Effective potentials induced by mixtures of patchy and hard co-solutes.

The addition of co-solutes to colloidal suspensions is often employed to induce tunable depletion interactions. In this work, we investigate effective colloidal interactions arising from binary co-solute mixtures of hard spheres and patchy particles. By changing the relative concentration of the two species, we show that the resulting effective potential Veff continuously changes from the one obtained for a single-component hard sphere co-solute to that mediated by the single-component patchy particle co-solute. Interestingly, we find that, independent of the relative concentration of the two components, the resulting Veff is additive, i.e., it is well-described by the linear combination of the effective interactions mediated by respective pure co-solutes. However, a breakdown of the additivity occurs when the co-solute mixture is close to the onset of a demixing transition. These results represent a step forward in understanding and predicting colloidal behavior in complex and crowded environments and for exploiting this knowledge to design targeted colloidal superstructures.

Polarizable and non-polarizable force fields: Protein folding, unfolding, and misfolding.

Molecular dynamics simulations are an invaluable tool to characterize the dynamic motions of proteins in atomistic detail. However, the accuracy of models derived from simulations inevitably relies on the quality of the underlying force field. Here, we present an evaluation of current non-polarizable and polarizable force fields (AMBER ff14SB, CHARMM 36m, GROMOS 54A7, and Drude 2013) based on the long-standing biophysical challenge of protein folding. We quantify the thermodynamics and kinetics of the ß-hairpin formation using Markov state models of the fast-folding mini-protein CLN025. Furthermore, we study the (partial) folding dynamics of two more complex systems, a villin headpiece variant and a WW domain. Surprisingly, the polarizable force field in our set, Drude 2013, consistently leads to destabilization of the native state, regardless of the secondary structure element present. All non-polarizable force fields, on the other hand, stably characterize the native state ensembles in most cases even when starting from a partially unfolded conformation. Focusing on CLN025, we find that the conformational space captured with AMBER ff14SB and CHARMM 36m is comparable, but the ensembles from CHARMM 36m simulations are clearly shifted toward disordered conformations. While the AMBER ff14SB ensemble overstabilizes the native fold, CHARMM 36m and GROMOS 54A7 ensembles both agree remarkably well with experimental state populations. In addition, GROMOS 54A7 also reproduces experimental folding times most accurately. Our results further indicate an over-stabilization of helical structures with AMBER ff14SB. Nevertheless, the presented investigations strongly imply that reliable (un)folding dynamics of small proteins can be captured in feasible computational time with current additive force fields.

Charge Anisotropy of Nitrogen: Where Chemical Intuition Fails.

For more than half a century computer simulations were developed and employed to study ensemble properties of a wide variety of atomic and molecular systems with tremendous success. Nowadays, a selection of force-fields is available that describe the interactions in such systems. A key feature of force-fields is an adequate description of the electrostatic potential (ESP). Several force-fields model the ESP via point charges positioned at the atom centers. A major shortcoming of this approach, its inability to model anisotropies in the ESP, can be mitigated using additional charge sites. It has been shown that nitrogen is the most problematic element abundant in many polymers as well as large molecules of biological origin. To tackle this issue, small organic molecules containing a single nitrogen atom were studied. In performing rigorous scans of the surroundings of these nitrogen atoms, positions where a single extra charge can enhance the ESP description the most were identified. Significant improvements are found for ammonia, amines, and amides. Interestingly, the optimal location for the extra charge does not correlate with the chemically intuitive position of the nitrogen lone pair. In fact, the placement of an extra charge in the lone-pair location does not lead to significant improvements in most cases.

Dynamics Rationalize Proteolytic Susceptibility of the Major Birch Pollen Allergen Bet v 1.

