Multidimensional Energy Landscape Research Articles

Machine Learning Derived Collective Variables for the Study of Protein Homodimerization in Membrane.

The accurate calculation of equilibrium constants for protein-protein association is of fundamental importance to quantitative biology and remains an outstanding challenge for computational biophysics. Traditionally, equilibrium constants have been computed from one-dimensional free energy surfaces derived from sampling along a single collective variable. Importantly, recent advances in enhanced sampling methodology have facilitated the characterization of multidimensional free energy landscapes, often exposing multiple thermodynamically important minima missed by more restrictive sampling methods. A key to the effectiveness of this multidimensional sampling approach is the identification of collective variables that effectively define the configurational space of dissociated and associated states. Here we present the application of two machine learning methods for the unbiased determination of collective variables for enhanced sampling and analysis of protein-protein association. Our results both validate prior work, based on intuition derived collective variables, and demonstrate the effectiveness of the machine learning methods for the identification of collective variables for association reactions in complex biomolecular systems.

Effective data-driven collective variables for free energy calculations from metadynamics of paths.

A variety of enhanced sampling (ES) methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is crucially dependent on the ability of the chosen CVs to capture the relevant slow degrees of freedom of the system. For complex processes, finding such CVs is the real challenge. Machine learning (ML) CVs offer, in principle, a solution to handle this problem. However, these methods rely on the availability of high-quality datasets-ideally incorporating information about physical pathways and transition states-which are difficult to access, therefore greatly limiting their domain of application. Here, we demonstrate how these datasets can be generated by means of ES simulations in trajectory space via the metadynamics of paths algorithm. The approach is expected to provide a general and efficient way to generate efficient ML-based CVs for the fast prediction of free energy landscapes in ES simulations. We demonstrate our approach with two numerical examples, a 2D model potential and the isomerization of alanine dipeptide, using deep targeted discriminant analysis as our ML-based CV of choice.

Toward Data-Driven Many-Body Simulations of Biomolecules in Solution: N-Methyl Acetamide as a Proxy for the Protein Backbone.

The development of molecular models with quantum-mechanical accuracy for predictive simulations of biomolecular systems has been a long-standing goal in the field of computational biophysics and biochemistry. As a first step toward a transferable force field for biomolecules entirely derived from "first-principles", we introduce a data-driven many-body energy (MB-nrg) potential energy function (PEF) for N-methylacetamide (NMA), a peptide bond capped by two methyl groups that is commonly used as a proxy for the protein backbone. The MB-nrg PEF is shown to accurately describe the energetics and structural properties of an isolated NMA molecule, including the normal modes of both cis and trans isomers and the energy variation along the isomerization path, as well as the multidimensional potential energy landscape of the NMA-H2O dimer in the gas phase. Importantly, we show that the MB-nrg PEF is fully transferable, enabling molecular dynamics simulations of NMA in solution with quantum-mechanical accuracy. Comparisons with results obtained with a popular pairwise-additive force field for biomolecules and a classical polarizable PEF demonstrate the ability of the MB-nrg PEF to accurately represent many-body effects in NMA-H2O interactions at both short and long distances, which is key to guaranteeing full transferability from the gas phase to the liquid phase.

How and When Does an Enzyme React? Unraveling α-Amylase Catalytic Activity with Enhanced Sampling Techniques

Enzymatic catalysis is a complex process that can involve multiple conformations of the enzyme:substrate complex and several competitive reaction pathways, resulting in a multi-dimensional free energy landscape. The study of enzymatic activity often requires deep knowledge of the system to establish the catalytic mechanism and identify the possible reactive conformations of the complex. Here, we present an enhanced sampling and machine learning-based approach to explore the catalytic reaction space and characterize the transformation from reactive to non-reactive conformations with minimal a priori knowledge of the system. We applied this approach to study the rate-determining step of the glycolysis reaction of maltopentose catalyzed by human pancreatic α-amylase, an important enzyme in glucose production as well as a major drug target for the treatment of type-II diabetes. We unravel the complexity of the enzymatic reaction, reveal three binding modes of the substrate within the active site, and highlight the role of water in the catalytic process and in the stepwise conversion of reaction-ready to non-reactive conformations. Overall, these insights offer atomistic details on the catalytic mechanism and dynamics of the active site, allowing one to shed light on two fundamental questions in enzymatic catalysis, that is how and when does an enzyme react?

