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Titus S. van Erp

Publications and source records attributed to Titus S. van Erp.

At least 19 recordsLinked to original sources
arXiv2026

Multi-Resolution Wire-Fencing for Efficient Path Sampling

Path sampling methods enable the computation of thermodynamic and kinetic properties through Monte Carlo (MC) moves that generate trajectories from short forward and backward molecular dynamics (MD) segments. Recently, the wire-fencing move was developed to achieve near-unity acceptance while also rapidly decorrelating successive paths, two properties that are usually in conflict in conventional MC schemes. However, in large systems, such as biomolecular simulations, the frame-saving frequency is often kept low to reduce storage requirements. Likewise, when evaluating the order parameter is expensive, frames are saved less frequently to reduce the associated cost. In either situation, this can severely limit the number of available shooting points, in extreme situations leaving only a single point, typically the one with the highest order parameter value, accessible for shooting. Repeated shootings may then originate from the same configuration, reducing sampling efficiency. Here, we introduce a multi-resolution variant of the wire-fencing move in which selected subtrajectories are propagated at higher temporal resolution than the stored trajectories. This refinement affects only the MC move and does not alter the structure or storage of the generated paths, but enhances the diffusion of shooting points along the trajectory and thereby improves sampling efficiency. The approach is demonstrated on two model systems and a realistic protein--ligand unbinding process, with the latter showing an estimated efficiency improvement of more than an order of magnitude.

cond-mat.stat-mech↗
arXiv2026

Anisotropic Defect Diffusion in Layered CsPbBr$_\mathrm{x}$I$_\mathrm{3-x}$ Perovskites

Mixed-halide perovskites offer a route to enhance phase stability and modify optoelectronic properties. Here, we use large-scale molecular dynamics simulations with a reactive force field to investigate defects in CsPbBr$_\mathrm{x}$I$_\mathrm{3-x}$ perovskites, focusing on how defect mobility can be controlled and the stability of the material improved by layered ordering of Br and I anions. Our results show that layered halide ordering induces strongly anisotropic defect diffusion: migration proceeds readily along the layers, whereas diffusion across them is strongly suppressed. For Cs defects, this anisotropy originates from directional lattice strain and the associated octahedral tilting, whereas halide migration is governed by an interplay between strain and preferential local halide bonding configurations.

cond-mat.mtrl-sci↗
arXiv2026

Is the Eyring Plot Misleading? A Case for Arrhenius Analysis of Activation Parameters

A common view in physical chemistry literature is that the Eyring representation, in which a linear fit of $\ln(k/T)$ versus $1/T$ is attempted, is more fundamental than the Arrhenius representation, $\ln(k)$ versus $1/T$. This perception is typically motivated by its derivation from statistical mechanics and quantum mechanics, and by the interpretation of the intercept in terms of the activation entropy $ΔS^\ddagger$, whereas the Arrhenius equation and its prefactor are often regarded as purely phenomenological. However, harmonic approximation models yield exact linearity in Arrhenius plots but not in Eyring plots, although for real experimental data both generally appear equally linear within typical experimental accuracy. Furthermore, the impression that the Eyring formulation is inherently quantum mechanical arises from the presence of the Planck constant in the prefactor, whereas this term results from normalization conventions in the partition function. This also highlights an interpretational issue in $ΔG^\ddagger$, which is based on partition functions of different dimensionality between reactant and transition state. This dimensional mismatch can be reformulated in an alternative representation that improves interpretability and reduces to an Arrhenius-type expression in which the prefactor is directly related to an entropy of activation. In this framework, both activation enthalpy and entropy obtained from an Arrhenius fit are arguably more physically relevant than the corresponding Eyring fit values.