Proteolytic susceptibility during endolysosomal degradation is decisive for allergic sensitization. In the major birch pollen allergen Bet v 1 most protease cleavage sites are located within its secondary structure elements, which are inherently inaccessible to proteases. The allergen thus must unfold locally, exposing the cleavage sites to become susceptible to proteolysis. Hence, allergen cleavage rates are presumed to be linked to their fold stability, i.e., unfolding probability. Yet, these locally unfolded structures have neither been captured in experiment nor simulation due to limitations in resolution and sampling time, respectively. Here, we perform classic and enhanced molecular dynamics (MD) simulations to quantify fold dynamics on extended timescales of Bet v 1a and two variants with higher and lower cleavage rates. Already at the nanosecond-timescale we observe a significantly higher flexibility for the destabilized variant compared to Bet v 1a and the proteolytically stabilized mutant. Estimating the thermodynamics and kinetics of local unfolding around an initial cleavage site, we find that the Bet v 1 variant with the highest cleavage rate also shows the highest probability for local unfolding. For the stabilized mutant on the other hand we only find minimal unfolding probability. These results strengthen the link between the conformational dynamics of allergen proteins and their stability during endolysosomal degradation. The presented approach further allows atomistic insights in the conformational ensemble of allergen proteins and provides probability estimates below experimental detection limits.

Glass polymorphism and liquid-liquid phase transition in aqueous solutions: experiments and computer simulations.

One of the most intriguing anomalies of water is its ability to exist as distinct amorphous ice forms (glass polymorphism or polyamorphism). This resonates well with the possible first-order liquid-liquid phase transition (LLPT) in the supercooled state, where ice is the stable phase. In this Perspective, we review experiments and computer simulations that search for LLPT and polyamorphism in aqueous solutions containing salts and alcohols. Most studies on ionic solutes are devoted to NaCl and LiCl; studies on alcohols have mainly focused on glycerol. Less attention has been paid to protein solutions and hydrophobic solutes, even though they reveal promising avenues. While all solutions show polyamorphism and an LLPT only in dilute, sub-eutectic mixtures, there are differences regarding the nature of the transition. Isocompositional transitions for varying mole fractions are observed in alcohol but not in ionic solutions. This is because water can surround alcohol molecules either in a low- or high-density configuration whereas for ionic solutes, the water ion hydration shell is forced into high-density structures. Consequently, the polyamorphic transition and the LLPT are prevented near the ions, but take place in patches of water within the solutions. We highlight discrepancies and different interpretations within the experimental community as well as the key challenges that need consideration when comparing experiments and simulations. We point out where reinterpretation of past studies helps to draw a unified, consistent picture. In addition to the literature review, we provide original experimental results. A list of eleven open questions that need further consideration is identified.

Glass polymorphism in TIP4P/2005 water: A description based on the potential energy landscape formalism.

The potential energy landscape (PEL) formalism is a statistical mechanical approach to describe supercooled liquids and glasses. Here, we use the PEL formalism to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) using computer simulations of the TIP4P/2005 molecular model of water. We find that the properties of the PEL sampled by the system during the LDA-HDA transformation exhibit anomalous behavior. In particular, at conditions where the change in density during the LDA-HDA transformation is approximately discontinuous, reminiscent of a first-order phase transition, we find that (i) the inherent structure (IS) energy, eIS(V), is a concave function of the volume and (ii) the IS pressure, PIS(V), exhibits a van der Waals-like loop. In addition, the curvature of the PEL at the IS is anomalous, a nonmonotonic function of V. In agreement with previous studies, our work suggests that conditions (i) and (ii) are necessary (but not sufficient) signatures of the PEL for the LDA-HDA transformation to be reminiscent of a first-order phase transition. We also find that one can identify two different regions of the PEL, one associated with LDA and another with HDA. Our computer simulations are performed using a wide range of compression/decompression and cooling rates. In particular, our slowest cooling rate (0.01 K/ns) is within the experimental rates employed in hyperquenching experiments to produce LDA. Interestingly, the LDA-HDA transformation pressure that we obtain at T = 80 K and at different rates extrapolates remarkably well to the corresponding experimental pressure.

q-Independent Slow Dynamics in Atomic and Molecular Systems.

Investigating million-atom systems for very long simulation times, we demonstrate that the collective density-density correlation time (τ_{α}) in simulated supercooled water and silica becomes wave-vector independent (q^{0}) when the probing wavelength is several times larger than the interparticle distance. The q independence of the collective density-density correlation functions, a feature clearly observed in light-scattering studies of some soft-matter systems, is thus a genuine feature of many (but not all) slow-dynamics systems, either atomic, molecular, or colloidal. Indeed, we show that when the dynamics of the density fluctuations includes particle-type diffusion, as in the case of the Lennard-Jones binary-mixture model, the q^{0} regime does not set in and the relaxation time continues to scale as τ_{α}∼q^{-2} even at small q.