Molecular insights into the stereospecificity of arginine in RNA tetraloop folding.

One of the hypotheses for the homochirality of amino acids in the context of the origin of life is that only a particular stereoisomer provides preferential stability to RNA folding by acting as a chemical chaperon. However, the effect at the molecular level is not well understood. This study provides a molecular understanding of such preferential stability for a small GAAA RNA tetraloop in the presence of chiral arginine through a multidimensional free energy landscape constructed using a combination of umbrella sampling and parallel bias metadynamics (PBMetaD) simulations. We show that the origin of the chirality difference in RNA folding-unfolding dynamics is due to differences in the configurational diversity of RNA in adopting various non-natural conformations that accompany the diverse binding modes of D-arginine and L-arginine. We show that while D-arginine stabilizes the native folded state of RNA, L-arginine destabilizes it. Furthermore, free energy calculations on the binding of D- and L-arginine reveal a specific geometric constraint that helps D-arginine to stack with the terminal base pairs of RNA and pushes L-arginine for groove binding.

CELLoGeNe - An energy landscape framework for logical networks controlling cell decisions

SummaryExperimental and computational efforts are constantly made to elucidate mechanisms controlling cell fate decisions during development and reprogramming. One powerful computational method is to consider cell commitment and reprogramming as movements in an energy landscape. Here, we develop Computation of Energy Landscapes of Logical Gene Networks (CELLoGeNe), which maps Boolean implementation of gene regulatory networks (GRNs) into energy landscapes. CELLoGeNe removes inadvertent symmetries in the energy landscapes normally arising from standard Boolean operators. Furthermore, CELLoGeNe provides tools to visualize and stochastically analyze the shapes of multi-dimensional energy landscapes corresponding to epigenetic landscapes for development and reprogramming. We demonstrate CELLoGeNe on two GRNs governing different aspects of induced pluripotent stem cells, identifying experimentally validated attractors and revealing potential reprogramming roadblocks. CELLoGeNe is a general framework that can be applied to various biological systems offering a broad picture of intracellular dynamics otherwise inaccessible with existing methods.

Mode-selective ballistic pathway to a metastable electronic phase.

Exploiting vibrational excitation for the dynamic control of material properties is an attractive goal with wide-ranging technological potential. Most metal-to-insulator transitions are mediated by few structural modes and are, thus, ideal candidates for selective driving toward a desired electronic phase. Such targeted navigation within a generally multi-dimensional potential energy landscape requires microscopic insight into the non-equilibrium pathway. However, the exact role of coherent inertial motion across the transition state has remained elusive. Here, we demonstrate mode-selective control over the metal-to-insulator phase transition of atomic indium wires on the Si(111) surface, monitored by ultrafast low-energy electron diffraction. We use tailored pulse sequences to individually enhance or suppress key phonon modes and thereby steer the collective atomic motion within the potential energy surface underlying the structural transformation. Ab initio molecular dynamics simulations demonstrate the ballistic character of the structural transition along the deformation vectors of the Peierls amplitude modes. Our work illustrates that coherent excitation of collective modes via exciton-phonon interactions evades entropic barriers and enables the dynamic control of materials functionality.

Direct Observation of Single-Protein Transition State Passage by Nanopore Ionic Current Jumps.

Conformational transitions of proteins are governed by chemical kinetics, often toggled by passage through an activated state separating two conformational ensembles. The passage time of a protein through the activated state can be too fast to be detected by single-molecule experiments without the aid of viscogenic agents. Here, we use high-bandwidth nanopore measurements to resolve microsecond-duration transitions that occur between conformational states of individual protein molecules partly blocking pore current. We measure the transition state passage time between folded and unfolded states of a two-state λ6-85 mutant and between metastable intermediates and the unfolded state of the multistate folder cytochrome c. Consistent with the principle of microscopic reversibility, the transition state passage time is the same for the forward and backward reactions. A passage time distribution whose tail is broader than a single exponential observed in cytochrome c suggests a multidimensional energy landscape for this protein.

Transferability of data-driven, many-body models for CO2 simulations in the vapor and liquid phases.