cond-mat.stat-mech↗
arXiv2026

Generalized Path Reweighting and History-Dependent Free Energies

Transition interface sampling (TIS) and replica exchange TIS (RETIS) are powerful methods for computing rates of rare events inaccessible to straightforward molecular dynamics (MD) simulations. Path reweighting extends their output, enabling the evaluation of diverse thermodynamic and kinetic quantities, including reaction prediction metrics, activation barriers, committor functions, and free energies. The recently developed Infinity-RETIS algorithm boosts parallel efficiency through asynchronous replica exchanges in the infinite-swap limit, eliminating the wall-time bottlenecks of conventional RETIS. This approach introduces fractional samples and biased sampling distributions, requiring a generalized path reweighting framework, for which we derive expressions demonstrating how exact dynamic and thermodynamic variables can be computed. We then focus on a special class of free energy surfaces defined by history-dependent conditions, whose values are influenced by kinetic factors such as particle mass and friction, unlike standard unconditional free energy surfaces. Even with suboptimal reaction coordinates, these conditional free energies can reveal kinetically relevant barriers that may be misrepresented by standard unconditional free energies, thereby providing a rigorous and versatile tool for characterizing complex molecular transitions.

physics.chem-ph↗
arXiv2025

Path sampling challenges in large biomolecular systems: RETIS and REPPTIS for ABL-imatinib kinetics

Predicting the kinetics of drug-protein interactions is crucial for understanding drug efficacy, particularly in personalized medicine, where protein mutations can significantly alter drug residence times. This study applies Replica Exchange Transition Interface Sampling (RETIS) and its Partial Path variant (REPPTIS) to investigate the dissociation kinetics of imatinib from Abelson nonreceptor tyrosine kinase (ABL) and mutants relevant to chronic myeloid leukemia therapy. These path-sampling methods offer a bias-free alternative to conventional approaches requiring qualitative predefined reaction coordinates. Nevertheless, the complex free-energy landscape of ABL-imatinib dissociation presents significant challenges. Multiple metastable states and orthogonal barriers lead to parallel unbinding pathways, complicating convergence in TIS-based methods. Despite employing computational efficiency strategies such as asynchronous replica exchange, full convergence remained elusive. This work provides a critical assessment of path sampling in high-dimensional biological systems, discussing the need for enhanced initialization strategies, advanced Monte Carlo path generation moves, and machine learning-derived reaction coordinates to improve kinetic predictions of drug dissociation with minimal prior knowledge.

physics.bio-ph↗
arXiv2022

Enhanced path sampling using subtrajectory Monte Carlo moves

Path sampling allows the study of rare events like chemical reactions, nucleation and protein folding via a Monte Carlo (MC) exploration in path space. Instead of configuration points, this method samples short molecular dynamics (MD) trajectories with specific start- and end-conditions. As in configuration MC, its efficiency highly depends on the types of MC moves. Since the last two decades, the central MC move for path sampling has been the so-called shooting move in which a perturbed phase point of the old path is propagated backward and forward in time to generate a new path. Recently, we proposed the subtrajectory moves, stone-skipping (SS) and web-throwing (WT), that are demonstrably more efficient. However, the one-step crossing requirement makes them somewhat more difficult to implement in combination with external MD programs or when the order parameter determination is expensive. In this article, we present strategies to address the issue. The most generic solution is a new member of subtrajectory moves, wire fencing (WF), that is less thrifty than the SS, but more versatile. This makes it easier to link path sampling codes with external MD packages and provides a practical solution for cases where the calculation of the order parameter is expensive or not a simple function of geometry. We demonstrate the WF move in a double well Langevin model, a thin film breaking transition based on classical force fields, and a smaller ruthenium redox reaction at the ab initio level in which the order parameter explicitly depends on the electron density.

