# Unravelling the Origins of Ice Nucleation on Organic Crystals

Gabriele C. Sosso  Department of Chemistry and Centre for Scientific
Computing, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United
Kingdom<EMAIL_ADDRESS>Thomas F. Whale  Institute for Climate and
Atmospheric Science, School of Earth and Environment, University of Leeds,
Leeds LS2 9JT, United Kingdom  Mark A. Holden  School of Earth and Environment
and School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom
Philipp Pedevilla  Thomas Young Centre, London Centre for Nanotechnology and
Department of Physics and Astronomy, University College London, Gower Street
London, London, WC1E 6BT, UK  Benjamin J. Murray  Institute for Climate and
Atmospheric Science, School of Earth and Environment, University of Leeds,
Leeds LS2 9JT, United Kingdom  Angelos Michaelides  Thomas Young Centre,
London Centre for Nanotechnology and Department of Physics and Astronomy,
University College London, Gower Street London, London, WC1E 6BT, UK

###### Abstract

Organic molecules such as steroids or amino acids form crystals that can
facilitate the formation of ice – arguably the most important phase transition
on earth. However, the origin of the ice nucleating ability of organic
crystals is still largely unknown. Here, we combine experiments and
simulations to unravel the microscopic details of ice formation on
cholesterol, a prototypical organic crystal widely used in cryopreservation.
We find that cholesterol – which is also a substantial component of cell
membranes – is an ice nucleating agent more potent than many inorganic
substrates, including the mineral feldspar (one of the most active ice
nucleating material in the atmosphere). Scanning electron microscopy
measurements reveal a variety of morphological features on the surfaces of
cholesterol crystals: this suggests that the topography of the surface is key
to the broad range of ice nucleating activity observed (from -4 to -20 C°). In
addition, we show via molecular simulations that cholesterol crystals aid the
formation of ice nuclei in a unconventional fashion. Rather than providing a
template for a flat ice-like contact layer (as found in the case of many
inorganic substrates), the flexibility of the cholesterol surface and its low
density of hydrophilic functional groups leads to the formation of molecular
cages involving both water molecules and terminal hydroxyl groups of the
cholesterol surface. These cages are made of 6- and, surprisingly, 5-membered
hydrogen bonded rings of water and hydroxyl groups that favour the nucleation
of hexagonal as well as cubic ice (a rare occurrence). We argue that the
phenomenal ice nucleating activity of steroids such as cholesterol (and
potentially of many other organic crystals) is due to (i) the ability of
flexible hydrophilic surfaces to form unconventional ice-templating structures
and (ii) the different nucleation sites offered by the diverse topography of
the crystalline surfaces. These findings clarify how exactly organic crystals
promote the formation of ice, thus paving the way toward the understanding of
ice formation in soft and biological matter - with obvious reverberations on
atmospheric science and cryobiology.

##  I Introduction

The freezing of liquid water into crystalline ice is a ubiquitous phenomenon
which is part of our everyday experience Bartels-Rausch (2013) and has
countless reverberations in fields as diverse as cryobiology Mocé et al.
(2010); Massie et al. (2014); Morris and Acton (2013) and atmospheric science
Murray et al. (2012); Slater et al. (2015). Strikingly, the overwhelming
majority of ice on earth forms heterogeneously, i.e. thanks to the presence of
substances, other than water itself, which facilitate the ice nucleation
process Murray et al. (2012); Sosso et al. (2016a). Much of what is known
about heterogeneous ice nucleation has come from the study of atmospherically
relevant ice nucleating agents Murray et al. (2012): in fact, heterogeneous
ice nucleation from supercooled water plays a critical role in the glaciation
of mixed phase clouds, which in turn influences the climate Lohmann and
Feichter (2005); Tan et al. (2016). A variety of substances are known to
nucleate ice efficiently in the atmosphere, including inorganic species such
as silver iodide Marcolli et al. (2016), feldspar Atkinson et al. (2013);
Harrison et al. (2016); Kiselev et al. (2017) as well as biological entities
such as the bacterium pseudomonas syringae Maki et al. (1974); Lindemann et
al. (1986); Pandey et al. (2016) or birch pollen Pummer et al. (2012).

Biological ice nucleating agents also play a key role in the ever-growing
field of cryobiology: in fact, the formation of ice in biological matter is
the cornerstone of cryotherapy and cryopreservation Morris and Acton (2013);
Bar Dolev et al. (2016), i.e. the long-term storage of frozen biological
material which is essential to enable cutting-edge technologies such as
regenerative medicine Asghar et al. (2014); Aijaz et al. (2018). A number of
organic crystals have been known to facilitate ice nucleation Fukuta and Mason
(1963); Fukuta (1966), and molecular crystals of steroids such as cholesterol
(CHL) Head (1961) are used to boost the formation of ice when cryopreserving
biological material Mocé et al. (2010); Massie et al. (2011). Importantly, CHL
molecules also represent a major component (up to 40%) of animal cell
membranes Krause and Regen (2014), thus prompting the question of whether this
steroid can play a role as ice nucleator in the context of ice formation in
biological matter.

However, the the microscopic details of heterogeneous ice nucleation on CHL -
and indeed on the vast majority of organic and inorganic compounds alike -
remain remarkably poorly understood Sosso et al. (2016a), although a
substantial body of experimental work has been devoted to assess the ice
nucleation ability of biological matter Fukuta (1966); Edwards and Evans
(1971); Pratt et al. (2009); Hoose et al. (2010); Wang et al. (2012); Davies
(2014); Liu et al. (2016); Campbell et al. (2017). In fact, the reason why
many biological ice nucleating agents display a far stronger ice nucleating
activity than most inorganic materials Murray et al. (2012); Sosso et al.
(2016a) is still largely unknown. Partly this is because obtaining molecular-
level insight into the nucleation process is still a formidable challenge for
experiments, and only very recently simulations of heterogeneous ice
nucleation have become feasible Sosso et al. (2016a); Zielke et al. (2016);
Zhang et al. (2014); Bi et al. (2016); Reinhardt and Doye (2014); Fraux and
Doye (2014); Pedevilla et al. (2017); Kiselev et al. (2017); Lupi et al.
(2017); Bi et al. (2017), largely thanks to the capabilities of the coarse
grained mW water model Molinero and Moore (2009). Indeed mW has played a
pivotal role in enabling systematic investigations of ice nucleation on e.g.
carbonaceous Lupi et al. (2014) or hydroxylated organic surfaces Qiu et al.
(2017). However, fully atomistic water models and enhanced sampling methods
are often required to take into account the subtleties of the hydrogen bond
network between water and complex impurities Sosso et al. (2016b, c).

