Absolute binding free energy calculations: On the accuracy of computational scoring of protein–ligand interactions

Calculating the absolute binding free energies is a challenging task. Reliable estimates of binding free energies should provide a guide for rational drug design. It should also provide us with deeper understanding of the correlation between protein structure and its function. Further applications may include identifying novel molecular scaffolds and optimizing lead compounds in computer‐aided drug design. Available options to evaluate the absolute binding free energies range from the rigorous but expensive free energy perturbation to the microscopic linear response approximation (LRA/β version) and related approaches including the linear interaction energy (LIE) to the more approximated and considerably faster scaled protein dipoles Langevin dipoles (PDLD/S‐LRA version) as well as the less rigorous molecular mechanics Poisson–Boltzmann/surface area (MM/PBSA) and generalized born/surface area (MM/GBSA) to the less accurate scoring functions. There is a need for an assessment of the performance of different approaches in terms of computer time and reliability. We present a comparative study of the LRA/β, the LIE, the PDLD/S‐LRA/β, and the more widely used MM/PBSA and assess their abilities to estimate the absolute binding energies. The LRA and LIE methods perform reasonably well but require specialized parameterization for the nonelectrostatic term. The PDLD/S‐LRA/β performs effectively without the need of reparameterization. Our assessment of the MM/PBSA is less optimistic. This approach appears to provide erroneous estimates of the absolute binding energies because of its incorrect entropies and the problematic treatment of electrostatic energies. Overall, the PDLD/S‐LRA/β appears to offer an appealing option for the final stages of massive screening approaches. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603.

The study of antibody-antigen interactions should greatly benefit from the development of quantitative models for the evaluation of binding free energies in proteins. The present work addresses this challenge by considering the test case of the binding free energies of phosphorylcholine analogs to the murine myeloma protein McPC603. This includes the evaluation of the differential binding energy as well as the absolute binding energies and their corresponding electrostatic contributions. Four different approaches are examined: the Protein Dipoles Langevin Dipoles (PDLD) method, the semi-microscopic PDLD (PDLD/S) method, a free energy perturbation (FEP) method based on an adiabatic charging procedure and a linear response approximation that accelerates the FEP calculation. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions. The determination of the hydrophobic energy involves an approach which considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. This treatment, which considers the protein as a harmonic system, views the steric forces as the restoring forces for the electrostatic interactions. The FEP method is found to give unreliable results with regular cut-off radii and starts to give quantitative results only in very expensive treatment with very large cut-off radii. The PDLD and PDLD/S methods are much faster than the FEP approach and give reasonable results for both the relative and absolute binding energies. The speed and simplicity of the PDLD/S method make it an effective strategy for interactive docking studies and indeed such an option is incorporated in the program MOLARIS. A component analysis of the different energy contributions of the FEP treatment and a similar PDLD analysis indicate that electrostatic effects provide the largest contribution to the differential binding energy, while the hydrophobic and steric contributions are much smaller. This finding lends further support to the idea that electrostatic interactions play a major role in determining the antigen specificity of McPC603.     

Binding free energy calculations of galectin-3-ligand interactions

Galectins show remarkable binding specificity towards beta-galactosides. A recently developed method for calculating binding free energies between a protein and its substrates has been used to evaluate the binding specificity of galectin-3. Five disaccharides and a tetrasaccharide were used as the substrates. The calculated binding free energies agree quite well with the experimental data and the ranking of binding affinities is well reproduced. For all the six protein-ligand complexes it was observed that electrostatic interactions oppose binding whereas the non-polar contributions drive complex formation. The observed binding specificity of galectin-3 for galactosides rather than glucosides is discussed in light of our results.     

On the calculation of binding free energies using continuum methods: Application to MHC class I protein-peptide interactions

