Hamiltonian replica-exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

Design-rules for stapled peptides with in vivo activity and their application to Mdm2/X antagonists

Although stapled α-helical peptides can address challenging targets, their advancement is impeded by poor understandings for making them cell permeable while avoiding off-target toxicities. By synthesizing >350 molecules, we present workflows for identifying stapled peptides against Mdm2(X) with in vivo activity and no off-target effects. Key insights include a clear correlation between lipophilicity and permeability, removal of positive charge to avoid off-target toxicities, judicious anionic residue placement to enhance solubility/behavior, optimization of C-terminal length/helicity to enhance potency, and optimization of staple type/number to avoid polypharmacology. Workflow application gives peptides with >292x improved cell proliferation potencies and no off-target cell proliferation effects ( > 3800x on-target index). Application of these 'design rules' to a distinct Mdm2(X) peptide series improves ( > 150x) cellular potencies and removes off-target toxicities. The outlined workflow should facilitate therapeutic impacts, especially for those targets such as Mdm2(X) that have hydrophobic interfaces and are targetable with a helical motif.

Stitched peptides as potential cell permeable inhibitors of oncogenic DAXX protein

DAXX (Death Domain Associated Protein 6) is frequently upregulated in various common cancers, and its suppression has been linked to reduced tumor progression. Consequently, DAXX has gained significant interest as a therapeutic target in such cancers. DAXX is known to function in several critical biological pathways including chromatin remodelling, transcription regulation, and DNA repair. Leveraging structural information, we have designed and developed a novel set of stapled/stitched peptides that specifically target a surface on the N-terminal helical bundle domain of DAXX. This surface serves as the anchor point for binding to multiple interaction partners, such as Rassf1C, p53, Mdm2, and ATRX, as well as for the auto-regulation of the DAXX N-terminal SUMO interaction motif (SIM). Our experiments demonstrate that these peptides effectively bind to and inhibit DAXX with a higher affinity than the known interaction partners. Furthermore, these peptides release the auto-inhibited SIM, enabling it to interact with SUMO-1. Importantly, we have developed stitched peptides that can enter cells, maintaining their intracellular concentrations at nanomolar levels even after 24 hours, without causing any membrane perturbation. Collectively, our findings suggest that these stitched peptides not only serve as valuable tools for probing the molecular interactions of DAXX but also hold potential as precursors to the development of therapeutic interventions.

Efficient and accurate calculation of proline cis/trans isomerization free energies from Hamiltonian replica exchange molecular dynamics simulations

Proline cis/trans isomerization plays an important role in many biological processes but occurs on time scales not accessible to brute-force molecular dynamics (MD) simulations. We have designed a new Hamiltonian replica exchange scheme, ω-bias potential replica exchange molecular dynamics (ωBP-REMD), to efficiently and accurately calculate proline cis/trans isomerization free energies. ωBP-REMD is applied to various proline-containing tripeptides and a biologically important proline residue in the N2-domain of the gene-3-protein of phage fd in the wildtype and mutant variants of the protein. Excellent cis/trans transition rates are obtained. Reweighting of the sampled probability distribution along the peptide bond dihedral angle allows construction of the corresponding free-energy profile and calculation of the cis/trans isomerization free energy with high statistical precision. Very good agreement with experimental data is obtained. ωBP-REMD outperforms standard umbrella sampling in terms of convergence and agreement with experiment and strongly reduces perturbation of the local structure near the proline residue.

Chitosan Polysaccharides from a Polarizable Multiscale Approach

We report simulations of chitosan polysaccharides in the aqueous phase, at infinite dilute conditions and zero ionic strength. Those simulations are performed by means of a polarizable multiscale modeling scheme that relies on a polarizable all atom force field to model solutes and on a polarizable solvent coarse grained approach. Force field parameters are assigned only from quantum chemistry ab initio data. We simulate chitosan monomer units, dimers and 50-long chains. Regarding the 50-long chains we simulate three sets of ten randomly built chain replica at three different pH conditions (corresponding to different chain protonation states, the chain degree of deacetylation is 85%). Our simulations show the persistence length of 50-long chitosan chains at strong acidic conditions (pH <5) to be 24 ± 2 nm (at weak/negligible ionic strength conditions), and to be 1 order of magnitude shorter at usual pH conditions. Our simulation data support the most recent simulation and experimental studies devoted to chitosan polysaccharides in the aqueous phase.

Computational methods for exploring protein conformations

Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.