In this work, we bring together experiments and simulations to take an
ambitious step forward in furthering our understanding of ice formation on
organic crystals. We focus on CHL, due to its relevance in cryopreservation
and its role within cellular membrane, unravelling microscopic motivations for
heterogeneous ice nucleation likely to be shared by many other organic
crystals. We find via micro-litre droplet nucleation measurements
($\mu$l-NIPI) that CHL crystals display an outstanding ice nucleation ability
(stronger than most inorganic ice nucleating agents), with freezing events
initiating at very mild supercooling $\Delta T_{S}=T_{\text{Melt}}-T$ = 4 K
down to $\Delta T_{S}$ = 20 K. Scanning electron microscopy suggests that the
activity of these crystals as ice nucleating agents across such a wide
temperature range could be due to the diverse topography of the surface of the
cholesterol crystals, which are likely to offer a variety of different
nucleation sites. In order to get a molecular-level insight into the mechanism
of ice formation on CHL crystals, we harness enhanced sampling simulations,
focusing on the hydroxylated (001) face of cholesterol monohydrate (CHLM) –
the most relevant surface (and polymorph, as discussed below) in biological
scenarios. We find that CHL crystals facilitate the formation of ice in a non-
conventional fashion: in contrast to what has been observed in the case of
inorganic substrates such as e.g. carbonaceous particles Lupi et al. (2014) or
clay minerals Sosso et al. (2016c), the flexibility of the CHLM surface and
the large spacing of its hydroxyl groups prevent the formation of a flat, ice-
like layer of water molecules at the water-crystal interface. Instead, the
hydroxyl groups participate in the formation of 5- and 6-membered hydrogen
bonded rings of water molecules forming peculiar molecular “cages” that
provide an effective template for the nucleation of both cubic and hexagonal
ice (a rare occurrence).

As a whole, our findings suggest that the formation of ice on CHL crystals
originates from the ability of their flexible hydrophilic surfaces to trigger
the formation of unconventional ice-templating molecular features. In
addition, different nucleation sites potentially offered by the diverse
topography of the crystal can further enhance the intrinsic ice nucleation
potential of CHL surfaces. This insight could help to understand ice formation
on a number of other organic compounds, from amino acid crystals Evans (1966);
Gavish et al. (1992) to bacterial fragments Wolber et al. (1986); Gurian-
Sherman and Lindow (1993) – as they are all characterised by the presence of
flexible hydrophilic surfaces displaying diverse topological features. In
addition, organic crystals such as cholesterol are positioned “in between”
inorganic and biological ice nucleating agents: they possess the order and the
crystalline surfaces of the former, and the complexity and flexibility of the
latter. This work thus paves the way to a molecular-level understanding of ice
formation in biological matter, tackling a substrate (CHL crystals) that
embeds unique features of very different classes of materials.

##  II Methods

###  $\mu$l-NIPI experiments and scanning electron microscopy measurements

The ice nucleation efficiency of CHLM was evaluated using an adapted version
of the $\mu$L Nucleation by Immersed Particles Instrument ($\mu$l-NIPI)
described in detail in Ref. Whale et al. (2015a). To make the flat plates we
dissolved 2g of pure CHL (Sigma Aldrich) in approximately 30 ml of hot ($\sim$
343 K) 95% ethanol (Sigma-Aldrich). The CHL solution was then allowed to cool
slowly, causing crystallisation of large (up to approx. 1 cm across) flat
plates of CHLM. Individual plates of CHLM of around 2mm diameter were then
recovered by vacuum filtration on a filter membrane and placed onto a thin
($\sim$ 0.1 mm) glass plate. The glass plate was then placed onto an EF600
Stirling cryocooler. A Picus Biohit electronic pipette was then used to
deposit 1 $\mu$l droplets of MilliQ water onto the separated CHLM plates. The
EF600 cryocooler was then used to reduce the temperature of the droplets at a
rate of 1 K/min. freezing was monitored using a camera. In this way the
droplet fraction frozen curve presented in Fig. 1a was built up. The data is
the result of several cooling runs as only about 10 droplets could be frozen
per experiment. It was important that plates were not in contact as ice
clearly propagated across the CHL surface, triggering neighbouring droplets
after an initial freezing events, when multiple droplets were placed on a
single plate.

In order to calculate the (surface) density of the active ice nucleation sites
($n_{s}$, commonly used to compare the ice nucleating efficiency of different
substances Murray et al. (2012)) on the CHLM surface (reported in Fig. 1) we
have used the following expression:

$\frac{n(T)}{N}=1-\exp{[-n_{s}\left(T\right)A]},$ (1)

where $n(T)$ is the number of droplets frozen at temperature $T$, $N$ is the
total number of droplets in the experiment and $A$ is the surface area of
nucleating agent per droplet. The value of $A$ for each droplet was measured
using the image analysis software imageJ, customarily used to quantify
particles size in biosciences Schneider et al. (2012). The resulting estimate
of the mean value of $A$ is 1.82 $\pm$ 0.46 mm2.

The uncertainties associated with the values of $n_{s}$ have been calculated
using Monte-Carlo simulations of possible active ice nucleation sites
distributions, propagated with the uncertainty associated with $A$ – as
described in Harrison et al. Harrison et al. (2016). These simulations
generate a list of possible values for the number of active sites per droplet
for a given experiment, given the observed freezing data. By repeating this
process a great many times, a distribution of the possible active site
distributions that can account for the freezing of each droplet is obtained.
The error bars for the CHLM $n_{s}$ data reported in Fig. 1 are generated by
propagating this distribution with the uncertainty in surface area of
cholesterol per droplet and taking the 95% confidence interval of the
resulting distribution. At high and low temperature ends of the reported data,
where the Poisson uncertainty (i.e. the error originating from the Monte-Carlo
simulations) is largest, the contribution of the uncertainty in surface area
amounts to approximately 25% of total uncertainty in $n_{s}(T)$, with the
Poisson uncertainty in the active site distribution accounting for the
remainder of the error bars.

Scanning electron microscopy (SEM) was performed on CHLM plates. These were
mounted on copper tape, then coated with 2 nm of iridium. SEM was performed
with an FEI Nova NanoSEM 450 in high vacuum mode, using an Everhart-Thornley
Detector (ETD).

### Molecular dynamics simulations

The computational setup we have used is depicted in Fig. 3a. A single layer of
CHL molecules, cleaved along the (001) plane (perpendicular to the normal to
the slab) was prepared by starting from the experimental cell parameters and
lattice positions Craven (1976). Specifically, a CHLM crystal system made of
two mirroring slabs (intercalated by water molecules, in a ratio of 1:1) was
cleaved along the (001) plane. The triclinc symmetry of the system (space
group $C1$) was preserved, and we have constructed a 3 by 3 supercell with in-
plane dimensions of 37.17 and 36.57 Å. We positioned 1923 water molecules
randomly atop this CHLM slab at the density of the TIP4P/Ice model Abascal et
al. (2005) at 300 K, and expanded the dimension of the simulation cell along
the normal to the slab to 100 Å. This setup allows for a physically meaningful
equilibration of the water at the density of interest at a given temperature,
but suffers from two distinct drawbacks: i) the CHLM slab possesses a net
dipole moment which is not compensated throughout the simulation cell and ii)
the presence of the water-vacuum interface can alter the structure and the
dynamics of the liquid film. However, we have previously addressed these
issues in previous work dealing with the hydroxylated (001) polar surface of
the clay mineral kaolinite Sosso et al. (2016b, c), concluding that such
details do not affect the mechanism nor the kinetics of ice formation. In
addition, the water film is thick enough to allow a bulk-like region to exist
in terms of both structure and dynamics. The effect of the water-vacuum
interface is therefore negligible. The slab considered in this work presents
the hydrophilic, -OH terminated heads of the CHL molecules to the water, in
agreement with experimental insight Abendan and Swift (2002). As we discuss in
the main text, the interaction between the hydroxyl groups (which display
amphoteric characteristics in terms of the hydrogen bond network) of CHL
molecules and water is responsible for the templating effect of CHLM crystals
which serves to promote ice nucleation.