This paper describes a methodology to calculate the binding free energy (ΔG) of a protein-ligand complex using a continuum model of the solvent. A formal thermodynamic cycle is used to decompose the binding free energy into electrostatic and non-electrostatic contributions. In this cycle, the reactants are discharged in water, associated as purely nonpolar entities, and the final complex is then recharged. The total electrostatic free energies of the protein, the ligand, and the complex in water are calculated with the finite difference Poisson-Boltzmann (FDPB) method. The nonpolar (hydrophobic) binding free energy is calculated using a free energy-surface area relationship, with a single alkane/water surface tension coefficient (γ_aw). The loss in backbone and side-chain configurational entropy upon binding is estimated and added to the electrostatic and the nonpolar components of ΔG. The methodology is applied to the binding of the murine MHC class I protein H-2K^b with three distinct peptides, and to the human MHC class I protein HLA-A2 in complex with five different peptides. Despite significant differences in the amino acid sequences of the different peptides, the experimental binding free energy differences (ΔΔG_exp) are quite small (<0.3 and <2.7 kcal/mol for the H-2K^b and HLA-A2 complexes, respectively). For each protein, the calculations are successful in reproducing a fairly small range of values for ΔΔG_calc (<4.4 and <5.2 kcal/mol, respectively) although the relative peptide binding affinities of H-2K^b and HLA-A2 are not reproduced. For all protein-peptide complexes that were treated, it was found that electrostatic interactions oppose binding whereas nonpolar interactions drive complex formation. The two types of interactions appear to be correlated in that larger nonpolar contributions to binding are generally opposed by increased electrostatic contributions favoring dissociation. The factors that drive the binding of peptides to MHC proteins are discussed in light of our results.     

Protein chemistry at membrane interfaces: non-additivity of electrostatic and hydrophobic interactions

Non-specific binding of proteins and peptides to charged membrane interfaces depends upon the combined contributions of hydrophobic (DeltaG(HPhi)) and electrostatic (DeltaG(ES)) free energies. If these are simply additive, then the observed free energy of binding (DeltaG(obs)) will be given by DeltaG(obs)=DeltaG(HPhi)+DeltaG(ES), where DeltaG(HPhi)=-sigma(NP)A(NP) and DeltaG(ES)=zFphi. In these expressions, A(NP) is the non-polar accessible area, sigma(NP) the non-polar solvation parameter, z the formal peptide valence, F the Faraday constant, and phi the membrane surface potential. But several lines of evidence suggest that hydrophobic and electrostatic binding free energies of proteins at membrane interfaces, such as those associated with cell signaling, are not simply additive. In order to explore this issue systematically, we have determined the interfacial partitioning free energies of variants of indolicidin, a cationic proline-rich antimicrobial peptide. The synthesized variants of the 13 residue peptide covered a wide range of hydrophobic free energies, which allowed us to examine the effect of hydrophobicity on electrostatic binding to membranes formed from mixtures of neutral and anionic lipids. Although DeltaG(obs) was always a linear function of DeltaG(HPhi), the slope depended upon anionic lipid content: the slope was 1.0 for pure, zwitterionic phosphocholine bilayers and 0.3 for pure phosphoglycerol membranes. DeltaG(obs) also varied linearly with surface potential, but the slope was smaller than the expected value, zF. As observed by others, this suggests an effective peptide valence z(eff) that is smaller than the formal valence z. Because of our systematic approach, we were able to establish a useful rule-of-thumb: z(eff) is reduced relative to z by about 20 % for each 3 kcal mol(-1) (1 kcal=4.184 kJ) favorable increase in DeltaG(HPhi). For neutral phosphocholine interfaces, we found that DeltaG(obs) could be predicted with remarkable accuracy using the Wimley-White experiment-based interfacial hydrophobicity scale.     

Empirical calculation of the relative free energies of peptide binding to the molecular chaperone DnaK

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Binding free energy calculations of adenosine deaminase inhibitors

The interactions between four inhibitors and adenosine deaminase (ADA) were examined by calculating their binding free energies after molecular dynamics simulations. A bonded model was used to represent the electrostatic potentials of the zinc coordination site. The charge distribution of the model was derived by using a two-stage electrostatic potential fitting calculations. The calculated binding free energies are in good agreement with the experimental data and the ranking of binding affinities is well reproduced. Notably, our findings suggest that non-polar contributions play an important role for ADA-inhibitor interactions.     

RNA binding small molecules: studies on t-RNA binding by cytotoxic plant alkaloids berberine, palmatine and the comparison to ethidium

The interaction of two natural protoberberine plant alkaloids berberine and palmatine with t-RNA(phe) was studied using various biophysical techniques and the data was compared with the binding of the classical DNA intercalator, ethidium. The results of optical thermal melting, differential scanning calorimetry and circular dichroism characterized the native cloverleaf structure of t-RNA under the conditions of the study. The strong binding of the alkaloids and ethidium to t-RNA was revealed from the absorption and fluorescence studies. The salt dependence of the binding constants enabled the dissection of the binding free energy to electrostatic and non-electrostatic contributions. This analysis revealed a surprisingly large favourable component of the non-electrostatic contribution to the binding of these charged alkaloids and ethidium to t-RNA. Isothermal titration calorimetric studies revealed that the binding of both the alkaloids is driven by a moderately favourable enthalpy decrease and a moderately favourable entropy increase while that of ethidium is driven by a large favourable enthalpy decrease. Taken together, the results suggest that the binding of these alkaloid molecules on the t-RNA structure appears to be mostly by partial intercalation while ethidium intercalates to the t-RNA. These results reveal the molecular aspects on the interaction of these alkaloids to t-RNA.     

