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A simple and quantitative method to evaluate ice recrystallization kinetics using the circle Hough transform algorithm Luuk L. C. Olijve, Anneloes S. Oude Vrielink, and Ilja K. Voets Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.5b01637 • Publication Date (Web): 20 Jun 2016 Downloaded from http://pubs.acs.org on June 25, 2016

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Crystal Growth & Design

A simple and quantitative method to evaluate ice recrystallization kinetics using the circle Hough transform algorithm 1,2

1,2

Luuk L.C. Olijve, Anneloes S. Oude Vrielink, Ilja K. Voets

1,2,3*

1

Institute for Complex Molecular Systems, Eindhoven University of Technology, Post Office Box 513, 5600 MD Eind2 hoven, Netherlands. Laboratory of Macromolecular and Organic Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, Post Office Box 513, 5600 MD Eindhoven, Netherlands. 3 Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, Post Office Box 513, 5600 MD Eindhoven, Netherlands. KEYWORDS ice recrystallization inhibition, antifreeze protein, image analysis, circle Hough transform, Ostwald ripening.

ABSTRACT: The formation of large ice crystals via recrystallization processes in foods and water-based materials often decreases the quality and structural integrity of the materials. Hence, there is a widespread academic and commercial interest in natural and synthetic ice crystal growth modifiers which inhibit the recrystallization of ice. Well-known natural ice crystal growth modifiers are antifreeze proteins (AFPs), which inhibit ice recrystallization by adsorbing on the surface of ice crystals. Reliable quantification of the ice recrystallization inhibition (IRI) efficiency is a long-sought goal. In this work, we describe a simple method to quantitatively evaluate IRI efficiency, based on automated image analysis using the circle Hough transform (CHT) algorithm. It enables robust and high throughput analysis of natural and synthetic ice recrystallization inhibitors. Here we use the method to evaluate the impact of a single point mutation in the ice-binding site of QAE on its IRI activity. We find that the T18N mutant of QAE has virtually the same effective ice recrystallization inhibitory concentration as the wild-type QAE. This is in contrast to thermal hysteresis activity, evaluated by cryoscopy or sonocrystallization, where the mutation greatly decreases the activity.

INTRODUCTION A predictive understanding of (re)crystallization processes would allow to create nanomaterials with novel or enhanced physical and chemical properties.1 For example, aligned porous materials and other complex structured polymer-inorganic composites have been created by directional freezing methods.2-4 Conversely, ice recrystallization can have a major detrimental impact on the quality and performance of many water-based materials such as foods, biological materials, paints.5-7 The force driving ice recrystallization is a lowering in the free energy of the system by a reduction in crystal/solution interface energy, due to; isomass, accretion and migration.8, 9 Isomass recrystallization involves the change in internal structure of ice crystals, and a reduction of crystal defects and surface irregularities. Accretive recrystallization describes the fusion of two neighboring ice crystals. The dominant mechanism at high sucrose concentration is migratory recrystallization (i.e., Ostwald ripening), wherein the mean ice crystal size increases while the number of ice crystals decreases, at a constant volume of ice. The inhibitory effect of antifreeze proteins

(AFPs) on the recrystallization of ice (termed ice recrystallization inhibition, IRI) has been extensively reported by Knight et al.10-13 AFPs are macromolecular ice crystal growth modifiers and are produced by many cold-adapted and freeze avoidant organisms to protect body tissues against freeze damage.14-16 AFPs adsorb onto the surface of ice crystals, thereby acting as an impurity on the ice crystal surface. As a result, the AFPs interfere with the attachment and detachment of water molecules on the ice grains, which completely arrests grain boundary migration. From an industrial perspective, there is a huge interest in inexpensive synthetic ice crystal growth modifiers able to inhibit the recrystallization process of ice.7 One major obstacle for the development of potent IRI-active compounds, however, is the lack of a reliable and highthroughput method to quantify IRI. Thin ice films with clearly visible grain boundaries are the primary requirement for a robust evaluation of IRI activity. This motivated the development of the “splat cooling” method, which involves dropping a 10 μL droplet of the analyte dissolved in PBS from a pipette through a

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three meter high plastic tube onto a cooled aluminum block (-80 oC).12 This produces a thin wafer of ice upon impact with the aluminum, which is subsequently trans-

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ferred to a microscope stage. A more convenient alternative, the “sucrose” method, was described by Smallwood et al. and

Figure 1. Optical micrographs of a 30 w/w% sucrose solution taken after 60, 70, 80 and 90 min show how large ice crystals with more concave boundaries (green) grow at the expense of smaller ice crystals (red and blue), i.e. Ostwald ripening. This spontaneous process is thermodynamically-driven and results in a lower free energy of the overall system by decreasing the specific surface area of the ice crystals. The Ostwald ripening process occurs via attachment and detachment of water molecules at the ice crystal surfaces via diffusion of water molecules through the liquid phase. For clarity, the size of the drawn circles is the same in all images.