The CHARMM36 Bjelkmar et al. (2010) force field was used to model the CHL
crystals, taking advantage of a recent update of this force field parameters
explicitly with respect to CHL Lim et al. (2012). In order to mimic the
experimental conditions, we have constrained the system at the experimental
lateral dimensions (detailed together with the computational geometry in the
SI), and we have also restrained the positions of the hydrophobic tail of each
CHL molecule (specifically, the carbon atoms C25, C26 and C27, see the inset
of Fig. S1 in the SI) by means of an harmonic potential characterised by a
spring constant of 10000 kJ/mol. All the other atoms within the CHLM slab are
unconstrained. We have verified that the thermal expansion of the crystal at
230 K ($\sim$ 0.1% with respect to each lateral dimension) does not alter the
structure nor the dynamics of the water-kaolinite interface. This setup is
thus as close as we can get to the realistic (001) hydrophilic surface of CHLM
within the CHARMM36 model. Implications of the flexibility of the CHLM slab
are discussed in the SI. The interaction between the water molecules have been
modelled using the TIP4P/Ice model Abascal et al. (2005), so that our results
are consistent with the homogeneous simulations of Ref. 57. The interaction
parameters between the clay and the water were obtained using the standard
Lorentz-Berthelot mixing rules Lorentz (1881).

Extreme care must be taken in order to correctly reproduce the structure and
the dynamics of the water-CHLM interface. The Forward Flux Sampling (FFS)
simulations reported in this work rely on a massive collection of unbiased
Molecular Dynamics (MD) runs, all of which have been performed using the
GROMACS package, version 4.6.7. The code was compiled in single-precision, in
order to alleviate the huge computational workload needed to converge the FFS
algorithm and because we have taken advantage of GPU acceleration, which is
not available in the double-precision version. The equations of motions were
integrated using a leap-frog integrator with a time step of 2 fs. The van der
Waals (non bonded) interactions were considered up to 10 Å, where a switching
function was used to bring them to zero at 12 Å. Electrostatic interactions
have been dealt with by means of an Ewald summation up to 12 Å. The NVT
ensemble was sampled at 230 K using a stochastic velocity rescaling thermostat
Bussi et al. (2007) with a very weak coupling constant of 4 ps in order to
avoid temperature gradients throughout the system. The geometry of the water
molecules (TIP4P/Ice being a rigid model) was constrained using the SETTLE
algorithm Miyamoto and Kollman (1992) while the P_LINCS algorithm Hess et al.
(1997) was used to constrain the O-H bonds within the clay. We have verified
that these settings reproduce the dynamical properties of water reported in
Ref. Haji-Akbari and Debenedetti (2015). The system was equilibrated at 300 K
for 10 ns, before being quenched to 230 K over 50 ns. This is the starting
point for the calculation of the initial flux rate for the FFS algorithm,
which lasted about 1.5 $\mu$s and thus allowed us to investigate the water-
CHLM interface as well (see e.g. Fig. 3).

##  III Results

###  III.1  Cholesterol promotes the formation of ice across a wide range of
temperatures

Figure 1: CHLM crystals promote the formation of ice across a wide range of
temperatures. (a) Droplet fraction frozen as a function of temperature for
1$\mu$l water droplets placed onto a CHLM substrate. (b) Ice-active surface
site density $n_{s}$ (see text and Methods section) values for the same data
reported for CHLM (CHL) in panel (a), together with $n_{s}$ values for
kaolinite (KAO) from Herbert et al. Herbert et al. (2014), BCS376 feldspar
(K-FELD) from Atkinson et al. Atkinson et al. (2013), graphene oxide (GRA)
from Whale et al. Whale et al. (2015b) and single-walled carbon nanotubes
(SWCN) also from Ref. 63. The uncertainty in terms of temperature associated
with the CHLM data is $\pm$ 0.4 K.

We start by experimentally investigating the ice nucleating ability of
cholesterol crystals - as a function of supercooling. CHL can crystallise into
two different polymorphs, namely anhydrous Shieh et al. (1977) (CHLA) and CHLM
Craven (1976). The latter is the most relevant to ice formation, as it
spontaneously forms in aqueous environments Craven (1976); Loomis et al.
(1979); Garti et al. (1981); Rapaport et al. (2001); Abendan and Swift (2002);
Solomonov et al. (2005). Conveniently, CHLM crystallises from a mixture of 95%
ethanol and 5% water as plates with the (001) surface forming the flat surface
of the plates Garti et al. (1981). The platey crystal habit of CHLM is
characteristic of CHLM as opposed to CHLA, which tends to crystallise as
needles. CHLM crystals display a layered structure: bilayers of CHL molecules
are stacked along the [001] direction, and facile cleavage along the (001)
planes leads to surfaces exposing either a -CH3 terminated, hydrophobic
surface or a -OH terminated, hydrophilic surface. Atomic and chemical force
microscopy measurements indicate that in aqueous and organic solution
conditions, the hydrophilic (001) surface is most abundantly found, in the
form of largely homogeneous crystalline faces Abendan and Swift (2002). Early
experimental evidence suggested substantial ice nucleation activity of CHLM at
very mild supercooling ($\Delta T_{S}$ = 5 K) Head (1961, 1962); Fukuta and
Mason (1963). The ice nucleation efficiency of CHLM was evaluated using an
adapted version of the $\mu$l-Nucleation by Immersed Particles Instrument
($\mu$l-NIPI) experiments $\mu$l-NIPI described in detail in Ref. 50.
Experiments were performed by placing droplets directly onto a surface of
crystalline CHLM. We used an electronic pipette to place 1 $\mu$l droplets of
water onto the (001) plane of plates of CHLM. The water droplets were then
cooled down at a rate of 1 K/min and freezing monitored using a camera. In
this way the fraction of frozen droplets can be determined as a function of
temperature. Note that as the crystalline surface is submerged in liquid water
these experiments are conducted at 100% relative humidity - i.e. in ”immersion
mode“ Vali et al. (2015).

