation by the time of onset. Identification of the time at which clearance significantly changes, per perpetrator drug, can guide the design of an optimal sampling schedule for future drug-drug interaction studies. The impact of a short-term combination of different perpetrator drugs on the paradigm CYP3A substrate midazolam was characterized and can define combination intervals in which no relevant interaction is to be expected.
Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.
Introduction:
Hydrocortisone is the standard of care in cortisol replacement therapy for congenital adrenal hyperplasia patients. Challenges in mimicking cortisol circadian rhythm and dosing individualization can be overcome by the support of mathematical modelling. Previously, a non-linear mixed-effects (NLME) model was developed based on clinical hydrocortisone pharmacokinetic (PK) pediatric and adult data. Additionally, a physiologically-based pharmacokinetic (PBPK) model was developed for adults and a pediatric model was obtained using maturation functions for relevant processes. In this work, a middle-out approach was applied. The aim was to investigate whether PBPK-derived maturation functions could provide a better description of hydrocortisone PK inter-individual variability when implemented in the NLME framework, with the goal of providing better individual predictions towards precision dosing at the patient level.
Methods:
Hydrocortisone PK data from 24 adrenal insufficiency pediatric patients and 30 adult healthy volunteers were used for NLME model development, while the PBPK model and maturation functions of clearance and cortisol binding globulin (CBG) were developed based on previous studies published in the literature.
Results:
Clearance (CL) estimates from both approaches were similar for children older than 1 year (CL/F increasing from around 150 L/h to 500 L/h), while CBG concentrations differed across the whole age range (CBG(NLME) stable around 0.5 mu M vs. steady increase from 0.35 to 0.8 mu M for CBG (PBPK)). PBPK-derived maturation functions were subsequently included in the NLME model. After inclusion of the maturation functions, none, a part of, or all parameters were re-estimated. However, the inclusion of CL and/or CBG maturation functions in the NLME model did not result in improved model performance for the CL maturation function (& UDelta;OFV > -15.36) and the re-estimation of parameters using the CBG maturation function most often led to unstable models or individual CL prediction bias.
Discussion:
Three explanations for the observed discrepancies could be postulated, i) non-considered maturation of processes such as absorption or first-pass effect, ii) lack of patients between 1 and 12 months, iii) lack of correction of PBPK CL maturation functions derived from urinary concentration ratio data for the renal function relative to adults. These should be investigated in the future to determine how NLME and PBPK methods can work towards deriving insights into pediatric hydrocortisone PK.
The chemical master equation (CME) is the fundamental evolution equation of the stochastic description of biochemical reaction kinetics. In most applications it is impossible to solve the CME directly due to its high dimensionality. Instead, indirect approaches based on realizations of the underlying Markov jump process are used, such as the stochastic simulation algorithm (SSA). In the SSA, however, every reaction event has to be resolved explicitly such that it becomes numerically inefficient when the system's dynamics include fast reaction processes or species with high population levels. In many hybrid approaches, such fast reactions are approximated as continuous processes or replaced by quasi-stationary distributions in either a stochastic or a deterministic context. Current hybrid approaches, however, almost exclusively rely on the computation of ensembles of stochastic realizations. We present a novel hybrid stochastic-deterministic approach to solve the CME directly. Our starting point is a partitioning of the molecular species into discrete and continuous species that induces a partitioning of the reactions into discrete-stochastic and continuous-deterministic processes. The approach is based on a WKB (Wentzel-Kramers-Brillouin) ansatz for the conditional probability distribution function (PDF) of the continuous species (given a discrete state) in combination with Laplace's method of integral approximation. The resulting hybrid stochastic-deterministic evolution equations comprise a CME with averaged propensities for the PDF of the discrete species that is coupled to an evolution equation of the related expected levels of the continuous species for each discrete state. In contrast to indirect hybrid methods, the impact of the evolution of discrete species on the dynamics of the continuous species has to be taken into account explicitly. The proposed approach is efficient whenever the number of discrete molecular species is small. We illustrate the performance of the new hybrid stochastic-deterministic approach in an application to model systems of biological interest.