Influence of a Ser111-phosphorylation on Rab1b GTPase conformational dynamics studied by advanced sampling simulations

Rab GTPases constitute the largest branch of the Ras protein superfamily that regulate intra-cellular membrane trafficking. Their signaling activity is mediated by the transition between an active GTP-bound state and an inactive GDP-bound state. In the inactive state the switch I and II segments adopt largely disordered flexible conformations, whereas in the active state these regions are in well-defined conformations. The switch I and II states are central for recognition of Rab GTPases by interacting partners. Phosphorylation of the Rab1b-GTPase at residue Ser111 (pS111) results in modulation of the signaling activity due to alterations of the protein interaction interface and also due to modulation of the conformational flexibility. We have studied the flexibility of native and pS111-Rab1b in complex with GTP or GDP using extensive Molecular Dynamics (MD) simulations and an advanced sampling method called DIhedral Angle-biasing potential Replica-Exchange Molecular dynamics (DIA-REMD). The DIA-REMD method promotes backbone and side chain dihedral transitions along a series of replica simulations in selected protein segments and through exchanges also improves sampling in an unbiased reference simulation. Application to the Rab1b system results in significantly enhanced sampling of different switch I/II conformational states in the GDP-bound Rab1b state. The pS111 modification is found to reduce the conformational flexibility even in the presence of GDP, which may influence signaling activities. The stabilizing effect can be attributed to the formation of additional surface salt bridges between Arg-residues and pS111 not present in the native structure. The DIA-REMD method could be a valuable approach for studying also other signaling proteins that contain flexible segments.

DESP: Deep Enhanced Sampling of Proteins' Conformation Spaces Using AI-Inspired Biasing Forces

The molecular structures (i.e., conformation spaces, CS) of bio-macromolecules and the dynamics that molecules exhibit are crucial to the understanding of the basis of many diseases and in the continuous attempts to retarget known drugs/medications, improve the efficacy of existing drugs, or develop novel drugs. These make a better understanding and the exploration of the CS of molecules a research hotspot. While it is generally easy to computationally explore the CS of small molecules (such as peptides and ligands), the exploration of the CS of a larger biomolecule beyond the local energy well and beyond the initial equilibrium structure of the molecule is generally nontrivial and can often be computationally prohibitive for molecules of considerable size. Therefore, research efforts in this area focus on the development of ways that systematically favor the sampling of new conformations while penalizing the resampling of previously sampled conformations. In this work, we present Deep Enhanced Sampling of Proteins’ Conformation Spaces Using AI-Inspired Biasing Forces (DESP), a technique for enhanced sampling that combines molecular dynamics (MD) simulations and deep neural networks (DNNs), in which biasing potentials for guiding the MD simulations are derived from the KL divergence between the DNN-learned latent space vectors of [a] the most recently sampled conformation and those of [b] the previously sampled conformations. Overall, DESP efficiently samples wide CS and outperforms conventional MD simulations as well as accelerated MD simulations. We acknowledge that this is an actively evolving research area, and we continue to further develop the techniques presented here and their derivatives tailored at achieving DNN-enhanced steered MD simulations and DNN-enhanced targeted MD simulations.

Evaluation of replica exchange with repulsive scaling approach for docking glycosaminoglycans

Glycosaminoglycans (GAGs), long linear periodic anionic polysaccharides, are key molecules in the extracellular matrix (ECM). Therefore, deciphering their role in the biologically relevant context is important for fundamental understanding of the processes ongoing in ECM and for establishing new strategies in the regenerative medicine. Although GAGs represent a number of computational challenges, molecular docking is a powerful tool for analysis of their interactions. Despite the recent development of GAG-specific docking approaches, there is plenty of room for improvement. Here, replica exchange molecular dynamics with repulsive scaling (REMD-RS) recently proved to be a successful approach for protein-protein complexes, was applied to dock GAGs. In this method, effective pairwise radii are increased in different Hamiltonian replicas. REMD-RS is shown to be an attractive alternative to classical docking approaches for GAGs. This work contributes to setting up of GAG-specific computational protocols and provides new insights into the nature of these biological systems.