Budke et al., wherein thin ice wafers were produced by rapid freezing of a 1 μL sample droplet of the analyte dissolved in 20-40% sucrose which was sandwiched between two cover slips.17, 18 A third assay, the “capillary” method, is equally practical, but only allowed for qualitative assessment of IRI activity by visual examination of the samples.19 Reported methods to quantify IRI rely on either manual determination of the mean largest crystal size or automated domain recognition software.7, 20-23 However, these methods suffer from numerous drawbacks: they do not allow for high-throughput measurements, are laborious, do not take a large number of small ice crystals into account or are sensitive to experimental variabilities in image acquisition. Budke et al. described a versatile alternative which relies on ImageTool software to identify individual ice crystals and quantitatively assess the recrystallization kinetics of ice.17 In this work, we introduce a simple, open source Matlab-based program to extract the rate of the recrystallization process of ice from micrographs taken during an IRI experiment. The circle Hough transform (CHT) algorithm is used to extract circular features from the micrographs taken during IRI experiments on thin wafers with 30 w/w% sucrose. The CHT algorithm is an attractive means to detect ice crystal sizes, because of its robustness in the presence of noise, occlusion, varying illumination and focus.24-26 Because of its practicality, the Hough transform algorithm is also applied for automated cell colony counting and analysis of crystallization trials.27, 28 Our CHT image analysis method of the IRI micrographs includes all (~200 or more) ice crystals in the images, which provides significant statistics to ensure reproducible and quantitative evaluation of ice recrystallization kinetics.

ICE RECRYSTALLIZATION KINECTIS For quantitative analysis of ice recrystallization kinetics we build upon previous work of Budke et al. which utilizes the theory of Lifshitz, Slyozov and Wagner (LSW theory) to describe Ostwald ripening processes.17, 29, 30 If the diffusion of liquid water molecules is dominating the kinetic process of ice recrystallization, then the LSW theory suggest that the temporal increase in mean crystal radius r follows:

(eq. 1) Where is the initial mean radius at time t = 0 min and the observed rate constant of recrystallization. This is applicable to our sandwich IRI assay on this wafers with 30 w/w% sucrose, which ensures large liquid fraction such that migratory recrystallization or Oswald ripening dominates. The ice crystal grains develop a rounded shape enabling automated detection of their contours with a home-written Matlab script that employs a circular search using a circle Hough transform. Our approach contrasts with previously reported methods of other labs in which only the size of the largest ice crystals were evaluated manually in the final images thus ignoring the disappearance of the smaller ice-crystals, which is an important factor in Ostwald-ripening. This is because Ostwald ripening involves the growth of large ice crystals at the expense of small ice crystals, so both large and small ice crystals have to be detected accurately to determine the rate of recrystallization. To this end, we employ a radial number average, , of the growing ice crystals which is given by:


(eq. 2)

∑ ∑

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Where ri is the radius of ice crystal i. From the time evolution of the mean ice crystal radius, we obtain the rate constant of recrystallization kd, from the slope of a fit of eq. (1) to the experimental data. Subsequently, the concentration dependent kd is described by the following equation:

(eq. 3)

Where kd0 is the value of the growth limiting rate constant at c = 0, ci the inhibitor concentration that represents the inflection point of the curve, and s is a parameter that determines the slope of the curve in the turnover region. Next, we take the derivative of eq. 3 to obtain the inflection point, i.e. ci. CIRCLE HOUGH TRANSFORM (CHT) A circle can be parametrized by its center with coordinates (a,b) and radius R. If the radius of a circle in an image is known,