Size dependence of dynamic fluctuations in liquid and supercooled water.

We study the evolution of dynamic fluctuations averaged over different space lengths and time scales to characterize spatially and temporally heterogeneous behavior of TIP4P/2005 water in liquid and supercooled states. Analyzing a 250 000 molecules simulated system, we provide evidence of the existence, upon supercooling, of a significant enhancement of spatially localized dynamic fluctuations stemming from regions of correlated mobile molecules. We show that both the magnitude of the departure from the value expected for the system-size dependence of an uncorrelated system and the system size at which such a trivial regime is finally recovered clearly increase upon supercooling. This provides a means to estimate an upper limit to the maximum length scale of influence of the regions of correlated mobile molecules. Notably, such an upper limit grows two orders of magnitude on cooling, reaching a value corresponding to a few thousand molecules at the lowest investigated temperature.

The Adam-Gibbs relation and the TIP4P/2005 model of water.

We report a numerical test of the Adam-Gibbs relation for the TIP4P/2005 model of water. The configurational entropy is here evaluated as the logarithm of the number of different basins in the potential energy landscape sampled in equilibrium conditions. Despite the non-monotonic behaviour which characterise the density dependence of the diffusion coefficient, the Adam-Gibbs relation is satisfied within the numerical precision in a wide range of densities and temperatures. We also show that expressions based on the excess entropy (the logarithm of the number of sampled microstates in phase space) fail in the region of densities where a tetrahedral hydrogen bond network develops.

Potential energy landscape of TIP4P/2005 water.

We report a numerical study of the statistical properties of the potential energy landscape of TIP4P/2005, one of the most accurate rigid water models. We show that, in the region where equilibrated configurations can be generated, a Gaussian landscape description is able to properly describe the model properties. We also find that the volume dependence of the landscape properties is consistent with the existence of a locus of density maxima in the phase diagram. The landscape-based equation of state accurately reproduces the TIP4P/2005 pressure-vs-volume curves, providing a sound extrapolation of the free-energy at low T. A positive-pressure liquid-liquid critical point is predicted by the resulting free-energy.

Experimental study of the polyamorphism of water. I. The isobaric transitions from amorphous ices to LDA at 4 MPa.

The existence of more than one solid amorphous state of water is an extraordinary feature. Since polyamorphism might be connected to the liquid-liquid critical point hypothesis, it is particularly important to study the relations amongst the different amorphous ices. Here we study the polyamorphic transformations of several high pressure amorphous ices to low-density amorphous ice (LDA) at 4 MPa by isobaric heating utilising in situ volumetry and ex situ X-ray diffraction. We find that very-high density amorphous ice (VHDA) and unannealed high density amorphous ice (HDA) show significant relaxation before transforming to LDA, whereby VHDA is seen to relax toward HDA. By contrast, expanded HDA shows almost no relaxation prior to the transformation. The transition to LDA itself obeys criteria for a first-order-like transition in all cases. In the case of VHDA, even macroscopic phase separation is observed. These findings suggest that HDA and LDA are two clearly distinct polyamorphs. We further present evidence that HDA reaches the metastable equilibrium at 140 K and 0.1 GPa but only comes close to that at 140 K and 0.2 GPa. The most important is the path independence of the amorphous phase reached at 140 K and 0.1 GPa.

Experimental study of the polyamorphism of water. II. The isobaric transitions between HDA and VHDA at intermediate and high pressures.

Since the first report of very-high density amorphous ice (VHDA) in 2001 [T. Loerting et al., Phys. Chem. Chem. Phys. 3, 5355-5357 (2001)], the status of VHDA as a distinct amorphous ice has been debated. We here study VHDA and its relation to expanded high density amorphous ice (eHDA) on the basis of isobaric heating experiments. VHDA was heated at 0.1 ≤ p ≤ 0.7 GPa, and eHDA was heated at 1.1 ≤ p ≤ 1.6 GPa to achieve interconversion. The behavior upon heating is monitored using in situ volumetry as well as ex situ X-ray diffraction and differential scanning calorimetry. We do not observe a sharp transition for any of the isobaric experiments. Instead, a continuous expansion (VHDA) or densification (eHDA) marks the interconversion. This suggests that a continuum of states exists between VHDA and HDA, at least in the temperature range studied here. This further suggests that VHDA is the most relaxed amorphous ice at high pressures and eHDA is the most relaxed amorphous ice at intermediate pressures. It remains unclear whether or not HDA and VHDA experience a sharp transition upon isothermal compression/decompression at low temperature.