Trypsin specificity as elucidated by LIE calculations, X-ray structures, and association constant measurements

The variation in inhibitor specificity for five different amine inhibitors bound to CST, BT, and the cold-adapted AST has been studied by use of association constant measurements, structural analysis of high-resolution crystal structures, and the LIE method. Experimental data show that AST binds the 1BZA and 2BEA inhibitors 0.8 and 0.5 kcal/mole more strongly than BT. However, structural interactions and orientations of the inhibitors within the S1 site have been found to be virtually identical in the three enzymes studied. For example, the four water molecules in the inhibitor-free structures of AST and BT are channeled into similar positions in the S1 site, and the nitrogen atom(s) of the inhibitors are found in two cationic binding sites denoted Position1 and Position2. The hydrophobic binding contributions for all five inhibitors, estimated by the LIE calculations, are also in the same order (-2.1 +/- 0.2 kcal/mole) for all three enzymes. Our hypothesis is therefore that the observed variation in inhibitor binding arises from different electrostatic interactions originating from residues outside the S1 site. This is well illustrated by AST, in which Asp 150 and Glu 221B, despite some distance from the S1 binding site, lower the electrostatic potential of the S1 site and thus enhance substrate binding. Because the trends in the experimentally determined binding energies were reproduced by the LIE calculations after adding the contribution from long-range interactions, we find this method very suitable for rational studies of protein-substrate interactions.     

Relative free energy of binding between antimicrobial peptides and SDS or DPC micelles

We present relative binding free energy calculations for six antimicrobial peptide-micelle systems, three peptides interacting with two types of micelles. The peptides are the scorpion derived antimicrobial peptide (AMP), IsCT and two of its analogues. The micelles are dodecylphosphatidylcholine (DPC) and sodium dodecylsulphate (SDS) micelles. The interfacial electrostatic properties of DPC and SDS micelles are assumed to be similar to those of zwitterionic mammalian and anionic bacterial membrane interfaces, respectively. We test the hypothesis that the binding strength between peptides and the anionic micelle SDS can provide information on peptide antimicrobial activity, since it is widely accepted that AMPs function by binding to and disrupting the predominantly anionic lipid bilayer of the bacterial cytoplasmic membrane. We also test the hypothesis that the binding strength between peptides and the zwitterionic micelle DPC can provide information on peptide haemolytic activities, since it is accepted that they also bind to and disrupt the zwitterionic membrane of mammalian cells. Equilibrium structures of the peptides, micelles and peptide-micelle complexes are obtained from more than 300 ns of molecular dynamics simulations. A thermodynamic cycle is introduced to compute the binding free energy from electrostatic, non-electrostatic and entropic contributions. We find relative binding free energy strengths between peptides and SDS to correlate with the experimentally measured rankings for peptide antimicrobial activities, and relative free energy binding strengths between peptides and DPC to correlate with the observed rankings for peptide haemolytic toxicities. These findings point to the importance of peptide-membrane binding strength for antimicrobial activity and haemolytic activity.     