In Fig. 1a we report the fraction of frozen droplets as a function of
temperature for CHLM. It can be seen that CHLM can induce ice nucleation at
temperatures as warm as 269 K. This agrees with previous studies which have
reported high nucleation temperatures for CHL in the immersion mode Mocé et
al. (2010); Massie et al. (2011). In here, we investigate the ice nucleating
ability of CHLM as a function of supercooling. As shown in Fig. 1a, the spread
of nucleation temperatures for the CHLM sheets is very broad, with some of
them freezing at temperatures as low as 252 K. To allow for a comparison of
the efficiency of ice nucleation by CHLM with other known nucleating species
we have calculated the ice-active surface site density ($n_{s}$) for CHLM on
the basis of the size of the contact patch of the water droplets with the CHL
plates. As explained in greater detail in the Methods section, $n_{s}$ is a
site specific measure of ice nucleation efficiency which does not take into
account the time dependence of ice nucleation, on the basis that the impact of
time dependence on heterogeneous ice nucleation is generally minimal Vali
(2014); Herbert et al. (2014); Vali et al. (2015). We have compared the ice
nucleating efficiency of CHLM with that of e.g. kaolinite powder Herbert et
al. (2014), which has commonly been regarded as an efficient ice nucleating
agent in the past Pruppacher and Klett (1997) and of BCS 376 feldspar powder,
which is known to nucleate ice highly efficiently Atkinson et al. (2013) and
was likely responsible for earlier observations of efficient ice nucleation in
kaolinite samples. It can be seen that CHLM nucleates ice far more efficiently
than kaolinite and more efficiently even than the feldspar at warm
temperatures. Thus, CHLM has the potential to be a highly efficient ice
nucleating agent in immersion mode across a wide range of temperatures - which
is the scenario typically encountered when dealing with cryobiological
applications.

###  III.2  The role of surface topography

Figure 2: CHLM crystals display a diverse surface topography. SEM images of
CHLM crystals, which predominantly expose {001} surfaces – consistent with
what has been reported in Ref. 54. It is quite clear that these plates possess
numerous topographical features, particularly steps and terraces.

As noted above the spread of freezing temperatures we report for CHLM is very
broad. This behaviour suggests that the nucleation behaviour of CHLM is
spatially heterogeneous, i.e. different parts of the surface nucleate ice with
differing efficiency. This is commonly known as _site specific_ nucleation
behaviour Vali (2014); Herbert et al. (2014); Vali et al. (2015); Vali (2008),
and it can be appreciated to a lesser extent for the other ice nucleating
agents considered in Fig. 1b. However, it is interesting to note that CHLM
crystals seem to lead to two different ice nucleation regimes, as can be
inferred from Fig. 1b (note the two different slopes characterising $n_{s}$ as
a function of temperature). As it is becoming increasingly clear that the
topography of the ice nucleating agents must play an important role in the
heterogeneous nucleation of ice from liquid water Gurganus et al. (2014); Bi
et al. (2017); Whale et al. (2017), we suspect that structural differences
between the crystalline areas covered by the water droplets are responsible
for the wide spread in nucleation temperatures observed. This hypothesis is
supported by the scanning electron microscope (SEM) images of the (001) face
of CHLM reported in Fig. 2. While the crystalline plates appear as mostly flat
and smooth within the resolution of $\sim$100 $\mu$m, it is clear that there
exist numerous defects, particularly steps and terraces, which can potentially
present opportunities for complicated surface geometries to occur. How exactly
the nanometric structure of crystalline ice nucleating agents affects the
kinetics of ice formation is still an open question (see e.g. Refs. 40; 32).
In fact, it would be expected that an atomically smooth and homogeneous CHL
surface would nucleate ice with a single nucleation rate and hence within a
far narrower range of temperatures than that reported in Fig. 1. The role of
specific defects and broadly speaking of the surface morphology to ice
formation on CHL - and the vast majority of biological nucleating agents, it
thus remains yet to be fully understood. For instance, it is not immediately
clear why CHLM crystals are much more effective than feldspar in promoting the
formation of ice. In the next section, we will address this issue by showing
that in addition to the topography of the surface, the formation of a peculiar
hydrogen bond network at the water-CHLM interface is key in determining the
ice nucleating ability of this compound.

###  III.3  The cholesterol-water interface

Figure 3: Structuring of water on the (001) hydroxylated face of CHLM. a)
Representative snapshot of a molecular dynamics simulation of a water slab in
contact with the (001) hydroxylated face of CHLM. The inset at the bottom
illustrates the arrangement of the hydroxyl group on the CHLM surface; an
hypothetical ice $I_{h}$ (001) plane (blue) is superimposed on part of the
image to highlight the absence of a structural match between -OH groups and
ice. b) Density profile of oxygen atoms belonging to either the -OH hydroxyl
groups of CHLM molecules (OCHL) or water molecules (O${}_{H_{2}O})$ along the
z-axis parallel to [001] direction, thus normal to the water-CHLM interface.
The zero of the x-axis corresponds to the average position of the $O_{CHL}$
atoms, while the shaded area in green identifies the water-CHLM interface.
Statistics have been accumulated over a 1.5 $\mu$s long simulation at 230 K.
c) Number of n-membered rings of hydrogen bonded water molecules at the water-
CHLM interface (Surf) or within the bulk of the water slab (Bulk), normalised
by the number of oxygen atoms in each region. Note that at the water-CHLM
interface oxygen atoms belonging to the CHLM -OH hydroxyl groups have also
been considered when computing the rings statistics.

In order to investigate the molecular-level details of the CHLM-water
interface, we have performed unbiased molecular dynamics simulations at strong
supercooling ($\Delta T_{S}$ = 42 K) employing the CHARMM36 Bjelkmar et al.
(2010); Lim et al. (2012) and the TIP4P/Ice Abascal et al. (2005) force fields
for CHL and water molecules respectively. Computational details and results
concerning the validation of our computational setup are reported in the
Methods section and in the Supplementary Information (SI) respectively, while
the computational geometry is depicted in Fig. 3a.

A water slab ($\sim$ 40 Å thick) is in contact with the hydroxylated (001)
surface of CHLM (CHLM${}^{-OH}_{001}$), modelled as a single layer of CHL
molecules. This surface is hydrophilic, due to the presence of amphoteric
hydroxyl groups. As CHL molecules are relatively bulky and the crystal is held
together by weak electrostatic interactions only, the arrangement of these -OH
groups on the CHLM surface is characterised by a broad distribution of large
OH-OH distances, ranging from 5.1 to 7.1 Å - as illustrated in Fig. 3a. Such a
pattern of hydroxyl groups does not straightforwardly match any particular
low-index Miller surface of either hexagonal or cubic ice. This is relevant,
as a good structural match between a substrate and ice Pedevilla et al. (2017)
has traditionally been considered as a ”requirement” of an effective ice
nucleating agent Turnbull and Vonnegut (1952).