Extending on the previous work by Riera et al. [J. Chem. Theory Comput. 16, 2246-2257 (2020)], we introduce a second generation family of data-driven many-body MB-nrg models for CO2 and systematically assess how the strength and anisotropy of the CO2-CO2 interactions affect the models' ability to predict vapor, liquid, and vapor-liquid equilibrium properties. Building upon the many-body expansion formalism, we construct a series of MB-nrg models by fitting one-body and two-body reference energies calculated at the coupled cluster level of theory for large monomer and dimer training sets. Advancing from the first generation models, we employ the charge model 5 scheme to determine the atomic charges and systematically scale the two-body energies to obtain more accurate descriptions of vapor, liquid, and vapor-liquid equilibrium properties. Challenges in model construction arise due to the anisotropic nature and small magnitude of the interaction energies in CO2, calling for the necessity of highly accurate descriptions of the multidimensional energy landscape of liquid CO2. These findings emphasize the key role played by the training set quality in the development of transferable, data-driven models, which, accurately representing high-dimensional many-body effects, can enable predictive computer simulations of molecular fluids across the entire phase diagram.

Out-of-Equilibrium Biophysical Chemistry: The Case for Multidimensional, Integrated Single-Molecule Approaches.

Out-of-equilibrium processes are ubiquitous across living organisms and all structural hierarchies of life. At the molecular scale, out-of-equilibrium processes (for example, enzyme catalysis, gene regulation, and motor protein functions) cause biological macromolecules to sample an ensemble of conformations over a wide range of time scales. Quantifying and conceptualizing the structure–dynamics to function relationship is challenging because continuously evolving multidimensional energy landscapes are necessary to describe nonequilibrium biological processes in biological macromolecules. In this perspective, we explore the challenges associated with state-of-the-art experimental techniques to understanding biological macromolecular function. We argue that it is time to revisit how we probe and model functional out-of-equilibrium biomolecular dynamics. We suggest that developing integrated single-molecule multiparametric force–fluorescence instruments and using advanced molecular dynamics simulations to study out-of-equilibrium biomolecules will provide a path towards understanding the principles of and mechanisms behind the structure–dynamics to function paradigm in biological macromolecules.

Unfolding of Dynamical Events in the Early Stage of Insulin Dimer Dissociation.

The dissociation of an insulin dimer is an important biochemical event that could also serve as a prototype of dissociations in similar biomolecular assemblies. We use a recently developed multidimensional free energy landscape for insulin dimer dissociation to unearth the microscopic and mechanistic aspects of the initial stages of the process that could hold the key to understanding the stability and the rate. The following sequence of events occurs in the initial stages: (i) The backbone hydrogen bonds break partially at the antiparallel β-sheet junction, (ii) the two α-helices (chain B) move away from each other while several residues (chain A) move closer, and (iii) a flow of adjacent water molecules occurs into the junction region. Interestingly, the intermonomeric center-to-center distance does not increase, but the number of native contacts exhibits a sharp decrease. Subsequent steps involve further disengagement of hydrophobic groups. This process is slow because of an entropic bottleneck created by the existence of the large configuration space available in the native state (NS), which is inhabited by low-frequency conformational fluctuations. We carry out a density-of-states analyses in the dimer NS to unearth distinctive features not present in the monomers. These low-frequency modes are also responsible for a large entropic stabilization of the NS. Hydrophobic disengagement in the early stage leads to the formation of a twisted intermediate state which itself is a metastable minimum (IS-1). The subsequent progress leads to another dimeric complex (IS-2), which is on the dissociative pathway and characterized by a further decrease in the native contacts. The dissociation process provides insights into the workings of a biomolecular assembly.

Monte Carlo Pathway Search (MCPS) for Exploring Permeation Pathways in High-Dimensional Conformational Space