DNA binding and bending by HMG boxes: energetic determinants of specificity

To clarify the physical basis of DNA binding specificity, the thermodynamic properties and DNA binding and bending abilities of the DNA binding domains (DBDs) of sequence-specific (SS) and non-sequence-specific (NSS) HMG box proteins were studied with various DNA recognition sequences using micro-calorimetric and optical methods. Temperature-induced unfolding of the free DBDs showed that their structure does not represent a single cooperative unit but is subdivided into two (in the case of NSS DBDs) or three (in the case of SS DBDs) sub-domains, which differ in stability. Both types of HMG box, most particularly SS, are partially unfolded even at room temperature but association with DNA results in stabilization and cooperation of all the sub-domains. Binding and bending measurements using fluorescence spectroscopy over a range of ionic strengths, combined with calorimetric data, allowed separation of the electrostatic and non-electrostatic components of the Gibbs energies of DNA binding, yielding their enthalpic and entropic terms and an estimate of their contributions to DNA binding and bending. In all cases electrostatic interactions dominate non-electrostatic in the association of a DBD with DNA. The main difference between SS and NSS complexes is that SS are formed with an enthalpy close to zero and a negative heat capacity effect, while NSS are formed with a very positive enthalpy and a positive heat capacity effect. This indicates that formation of SS HMG box-DNA complexes is specified by extensive van der Waals contacts between apolar groups, i.e. a more tightly packed interface forms than in NSS complexes. The other principal difference is that DNA bending by the NSS DBDs is driven almost entirely by the electrostatic component of the binding energy, while DNA bending by SS DBDs is driven mainly by the non-electrostatic component. The basic extensions of both categories of HMG box play a similar role in DNA binding and bending, making solely electrostatic interactions with the DNA.     

Calculation of HyHel10-lysozyme binding free energy changes: Effect of ten point mutations

The change in free energy of binding of hen egg white lysozyme (HEL) to the antibody HyHel-10 arising from ten point mutations in HEL (D101K, D101G, K96M, K97D, K97G, K97G, R21E, R21K, W62Y, and W63Y) was calculated using a combination of the finite difference Poisson-Boltzmann method for the electrostatic contribution, a solvent accessible surface area term for the non-polar contribution, and rotamer counting for the sidechain entropy contribution. Comparison of experimental and calculated results indicate that because of pKa shifts in some of the mutated residues, primarily those involving Aspartate or Glutamate, proton uptake or release occurs in binding. When this effect was incorporated into the binding free energy calculations, the agreement with experiment improved significantly, and resulted in a mean error of about 1.9 kcal/mole. Thus these calculations predict that there should be a significant pH dependence to the change in binding caused by these mutations. The other major contributions to binding energy changes comes from solvation and charge charge interactions, which tend to oppose each other. Smaller contributions come from nonpolar interactions and sidechain entropy changes. The structures of the HyHel-10-HEL complexes with mutant HEL were obtained by modeling, and the effect of the modeled structure on the calculations was also examined. “Knowledge based” modeling and automatic generation of models using molecular mechanics produced comparable results. Proteins 33:39–48, 1998. © 1998 Wiley-Liss, Inc.     

Salt-dependent binding of iron(II) mixed-ligand complexes containing 1,10-phenanthroline and dipyrido[3,2-a:2',3'-c]phenazine to calf thymus DNA

The salt-dependent binding of racemic iron(II) mixed-ligand complex containing 1,10-phenanthroline (phen) and dipyrido[3,2-a:2',3'-c]phenazine (dppz), [Fe(phen)2(dppz)]2+ to calf thymus DNA (ct-DNA) has been characterized by UV-VIS spectrophotometric titration. The equilibrium binding constant (Kb) of the iron(II) complex to ct-DNA decreases with the salt concentration in the solution. The slope, SK=(deltalog Kb/deltalog [Na2+]) has been found to be 0.49, suggesting that, in addition to intercalation, considerable electrostatic interaction is also involved in the ct-DNA binding of [Fe(phen)2(dppz)]2+. The calculation of non-electrostatic binding constant (Kt(o)) based on polyelectrolyte theory has revealed that the non-electrostatic contribution to the total binding constant (Kb) increases significantly with the increase in [Na+] and reaches 36% at 0.1 M NaCl. On the other hand, the contribution of the non-electrostatic binding free energy (DeltaGt(o)) to the total binding free energy change (DeltaGo) is considerably large, i.e. 87% at [Na+]=0.1 M, suggesting that the stabilization of the DNA binding is mostly due to the contribution of non-electrostatic process. Moreover, the effect of specific ligand substitutions on DeltaGo has been rigorously evaluated using the quantity DeltaDeltaGt(o), i.e. the difference in DeltaGt(o) relative to that of the parent iron(II) complex, [Fe(phen)3]2+, indicating that each substitution of phen by dip and dppz contributes 7.5 and 17.5 kJ mol(-1), respectively to more favorable ct-DNA binding.     

