Combined molecular dynamics and neural network method for predicting protein antifreeze activity

On the engulfment of antifreeze proteins by ice

Antifreeze proteins (AFPs) are remarkable biomolecules that suppress ice formation at trace concentrations. To inhibit ice growth, AFPs must not only bind to ice crystals, but also resist engulfment by ice. The highest supercooling, [Formula: see text], for which AFPs are able to resist engulfment is widely believed to scale as the inverse of the separation, [Formula: see text], between bound AFPs, whereas its dependence on the molecular characteristics of the AFP remains poorly understood. By using specialized molecular simulations and interfacial thermodynamics, here, we show that in contrast with conventional wisdom, [Formula: see text] scales as [Formula: see text] and not as [Formula: see text]. We further show that [Formula: see text] is proportional to AFP size and that diverse naturally occurring AFPs are optimal at resisting engulfment by ice. By facilitating the development of AFP structure-function relationships, we hope that our findings will pave the way for the rational design of AFPs.

Long-range, water-mediated interaction between a moderately active antifreeze protein molecule and the surface of ice

Using molecular dynamics simulations, we show that a molecule of moderately active antifreeze protein (type III AFP, QAE HPLC-12 isoform) is able to interact with ice in an indirect manner. This interaction occurs between the ice binding site (IBS) of the AFP III molecule and the surface of ice, and it is mediated by liquid water, which separates these surfaces. As a result, the AFP III molecule positions itself at a specific orientation and distance relative to the surface of ice, which enables the effective binding (via hydrogen bonds) of the molecule with the nascent ice surface. Our results show that the final adsorption of the AFP III molecule on the surface of ice is not achieved by chaotic diffusion movements, but it is preceded by a remote, water-mediated interaction between the IBS and the surface of ice. The key factor that determines the existence of this interaction is the ability of water molecules to spontaneously form large, high-volume aggregates that can be anchored to both the IBS of the AFP molecule and the surface of ice. The results presented in this work for AFP III are in full agreement with the ones obtained by us previously for hyperactive CfAFP, which indicates that the mechanism of the remote interaction of these molecules with ice remains unchanged despite significant differences in the molecular structure of their ice binding sites. For that reason, we can expect that also other types of AFPs interact with the ice surface according to an analogous mechanism.

Computational Design of Peptides for Biomaterials Applications

Computer-aided molecular design and protein engineering emerge as promising and active subjects in bioengineering and biotechnological applications. On one hand, due to the advancing computing power in the past decade, modeling toolkits and force fields have been put to use for accurate multiscale modeling of biomolecules including lipid, protein, carbohydrate, and nucleic acids. On the other hand, machine learning emerges as a revolutionary data analysis tool that promises to leverage physicochemical properties and structural information obtained from modeling in order to build quantitative protein structure-function relationships. We review recent computational works that utilize state-of-the-art computational methods to engineer peptides and proteins for various emerging biomedical, antimicrobial, and antifreeze applications. We also discuss challenges and possible future directions toward developing a roadmap for efficient biomolecular design and engineering.

Analysis of Ice-Binding Protein Evolution

Discovering novel ice-binding proteins (IBPs) is important for understanding the evolution of IBPs but it is difficult to determine where resources should be directed in the search for novel IBPs. For this reason, we developed a simple bioinformatic approach for aiding in the determination of where to direct efforts in the search for IBPs. First, BLAST is used to obtain a candidate list of putative IBPs. Next, phylogenetic trees are constructed to map the candidate list of putative IBPs to determine if any patterns are forming. These candidate putative IBPs and their patterns are then assessed through the production of ancestral sequences and reverse BLAST searches, in addition to the use of IBP calculators, to determine which sequences should be cut to produce the final putative IBP list. Finally, we explain an avenue to investigate these putative IBPs further for the development of hypotheses on their evolution.