Antibiotic resistance of Gram-negative bacteria is largely attributed to the low permeability of their outer membrane (OM). Antibiotics crossing the OM typically do so through OM porins; therefore, understanding mechanisms facilitating this permeation would aid in antibiotic development. Molecular dynamics (MD) simulations provide key structural information on relevant molecular processes; however, simulating OM porin permeation is challenging, because antibiotic permeation occurs on timescales not feasibly attained with equilibrium MD due to hindrance by a constriction region (CR) within these porins. The CR also hinders antibiotic reorientation meaning translation and rotation are slow degrees of freedom requiring extensive simulation or expensive enhanced sampling techniques to satisfactorily sample. To overcome these challenges, we developed MCPS to efficiently sample high-dimensional permeation pathways through OM porins from the extracellular to periplasmic side. First, a multidimensional energy landscape is created by placing the antibiotic in all possible poses within translational and rotational space and evaluating antibiotic-protein interaction energy for each pose. Then, Monte Carlo (MC) moves are used to walk through this landscape to determine favorable trajectories connecting extracellular and periplasmic spaces. Since rotation and translation are slow degrees of freedom, limited changes in antibiotic orientation and position are allowed in each MC move. After obtaining multiple trajectories to comprehensively sample the possible pathways, most likely permeation pathways are identified using Dijkstra's algorithm. MCPS was used to study permeation of ampicillin through OmpF, an abundant E. Coli porin. We found ampicillin adopts a similar orientation as in the ampicillin-bound OmpF crystal structure at the CR entrance before diverging into two pathways with differing orientations and protein interactions. This application demonstrates MCPS effectiveness to obtain descriptive structural information for antibiotic permeation using few computational resources, indicating its potential for screening multiple antibiotics.

Forced deterministic dynamics on a random energy landscape: Implications for the physics of amorphous solids.

The dynamics of supercooled liquids and plastically deformed amorphous solids is known to be dominated by the structure of their rough energy landscapes. Recent experiments and simulations on amorphous solids subjected to oscillatory shear at athermal conditions have shown that for small strain amplitudes these systems reach limit cycles of different periodicities after a transient. However, for larger strain amplitudes the transients become longer and for strain amplitudes exceeding a critical value the system reaches a diffusive steady state. This behavior cannot be explained using the current mean-field models of amorphous plasticity. Here we show that this phenomenology can be described and explained using a simple model of forced dynamics on a multidimensional random energy landscape. In this model, the existence of limit cycles can be ascribed to confinement of the dynamics to a small part of the energy landscape which leads to self-intersection of state-space trajectories and the transition to the diffusive regime for larger forcing amplitudes occurs when the forcing overcomes this confinement.

Deciphering the Self-Cleavage Reaction Mechanism of Hairpin Ribozyme.

Hairpin ribozyme catalyzes the reversible self-cleavage of phosphodiester bonds which plays prominent roles in key biological processes involving RNAs. Despite impressive advances on ribozymatic self-cleavage, critical aspects of its molecular reaction mechanism remain controversially debated. Here, we generate and analyze the multidimensional free energy landscape that underlies the reaction using extensive QM/MM metadynamics simulations to investigate in detail the full self-cleavage mechanism. This allows us to answer several pertinent yet controversial questions concerning activation of the 2'-OH group, the mechanistic role of water molecules present in the active site, and the full reaction pathway including the structures of transition states and intermediates. Importantly, we find that a sufficiently unrestricted reaction subspace must be mapped using accelerated sampling methods in order to compute the underlying free energy landscape. It is shown that lower-dimensional sampling where the bond formation and cleavage steps are coupled does not allow the system to sufficiently explore the landscape. On the basis of a three-dimensional free energy surface spanned by flexible generalized coordinates, we find that 2'-OH is indirectly activated by adjacent G8 nucleobase in conjunction with stabilizing H-bonding involving water. This allows the proton of the 2'-OH group to directly migrate toward the 5'-leaving group via a nonbridging oxygen of the phosphodiester link. At variance with similar enzymatic processes where water wires connected to protonable side chains of the protein matrix act as transient proton shuttles, no such de/reprotonation events of water molecules are found to be involved in this ribozymatic transesterification. Overall, our results support an acid-catalyzed reaction mechanism where A38 nucleobase directly acts as an acid whereas G8, in stark contrast, participates only indirectly via stabilizing the nascent nucleophile for subsequent attack. Moreover, we conclude that self-cleavage of hairpin ribozyme follows an AN + DN two-step associative pathway where the rate-determining step is the cleavage of the phosphodiester bond. These results provide a major advancement in our understanding of the unique catalytic mechanism of hairpin ribozyme which will fruitfully impact on the design of synthetic ribozymes.

Multidimensional Global Optimization and Robustness Analysis in the Context of Protein-Ligand Binding.