Supercooled and glassy water: Metastable liquid(s), amorphous solid(s), and a no-man's land.

We review the recent research on supercooled and glassy water, focusing on the possible origins of its complex behavior. We stress the central role played by the strong directionality of the water-water interaction and by the competition between local energy, local entropy, and local density. In this context we discuss the phenomenon of polyamorphism (i.e., the existence of more than one disordered solid state), emphasizing both the role of the preparation protocols and the transformation between the different disordered ices. Finally, we present the ongoing debate on the possibility of linking polyamorphism with a liquid-liquid transition that could take place in the no-man's land, the temperature-pressure window in which homogeneous nucleation prevents the investigation of water in its metastable liquid form.

Relaxation dynamics and transformation kinetics of deeply supercooled water: Temperature, pressure, doping, and proton/deuteron isotope effects.

Above its glass transition, the equilibrated high-density amorphous ice (HDA) transforms to the low-density pendant (LDA). The temperature dependence of the transformation is monitored at ambient pressure using dielectric spectroscopy and at elevated pressures using dilatometry. It is found that near the glass transition temperature of deuterated samples, the transformation kinetics is 300 times slower than the structural relaxation, while for protonated samples, the time scale separation is at least 30 000 and insensitive to doping. The kinetics of the HDA to LDA transformation lacks a proton/deuteron isotope effect, revealing that this process is dominated by the restructuring of the oxygen network. The x-ray diffraction experiments performed on samples at intermediate transition stages reflect a linear combination of the LDA and HDA patterns implying a macroscopic phase separation, instead of a local intermixing of the two amorphous states.

Condensation and Demixing in Solutions of DNA Nanostars and Their Mixtures.

We present a numerical/theoretical approach to efficiently evaluate the phase diagram of self-assembling DNA nanostars. Combining input information based on a realistic coarse-grained DNA potential with the Wertheim association theory, we derive a parameter-free thermodynamic description of these systems. We apply this method to investigate the phase behavior of single components and mixtures of DNA nanostars with different numbers of sticky arms, elucidating the role of the system functionality and of salt concentration. Specifically, we evaluate the propensity to demix, the gas-liquid phase boundaries and the location of the critical points. The predicted critical parameters compare very well with existing experimental results for the available compositions. The approach developed here is very general, easily extensible to other all-DNA systems, and provides guidance for future experiments.

The glass transition in high-density amorphous ice.

There has been a long controversy regarding the glass transition in low-density amorphous ice (LDA). The central question is whether or not it transforms to an ultraviscous liquid state above 136 K at ambient pressure prior to crystallization. Currently, the most widespread interpretation of the experimental findings is in terms of a transformation to a superstrong liquid above 136 K. In the last decade some work has also been devoted to the study of the glass transition in high-density amorphous ice (HDA) which is in the focus of the present review. At ambient pressure HDA is metastable against both ice I and LDA, whereas at > 0.2 GPa HDA is no longer metastable against LDA, but merely against high-pressure forms of crystalline ice. The first experimental observation interpreted as the glass transition of HDA was made using in situ methods by Mishima, who reported a glass transition temperature Tg of 160 K at 0.40 GPa. Soon thereafter Andersson and Inaba reported a much lower glass transition temperature of 122 K at 1.0 GPa. Based on the pressure dependence of HDA's Tg measured in Innsbruck, we suggest that they were in fact probing the distinct glass transition of very high-density amorphous ice (VHDA). Very recently the glass transition in HDA was also observed at ambient pressure at 116 K. That is, LDA and HDA show two distinct glass transitions, clearly separated by about 20 K at ambient pressure. In summary, this suggests that three glass transition lines can be defined in the p-T plane for LDA, HDA, and VHDA.

Temperature-induced amorphisation of hexagonal ice.