Interestingly, despite the presence of the hydroxyl groups, the density
profile of the oxygen atoms of the water molecules on CHLM reported in Fig. 3b
resembles that for water at hydrophobic walls Harrach and Drossel (2014). The
enhancement ($\sim$ 30% in Fig. 3b) of the density, within the first peak of
the profile, compared to its value in the bulk of the water slab, is much
smaller than that (typically a factor four or six) observed for e.g. water in
contact with hydrophilic walls – or indeed water on kaolinite. This is
because, the outer layer of the CHLM crystals is much more mobile/flexible
than that of kaolinite: this is not surprising, as we are comparing a
molecular organic crystal (held together by van der Waals interactions) with a
(covalently bonded) clay mineral. Importantly, it is reasonable to assume that
a similar degree of flexibility characterises the majority of organic crystals
containing long molecules such as steroids. This is relevant to ice formation
because, as discussed in e.g. Ref. 43, the structural fluctuations of
organic/biological ice nucleating particles can strongly affect the kinetics
of ice nucleation. In fact, we have shown in Ref. 45 that the same argument
holds in the case of kaolinite as well: for instance, a “frozen” kaolinite
surface (atoms are kept fixed during MD simulations) leads to nonphysically
fast ice nucleation rates.

Figure 4: The formation of unconventional ice-templating molecular structures:
hydrogen bonded cages. a) A hydroxyl group (purple) of CHLM participates into
a hydrogen bonded cage of water molecules. b) A single hydrogen bonded cage
(top view), which constitutes the building block of cubic ice (panel c, side
view). Note that these cages are made of both 6-membered (panel d, side view)
and 5-membered (panel e, side view) hydrogen bonded rings, involving water
molecules as well as a hydroxyl group provided by the CHLM surface.

Because of this flexibility of the CHL molecules and the low-density of
hydroxyl groups at the water-CHLM interface, we did not observe (within a 200
ns time scale) the formation of an ordered, ice-like over-layer of water
molecules, in contrast with what is generally found in the case of idealised
crystalline surfaces Fitzner et al. (2015), carbonaceous particles Lupi et al.
(2014) or kaolinite crystals Sosso et al. (2016c, b). In fact, most inorganic
substrates are characterised by surfaces where atomic/molecular species are
tightly packed, and can thus potentially provide a high density of functional
groups for supercooled water to interact with, typically by forming a more or
less ordered overlayer sitting on top of the crystalline surface. In the case
of the water-CHLM interface, however, water molecules can partially infiltrate
the outer layer of the CHLM surface (see Fig. 3a and Fig. 3b) due to the
relatively large spacing between the CHL molecules and the flexibility of the
surface itself. As a net result, despite the absence of a flat overlayer of
ice-like water molecules, the amphoteric character of the hydroxyl groups does
facilitate the formation of a network of hydrogen bonded rings of water
molecules as well as hydroxyl groups, as illustrated in Fig. 3c. In
particular, we observe the emergence of 6-membered rings of hydrogen bonded
water molecules and hydroxyl groups. These rings are the building blocks of
both hexagonal (ice $I_{h}$) and cubic (ice $I_{c}$) ice, and are the most
abundant species in bulk water. Note that the occurrence of these rings is
actually even more pronounced in the proximity of the CHLM-water interface
(red/orange points/curve in Fig. 3c). Surprisingly, there is also an increase
in the number of 5-membered water/hydroxyl rings at the crystal-liquid
interface. Pentagonal rings are thought to frustrate the homogeneous formation
of ice Shintani and Tanaka (2006); however, in this case both 6- and
5-membered rings alike contribute to the formation of ice-like fluctuations
such as the ”cage” shown in Fig. 4a. These cages are indeed the building
blocks of ice $I_{c}$ (see Fig. 4b and Fig. 4c), and involve hydrogen bonds
between water molecules and hydroxyl groups, as depicted in Fig. 4d and Fig.
4e. Thus, in this heterogeneous nucleation scenario, the presence of
5-membered rings in not detrimental; on the contrary, they lead to the
formation of ice-like fluctuations of the water network at the water-
CHLM${}^{-OH}_{001}$ interface.

We note that the emergence of these cages is the reason why we have chosen to
consider as the ”interfacial layer” those water molecules within 5.0 Å from
the average position of the oxygens of the CHL hydroxyl groups - as
illustrated by the shaded region in Fig. 3b. As shown in e.g. Ref. 80, the
definition of this water layer can have an impact on the analysis of the
structure of - in this case - the water-CHLM interface. While the interfacial
layer can be chosen on the basis on indicators such as the first or second
minimum of the density profile (see Fig. 3b), we have found that the rather
generous cutoff of 5.0 Å is sufficient to accommodate the substantial extent
of the hydrogen bonded cages depicted in Fig. 4d and Fig. 3e. We have also
verified that by choosing the second minimum of the density profile ($\sim$7Å)
our results, including the trends within the rings statistics reported in Fig.
3c, are basically unchanged.

Our findings thus contribute the growing body of evidence Fitzner et al.
(2015); Qiu et al. (2017); Bi et al. (2017) that the structural mismatch
argument alone cannot be deemed as neither a sufficient nor a necessary
criteria to assess, let alone to predict, the ice nucleating ability of a
given substrate Pedevilla et al. (2017). This is bound to be especially true
in the case of biological ice nucleating agents such as macromolecules Pummer
et al. (2012), where the notion itself of a lattice mismatch is ill defined.
In fact, we argue that organic crystals such as cholesterol lie halfway in
between inorganic (e.g. mineral crystals) and biological (e.g. bacterial
fragments) ice nucleating agents, as they are characterised by the relatively
flat and (in this case) -OH regularly patterned surfaces of the former while
showing the flexibility of the latter. This is particularly relevant for CHL,
which is a substantial component of animal cellular membranes Krause and Regen
(2014) and could thus contribute to promote the heterogeneous formation of ice
in biological matter – a possibility we will investigate in future work. In
this respect, it is interesting to note that very recent simulations Hudait et
al. (2018) suggest that ice can bind to antifreeze proteins via “anchored
clathrate” motifs not dissimilar to the molecular cages discussed above.

###  III.4  Ice nucleation mechanism and kinetics

In order to characterise the mechanism as well as the kinetics of ice
nucleation on CHLM${}^{-OH}_{001}$ we have performed forward flux sampling
(FFS) simulations Allen et al. (2009); Li et al. (2011, 2013); Valeriani et
al. (2005); Wang et al. (2009); Bi and Li (2014); Gianetti et al. (2016);
Haji-Akbari and Debenedetti (2017). While other enhanced sampling techniques
are in principle available, such as metadynamics Laio and Parrinello (2002),
transition path sampling Bolhuis et al. (2002), and seeded molecular dynamics
Espinosa et al. (2016), FFS represents a “gold standard” approach when dealing
with ice nucleation (see e.g. Refs. 57; 35; 44; 89; 93). This method involves
partitioning the path from (in this case) liquid water to ice, described by an
order parameter $\lambda$, into a collection of interfaces $\lambda_{i}$.
Here, $\lambda$ corresponds to the number of water molecules within the
largest ice nucleus, which can be located either in the bulk of the water slab
or at the water-CHLM${}^{-OH}_{001}$ interface. A diffuse crystal-liquid
interface has been taken into account into the definition of $\lambda$, which
relies on local bond order parameters (see SI and Ref. 94), consistent with
Ref. 44. Starting from the natural fluctuations of liquid water toward the ice
phase, i.e. pre-critical ice nuclei as sampled within $\mu$s long unbiased MD
simulations, the nucleation rate $\mathcal{J}$ can be obtained as the product
of the flux $\Phi_{\lambda_{0}}$ by which the system reached the first
interface $\lambda_{0}$, times the product of the sequence of the individual
crossing probabilities $P(\lambda_{i}|\lambda_{i-1})$:

$\mathcal{J}={\Phi}_{\lambda_{0}}\prod_{i=1}^{N_{\lambda}}P(\lambda_{i}|\lambda_{i-1})$
(2)

In this way, the (exceedingly small) total probability
$P(\lambda_{ice}|\lambda_{0})$ for a certain MD trajectory to reach the ice
basin is decomposed in a collection of (manageable) crossing probabilities
which we compute by a large number (103 to 105) of unbiased MD trial runs from
$\lambda_{i-1}$ to $\lambda_{i}$. Further details about the FFS algorithm can
be found in the SI. We note that we have used the same water model (TIP4P/Ice)
at the same strong supercooling ($\Delta T_{S}$=42 K) as employed previously
to compute the homogeneous ice nucleation rate and the heterogeneous ice
nucleation rate on kaolinite, a clay mineral of relevance to atmospheric
science. As such, we can compare directly our results with those of Refs. 57
and 44.

From the very early stages of the nucleation process, we observe a strong
preference for ice to form at the water-CHLM${}^{-OH}_{001}$ interface – as
opposed to within the bulk of the water slab. In fact, $\sim$ 75% of the pre-
critical ice nuclei we observe as natural fluctuations of the supercooled
water network ($\lambda$=0) sit on top of the CHLM${}^{-OH}_{001}$ surface.
The calculated growth probability $P(\lambda|\lambda_{0})$ as a function of
lambda, together with the fraction of ice nuclei that can be found at the
water-CHLM${}^{-OH}_{001}$ interface are reported in the SI (Fig. S2b). By the
time the FFS algorithm has reached $\lambda$=125, no nuclei within the bulk of
the water slab survive. We have observed a similar trend in the case of ice
nucleation on the hydroxylated (001) basal face of kaolinite Sosso et al.
(2016b), but the fraction of ice nuclei at the water-kaolinite interface at
the initial stages of the FFS algorithm was much smaller ($\sim$ 25%). This
suggests that pre-critical ice-like fluctuations, which we have recently
investigated in the broader context of heterogeneous crystal nucleation
Fitzner et al. (2017), are much more likely to occur at the surface of CHLM
compared to kaolinite.

The mechanism of ice nucleation at the water-CHLM${}^{-OH}_{001}$ interface is
illustrated in Fig. 5: the early stages involve the formation of elongated,
almost one dimensional, linear, chain-like ice nuclei preferentially along
specific directions (see SI), due to the particular arrangement of the -OH
hydroxyl groups on the CHLM${}^{-OH}_{001}$ surface. However, larger nuclei
(corresponding to increasing values of $\lambda$) progressively assume a more
isotropic shape, as indicated by the evolution of the asphericity parameter
$\alpha$ (equal to 1 and 0 for a infinitely elongated rod and a perfect sphere
respectively) as a function of $\lambda$. At the same time, the 1D character
of the nuclei evolves toward a more compact geometry, with a significant
growth along the [001] direction (z-axis) normal to the water-
CHLM${}^{-OH}_{001}$ interface, as demonstrated by the trend of the dimension
$\Delta Z$ of the ice nuclei along that axis, also reported in Fig. 5. The
resulting morphology of the ice crystals, though, remains to be investigated
because of the emergence of finite size effects. Overall, the evolution of the
ice nuclei within the early stage of ice nucleation at the water-
CHLM${}^{-OH}_{001}$ interface possesses some similarities with the case of
ice formation on kaolinite Sosso et al. (2016b), where ice nuclei spread into
a 2D, planar geometry before stacking additional ice layers along the normal
to the water-kaolinite interface, once the critical nucleus has been reached.
Thus, these findings suggest that the nature of the early stages of
heterogeneous ice nucleation at strong supercooling ($\Delta T_{S}$ = 42 K)
has a strong anisotropic character, in stark contrast with the assumptions
prescribed by classical nucleation theory (CNT) Cabriolu and Li (2015).

In fact, CNT does not take into account the molecular structure nor the
”chemistry” of the substrate: these aspects are only implicitly included into
the value of the contact angle of the ice nuclei with respect to the
substrate. However, microscopic features such as the particular arrangement of
the hydroxyl groups on the CHLM surface can influence the shape and the
energetics of the ice nuclei. In the case of ice on CHLM, water molecules at
the water-cholesterol interface find convenient to harness the directionality
of the -OH pattern (see Fig. 3a and Fig. 3 in the SI) to form anisotropic ice
nuclei (see Fig. 5 and Fig. 3 in the SI), which are likely to be characterised
by a much smaller interfacial energy if compared to the hemispherical shape
predicated by CNT in the case of perfectly flat, featureless substrates. We
note however that in order to probe this aspect of CNT quantitatively, it
would be desirable to improve the current enhanced sampling techniques to take
into account milder supercooling - and thus larger critical ice nuclei.

The ice nucleation rate on the CHLM${}^{-OH}_{001}$ surface obtained from our
FFS simulations is 1027±3 s-1m-3, about 20 orders of magnitude larger than the
homogeneous ice nucleation rate at the same supercooling – calculated via FFS
simulations using the same water model Haji-Akbari and Debenedetti (2015).
This spectacular enhancement of the kinetics of ice formation is due to the
small heterogeneous critical nucleus size $N^{*}_{\text{H}}$, which we
estimate (as discussed in detail in the SI) to contain 250 $\pm$ 50 water
molecules – a number consistent with the predictions of CNT (see SI and Ref.
44). Interestingly, these results are very similar to what we have previously
obtained in the case of ice formation on kaolinite Sosso et al. (2016b), where
we calculated $\mathcal{J}$ = 1026±2 s-1m-3 and $N^{*}_{\text{H}}$ = 225 $\pm$
25\. However, it has to be said that the FFS simulations performed in this
work (as opposed to the case of kaolinite Sosso et al. (2016b)) may be
suffering from finite size effects (discussed in the SI), which could both
enhance the kinetics of ice nucleation (as the ice nuclei feel the influence
of their periodic images) and/or hamper the growth of ice crystals (as the
simulation box most likely does not match the periodicity of the growing ice
crystal). Our estimates of $\mathcal{J}$ and $N^{*}_{\text{H}}$ have therefore
to be taken with care.

The fact that the kinetics of ice formation on the CHLM${}^{-OH}_{001}$
surface seems to be comparable with that of an inorganic crystal such as
kaolinite is not entirely unexpected, as the (001) hydroxylated surface of
kaolinite also presents -OH groups at the water-crystal interface which are
capable of templating the formation of ice-like structures. However,
supercooled water on kaolinite forms a dense, hexagonal ordered overlayer of
ice-like molecules sitting on top of the hydroxyl groups Sosso et al. (2016c),
while, as we have discussed in the previous section, water molecules can
partially infiltrate the CHLM${}^{-OH}_{001}$ surface to form 5- and 6-
membered hydrogen bonded rings, resulting in a much less ordered and way less
dense overlayer. As both substrates (kaolinite and CHLM) are characterised by
the presence of hydroxyl groups which facilitate the formation of ice, the
much faster kinetics of ice nucleation we have observed experimentally for
CHLM compared to kaolinite (especially at mild supercooling, Fig. 1b) is
likely to be due to the different surface topography of the two compounds.