Figure 2. Illustration of the circle Hough transform (CHT). (A) The center coordinate (a,b) indicated in red of a circle of known radius R (black line) is determined from the intersection of circles with R (grey line) and an origin given by a pixel (black point) with coordinate (x,y) on the ice grain contour obtained by Canny edge detection (see main text for more information). (B) If the radius R of the circle in the image is unknown, conical surfaces are formulated from each edge coordinate instead of circles to determine the parameter triplet (a,b,R) of a circle in the image.

then the CHT algorithm formulates a circle from each geometric edge pixel (x,y) in parameter space. The position of the circle center can be identified by the intersection point of all circles (Figure 2A). In practice, an accumulator matrix is introduced to find the intersection point in parameter space. The voting number for an element in the accumulator matrix is increased if a formulated circle from an edge pixel (x,y) in parameter space passes through. The local maximum in the accumulator matrix corresponds to the circle center in the original image. If the radius of a circle in an image is unknown, the parameter triplet (a,b,R) of a circle is determined from 3D parameter space (Figure 2B). Instead of circles, conical surfaces are calculated from each edge pixel (x,y). Circle

center coordinates (a,b) and radius R are determined using similar accumulator and voting methods. EXPERIMENTAL Recombinant expression and purification of QAE wild-type and QAE T18N was performed as described previously. 31 The AFGP1-5, which was purified from Antarctic tooth fish blood serum by gel filtration chromatography, were kindly provided by prof. Art DeVries and dr. Konrad Meister. Optical microscopy experiments were carried out on a Jeneval polarization microscope equipped with a Linkam TMS94 temperature control unit operating in transmission mode. Samples were prepared in ultra-pure water and measured in pre-filtered 30 w/w% sucrose. A 1 μL sample droplet in 30 w/w% sucrose is sandwiched between two cleaned glass slides (ø = 12 mm, MenzelGläser) and was placed on a temperature-controlled silver block inside the Linkam stage. Glass slides were cleaned by subsequent one-minute sonication treatments; in acetone, ethanol and isopropanol, after which they were dried with air flow. During IRI experiments ,samples were kept under a nitrogen stream to avoid water condensation from ambient air during the experiment. The sample is rapidly cooled to -40 oC at a rate of 20 oC/min to produce polycrystalline ice, re-heated to -7 oC at a rate of 10 o C/min at which the sample is at held constant temperature for 120 min. Micrographs of 512 × 384 µm are taken at regular time intervals, and at continuous auto-exposure, using a Lumenera Infinity 1 CMOS camera. The micrographs obtained from the IRI experiment were analyzed using a home-written image analysis program (Matlab), which employs a Canny edge detection (CED) from a tresholded gray level image followed by a circular search using a circle Hough transform (CHT) (Matlab function imfindcircles, which is part of the Image Processing Toolbox). These steps are exemplified in Figure 3. The program evaluates all images obtained in an IRI experiment and determines the number average radius of the ice crystals for each image. The rate constant of recrystallization is obtained after fitting an experimental data set to eq. 1. Full analysis of one data set of 20 images takes 5-10 min on a normal desktop computer. The Matlab script is available in the free online supplementary information.



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Figure 3. Overview of the image analysis process employing the circle Hough transform (CHT) to detect the centers and radii of individual growing ice crystals. A threshold is applied to a micrograph (30 w/w% sucrose solution after 35 min) to obtain a binary image. The thresholding is followed by a Canny edge detection after which ice crystals are detected by the CHT procedure (indicated by red circles). The number average radius is calculated after size binning of the detected circles.

RESULTS AND DISCUSSION Different methods (splat cooling, sucrose, capillary) are reported for the formation of thin ice wafers with well distinguishable grain boundaries, all using different concentrations of colligative additives (e.g., salts, sucrose) and annealing temperatures. We have standardized our experiments to the sucrose method (30 w/w% sucrose, annealing temperature T = -7 oC), where a 1 μL sample droplet is sandwiched between two cover slides. This gives in general well defined ice grain boundaries with concave morphologies, and minimizes accretion of ice crystals.

Figure 4. Circle detection (red circles) of micrographs of 20 mM Tris-HCl, pH 7.9, 30 w/w% sucrose at -7 °C. As the mean ice crystal grain size increases with time, progressively larger circles are obtained for micrographs collected at longer annealing times.


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Figure 6. Ice recrystallization inhibition efficiency of antifreeze glycoproteins (AFGP1-5).

Figure 5: Triplo measurements of a 30 w/w% sucrose solution to demonstrate the reproducibility of the CHT analysis 3 procedure, with (A) the radius Rn vs time and (B) ice volume fraction vs time.