Divergent Mechanisms of Ice Growth Inhibition by Antifreeze Proteins

Antifreeze proteins (AFPs) are biomolecules that can bind to ice and hinder its growth, thus holding significant potential for biotechnological and biomedical applications. AFPs are a subset of ice-binding proteins (IBPs) and are found in various organisms across different life kingdoms. This mini-review investigates the underlying mechanisms by which AFPs impede ice growth, emphasizing the disparities between hyperactive and moderate AFPs. Hyperactive AFPs exhibit heightened thermal hysteresis (TH) activity and can bind to both the basal and prism planes of ice crystals, enabling them to endure extremely cold temperatures. In contrast, moderate AFPs predominantly bind to the prism/pyramidal planes and demonstrate lower TH activity. The structural diversity of AFPs and the presence of ordered water molecules on their ice-binding sites (IBS) have been subjects of debate among researchers. Multiple hypotheses have been proposed concerning the significance of ordered water molecules in ice binding. Gaining insights into the binding dynamics and the factors influencing TH activity in AFPs is crucial for the development of efficient synthetic compounds and the establishment of comprehensive models to elucidate ice growth inhibition. Here we emphasize the necessity for further research to unravel the mechanisms of AFPs and presents a pathway for constructing models capable of comprehensively explaining their inhibitory effects on ice growth.

Engulfment Avalanches and Thermal Hysteresis for Antifreeze Proteins on Supercooled Ice

Antifreeze proteins (AFPs) bind to the ice-water surface and prevent ice growth at temperatures below 0 °C through a Gibbs-Thomson effect. Each adsorbed AFP creates a metastable depression on the surface that locally resists ice growth, until ice engulfs the AFP. We recently predicted the susceptibility to engulfment as a function of AFP size, distance between AFPs, and supercooling [ J. Chem. Phys. 2023, 158, 094501]. For an ensemble of AFPs adsorbed on the ice surface, the most isolated AFPs are the most susceptible, and when an isolated AFP gets engulfed, its former neighbors become more isolated and more susceptible to engulfment. Thus, an initial engulfment event can trigger an avalanche of subsequent engulfment events, leading to a sudden surge of unrestrained ice growth. This work develops a model to predict the supercooling at which the first engulfment event will occur for an ensemble of randomly distributed AFP pinning sites on an ice surface. Specifically, we formulate an inhomogeneous survival probability that accounts for the AFP coverage, the distribution of AFP neighbor distances, the resulting ensemble of engulfment rates, the ice surface area, and the cooling rate. We use the model to predict thermal hysteresis trends and compare with experimental data.

Free energy barriers for anti-freeze protein engulfment in ice: Effects of supercooling, footprint size, and spatial separation

Anti-freeze proteins (AFPs) protect organisms at freezing conditions by attaching to the ice surface and arresting its growth. Each adsorbed AFP locally pins the ice surface, resulting in a metastable dimple for which the interfacial forces counteract the driving force for growth. As supercooling increases, these metastable dimples become deeper, until metastability is lost in an engulfment event where the ice irreversibly swallows the AFP. Engulfment resembles nucleation in some respects, and this paper develops a model for the "critical profile" and free energy barrier for the engulfment process. Specifically, we variationally optimize the ice-water interface and estimate the free energy barrier as a function of the supercooling, the AFP footprint size, and the distance to neighboring AFPs on the ice surface. Finally, we use symbolic regression to derive a simple closed-form expression for the free energy barrier as a function of two physically interpretable, dimensionless parameters.