physics.chem-ph↗
arXiv2022

Exchanging replicas with unequal cost, infinitely and permanently

We developed a replica exchange method that is effectively parallelizable even if the computational cost of the Monte Carlo moves in the parallel replicas are considerably different, for instance, because the replicas run on different type of processor units or because of the algorithmic complexity. To prove detailed-balance, we make a paradigm shift from the common conceptual viewpoint in which the set of parallel replicas represents a high-dimensional superstate, to an ensemble based criterion in which the other ensembles represent an environment that might or might not participate in the Monte Carlo move. In addition, based on a recent algorithm for computing permanents, we effectively increase the exchange rate to infinite without the steep factorial scaling as function of the number of replicas. We illustrate the effectiveness of the replica exchange methodology by combining it with a quantitative path sampling method, replica exchange transition interface sampling (RETIS), in which the costs for a Monte Carlo move can vary enormously as paths in a RETIS algorithm do not have the same length and the average path lengths tend to vary considerably for the different path ensembles that run in parallel. This combination, coined $\infty$RETIS, was tested on three model systems.

physics.comp-ph↗
arXiv2012

The dynamics of the DNA denaturation transition

The dynamics of the DNA denaturation is studied using the Peyrard-Bishop-Dauxois model. The denaturation rate of double stranded polymers decreases exponentially as function of length below the denaturation temperature. Above Tc, the rate shows a minimum, but then increases as function of length. We also examine the influence of sequence and solvent friction. Molecules having the same number of weak and strong base-pairs can have significantly different opening rates depending on the order of base-pairs.

physics.bio-ph↗
arXiv2011

Dynamical Rare event simulation techniques for equilibrium and non-equilibrium systems

I give an overview of rare event simulation techniques to generate dynamical pathways across high free energy barriers. The methods on which I will concentrate are the reactive flux approach, transition path sampling, (replica-exchange) transition interface sampling, partial path sampling/milestoning, and forward flux sampling. These methods have in common that they aim to simulate true molecular dynamics trajectories at a much faster rate than naive brute force molecular dynamics. The advantages and disadvantages of these methods are discussed and compared for a simple one-dimensional test system. These numerical results reveal some important pitfalls of the present non-equilibrium methods that have no easy solution and show that caution is necessary when interpreting their results.

cond-mat.stat-mech↗
arXiv2010

Kinetics of intermediate-mediated self-assembly in nano-sized materials: a generic model

We propose in this paper a generic model of a non-standard aggregation mechanism for self-assembly processes of a class of materials involving the mediation of intermediates consisting of a polydisperse population of nano-sized particles. The model accounts for a long induction period in the process. The proposed mechanism also gives insight on future experiments aiming at a more comprehensive picture of the role of self-organization in self-assembly processes.

cond-mat.mes-hall↗
arXiv2007

Efficient path sampling on multiple reaction channels

Due to the time scale problem, rare events are not accessible by straight forward molecular dynamics. The presence of multiple reaction channels complicates the problem even further. The feasibility of the standard free energy based methods relies strongly on the success in finding a proper reaction coordinate. This can be very difficult task in high-dimensional complex systems and even more if several distinct reaction channels exist. Moreover, even if a proper reaction coordinate can be found, ergodic sampling will be a challenge. In this article, we discuss the recent advancements of path sampling methods to tackle this problem. We argue why the path sampling methods, via the transition interface sampling technique, is less sensitive to the choice of reaction coordinate. Moreover, we review a new algorithm, parallel path swapping, that can dramatically improve the ergodic sampling of trajectories for the multiple reaction channel systems.

cond-mat.stat-mech↗
arXiv2007

Reaction rate calculation by parallel path swapping

The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we have devised a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We have tested the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor 20.

cond-mat.stat-mech↗
arXiv2007

Prospects of Transition Interface Sampling simulations for the theoretical study of zeolite synthesis

The transition interface sampling (TIS) technique allows to overcome large free energy barriers within reasonable simulation time, which is impossible for straightforward molecular dynamics. Still, the method does not impose an artificial driving force, but it surmounts the timescale problem by an importance sampling of true dynamical pathways. Recently, it was shown that the efficiency of TIS to calculate reaction rates is less sensitive to the choice of reaction coordinate than those of the standard free energy based techniques. This could be an important advantage in complex systems for which a good reaction coordinate is usually very difficult to find. We explain the principles of this method and discuss some of the promising applications related to zeolite formation.