An overview of the image processing steps for extracting the circular features from the micrographs is illustrated in Figure 3. First, the original micrograph is converted to a binary image by applying a threshold, after which a Canny edge detection is applied to identify the contours of the ice grains. Next, the CHT analysis is applied resulting in the detected circles indicated in red. A radius distribution profile is generated from which the number average radius (Rn3) is calculated according to Eq. 2.

The time evolution of a typical IRI experiment with buffer in presence of 30 w/w% sucrose is shown in Figure 4. The number average radius increases from Rn ~ 3.5 µm at t = 1 min, to Rn ~ 7,2 µm at t = 90 min. Sometimes ice crystals are detected twice, a radius is over- or underestimated, or an ice crystal remains undetected. However, this has relatively little influence on the ci. The timeevolution of the number average radius Rn can be evaluated using a linear growth function (Eq. 1, Figure 5A), indicating that the kinetics of ice recrystallization in the presence of 30 w/w% sucrose is dominated by the diffusion of water molecules as proposed by the LSW theory on Ostwald ripening processes. To demonstrate the reproducibility of the CHT analysis, three independent experiments of a 30 w/w% sucrose sample were performed. The obtained average recrystallization constant is kd = 4.01 ± 0.17 μm3/min. Furthermore, the LSW theory underlines that the total ice volume fraction remains constant during the Ostwald ripening process, which is evident from Figure 5B. The ice recrystallization inhibition efficiency of antifreeze glycoproteins (AFGP1-5) is analyzed using the CHT procedure.32 IRI experiments were performed over a wide protein concentration range and the recrystallization inhibition efficiency estimated from the inflection point of the s-curve (Eq. 3, Figure 6). The data demonstrates that ice recrystallization kinetics is dramatically reduced at concentrations > 0.01 μM to nearly 0 μm3/min and grain boundary migration processes are completely arrested. A concentration of ci = 3 · 10-3 ± 5 · 10-3 μM marks the inflection point and at lower concentrations the recrystallization constant is similar to 30 w/w% sucrose solution. The value for the effective inhibitory concentration ci obtained using the CHT analysis procedure is in reasonable agreement to reported values (ci = 0.001 μM) by Budke et al.33



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Furthermore, the method described was used to test the influence of the single amino acid mutation T18N in the ice-binding site of the ocean pout type III antifreeze protein QAE on its ice recrystallization inhibition activity. This particular mutation is deleterious for TH activity as shown by nanoliter osmometry and sonocrystallization methods. Graether et al. showed a 90% decrease in activity by nanoliter osmometry, 34 while Meister et al. reported that virtually no freezing plateau could be observed for the T18N mutant by sonocrystallization. Furthermore, no ice-like waters were observed at the ice binding site of the T18N mutant by SFG.31 Surprisingly the T18N mutation has relatively little effect on the ice recrystallization inhibition activity of QAE. As shown in Figure 7, wild-type QAE has an ci ~ 4 ± 2 µM, and QAE T18N has an ci ~ 5 ± 2 µM. These results indicate for the first time that mutations in the ice binding site of ice binding proteins can have a markedly different effect on the protein’s thermal hysteresis compared to the ice recrystallization inhibition activity. These findings are in line with a recent systematic investigation on all major classes of antifreeze proteins demonstrating that thermal hysteresis and IRI activity are not correlated. 32

Figure 7. Ice recrystallization inhibition efficiency of re-

combinant type III AFP QAE (wild-type, ci ~ 4 ± 2 µM) and QAE T18N (ci ~ 5 ± 2 µM). CONCLUSION A number of methods have been reported to quantitatively assess the recrystallization kinetics of ice. We have critically evaluated the advantages and disadvantages of those methods, and in this work provide a general method that is simple yet efficient. An circle Hough transform (CHT) based algorithm is used as a robust and automatic method to extract ice recrystallization rates from the micrographs of AFP solutions in 30 w/w% sucrose sandwiched between two glass coverslides. The analysis takes minimal computational time and eliminates any need for manual estimation of the size or the mean radius of ice crystal grains. The large number of detected ice crystals in each image gives significant statistics to ensure reproducibility of the calculated number average radius. The methodology described in this work can be used to quantitatively evaluate the recrystallization inhibition efficiency of natural and synthetic ice crystal modifiers. We determined the impact of a single-


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site mutation in the ice-binding site of ocean pout type III AFP on its IRI activity, which is known to dramatically reduce thermal hysteresis activity. By contrast, the T18N mutant has the same IRI activity as the wild-type QAE.