Molecular Factors of Ice Growth Inhibition for Hyperactive and Globular Antifreeze Proteins: Insights from Molecular Dynamics Simulation

The molecular mechanism behind the ice growth inhibition by antifreeze proteins (AFPs) is yet to be understood completely. Also, what physical parameters differentiate between the AFP and non-AFP are largely unknown. Thus, to get an atomistic overview of the differential antifreeze activities of different classes of AFPs, we have studied ice growth from different ice surfaces in the presence of a moderately active globular type III AFP and a hyperactive spruce budworm (sbw) AFP. Results are compared with the observations of ice growth simulations in the presence of topologically similar non-AFPs using all-atom molecular dynamics simulations. Simulation data suggest that the ice surface coverage is a critical factor in ice growth inhibition. Due to the presence of an ice binding surface (IBS), AFPs form a high affinity complex with ice, accompanied by a transition of hydration water around the IBS from clathrate-like to ice-like. Several residues around the periphery of the IBS anchor the AFP to the curved ice surface mediated by multiple strong hydrogen bonds, stabilizing the complex immensely. In the high surface coverage regime, the slow unbinding kinetics dominates over the ice growth kinetics and thus facilitates the ice growth inhibition. Due to the non-availability of a proper IBS, non-AFPs form a low-affinity complex with the growing ice surface. As a result, the non-AFPs are continuously repelled by the surface. If the concentration of AFPs is low, then the effective surface coverage is reduced significantly. In this low surface coverage regime, AFPs can also behave like impurities and are engulfed by the growing ice crystal.

Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon's needle, requires the rods to "land," with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.

Molecular evidence of intertidal habitats selecting for repeated ice-binding protein evolution in invertebrates

Ice-binding proteins (IBPs) have evolved independently in multiple taxonomic groups to improve their survival at sub-zero temperatures. Intertidal invertebrates in temperate and polar regions frequently encounter sub-zero temperatures, yet there is little information on IBPs in these organisms. We hypothesized that there are far more IBPs than are currently known and that the occurrence of freezing in the intertidal zone selects for these proteins. We compiled a list of genome-sequenced invertebrates across multiple habitats and a list of known IBP sequences and used BLAST to identify a wide array of putative IBPs in those invertebrates. We found that the probability of an invertebrate species having an IBP was significantly greater in intertidal species than in those primarily found in open ocean or freshwater habitats. These intertidal IBPs had high sequence similarity to fish and tick antifreeze glycoproteins and fish type II antifreeze proteins. Previously established classifiers based on machine learning techniques further predicted ice-binding activity in the majority of our newly identified putative IBPs. We investigated the potential evolutionary origin of one putative IBP from the hard-shelled mussel Mytilus coruscus and suggest that it arose through gene duplication and neofunctionalization. We show that IBPs likely readily evolve in response to freezing risk and that there is an array of uncharacterized IBPs, and highlight the need for broader laboratory-based surveys of the diversity of ice-binding activity across diverse taxonomic and ecological groups.

Molecular simulations of proteins: From simplified physical interactions to complex biological phenomena

Molecular dynamics simulation is the most popular computational technique for investigating the structural and dynamical behaviour of proteins, in search of the molecular basis of their function. Far from being a completely settled field of research, simulations are still evolving to best capture the essential features of the atomic interactions that govern a protein's inner motions. Modern force fields are becoming increasingly accurate in providing a physical description adequate to this purpose, and allow us to model complex biological systems under fairly realistic conditions. Furthermore, the use of accelerated sampling techniques is improving our access to the observation of progressively larger molecular structures, longer time scales, and more hidden functional events. In this review, the basic principles of molecular dynamics simulations and a number of key applications in the area of protein science are summarized, and some of the most important results are discussed. Examples include the study of the structure, dynamics and binding properties of 'difficult' targets, such as intrinsically disordered proteins and membrane receptors, and the investigation of challenging phenomena like hydration-driven processes and protein aggregation. The findings described provide an overall picture of the current state of this research field, and indicate new perspectives on the road ahead to the upcoming future of molecular simulations.