cond-mat.stat-mech↗
arXiv2006

Bubbles and denaturation in DNA

The local opening of DNA is an intriguing phenomenon from a statistical physics point of view, but is also essential for its biological function. For instance, the transcription and replication of our genetic code can not take place without the unwinding of the DNA double helix. Although these biological processes are driven by proteins, there might well be a relation between these biological openings and the spontaneous bubble formation due to thermal fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois model, have fairly accurately reproduced some experimental denaturation curves and the sharp phase transition in the thermodynamic limit. It is, hence, tempting to see whether these models could be used to predict the biological activity of DNA. In a previous study, we introduced a method that allows to obtain very accurate results on this subject, which showed that some previous claims in this direction, based on molecular dynamics studies, were premature. This could either imply that the present PBD should be improved or that biological activity can only be predicted in a more complex frame work that involves interactions with proteins and super helical stresses. In this article, we give detailed description of the statistical method introduced before. Moreover, for several DNA sequences, we give a thorough analysis of the bubble-statistics as function of position and bubble size and the so-called $l$-denaturation curves that can be measured experimentally. These show that some important experimental observations are missing in the present model. We discuss how the present model could be improved.

physics.bio-ph↗
arXiv2006

Efficiency analysis of reaction rate calculation methods using analytical models I: The 2D sharp barrier

We analyze the efficiency of different methods for the calculation of reaction rates in the case of two simple analytical benchmark systems. Two classes of methods are considered: the first are based on the free energy calculation along a reaction coordinate and the calculation of the transmission coefficient, the second on the sampling of dynamical pathways. We give scaling rules for how this efficiency depends on barrier height and width, and we hand out simple optimization rules for the method-specific parameters. We show that the path sampling methods, using the transition interface sampling technique, become exceedingly more efficient than the others when the reaction coordinate is not the optimal one.

cond-mat.stat-mech↗
arXiv2005

Can one predict DNA Transcription Start Sites by studying bubbles?

It has been speculated that bubble formation of several base-pairs due to thermal fluctuations is indicatory for biological active sites. Recent evidence, based on experiments and molecular dynamics (MD) simulations using the Peyrard-Bishop-Dauxois model, seems to point in this direction. However, sufficiently large bubbles appear only seldom which makes an accurate calculation difficult even for minimal models. In this letter, we introduce a new method that is orders of magnitude faster than MD. Using this method we show that the present evidence is unsubstantiated.

physics.bio-ph↗
arXiv2004

Breakdown of Lindstedt Expansion for Chaotic Maps

In a previous paper of one of us [Europhys. Lett. 59 (2002), 330--336] the validity of Greene's method for determining the critical constant of the standard map (SM) was questioned on the basis of some numerical findings. Here we come back to that analysis and we provide an interpretation of the numerical results by showing that no contradiction is found with respect to Greene's method. We show that the previous results based on the expansion in Lindstedt series do correspond to the transition value but for a different map: the semi-standard map (SSM). Moreover, we study the expansion obtained from the SM and SSM by suppressing the small divisors. The first case turns out to be related to Kepler's equation after a proper transformation of variables. In both cases we give an analytical solution for the radius of convergence, that represents the singularity in the complex plane closest to the origin. Also here, the radius of convergence of the SM's analogue turns out to be lower than the one of the SSM. However, despite the absence of small denominators these two radii are lower than the ones of the true maps for golden mean winding numbers. Finally, the analyticity domain and, in particular, the critical constant for the two maps without small divisors are studied analytically and numerically. The analyticity domain appears to be an perfect circle for the SSM analogue, while it is stretched along the real axis for the SM analogue yielding a critical constant that is larger than its radius of convergence.

cond-mat.other↗