Figure 5: The early stages of ice nucleation at the water-CHLM${}^{-OH}_{001}$
interface involve non-spherical ice crystallites. Asphericity parameter
$\alpha$ and spatial extent of the ice nuclei along the direction normal to
the CHLM slab $\Delta Z$ as a function of $\lambda$ for ice nuclei at the
water-CHLM${}^{-OH}_{001}$ interface. The insets correspond to top and side
views of typical ice nuclei forming at the water-CHLM${}^{-OH}_{001}$
interface, containing about 100 (top) and 245 (bottom) water molecules.

###  III.5  Competition between cubic and hexagonal ice

Figure 6: Competition between cubic (blue/cyan spheres/sticks) and hexagonal
(red/orange spheres/sticks) ice within the early stage of ice nucleation at
the water-CHLM${}^{-OH}_{001}$ interface. The average number of double diamond
and hexagonal cages (DDC and HC, the building block of ice $I_{c}$ and ice
$I_{h}$ respectively) is reported as a function of the order parameter
$\lambda$. Insets on the left show representative ice $I_{c}$ and ice $I_{h}$
fluctuations (top view) at the first FFS interface ($\lambda$=80). Insets on
the right show representative ice nuclei at $\lambda$=165 and 260, where the
competition between the two polymorphs becomes more evident. The dashed
(green) lines/arrows indicate the crystallographic plane/direction along with
ice $I_{h}$ has the possibility to grow on top of ice $I_{c}$.

At the strong supercooling considered here ($\Delta T_{S}$ = 42 K),
homogeneous ice nucleation results in a mixture of ice $I_{c}$ and ice $I_{h}$
known as stacking disordered ice $I_{sd}$ Moore and Molinero (2011); Hansen et
al. (2008); Malkin et al. (2014). However, things can be quite different in
the heterogeneous case. For instance, the hydroxylated (001) basal face of
kaolinite promotes exclusively the formation of the primary prism face of ice
$I_{h}$ Sosso et al. (2016b, c). In the case of the CHLM${}^{-OH}_{001}$
surface, we observe both ice $I_{c}$ and ice $I_{h}$ nuclei at the very early
stages of the nucleation process, as depicted in the inset (left side) of Fig.
6. These ice-like fluctuations originate from the templating effect of the
hydroxyl groups on the CHLM surface, as illustrated in Fig. 4a-e (and Fig.S3
in the SI). In principle, even if ice $I_{c}$ nuclei are three times more
abundant than ice $I_{h}$ nuclei at the first FFS interface ($\lambda=80$), we
would expect the formation of ice on the CHLM${}^{-OH}_{001}$ surface to
proceed via the growth of ice $I_{sd}$. In fact, as shown in Fig. 6, the
competition between the growth of two ice polytypes at 230 K (i.e. $\Delta
T$=42 K) is dominated by ice $I_{c}$: by the time the ice nuclei have reached
a post-critical size (e.g. $\lambda=360$), the average number of Hexagonal
Cages (HC Haji-Akbari and Debenedetti (2015), the building blocks of ice
$I_{h}$) is still about three times larger than that of DDC (Double Diamond
Cages Haji-Akbari and Debenedetti (2015), the building blocks of ice $I_{c}$).

Interestingly, despite the predominance of ice $I_{c}$ within the growing ice
nuclei, ice $I_{h}$ can still form and grow along a specific direction (the
[111] of the cubic phase) on top of ice $I_{c}$ crystals (which in turn grow
along the [100] direction, normal to the plane of the water-
CHLM${}^{-OH}_{001}$ interface), as illustrated in the insets (right side) of
Fig. 6. The coexistence of ice $I_{c}$ and ice $I_{h}$ is thus likely to
result in ice $I_{sd}$ crystals at strong supercooling. However, at milder
supercooling ice $I_{h}$ fluctuations are expected to become more relevant,
and in fact experimental evidence suggests that the macroscopic crystalline
habit of ice crystals grown on CHLM at $\Delta T$=2 K is indeed that of ice
$I_{h}$ Fukuta (1966). Importantly, we did not observe such a competition
between ice $I_{c}$ and ice $I_{h}$ in the case of kaolinite, where the cubic
polytype is basically absent throughout the whole nucleation process Sosso et
al. (2016b, c). In fact, we argue that, in the case of CHLM crystals,
different nucleation sites (whose exact nature remains to be determined) could
promote chiefly ice $I_{c}$ or ice $I_{h}$ according to the different degree
of supercooling, thus contributing to unravel the strong ice nucleating
ability of CHLM crystals along such a wide range of temperatures. This
argument would suggest that the multi-component nature of ice nucleation on
biological matter could be at least partially attributed to a greater variety
of nucleation sites – as well as the specific templating effect of functional
groups acting as hydrogen bond donor and/or acceptors with respect to
supercooled liquid water. Moreover, we have shown in this work that some of
these functional groups - such as the hydroxyl groups characterising the
water-CHLM${}^{-OH}_{001}$ interface - can even promote a different ice
polytype at the same time, possibly according to different supercooling.

Finally, we note that, in agreement with previous simulations of ice
nucleation Sosso et al. (2016c); Qiu et al. (2017), the flexibility of the
CHLM${}^{-OH}_{001}$ has an impact on the extent and the structure of the ice-
like fluctuations at the CHLM${}^{-OH}_{001}$-water interface, and that the
anhydrous crystalline phase of CHL also displays substantial ice nucleating
potential. These two aspects are both addressed in detail in the SI.

##  IV  Conclusions

By means of a blend of experiments and simulations, we have unravelled the the
origins of ice nucleation on cholesterol (CHL), a prototypical organic crystal
of relevance to cryopreservation. Our results suggest that its exceptional ice
nucleating activity stems from the ability of its flexible hydrophilic surface
to form unconventional ice-templating structures – specifically, hydrogen
bonded cages comprising 6- as well as 5-membered rings. In addition, the
experimental evidence reported here suggests that the intrinsic potential of
cholesterol to nucleate ice may potentially be enhanced by specific
topological features of the crystalline habit. In particular, droplet freezing
measurements show that cholesterol promotes the heterogeneous formation of ice
across a wide range of temperatures (from -4 to -20 C°). In fact, we find that
CHLM crystals nucleate ice far better than the mineral feldspar, which is one
of the most effective inorganic ice nucleating agents of relevance to
atmospheric science. Moreover, electron microscopy measurements suggest that
the broad range of freezing temperatures we observe for CHLM crystals may be
due to the coexistence of diverse structural features of the crystalline
surface, which in turn can act as different nucleation sites. The microscopic
structure of the latter remains to be assessed, but the possibility that
different parts of the CHLM surface may nucleate ice with different efficiency
suggests that surface topography can play an important role in determining the
ice nucleating ability of organic crystals.