Diffusion Attachment Model for Long Helical Antifreeze Proteins to Ice

Some of the most potent antifreeze proteins (AFPs) are approximately rigid helical structures that bind with one side in contact with the ice surface at specific orientations. These AFPs take random orientations in solution; however, most orientations become sterically inaccessible as the AFP approaches the ice surface. The effect of these inaccessible orientations on the rate of adsorption of AFP to ice has never been explored. Here, we present a diffusion-controlled theory of adsorption kinetics that accounts for these orientational restrictions to predict a rate constant for adsorption (k_on, in m/s) as a function of the length and width of the AFP molecules. We find that k_on decreases with length and diameter of the AFP and is almost proportional to the inverse of the area of the binding surface. We demonstrate that the restricted orientations create an entropic barrier to AFP adsorption, which we compute to be approximately 7 k_BT for most AFPs and up to 9 k_BT for Maxi, the largest known AFP. We compare the entropic resistance 1/k_on to resistances for diffusion through boundary layers and across typical distances in the extracellular matrix and find that these entropic and diffusion resistances could become comparable in the small confined spaces of biological environments.

Antifreeze proteins and their biomimetics for cell cryopreservation: Mechanism, function and application-A review

Cell-based therapy is a promising technology for intractable diseases and health care applications, in which cryopreservation has become an essential procedure to realize the production of therapeutic cells. Ice recrystallization is the major factor that affects the post-thaw viability of cells. As a typical series of biomacromolecules with ice recrystallization inhibition (IRI) activity, antifreeze proteins (AFPs) have been employed in cell cryopreservation. Meanwhile, synthesized materials with IRI activity have emerged in the name of biomimetics of AFPs to expand their availability and practicality. However, fabrication of AFPs mimetics is in a chaotic period. There remains little commonality among different AFPs mimetics, then it is difficult to set guidelines on their design. With no doubt, a comprehensive understanding on the antifreezing mechanism of AFPs in molecular level will enable us to rebuild the function of AFPs, and provide convenience to clarify the relationship between structure and function of these early stage biomimetics. In this review, we would discuss those previously reported biomimetics to summarize their structure characteristics concerning the IRI activity and attempt to develop a roadmap for guiding the design of novel AFPs mimetics.

High Water Density at Non-Ice-Binding Surfaces Contributes to the Hyperactivity of Antifreeze Proteins

Antifreeze proteins (AFPs) can bind to ice nuclei thereby inhibiting their growth and their hydration shell is believed to play a fundamental role. Here, we use molecular dynamics simulations to characterize the hydration shell of four moderately-active and four hyperactive AFPs. The local water density around the ice-binding-surface (IBS) is found to be lower than that around the non-ice-binding surface (NIBS) and this difference correlates with the higher hydrophobicity of the former. While the water-density increase (with respect to bulk) around the IBS is similar between moderately-active and hyperactive AFPs, it differs around the NIBS, being higher for the hyperactive AFPs. We hypothesize that while the lower water density at the IBS can pave the way to protein binding to ice nuclei, irrespective of the antifreeze activity, the higher density at the NIBS of the hyperactive AFPs contribute to their enhanced ability in inhibiting ice growth around the bound AFPs.

Genetic Algorithm Approach for the Optimization of Protein Antifreeze Activity Using Molecular Simulations

Antifreeze proteins (AFPs) are of much interest for their ability to inhibit ice growth at low concentrations. In this work, we present a genetic algorithm for the in silico design of AFP mutants with improved antifreeze activity, measured as the predicted thermal hysteresis at a fixed concentration, ΔT_C. Central to the algorithm is our recently developed neural network method for predicting ΔT_C from molecular simulations [Kozuch et al., PNAS, 115, 13252 (2018)]. Applying the algorithm to three structurally diverse AFPs, wfAFP, rQAE, and RiAFP, we find that significantly improved mutants are discovered for rQAE and RiAFP. Testing of the optimized mutants shows an increase in ΔT_C of 0.572 ± 0.11 K (262 ± 50.6%) and 1.33 ± 0.14 K (39.9 ± 4.19%) over the native structures for rQAE and RiAFP, respectively. Structural analysis of the optimized mutants reveals that the algorithm is able to exploit two pathways for enhancing the predicted antifreeze activity of the mutants: (1) increasing the local order of surface waters by encouraging the formation of internal water channels in the protein and (2) increasing the total ice-binding area by improving the planar structure of the ice-binding surface. Additionally, analysis of all mutants explored by the algorithm reveals that a subset of residues, mainly nonpolar, are particularly helpful in improving antifreeze activity at the ice-binding surface.