Accuracy of protein-ligand binding free energy calculations utilizing implicit solvent models is critically affected by parameters of the underlying dielectric boundary, specifically, the atomic and water probe radii. Here, a global multidimensional optimization pipeline is developed to find optimal atomic radii specifically for protein-ligand binding calculations in implicit solvent. The computational pipeline has these three key components: (1) a massively parallel implementation of a deterministic global optimization algorithm (VTDIRECT95), (2) an accurate yet reasonably fast generalized Born implicit solvent model (GBNSR6), and (3) a novel robustness metric that helps distinguish between nearly degenerate local minima via a postprocessing step of the optimization. A graph-based "kT-connectivity" approach to explore and visualize the multidimensional energy landscape is proposed: local minima that can be reached from the global minimum without exceeding a given energy threshold (kT) are considered to be connected. As an illustration of the capabilities of the optimization pipeline, we apply it to find a global optimum in the space of just five radii: four atomic (O, H, N, and C) radii and water probe radius. The optimized radii, ρW = 1.37 Å, ρC = 1.40 Å, ρH = 1.55 Å, ρN = 2.35 Å, and ρO = 1.28 Å, lead to a closer agreement of electrostatic binding free energies with the explicit solvent reference than two commonly used sets of radii previously optimized for small molecules. At the same time, the ability of the optimizer to find the global optimum reveals fundamental limits of the common two-dielectric implicit solvation model: the computed electrostatic binding free energies are still almost 4 kcal/mol away from the explicit solvent reference. The proposed computational approach opens the possibility to further improve the accuracy of practical computational protocols for binding free energy calculations.

Spatially varying colloidal phase behavior on multi-dimensional energy landscapes.

A method is reported to determine equilibrium concentration profiles and local phase behavior of colloids on multi-dimensional energy landscapes. A general expression is derived based on local particle concentration and osmotic pressure differences that are balanced by forces on colloids due to energy landscape gradients. This analysis is applied to colloidal particles in high frequency AC electric fields within octupolar electrodes, where the energy landscape can be shaped in two dimensions. These results are also directly applicable to any particles having induced dipoles in spatially non-uniform electromagnetic fields. Predictions based on modeling colloids with an effective hard disk equation of state indicate inhomogeneous solid and fluid states coexisting on different shaped energy landscapes including multiple minima. Model predictions show excellent agreement with time-averaged Brownian dynamic simulations at equilibrium. Findings demonstrate a general approach to understand colloidal phase behavior on energy landscapes due to external fields, which could enable control of colloidal microstructures on morphing energy landscapes and the inverse design of fields to assemble hierarchically structured colloidal materials.

Combined Force-Frequency Sampling for Simulation of Systems Having Rugged Free Energy Landscapes.

An adaptive, machine learning-based sampling method is presented for simulation of systems having rugged, multidimensional free energy landscapes. The method's main strength resides in its ability to learn both from the frequency of visits to distinct states and the generalized force estimates that arise in a system as it evolves in phase space. This is accomplished by introducing a self-integrating artificial neural network, which generates an estimate of the free energy directly from its derivatives. The usefulness of the proposed combined approach is examined in the context of two concrete examples, namely, an alanine dipeptide molecule in water and a polymer diffusing through a narrow pore. This new method is found to be robust, faster, and more accurate than approaches that rely only on frequency-based or generalized force-based estimations. After combining the proposed approach with overfill protection and support for sparse data storage and training, the method is shown to be more effective than comparable, previously available techniques and capable of scaling efficiently to larger numbers of collective variables.

Resonance Raman Spectroscopy and Imaging of Franck-Condon Vibrational Activity and Morphology in Conjugated Polymers for Solar Cells.