Macrocyclization of an all-d linear α-helical peptide imparts cellular permeability

Peptide-based molecules hold great potential as targeted inhibitors of intracellular protein-protein interactions (PPIs). Indeed, the vast diversity of chemical space conferred through their primary, secondary and tertiary structures allows these molecules to be applied to targets that are typically deemed intractable via small molecules. However, the development of peptide therapeutics has been hindered by their limited conformational stability, proteolytic sensitivity and cell permeability. Several contemporary peptide design strategies are aimed at addressing these issues. Strategic macrocyclization through optimally placed chemical braces such as olefinic hydrocarbon crosslinks, commonly referred to as staples, may improve peptide properties by (i) restricting conformational freedom to improve target affinities, (ii) improving proteolytic resistance, and (iii) enhancing cell permeability. As a second strategy, molecules constructed entirely from d-amino acids are hyper-resistant to proteolytic cleavage, but generally lack conformational stability and membrane permeability. Since neither approach is a complete solution, we have combined these strategies to identify the first examples of all-d α-helical stapled and stitched peptides. As a template, we used a recently reported all d-linear peptide that is a potent inhibitor of the p53-Mdm2 interaction, but is devoid of cellular activity. To design both stapled and stitched all-d-peptide analogues, we used computational modelling to predict optimal staple placement. The resultant novel macrocyclic all d-peptide was determined to exhibit increased α-helicity, improved target binding, complete proteolytic stability and, most notably, cellular activity.

Influence of Calcium Binding on Conformations and Motions of Anionic Polyamino Acids. Effect of Side Chain Length

Investigation of the effect of CaCl2 salt on conformations of two anionic poly(amino acids) with different side chain lengths, poly-(α-l glutamic acid) (PGA) and poly-(α-l aspartic acid) (PASA), was performed by atomistic molecular dynamics (MD) simulations. The simulations were performed using both unbiased MD and the Hamiltonian replica exchange (HRE) method. The results show that at low CaCl2 concentration adsorption of Ca2+ ions lead to a significant chain size reduction for both PGA and PASA. With the increase in concentration, the chains sizes partially recover due to electrostatic repulsion between the adsorbed Ca2+ ions. Here, the side chain length becomes important. Due to the longer side chain and its ability to distance the charged groups with adsorbed ions from both each other and the backbone, PGA remains longer in the collapsed state as the CaCl2 concentration is increased. The analysis of the distribution of the mineral ions suggests that both poly(amino acids) should induce the formation of mineral with the same structure of the crystal cell.

pH-Induced Changes in Polypeptide Conformation: Force-Field Comparison with Experimental Validation

Microsecond-long all-atom molecular dynamics (MD) simulations, circular dichroism, laser Doppler velocimetry, and dynamic light-scattering techniques have been used to investigate pH-induced changes in the secondary structure, charge, and conformation of poly l-lysine (PLL) and poly l-glutamic acid (PGA). The employed combination of the experimental methods reveals for both PLL and PGA a narrow pH range at which they are charged enough to form stable colloidal suspensions, maintaining their α-helix content above 60%; an elevated charge state of the peptides required for colloidal stability promotes the peptide solvation as a random coil. To obtain a more microscopic view on the conformations and to verify the modeling performance, peptide secondary structure and conformations rising in MD simulations are also examined using three different force fields, i.e., OPLS-AA, CHARMM27, and AMBER99SB*-ILDNP. Ramachandran plots reveal that in the examined setup the α-helix content is systematically overestimated in CHARMM27, while OPLS-AA overestimates the β-sheet fraction at lower ionization degrees. At high ionization degrees, the OPLS-AA force-field-predicted secondary structure fractions match the experimentally measured distribution most closely. However, the pH-induced changes in PLL and PGA secondary structure are reasonably captured only by the AMBER99SB*-ILDNP force field, with the exception of the fully charged PGA in which the α-helix content is overestimated. The comparison to simulations results shows that the examined force fields involve significant deviations in their predictions for charged homopolypeptides. The detailed mapping of secondary structure dependency on pH for the polypeptides, especially finding the stable colloidal α-helical regime for both examined peptides, has significant potential for practical applications of the charged homopolypeptides. The findings raise attention especially to the pH fine tuning as an underappreciated control factor in surface modification and self-assembly.

Amyloid Evolution: Antiparallel Replaced by Parallel

Several atomic structures have now been found for micrometer-scale amyloid fibrils or elongated microcrystals using a range of methods, including NMR, electron microscopy, and X-ray crystallography, with parallel β-sheet appearing as the most common secondary structure. The etiology of amyloid disease, however, indicates nanometer-scale assemblies of only tens of peptides as significant agents of cytotoxicity and contagion. By combining solution X-ray with molecular dynamics, we show that antiparallel structure dominates at the first stages of aggregation for a specific set of peptides, being replaced by parallel at large length scales only. This divergence in structure between small and large amyloid aggregates should inform future design of molecular therapeutics against nucleation or intercellular transmission of amyloid. Calculations and an overview from the literature argue that antiparallel order should be the first appearance of structure in many or most amyloid aggregation processes, regardless of the endpoint. Exceptions to this finding should exist, depending inevitably on the sequence and on solution conditions.