Background and objective Optimisation of hydrocortisone replacement therapy in children is challenging as there is currently no licensed formulation and dose in Europe for children under 6 years of age. In addition, hydrocortisone has non-linear pharmacokinetics caused by saturable plasma protein binding. A paediatric hydrocortisone formulation, Infacort (R) oral hydrocortisone granules with taste masking, has therefore been developed. The objective of this study was to establish a population pharmacokinetic model based on studies in healthy adult volunteers to predict hydrocortisone exposure in paediatric patients with adrenal insufficiency. Methods Cortisol and binding protein concentrations were evaluated in the absence and presence of dexamethasone in healthy volunteers (n = 30). Dexamethasone was used to suppress endogenous cortisol concentrations prior to and after single doses of 0.5, 2, 5 and 10 mg of Infacort (R) or 20 mg of Infacort (R)/hydrocortisone tablet/hydrocortisone intravenously. A plasma protein binding model was established using unbound and total cortisol concentrations, and sequentially integrated into the pharmacokinetic model. Results Both specific (non-linear) and non-specific (linear) protein binding were included in the cortisol binding model. A two-compartment disposition model with saturable absorption and constant endogenous cortisol baseline (Baseline (cort),15.5 nmol/L) described the data accurately. The predicted cortisol exposure for a given dose varied considerably within a small body weight range in individuals weighing < 20 kg. Conclusions Our semi-mechanistic population pharmacokinetic model for hydrocortisone captures the complex pharmacokinetics of hydrocortisone in a simplified but comprehensive framework. The predicted cortisol exposure indicated the importance of defining an accurate hydrocortisone dose to mimic physiological concentrations for neonates and infants weighing < 20 kg.
Model-informed precision dosing (MIPD) is a quantitative dosing framework that combines prior knowledge on the drug-disease-patient system with patient data from therapeutic drug/ biomarker monitoring (TDM) to support individualized dosing in ongoing treatment. Structural models and prior parameter distributions used in MIPD approaches typically build on prior clinical trials that involve only a limited number of patients selected according to some exclusion/inclusion criteria. Compared to the prior clinical trial population, the patient population in clinical practice can be expected to also include altered behavior and/or increased interindividual variability, the extent of which, however, is typically unknown. Here, we address the question of how to adapt and refine models on the level of the model parameters to better reflect this real-world diversity. We propose an approach for continued learning across patients during MIPD using a sequential hierarchical Bayesian framework. The approach builds on two stages to separate the update of the individual patient parameters from updating the population parameters. Consequently, it enables continued learning across hospitals or study centers, because only summary patient data (on the level of model parameters) need to be shared, but no individual TDM data. We illustrate this continued learning approach with neutrophil-guided dosing of paclitaxel. The present study constitutes an important step toward building confidence in MIPD and eventually establishing MIPD increasingly in everyday therapeutic use.
Cell-level kinetic models for therapeutically relevant processes increasingly benefit the early stages of drug development. Later stages of the drug development processes, however, rely on pharmacokinetic compartment models while cell-level dynamics are typically neglected. We here present a systematic approach to integrate cell-level kinetic models and pharmacokinetic compartment models. Incorporating target dynamics into pharmacokinetic models is especially useful for the development of therapeutic antibodies because their effect and pharmacokinetics are inherently interdependent. The approach is illustrated by analysing the F(ab)-mediated inhibitory effect of therapeutic antibodies targeting the epidermal growth factor receptor. We build a multi-level model for anti-EGFR antibodies by combining a systems biology model with in vitro determined parameters and a pharmacokinetic model based on in vivo pharmacokinetic data. Using this model, we investigated in silico the impact of biochemical properties of anti-EGFR antibodies on their F(ab)-mediated inhibitory effect. The multi-level model suggests that the F(ab)-mediated inhibitory effect saturates with increasing drug-receptor affinity, thereby limiting the impact of increasing antibody affinity on improving the effect. This indicates that observed differences in the therapeutic effects of high affinity antibodies in the market and in clinical development may result mainly from Fc-mediated indirect mechanisms such as antibody-dependent cell cytotoxicity.
Understanding and reducing complex systems pharmacology models based on a novel input-response index
(2018)
A growing understanding of complex processes in biology has led to large-scale mechanistic models of pharmacologically relevant processes. These models are increasingly used to study the response of the system to a given input or stimulus, e.g., after drug administration. Understanding the input–response relationship, however, is often a challenging task due to the complexity of the interactions between its constituents as well as the size of the models. An approach that quantifies the importance of the different constituents for a given input–output relationship and allows to reduce the dynamics to its essential features is therefore highly desirable. In this article, we present a novel state- and time-dependent quantity called the input–response index that quantifies the importance of state variables for a given input–response relationship at a particular time. It is based on the concept of time-bounded controllability and observability, and defined with respect to a reference dynamics. In application to the brown snake venom–fibrinogen (Fg) network, the input–response indices give insight into the coordinated action of specific coagulation factors and about those factors that contribute only little to the response. We demonstrate how the indices can be used to reduce large-scale models in a two-step procedure: (i) elimination of states whose dynamics have only minor impact on the input–response relationship, and (ii) proper lumping of the remaining (lower order) model. In application to the brown snake venom–fibrinogen network, this resulted in a reduction from 62 to 8 state variables in the first step, and a further reduction to 5 state variables in the second step. We further illustrate that the sequence, in which a recursive algorithm eliminates and/or lumps state variables, has an impact on the final reduced model. The input–response indices are particularly suited to determine an informed sequence, since they are based on the dynamics of the original system. In summary, the novel measure of importance provides a powerful tool for analysing the complex dynamics of large-scale systems and a means for very efficient model order reduction of nonlinear systems.