We systematically studied the competition between polymorphic transformations and amorphisation of hexagonal ice on isobaric heating from 77 K to 155-170 K at pressures between 0.50 and 1.00 GPa. This competition is analysed here systematically by in situ dilatometry and ex situ X-ray diffraction and calorimetry. Volume vs. temperature curves were analysed using a novel fitting approach in order to understand the underlying mechanism. Hexagonal ice undergoes solid-state-transformation to ice IX/III at 0.50 and 0.60 GPa and to a mixture of ices IX/III and IV at 0.70 and 0.80 GPa. Possibly a tiny fraction of amorphous intermediate is transiently formed in this pressure range. At 0.85 GPa the amorphisation process becomes competitive, and leads to very high-density amorphous ice (VHDA) as by-product. At 0.90 and 0.95 GPa VHDA is the main product and at 1.00 GPa only VHDA is found. This represents the first observation of temperature-induced amorphisation (TIA) for hexagonal ice using diffraction methods. Our analysis suggests TIA to be a first-order phase transition which, by contrast to pressure-induced amorphisation (PIA), does not involve a precursor process. We suggest interpreting TIA as thermodynamic melting of ice followed by immediate vitrification rather than as mechanical collapse of hexagonal ice. The activation energies for amorphisation and polymorphic transformation are equal at ∼0.75 GPa. At 1.00 GPa the activation energy for amorphisation of hexagonal ice is lower by about 6 kJ mol(-1) than the activation energy for polymorphic transitions.

Water's second glass transition.

The glassy states of water are of common interest as the majority of H2O in space is in the glassy state and especially because a proper description of this phenomenon is considered to be the key to our understanding why liquid water shows exceptional properties, different from all other liquids. The occurrence of water's calorimetric glass transition of low-density amorphous ice at 136 K has been discussed controversially for many years because its calorimetric signature is very feeble. Here, we report that high-density amorphous ice at ambient pressure shows a distinct calorimetric glass transitions at 116 K and present evidence that this second glass transition involves liquid-like translational mobility of water molecules. This "double Tg scenario" is related to the coexistence of two liquid phases. The calorimetric signature of the second glass transition is much less feeble, with a heat capacity increase at Tg,2 about five times as large as at Tg,1. By using broadband-dielectric spectroscopy we resolve loss peaks yielding relaxation times near 100 s at 126 K for low-density amorphous ice and at 110 K for high-density amorphous ice as signatures of these two distinct glass transitions. Temperature-dependent dielectric data and heating-rate-dependent calorimetric data allow us to construct the relaxation map for the two distinct phases of water and to extract fragility indices m = 14 for the low-density and m = 20-25 for the high-density liquid. Thus, low-density liquid is classified as the strongest of all liquids known ("superstrong"), and also high-density liquid is classified as a strong liquid.

Limits of metastability in amorphous ices: the neutron scattering Debye-Waller factor.

Recently, it became clear that relaxation effects in amorphous ices play a very important role that has previously been overlooked. The thermodynamic history of amorphous samples strongly affects their transition behavior. In particular, well-relaxed samples show higher thermal stability, thereby providing a larger window to investigate their glass transitions. We here present neutron scattering experiments using fixed elastic window scans on relaxed forms of amorphous ice, namely expanded high density amorphous ice (eHDA), a variant of low density amorphous ice (LDA-II) and hyperquenched glassy water (HGW). These amorphous ices are expected to be true glassy counterparts of deeply supercooled liquid water, therefore fast precursor dynamics of structural relaxation are expected to appear below the calorimetric glass transition temperature. The Debye-Waller factor shows a very weak sub-T(g) anomaly in some of the samples, which might be the signature of such fast precursor dynamics. However, we cannot find this behavior consistently in all samples at all reciprocal length scales of momentum transfer.

Relaxation time of high-density amorphous ice.

Amorphous water plays a fundamental role in astrophysics, cryoelectron microscopy, hydration of matter, and our understanding of anomalous liquid water properties. Yet, the characteristics of the relaxation processes taking place in high-density amorphous ice (HDA) are unknown. We here reveal that the relaxation processes in HDA at 110-135 K at 0.1-0.2 GPa are of collective and global nature, resembling the alpha relaxation in glassy material. Measured relaxation times suggest liquid-like relaxation characteristics in the vicinity of the crystallization temperature at 145 K. By carefully relaxing pressurized HDA for several hours at 135 K, we produce a state that is closer to the ideal glass state than all HDA states discussed so far in literature.