The Dual Interactions of p53 with MDM2 and p300: Implications for the Design of MDM2 Inhibitors

Proteins that limit the activity of the tumour suppressor protein p53 are increasingly being targeted for inhibition in a variety of cancers. In addition to the development of small molecules, there has been interest in developing constrained (stapled) peptide inhibitors. A stapled peptide ALRN_6924 that activates p53 by preventing its interaction with its negative regulator Mdm2 has entered clinical trials. This stapled peptide mimics the interaction of p53 with Mdm2. The chances that this peptide could bind to other proteins that may also interact with the Mdm2-binding region of p53 are high; one such protein is the CREB binding protein (CBP)/p300. It has been established that phosphorylated p53 is released from Mdm2 and binds to p300, orchestrating the transcriptional program. We investigate whether molecules such as ALRN_6924 would bind to p300 and, to do so, we used molecular simulations to explore the binding of ATSP_7041, which is an analogue of ALRN_6924. Our study shows that ATSP_7041 preferentially binds to Mdm2 over p300; however, upon phosphorylation, it appears to have a higher affinity for p300. This could result in attenuation of the amount of free p300 available for interacting with p53, and hence reduce its transcriptional efficacy. Our study highlights the importance of assessing off-target effects of peptide inhibitors, particularly guided by the understanding of the networks of protein-protein interactions (PPIs) that are being targeted.

Incorporation of Putative Helix-Breaking Amino Acids in the Design of Novel Stapled Peptides: Exploring Biophysical and Cellular Permeability Properties

Stapled α-helical peptides represent an emerging superclass of macrocyclic molecules with drug-like properties, including high-affinity target binding, protease resistance, and membrane permeability. As a model system for probing the chemical space available for optimizing these properties, we focused on dual Mdm2/MdmX antagonist stapled peptides related to the p53 N-terminus. Specifically, we first generated a library of ATSP-7041 (Chang et al., 2013) analogs iteratively modified by L-Ala and D-amino acids. Single L-Ala substitutions beyond the Mdm2/(X) binding interfacial residues (i.e., Phe3, Trp7, and Cba10) had minimal effects on target binding, α-helical content, and cellular activity. Similar binding affinities and cellular activities were noted at non-interfacial positions when the template residues were substituted with their d-amino acid counterparts, despite the fact that d-amino acid residues typically 'break' right-handed α-helices. d-amino acid substitutions at the interfacial residues Phe3 and Cba10 resulted in the expected decreases in binding affinity and cellular activity. Surprisingly, substitution at the remaining interfacial position with its d-amino acid equivalent (i.e., Trp7 to d-Trp7) was fully tolerated, both in terms of its binding affinity and cellular activity. An X-ray structure of the d-Trp7-modified peptide was determined and revealed that the indole side chain was able to interact optimally with its Mdm2 binding site by a slight global re-orientation of the stapled peptide. To further investigate the comparative effects of d-amino acid substitutions we used linear analogs of ATSP-7041, where we replaced the stapling amino acids by Aib (i.e., R84 to Aib4 and S511 to Aib11) to retain the helix-inducing properties of α-methylation. The resultant analog sequence Ac-Leu-Thr-Phe-Aib-Glu-Tyr-Trp-Gln-Leu-Cba-Aib-Ser-Ala-Ala-NH2 exhibited high-affinity target binding (Mdm2 Kd = 43 nM) and significant α-helicity in circular dichroism studies. Relative to this linear ATSP-7041 analog, several d-amino acid substitutions at Mdm2(X) non-binding residues (e.g., d-Glu5, d-Gln8, and d-Leu9) demonstrated decreased binding and α-helicity. Importantly, circular dichroism (CD) spectroscopy showed that although helicity was indeed disrupted by d-amino acids in linear versions of our template sequence, stapled molecules tolerated these residues well. Further studies on stapled peptides incorporating N-methylated amino acids, l-Pro, or Gly substitutions showed that despite some positional dependence, these helix-breaking residues were also generally tolerated in terms of secondary structure, binding affinity, and cellular activity. Overall, macrocyclization by hydrocarbon stapling appears to overcome the destabilization of α-helicity by helix breaking residues and, in the specific case of d-Trp7-modification, a highly potent ATSP-7041 analog (Mdm2 Kd = 30 nM; cellular EC50 = 600 nM) was identified. Our findings provide incentive for future studies to expand the chemical diversity of macrocyclic α-helical peptides (e.g., d-amino acid modifications) to explore their biophysical properties and cellular permeability. Indeed, using the library of 50 peptides generated in this study, a good correlation between cellular permeability and lipophilicity was observed.