Antifreeze proteins and homogeneous nucleation: On the physical determinants impeding ice crystal growth

Antifreeze proteins (AFPs) are biopolymers capable of interfering with ice growth. Their antifreeze action is commonly understood considering that the AFPs, by pinning the ice surface, force the crystal-liquid interface to bend forming an ice meniscus, causing an increase in the surface free energy and resulting in a decrease in the freezing point ΔT^max. Here, we present an extensive computational study for a model protein adsorbed on a TIP4P/Ice crystal, computing ΔT^max as a function of the average distance d between AFPs, with simulations spanning over 1 µs. First, we show that the lower the d, the larger the ΔT^max. Then, we find that the water-ice-protein contact angle along the line ΔT^max(d) is always larger than 0°, and we provide a theoretical interpretation. We compute the curvature radius of the stable solid-liquid interface at a given supercooling ΔT ≤ ΔT^max, connecting it with the critical ice nucleus at ΔT. Finally, we discuss the antifreeze capability of AFPs in terms of the protein-water and protein-ice interactions. Our findings establish a unified description of the AFPs in the contest of homogeneous ice nucleation, elucidating key aspects of the antifreeze mechanisms and paving the way for the design of novel ice-controlling materials.

Insights into the interactions of bisphenol and phthalate compounds with unamended and carnitine-amended montmorillonite clays

Montmorillonite clays could be promising sorbents to mitigate toxic compound exposures. Bisphenols A (BPA) and S (BPS) as well as phthalates, dibutyl phthalate (DBP) and di-2-ethylhexyl phthalate (DEHP), are ubiquitous environmental contaminants linked to adverse health effects. Here, we combined computational and experimental methods to investigate the ability of montmorillonite clays to sorb these compounds. Molecular dynamics simulations predicted that parent, unamended, clay has higher binding propensity for BPA and BPS than for DBP and DEHP; carnitine-amended clay improved BPA and BPS binding, through carnitine simultaneously anchoring to the clay through its quaternary ammonium cation and forming hydrogen bonds with BPA and BPS. Experimental isothermal analysis confirmed that carnitine-amended clay has enhanced BPA binding capacity, affinity and enthalpy. Our studies demonstrate how computational and experimental methods, combined, can characterize clay binding and sorption of toxic compounds, paving the way for future investigation of clays to reduce BPA and BPS exposure.

Inhibition of Bacterial Ice Nucleators Is Not an Intrinsic Property of Antifreeze Proteins

Cold-adapted organisms use antifreeze proteins (AFPs) or ice-nucleating proteins (INPs) for the survival in freezing habitats. AFPs have been reported to be able to inhibit the activity of INPs, a property that would be of great physiological relevance. The generality of this effect is not understood, and for the few known examples of INP inhibition by AFPs, the molecular mechanisms remain unclear. Here, we report a comprehensive evaluation of the effects of five different AFPs on the activity of bacterial ice nucleators using a high-throughput ice nucleation assay. We find that bacterial INPs are inhibited by certain AFPs, while others show no effect. Thus, the ability to inhibit the activity of INPs is not an intrinsic property of AFPs, and the interactions of INPs and different AFPs proceed through protein-specific rather than universal molecular mechanisms.