ASSOCIATED CONTENT Supporting Information. The Matlab script for image analysis is free available in the online supplementary infor3 mation. Furthermore, Rn versus time plots of QAE WT, QAE T18N and AFGP1-5 are included, as well as sonocrystallization measurements with QAE WT and QAE T18N. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *[email protected]

Author Contributions I.K.V. conceived the project, I.K.V. and L.L.C.O. designed the experiments, L.L.C.O. and A.OV. performed and analyzed the data, I.K.V., L.L.C.O. and A.OV. wrote the manuscript.

Funding Sources This work has financially been supported by NWO (Veni grant 700.10.406) and the European Union (FP7-PEOPLE-288 2011-CIG contract 293788, ERC-2014-StG contract 635928).

ACKNOWLEDGMENT AFGP protein samples were kindly provided by Prof. Art DeVries and dr. Konrad Meister.

ABBREVIATIONS IRI, ice recrystallization inhibition; CHT, circle Hough transform; AF(G)P, antifreeze (glyco)protein; LSW, LifShitz, Slyozov and Wagner theory on Ostwald ripening.

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For Table of Contents Use Only A simple and quantitative method for evaluating ice recrystallization kinetics using the circle Hough transform algorithm

Luuk L.C. Olijve, Anneloes S. Oude Vrielink, Ilja K. Voets

Macromolecular ice crystal growth modifiers such as antifreeze proteins are able to inhibit the recrystallization of ice. In this work, we describes a simple method to quantitatively evaluate ice recrystallization inhibition (IRI) efficiency, based on automated image analysis using the circle Hough transform (CHT) algorithm, which provides a platform for the robust and high throughput analysis of natural and synthetic ice recrystallization inhibitors.

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Figure 1. Optical micrographs of a 30 w/w% sucrose solution taken after 60, 70, 80 and 90 min show how large ice crystals with more concave boundaries (green) grow at the expense of smaller ice crystals (red and blue), i.e. Ostwald ripening. This spontaneous process is thermodynamically-driven and results in a lower free energy of the overall system by decreasing the specific surface area of the ice crystals. The Ostwald ripening process occurs via attachment and detachment of water mole-cules at the ice crystal surfaces via diffusion of water molecules through the liquid phase. For clarity, the size of the drawn circles is the same in all images. 178x38mm (300 x 300 DPI)


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Figure 2. Illustration of the circle Hough transform (CHT). (A) The center coordinate (a,b) indicated in red of a circle of known radius R (black line) is determined from the intersection of circles with R (grey line) and an origin given by a pixel (black point) with coordinate (x,y) on the ice grain contour obtained by Canny edge detection (see main text for more information). (B) If the radius R of the circle in the image is unknown, conical surfaces are formulated from each edge coordinate instead of circles to determine the parameter triplet (a,b,R) of a circle in the image. 81x34mm (300 x 300 DPI)



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Figure 3. Overview of the image analysis process employing the circle Hough transform (CHT) to detect the centers and radii of individual growing ice crystals. A threshold is ap-plied to a micrograph (30 w/w% sucrose solution after 35 min) to obtain a BW image. The thresholding is followed by a Canny edge detection and the circular ice crystals detect-ed by the CHT procedure (indicated by red circles). The radius number average is calculated from after size binning of the detected circles. 82x100mm (300 x 300 DPI)


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Figure 4. Time evolution of the circle detection. The detected ice crystals are indicated by a red circle. Sample measured in 30 w/w% sucrose at a constant temperature of -7 oC. 177x42mm (300 x 300 DPI)



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Figure 5: Triplo measurements of a 30 w/w% sucrose solu-tion to demonstrate the reproducibility of the CHT analysis procedure, with (A) the radius Rn3 vs time and (B) ice vol-ume fraction vs time. 83x120mm (300 x 300 DPI)


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Figure 6. Ice recrystallization inhibition efficiency of anti-freeze glycoproteins (AFGP1-5). Insets show the micrograph after 90 min at a concentration of 6.7e-5 µM (left) and 0.13 µM (right). 85x64mm (300 x 300 DPI)


A Simple and Quantitative Method to Evaluate Ice ... - ACS Publications

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