Surprisingly, we find that CHLM crystals, despite being exceptionally good ice
nucleating agents, do not provide a conventional template for ice to form.
Specifically, molecular simulations reveal that, as opposed to what has been
reported for supercooled water in contact with simple model substrates (e.g.
Lennard-Jones crystals, which allow to rapidly explore different surface
geometries Fitzner et al. (2015)) and/or inorganic materials (such as
carbonaceous particles Lupi et al. (2014), or clay minerals Sosso et al.
(2016c, b)), water on the (001) hydroxylated surface of cholesterol
monohydrate (the most abundant interface in aqueous environments) does not
form an ordered, dense, ice-like overlayer. Instead, due to the flexibility of
the CHLM surface and its relatively low density of hydroxyl groups, water
molecules partially infiltrate the crystal, forming a network of both 6- and
5-membered hydrogen bonded rings. The latter involve water molecules as well
as hydroxyl groups provided by CHL molecules. While some of these structural
features (particularly pentagonal rings) are known to hinder homogeneous water
freezing, we find that they actually facilitate the heterogeneous formation of
both hexagonal and cubic ice on CHLM crystals. In fact, enhanced sampling
simulations suggest the emergence of stacking disordered ice (a mixture of the
two polytypes) at the water-CHLM interface. This is in stark contrast with
what we have previously observed in the case of e.g. the clay mineral
kaolinite, where only the hexagonal polytype was observed along the whole
nucleation process Sosso et al. (2016b). In fact, more often than not a given
crystalline substrate nucleates exclusively one of the two ice polytypes Sosso
et al. (2016a); Kiselev et al. (2017). Moreover, we find that the nucleation
rate of ice on CHLM crystals is basically identical to that we have previously
calculated in the case of kaolinite - at the same strong supercooling ($\Delta
T_{S}$ = 42 K). Kaolinite and CHLM are both characterised by an hydrogen bond
network capable of facilitating the formation of ice nuclei: thus, the
substantial difference in the ice nucleating ability we observe experimentally
for these two compounds is most likely rooted into their surface topography.
In fact, the $n_{s}$ data reported in Fig. 1b suggest that two populations of
potentially different ice nucleating sites may coexist on the CHLM surface.
The change in the slope of the CHLM data is reminiscent of that observed for
freezing spectra for birch pollen O’Sullivan et al. (2015); Pummer et al.
(2012), which has been attributed to the presence of two different ice
nucleating macromolecules Augustin et al. (2013). Similarly, we argue that
there may be two different broad classes of ice nucleating sites on CHLM,
represented by the two different slopes in the freezing spectra. Due to the
spatially sporadic nature of the highly active sites, which are not present in
every millimetre diameter droplet, it seems likely that these two different
classes of ice nucleation sites are related to specific defects or the diverse
topography of the CHLM, rather than any factors related to the bulk molecular
structure of CHLM.

In addition, the emergence of stacking disordered ice phases during the
heterogeneous formation of ice has been experimentally observed Malkin et al.
(2014), and consequently ascribed to different crystal growth regimes. Our
results offer the intriguing prospect that the nucleation process itself may
favour, in some cases, the formation of stacking disordered ices. Thus, we
argue that the dramatic ice nucleation ability of certain organic materials
may be traced down not only to the formation of a network of hydrogen bonds
between water and the nucleation sites, but also to the capability of specific
surfaces to promote at the same time different ice polytypes as a function of
supercooling. In order to verify this hypothesis, though, we would need to
investigate ice nucleation on CHLM at milder supercooling. To this end, an
heterogeneous seeded molecular dynamics approach is currently being validated
Pedevilla et al. (2018). Our results also suggest that organic crystals sit in
between inorganic and biological materials, when it comes to promoting the
formation of ice: substrates like CHLM are characterised by relatively flat
surfaces exposing an array of amphoteric functional groups, much like several
inorganic ice nucleating agents (e.g. kaolinite, feldspar, hydroxylated
graphene), but the flexibility of the surface and the low density of such
functional groups is typical of biological nucleating agents such as
macromolecules and bacterial fragments. This is especially relevant in the
case of CHL, a molecule which is not only used in crystalline form as an ice
nucleating agent in cryopreservation applications, but that significantly
contributes to the composition of animal cell membranes as well.

In summary, the experiments and simulations presented in this work indicate
that cholesterol crystals are incredibly efficient ice nucleating agents,
active across a broad range of supercooling. We show that such strong ice
nucleating activity is due to the intrinsic potential of the flexible
amphoteric surfaces of CHLM to form unconventional ice-templating molecular
structures. It is likely that microscopic structural features of the crystals
could further enhance the ability of CHLM (and potentially of other organic
crystals) to form ice, by offering a diverse array of nucleating sites. In
fact, we believe that for an ice nucleating agent to be very efficient, a
combination of interfacial “chemistry” and surface topography is generally
required. This interplay could thus be the key to understand the heterogeneous
formation of ice on molecular organic crystals, and it may provide a starting
point for the investigation of ice in soft and biological matter at the
molecular level. In particular, tailoring the microscopic structure of the
substrate and modifying the nature as well as the density of hydrogen-bonding
functional groups at the water-substrate interface can be seen as two
different routes to engineer the ice nucleating ability of novel
cryoprotectants, the design of which, at the moment, largely relies on the
high-throughput screening of whole libraries of different compounds. The
absence of a proper structure-to-function paradigm is perhaps the most
pressing challenge in cryobiology: this is why future work will be devoted to
assess whether and how hydrogen-bonding functional groups other than hydroxyls
would be equally effective to enhance the kinetics of heterogeneous ice
nucleation.

## Conflicts of interest

There are no conflicts to declare.

## Acknowledgements

This work was supported by the European Research Council (ERC) under the
European Union’s Seventh Framework Programme: Grant Agreement number 616121
(HeteroIce project [AM, PP, GCS]), Grant Agreement number 632272 (IceControl
project [TFW, BJM]) and Grant Agreement number 648661 (MarineIce project [TFW,
BJM]). MAH and BJM are also supported by the Engineering Physical Sciences
Research Council (EPSRC) via the Research Grant number EP/M003027/1. GCS and
PP acknowledge the use of the UCL Grace and Legion High Performance Computing
Facilities, the use of Emerald, a GPU-accelerated High Performance Computer,
made available by the Science & Engineering South Consortium operated in
partnership with the STFC Rutherford-Appleton Laboratory and the use of ARCHER
UK National Supercomputing Service (http://www.archer.ac.uk) through the
Materials Chemistry Consortium via the EPSRC grant number EP/L000202. The
Forward Flux Sampling simulations were supported by a grant from the Swiss
National Supercomputing Centre (CSCS; project ID s758).

## Supplementary Information

Supplementary Information (SI) can be found at:
http://www.rsc.org/suppdata/c8/sc/c8sc02753f/c8sc02753f1.pdf

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