Deciphering the Role of the Non-ice-binding Surface in the Antifreeze Activity of Hyperactive Antifreeze Proteins

Antifreeze proteins (AFPs) show thermal hysteresis through specific interaction with the ice crystal. Hyperactive AFPs interact with the ice surface through a threonine-rich motif present at their ice-binding surface (IBS). Ordering of water around the IBS was extensively investigated. However, the role of non-IBS in ice growth inhibition is yet to be understood completely. The present study explores the nature of hydration and its length-scale evaluation around the non-IBS for hyperactive AFPs. We observed that the hydration layer of non-IBS is liquid-like, even in highly supercooled conditions, and the nature of hydration is drastically different from the hydration pattern of non-AFP surfaces. In similar conditions, the hydration layer around the IBS is ice-like ordered. Non-IBS of the hyperactive AFP exposes toward the bulk and is able to maintain the liquid-like character of its hydration water up to 15 Å. We also find that the amino acid compositions and their spatial distribution on the non-IBS are markedly different from those of the IBS and non-AFP surfaces. These results elucidate the combined role of IBS and non-IBS in ice-growth inhibition. While IBS is required to adsorb on ice efficiently, the exposed non-IBS may prevent ice nucleation/growth on top of the bound AFPs.

AFP-LSE: Antifreeze Proteins Prediction Using Latent Space Encoding of Composition of k-Spaced Amino Acid Pairs

Species living in extremely cold environments resist the freezing conditions through antifreeze proteins (AFPs). Apart from being essential proteins for various organisms living in sub-zero temperatures, AFPs have numerous applications in different industries. They possess very small resemblance to each other and cannot be easily identified using simple search algorithms such as BLAST and PSI-BLAST. Diverse AFPs found in fishes (Type I, II, III, IV and antifreeze glycoproteins (AFGPs)), are sub-types and show low sequence and structural similarity, making their accurate prediction challenging. Although several machine-learning methods have been proposed for the classification of AFPs, prediction methods that have greater reliability are required. In this paper, we propose a novel machine-learning-based approach for the prediction of AFP sequences using latent space learning through a deep auto-encoder method. For latent space pruning, we use the output of the auto-encoder with a deep neural network classifier to learn the non-linear mapping of the protein sequence descriptor and class label. The proposed method outperformed the existing methods, yielding excellent results in comparison. A comprehensive ablation study is performed, and the proposed method is evaluated in terms of widely used performance measures. In particular, the proposed method demonstrated a high Matthews correlation coefficient of 0.52, F-score of 0.49, and Youden’s index of 0.81 on an independent test dataset, thereby outperforming the existing methods for AFP prediction.

Computational Study of Differences between Antifreeze Activity of Type-III Antifreeze Protein from Ocean Pout and Its Mutant

The antifreeze activity of a type-III antifreeze protein (AFP) expressed in ocean pout (Zoarces americanus) is compared with that of a specific mutant (T18N) using all-atom molecular dynamics simulations. The antifreeze activity of the mutant is only 10% of the wild-type AFP. The results from this simulation study revealed the following insights into the mechanism of antifreeze action by type-III AFPs. The AFP gets adsorbed to the advancing ice front due to its hydrophobic nature. A part of the hydrophobicity is caused by the presence of clathrate structure of water molecules near the ice-binding surface (IBS). The mutation in the AFP disrupts this structure and thereby reduces the ability of the mutant to adsorb to the ice-water interface leading to the loss of antifreeze activity. The mutation, however, has no effect on the ability of the adsorbed protein to bind to the growing ice phase. Simulations also revealed that all surfaces of the protein can bind to the ice phase, although the IBS is the preferred surface.

The properties, biotechnologies, and applications of antifreeze proteins

By natural selection, organisms evolve different solutions to cope with extremely cold weather. The emergence of an antifreeze protein gene is one of the most momentous solutions. Antifreeze proteins possess an importantly functional ability for organisms to survive in cold environments and are widely found in various cold-tolerant species. In this review, we summarize the origin of antifreeze proteins, describe the diversity of their species-specific properties and functions, and highlight the related biotechnology on the basis of both laboratory tests and bioinformatics analysis. The most recent advances in the applications of antifreeze proteins are also discussed. We expect that this systematic review will contribute to the comprehensive knowledge of antifreeze proteins to readers.