Binding free energy of selected anticancer compounds to DNA--theoretical calculations

Many studies have elucidated structures and thermodynamics of complexes formed by different ligands with DNA. However, in most cases structural and free energy binding studies were not correlated with each other because of the problem of identifying which experimental free energy of binding corresponds to which experimental DNA-ligand structure. In the present work, Poisson-Boltzmann and solvent-accessible surface area methods were used to predict unknown modes of interaction between DNA and three different ligands: mitoxantrone and two pyrimidoacridine derivatives. In parallel, experimental measurements of binding free energy for the studied complexes were performed to compare experimental and calculated values. Our studies showed that the calculated values of free energy are only close to experimental data for some models of interaction between ligands and DNA. Based on this correlation, the most likely models of DNA-ligand complexes were postulated: (i) mitoxantrone and one derivative of pyrimidoacridine, both with two charged side chains, intercalate from the minor groove of DNA and bind with both chains in this groove; (ii) pyrimidoacridine, with only one side chain, very likely does not intercalate into DNA at all. Additionally, the non-electrostatic and electrostatic parts of the calculated binding free energy for the DNA-ligands studied are discussed.     

Probing the effect of point mutations at protein-protein interfaces with free energy calculations

We have studied the effect of point mutations of the primary binding residue (P1) at the protein-protein interface in complexes of chymotrypsin and elastase with the third domain of the turkey ovomucoid inhibitor and in trypsin with the bovine pancreatic trypsin inhibitor, using molecular dynamics simulations combined with the linear interaction energy (LIE) approach. A total of 56 mutants have been constructed and docked into their host proteins. The free energy of binding could be reliably calculated for 52 of these mutants that could unambiguously be fitted into the binding sites. We find that the predicted binding free energies are in very good agreement with experimental data with mean unsigned errors between 0.50 and 1.03 kcal/mol. It is also evident that the standard LIE model used to study small drug-like ligand binding to proteins is not suitable for protein-protein interactions. Three different LIE models were therefore tested for each of the series of protein-protein complexes included, and the best models for each system turn out to be very similar. The difference in parameterization between small drug-like compounds and protein point mutations is attributed to the preorganization of the binding surface. Our results clearly demonstrate the potential of free energy calculations for probing the effect of point mutations at protein-protein interfaces and for exploring the principles of specificity of hot spots at the interface.     

Free energy calculations show that acidic P1 variants undergo large pKa shifts upon binding to trypsin

Serine proteinases and their protein inhibitors belong to one of the most comprehensively studied models of protein-protein interactions. It is well established that the narrow trypsin specificity is caused by the presence of a negatively charged aspartate at the specificity pocket. X-ray crystallography as well as association measurements revealed, surprisingly, that BPTI with glutamatic acid as the primary binding (P1) residue was able to bind to trypsin. Previous free energy calculations showed that there was a substantially unfavorable binding free energy associated with accommodation of ionized P1 Glu at the S1-site of trypsin. In this study, the binding of P1 Glu to trypsin has been systematically investigated in terms of the protonation states of P1 Glu and Asp189, the orientation of Gln192, as well as the possible presence of counterions using the linear interaction energy (LIE) approach and the free energy perturbation (FEP) method. Twenty-four conceivable binding arrangements were evaluated and quantitative agreement with experiments is obtained when the P1 Glu binds in its protonated from. The results suggest that P1 Glu is one of the variants of BPTI that inhibit trypsin strongest at low pH, contrary to the specificity profile of trypsin, suggesting a new regulation mechanism of trypsin-like enzymes.     

Improving the iterative Linear Interaction Energy approach using automated recognition of configurational transitions

Recently an iterative method was proposed to enhance the accuracy and efficiency of ligand-protein binding affinity prediction through linear interaction energy (LIE) theory. For ligand binding to flexible Cytochrome P450s (CYPs), this method was shown to decrease the root-mean-square error and standard deviation of error prediction by combining interaction energies of simulations starting from different conformations. Thereby, different parts of protein-ligand conformational space are sampled in parallel simulations. The iterative LIE framework relies on the assumption that separate simulations explore different local parts of phase space, and do not show transitions to other parts of configurational space that are already covered in parallel simulations. In this work, a method is proposed to (automatically) detect such transitions during the simulations that are performed to construct LIE models and to predict binding affinities. Using noise-canceling techniques and splines to fit time series of the raw data for the interaction energies, transitions during simulation between different parts of phase space are identified. Boolean selection criteria are then applied to determine which parts of the interaction energy trajectories are to be used as input for the LIE calculations. Here we show that this filtering approach benefits the predictive quality of our previous CYP 2D6-aryloxypropanolamine LIE model. In addition, an analysis is performed of the gain in computational efficiency that can be obtained from monitoring simulations using the proposed filtering method and by prematurely terminating simulations accordingly.