Vibrational reorganization influences photophysical outcomes in conjugated polymers used as active materials for optoelectronic devices. Excited state geometric rearrangements typically involve many displaced vibrations, yet most materials design schemes rely solely on pure electronic models with limited predictive capability. Although the coupling of vibrational motions to electronic processes occurs over a broad range of time scales, resolving structural displacements immediately following photon absorption can be particularly insightful for understanding the intrinsic stabilities of excited states. These Franck-Condon vibrational relaxation processes occur on time scales of <1 ps in polymers and mainly involve high-frequency skeletal motions. Establishing correlations between Franck-Condon vibrational reorganization and steady-state material properties could generate new avenues for informing materials design, which is especially important in the fast-paced field of organic photovoltaics (OPV) where seemingly elegant strategies often fail but molecular-level insights are usually lacking. The goal of this Account is to highlight relationships between molecular structure, packing, and vibrational reorganization in OPV systems, such as blends of conjugated polymers with fullerenes. Resonance Raman spectroscopy (RRS) is a sensitive probe of Franck-Condon activity in OPV materials, and signals are bolstered by large resonance enhancements and low backgrounds from quantitative fluorescence quenching. Our group has undertaken extensive RRS investigations of heterogeneous OPV materials in functioning device environments to uncover new insights of the multidimensional excited state potential energy landscape and fluctuations with local morphology. Time-dependent quantum mechanical approaches facilitate this effort by providing an intuitive theoretical framework to access dynamical perspectives of Raman transitions. Moreover, dynamics regimes of Franck-Condon excited state structural evolution can be selected simply by tuning excitation energies. This excitation detuning approach also reveals structurally and electronically distinct conformers with unique Franck-Condon signatures typically concealed under inhomogeneously broadened absorption line shapes. Interestingly, long and rich progressions of overtone and combination transitions-rare for large molecules with multiple displaced modes-are frequently resolved that exhibit strong sensitivity to the local chromophore environment. These harmonic features encode useful dynamics information by serving as internal "clocks" of Franck-Condon vibrational activity in addition to enabling quantitative estimates of mode-specific displacements. RRS attributes may be further exploited to perform noninvasive imaging of functioning OPV devices in concert with variable frequency electrical imaging probes. This approach generates direct spatial correlations between morphology-dependent Franck-Condon vibrational activity and material performance metrics (e.g., photocurrent generation) on submicrometer size scales.

Mechanical unfolding of spectrin reveals a super-exponential dependence of unfolding rate on force

We investigated the mechanical unfolding of single spectrin molecules over a broad range of loading rates and thus unfolding forces by combining magnetic tweezers with atomic force microscopy. We find that the mean unfolding force increases logarithmically with loading rate at low loading rates, but the increase slows at loading rates above 1pN/s. This behavior indicates an unfolding rate that increases exponentially with the applied force at low forces, as expected on the basis of one-dimensional models of protein unfolding. At higher forces, however, the increase of the unfolding rate with the force becomes faster than exponential, which may indicate anti-Hammond behavior where the structures of the folded and transition states become more different as their free energies become more similar. Such behavior is rarely observed and can be explained by either a change in the unfolding pathway or as a reflection of a multidimensional energy landscape of proteins under force.

Residue-Specialized Membrane Poration Kinetics of Melittin and Its Variants: Insight from Mechanistic Landscapes**Supported by the National Natural Science Foundation of China under Grant Nos. 21422404, 21774092, U1532108, and 21728502; the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions; and the Natural Science Foundation of Jiangsu Province of China under Grant Nos. BK20171207 and BK20171210

Pore-forming peptides have promising potentials for biomedical uses due to their ability to permeabilize cell membranes. However, to molecularly engineer them for practical applications is still blocked by the poor understanding of the specific roles of individual residues in peptides’ activity. Herein, using an advanced computational approach that combines Coarse-Grained molecular dynamics and well-tempered metadynamics, the membrane activities of melittin, a representative pore-forming peptide, and its gain-of-function variants, are characterized from the kinetics and thermodynamics perspectives. Unbiased simulations elucidate the molecular details of peptide-induced membrane poration; during which, some vital intermediate states, including the aggregation and U-shape configuration formation of peptides in the membrane, are observed and further applied as collective variables to construct the multi-dimensional free energy landscapes of the peptide-membrane interactions. Such a combination of kinetic and thermodynamic descriptions of the interaction process provides crucial information of residue-specialized contribution in chain conformation and consequently membrane perforation ability of the peptide. It is found that residues at the kink part (e.g. Thr) determine the chain flexibility and U-shape bending of the peptide, while residues near the C-terminus (e.g. Arg and Lys) are responsible for recruiting neighboring peptides for inter-molecular cooperation; the probable reaction pathway and the poration efficiency are consequently regulated. These results are helpful for a comprehensive understanding of the complicated molecular mechanism of pore-forming peptides and pave the way to rationally design and/or engineer the peptides for practical applications.