Deep learning predicts path-dependent plasticity

We show that material plasticity can be precisely and efficiently predicted by deep-learning methods. This approach is fundamentally different from the century-old theory of continuum plasticity because it is not iteratively tracing the yield surface, neither does it require the notion of effective strain or stress at the macroscopic level. Instead, we use representative computer simulations of materials, including microstructure and constituents, load them along different deformation paths, and then learn the reversible, irreversible, and history-dependent phenomena directly from data. We demonstrate that complex phenomena such as distortional hardening can be predicted within 0.5% error. The generality of the methodology and widespread importance of plasticity in designing structures and materials make it useful to a myriad of fields.

Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress–strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning.

Peptidic Antifreeze Materials: Prospects and Challenges

Necessitated by the subzero temperatures and seasonal exposure to ice, various organisms have developed a remarkably effective means to survive the harsh climate of their natural habitats. Their ice-binding (glyco)proteins keep the nucleation and growth of ice crystals in check by recognizing and binding to specific ice crystal faces, which arrests further ice growth and inhibits ice recrystallization (IRI). Inspired by the success of this adaptive strategy, various approaches have been proposed over the past decades to engineer materials that harness these cryoprotective features. In this review we discuss the prospects and challenges associated with these advances focusing in particular on peptidic antifreeze materials both identical and akin to natural ice-binding proteins (IBPs). We address the latest advances in their design, synthesis, characterization and application in preservation of biologics and foods. Particular attention is devoted to insights in structure-activity relations culminating in the synthesis of de novo peptide analogues. These are sequences that resemble but are not identical to naturally occurring IBPs. We also draw attention to impactful developments in solid-phase peptide synthesis and 'greener' synthesis routes, which may aid to overcome one of the major bottlenecks in the translation of this technology: unavailability of large quantities of low-cost antifreeze materials with excellent IRI activity at (sub)micromolar concentrations.

Hydration Shell of Antifreeze Proteins: Unveiling the Role of Non-Ice-Binding Surfaces

Antifreeze proteins (AFPs) have the ability to inhibit ice growth by binding to ice nuclei. Their ice-binding mechanism is still unclear, yet the hydration layer is thought to play a fundamental role. Here, we use molecular dynamics simulations to characterize the hydration shell of two AFPs and two non-AFPs. The calculated shell thickness and density of the AFPs do not feature any relevant difference with respect to the non-AFPs. Moreover, the hydration shell density is always higher than the bulk density and, thus, no low-density, ice-like layer is detected at the ice-binding surface (IBS) of AFPs. Instead, we observe local water-density differences in AFPs between the IBS (lower density) and the non-IBS (higher density). The lower solvent density at the ice-binding site can pave the way to the protein binding to ice nuclei, while the higher solvent density at the non-ice-binding surfaces might provide protection against ice growth.

Ice-binding proteins and the applicability and limitations of the kinetic pinning model

Ice-binding proteins (IBPs) are unique molecules that bind to and are active on the interface between two phases of water: ice and liquid water. This property allows them to affect ice growth in multiple ways: shaping ice crystals, suppressing the freezing point, inhibiting recrystallization and promoting nucleation. Advances in the protein's production technologies make these proteins promising agents for medical applications among others. Here, we focus on a special class of IBPs that suppress freezing by causing thermal hysteresis (TH): antifreeze proteins (AFPs). The kinetic pinning model describes the dynamics of a growing ice face with proteins binding to it, which eventually slow it down to a halt. We use the kinetic pinning model, with some adjustments made, to study the TH dependence on the solution's concentration of AFPs by fitting the model to published experimental data. We find this model describes the activity of (moderate) type III AFPs well, but is inadequate for the (hyperactive) Tenebrio molitor AFPs. We also find the engulfment resistance to be a key parameter, which depends on the protein's size. Finally, we explain intuitively how TH depends on the seeding time of the ice crystal in the protein solution. Using this insight, we explain the discrepancy in TH measurements between different assays. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.