Hamiltonian replica exchange simulations of glucose oxidase adsorption on charged surfaces

Hamiltonian replica exchange Monte Carlo simulations efficiently identify the lowest-energy orientations of proteins on charged surfaces at variable ionic strengths.

Using the multi-objective optimization replica exchange Monte Carlo enhanced sampling method for protein-small molecule docking

Background

In this study, we extended the replica exchange Monte Carlo (REMC) sampling method to protein–small molecule docking conformational prediction using RosettaLigand. In contrast to the traditional Monte Carlo (MC) and REMC sampling methods, these methods use multi-objective optimization Pareto front information to facilitate the selection of replicas for exchange.

Results

The Pareto front information generated to select lower energy conformations as representative conformation structure replicas can facilitate the convergence of the available conformational space, including available near-native structures. Furthermore, our approach directly provides min-min scenario Pareto optimal solutions, as well as a hybrid of the min-min and max-min scenario Pareto optimal solutions with lower energy conformations for use as structure templates in the REMC sampling method. These methods were validated based on a thorough analysis of a benchmark data set containing 16 benchmark test cases. An in-depth comparison between MC, REMC, multi-objective optimization-REMC (MO-REMC), and hybrid MO-REMC (HMO-REMC) sampling methods was performed to illustrate the differences between the four conformational search strategies.

Conclusions

Our findings demonstrate that the MO-REMC and HMO-REMC conformational sampling methods are powerful approaches for obtaining protein–small molecule docking conformational predictions based on the binding energy of complexes in RosettaLigand.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Folding Atomistic Proteins in Explicit Solvent Using Simulated Tempering

Following a previous report on a coarse-grained protein model in implicit solvent, we applied simulated tempering (ST) with on-the-fly Helmholtz free energy (weight factors) determination to the folding or aggregation of seven proteins with the CHARMM, OPLS, and AMBER protein, and the SPC and TIP3P water force fields. For efficiency and reliability, we also performed replica exchange molecular dynamics (REMD) simulations on the alanine di- and deca-peptide, and the dimer of the Aβ16-22 Alzheimer's fragment, and used experimental data and previous simulation results on the chignolin, beta3s, Trp-cage, and WW domain peptides of 10-37 amino acids. The sampling with ST is found to be more efficient than with REMD for a much lower CPU cost. Starting from unfolded or extended conformations, the WW domain and the Trp-cage peptide fold to their NMR structures with a backbone RMSD of 2.0 and 1 Å. Remarkably, the ST simulation explores transient non-native topologies for Trp-cage that have been rarely discussed by other simulations. Our ST simulations also show that the CHARMM22* force field has limitations in describing accurately the beta3s peptide. Taken together, these results open the door to the study of the configurations of single proteins, protein aggregates, and any molecular systems at atomic details in explicit solvent using a single normal CPU. They also demonstrate that our ST scheme can be used with any force field ranging from quantum mechanics to coarse-grain and atomistic.

Enhancing constant-pH simulation in explicit solvent with a two-dimensional replica exchange method

We present a new method for enhanced sampling for constant-pH simulations in explicit water based on a two-dimensional (2D) replica exchange scheme. The new method is a significant extension of our previously developed constant-pH simulation method, which is based on enveloping distribution sampling (EDS) coupled with a one-dimensional (1D) Hamiltonian exchange method (HREM). EDS constructs a hybrid Hamiltonian from multiple discrete end state Hamiltonians that, in this case, represent different protonation states of the system. The ruggedness and heights of the hybrid Hamiltonian's energy barriers can be tuned by the smoothness parameter. Within the context of the 1D EDS-HREM method, exchanges are performed between replicas with different smoothness parameters, allowing frequent protonation-state transitions and sampling of conformations that are favored by the end-state Hamiltonians. In this work, the 1D method is extended to 2D with an additional dimension, external pH. Within the context of the 2D method (2D EDS-HREM), exchanges are performed on a lattice of Hamiltonians with different pH conditions and smoothness parameters. We demonstrate that both the 1D and 2D methods exactly reproduce the thermodynamic properties of the semigrand canonical (SGC) ensemble of a system at a given pH. We have tested our new 2D method on aspartic acid, glutamic acid, lysine, a four residue peptide (sequence KAAE), and snake cardiotoxin. In all cases, the 2D method converges faster and without loss of precision; the only limitation is a loss of flexibility in how CPU time is employed. The results for snake cardiotoxin demonstrate that the 2D method enhances protonation-state transitions, samples a wider conformational space with the same amount of computational resources, and converges significantly faster overall than the original 1D method.

Evaluation of enhanced sampling provided by accelerated molecular dynamics with Hamiltonian replica exchange methods

Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency.