# Milk gel formation and properties: impact of whey protein aggregates

Erik Juste, Jeehyun Lee, Thomas Croguennec

► To cite this version:

Erik Juste, Jeehyun Lee, Thomas Croguennec. Milk gel formation and properties: impact of whey protein aggregates. 2025. hal-05163215

HAL Id: hal-05163215

https://hal.science/hal-05163215v1

Preprint submitted on 15 Jul 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Journal Pre-proof

Milk gel formation and properties: impact of whey protein aggregates

Erik Juste, Jeehyun Lee, Thomas Croguennec

PII: S0958-6946(25)00173-6

DOI: https://doi.org/10.1016/j.idairyj.2025.106354

Reference: INDA 106354

To appear in: *International Dairy Journal*

Received Date: 1 May 2025

Revised Date: 3 July 2025

Accepted Date: 10 July 2025

<figure><img src="image_2.png" /></figure>

Please cite this article as: Juste, E., Lee, J., Croguennec, T., Milk gel formation and properties: impact of whey protein aggregates, *International Dairy Journal*, https://doi.org/10.1016/j.idairyj.2025.106354.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2025 Published by Elsevier Ltd.
1 Milk gel formation and properties: impact of whey protein aggregates

2 Erik Juste, Jeehyun Lee*, Thomas Croguennec

3 INRAE, Institut Agro, STLO, 35042 Rennes, France

4 erik.juste@institut-agro.fr; jeehyun.lee@institut-agro.fr; thomas.croguennec@institut-agro.fr

5 *Corresponding author.

6 Keywords

7 casein micelle; aggregation; coagulation; soft matter; enzymatic gel; acid gel

8 Abstract

9 Whey protein aggregation has been used in cheesemaking to increase the yield. This review examines 10 rennet- and acid-induced milk gelation in the presence of whey protein aggregates. In situ aggregates, 11 formed during milk heating, impair enzymatic gelation by hindering casein micelle aggregation but 12 enhance acid gel strength. Ex situ aggregates, pre-formed and added in milk, exhibit various 13 morphologies. They alter gelation dynamics and gel properties differently compared to in situ 14 aggregates. However, this research area remains highly underexplored. Physics-based models may give 15 insights on underlying mechanisms of gel formation but lack specificity for casein micelle dynamics 16 and show limits in integrating whey protein aggregates. Future research must prioritise mechanistic 17 insights into interactions between whey protein aggregates and casein micelles. Such advances could 18 optimise ex situ aggregates structure and properties for innovative cheesemaking, balancing texture, 19 nutrition and yield.

20 1. Introduction

21 In cheesemaking, milk gelation occurs through two main pathways: enzyme-induced gelation and acid- 22 induced gelation, or sometimes a combination of both. Both involve destabilisation of the colloidal 23 suspension of casein micelles (CMs), followed by its clotting and the formation of a colloidal gel filling 24 the entire milk volume *via* an arrested phase separation mechanism. The milk gel is then cut to release 25 whey, and the curd is further processed to complete the cheesemaking process. One of the concerns of 26 cheesemakers is to maximise cheese yield, which depends on the fat, protein and moisture contents 27 retained in the curd. Milk components which do not contribute to the dairy gel network, and which are 28 likely to be expelled in whey during draining, such as whey proteins (WPs), fat, and water, must be 29 retained as much as possible in the matrix, while controlling the final product quality in terms of texture 30 and taste. Milk heating is the main lever for increasing WP retention in cheese curds (Britten & Giroux, 31 2022), with the additional aim of exploiting their nutritional value, water holding capacity and 32 functional properties.
During milk heating, WPs are mainly denatured/aggregated into micellar WP/κ-casein complexes and soluble WP/κ-casein complexes. In the following sections, the terms *in situ* denaturation/aggregation of WPs or *in situ* aggregates are employed when WPs and CMs are heated together (Figure 1). These *in situ* aggregates improve WP retention in the curd during both spontaneous syneresis and draining. WPs can also be denatured/aggregated in the absence of CMs, for instance when heating cheese whey or WP solutions. The obtained WP aggregates can be incorporated into cheese milk to improve curd WP retention and to tune cheese properties. The terms *ex situ* denaturation/aggregation of WPs or *ex situ* aggregates are used when the proteins in cheese whey or in WP solutions are first heated independently, and then introduced in cheese milk (Figure 1).

Despite the common industrial practice of preparing WP aggregates from whey or concentrated whey, the scientific literature on their use in cheesemaking is limited in contrast to that of patents describing their production and use to tune cheese curd properties. The molecular mechanisms behind the milk gelling properties after adding WP aggregates in milk is poorly understood. One plausible reason could be that the milk conditions (pH, calcium content, temperature) at renneting vary across studies and affect the interactions between WP aggregates and CMs. The contribution of the shape, size, number, and surface properties of the WP aggregates added in cheese milk have been little studied. Additionally, once incorporated into a dairy matrix, WP aggregates may undergo structural changes. This complicates the understanding of milk gelation in the presence of WP aggregates due to the difference in pH and salt content between the conditions used for their formation and those met in the dairy matrix (Chen et al., 2022).

The present review aims to gather and synthesise knowledge on enzymatic- and acid-induced milk gelation in the presence of WP aggregates, with the focus on gels obtained from skim milk. The conditions used for *in situ* and *ex situ* denaturation/aggregation of the WPs could affect the structure and functionalities of heat-induced aggregates and milk gelation properties. However, while heat-induced WP aggregates have been extensively described in the literature, their properties in cheese matrices are scarcer. Hence, this review will cover i) documented *in situ* and *ex situ* aggregates, ii) their reported uses and impacts in cheese and cheese-like products and iii) how these aggregates modify both enzymatic- and acid-induced gelation processes. Moreover, underlying milk gel formation mechanisms will be discussed through models based on colloidal science and soft matter physics.

## 2. Milk gelation: several pathways from homogenous dispersion to continuous colloidal network

### 2.1. Enzyme-induced gelation

The rennet-induced gelation of milk has long been studied and was recently reviewed by Horne and Lucey (2017). Adding rennet or rennet-like enzymes into the milk is a key step in cheesemaking.
Although the gelation process is not completely understood (Salvador *et al.*, 2022), three phases are generally recognised:

i) the enzymatic hydrolysis of κ-casein, which protrudes onto the surface of the CMs and stabilises them against aggregation in milk. The release of the hydrophilic and negatively charged C-terminal part of κ-casein in the whey leaves a destabilised para-CM;

ii) when 80 to 90 % of κ-casein is hydrolysed, para-CM aggregation occurs through the formation of weak interactions and calcium bridges. This results in CM clusters that are progressively linked together by intercluster bonds (Britten & Giroux, 2022) into a continuous network that spans the whole volume of milk;

iii) the strengthening of the three-dimensional network takes place, and its structure varies over time (Bauland *et al.*, 2024).

As soon as the gel is formed, almost all the para-CM become part of the network. Gel firming takes place through structural rearrangements of the network at several length scales without macrosynerisis (absence of whey released out of the gel). Measurements of the Young modulus of individual CMs (Bauland *et al.* 2022) suggest that each para-CM deformability influences the kinetics of structural rearrangement of the CM network and the macroscopic properties of the gel.

At supramolecular scale, para-CM tend to fuse after aggregation. This fusion is assumed to decrease centre-to-centre interparticle distance, creating stress inhomogeneity in the network due to different ability of the network strands to relax stress by bending or stretching. At a larger scale, thin supporting strands accumulating excessive stress break and their stress-free loose ends restructure and form new junctions with other strands (van Vliet *et al.*, 1991). This leads to the formation of larger, more compact clusters and thicker, more straightened strands which cause other thinner strands to snap. Initially, this rearrangement leads to gel firming but an excessive breaking of intercluster bonds can weaken the gel.

This evolution is common for fractal colloidal gels and explains both the microsyneresis (solid-liquid phase separation inside the gel) and the enlargement of gel pores (Cipelletti *et al.*, 2000). The syneresis of rennet gels was recently reviewed by Fagan *et al*. (2017). When the gel adheres to surfaces, i.e., to walls and is undisturbed, macrosyneresis is usually not observed because para-CM contraction is balanced by other forces (adhesion, surface tension). This explains why cheesemaking includes cutting the milk gel into curd grains: the newly created free surfaces allow the macrosyneresis to occur as para-CM network contracts and expels whey. Increasing the intensity of cutting and stirring as well as the temperature, are the main technological means to control syneresis and thus cheese dry matter content.

Smaller curd grains reduce the distance whey must travel to reach a free surface, thereby facilitating whey expulsion (Dejmek & Walstra, 2004). Increasing the temperature of the curd grain/whey mixture up to 55–56 °C reduces the viscosity of the whey and increases the contraction of the gel network, accelerating whey drainage in the case of hard cheeses.
## 2.2. Acid-induced gelation

Acid milk gelation, recently reviewed by Lucey (2017), mainly occurs through fermentation by lactic acid bacteria, whose growth results in the progressive accumulation of lactic acid. This gradually lowers the pH of milk, leading to i) the solubilisation of calcium phosphate nanoclusters naturally present within CMs, ii) the protonation of negative charges on the surface of CMs and finally iii) their destabilisation.

In unheated milk, down to pH 5.5, the supramolecular structure of CMs remains mostly unchanged despite their notable variation in mineral composition (Marchin et al., 2007). At pH 5.4, once the majority of calcium phosphate is solubilised, CMs begin to swell and fuse together into flocks of fractal nature (Gastaldi et al., 1996). Under pH 5.3, CMs flocks densify until they further aggregate into a particulate gel network at pH 4.7–4.8 (Dalgleish & Corredig, 2012).

By studying the temperature dependency of G' and G'' of acid milk gels, Roefs and van Vliet (1990) showed that acid milk gels are physical gels, which mechanical properties are indirectly driven by the effects of electrostatic and hydrophobic interactions on the conformation of milk proteins. Compared to enzymatic gels, they are more brittle and fragile (Lucey, 2017) and their structure rearranges less over time (van Vliet et al., 1991). Still, acid gels are dynamic due to the progressive fusion of CMs and the breaking of casein strands, as shown by the evolution of their rheological parameters (van Vliet et al., 1991), but their syneresis is more limited due to the lower degree of rearrangement of the casein network (van Vliet & Walstra, 1994).

Casein's water retention is low at acidic pH, resulting in a spontaneous self-decelerating flow of whey through the gel pores upon slicing (Castillo et al., 2000). However, the amount of whey that spontaneously drains off is low due to the low contraction ability of the acid milk gel. To achieve target curd dry matter content, whey drainage is usually accelerated by using a curd/whey separator (filter press, centrifugal separator, ultrafiltration).

# 3. Milk gelation in the presence of *in situ* aggregates

## 3.1. Formation of *in situ* WP aggregates

Pre-heating milk between 60 and 75°C denatures a small number of WPs (Guyomarc'h, 2006). At this temperature, interactions between WPs and caseins or CMs, if any, are limited. At temperatures above 75 °C, WPs are involved in the formation of various complexes with caseins and their quantity increases with the heat treatment intensity (Markoska et al., 2021). Their formation is consecutive to the heat-induced unfolding of WPs, which increases their surface hydrophobicity and exposes reactive thiol groups. These reactive WPs are preliminary linked by thiol-disulphide bonds, over hydrophobic, and electrostatic/ionic interactions (Li et al., 2021). Heating WPs within milk corresponds to the *in situ* formation of WP aggregates (Figure 1).
Donato and Guyomarc'h (2009) reviewed the structure of WP/κ-casein complexes and their distribution between the colloidal phase and serum phase during the heat treatment of skim milk. The growth of the complexes is limited by the number of native WPs in milk, and especially beta-lactoglobulin (β-Lg), which associates with κ-casein through thiol-disulphide exchanges upon heating. The complexes are either bound on the surface of the CMs with a molar ratio of 0.5-3.5 WPs to 1 κ-casein, or in the serum phase of milk (unbound aggregates), with a ratio of 1-5 WPs to 1 κ-casein. The prior aggregation of WPs into WP aggregates is not a prerequisite for the formation of WP/κ-casein complexes, as native WPs, once denatured, can bind directly to κ-casein.

Increasing the time and temperature of milk heat treatment increases the number of denatured WPs and WP/casein complexes (Čurlej et al., 2022). Increasing the pH of the milk to 6.7 prior to heating increases the WP denaturation, decreases the average size of the complexes and the proportion of WP/κ-casein bound to CMs, compared to lower pH (6.5-6.55) (Anema & Li, 2003). However, the underlying mechanisms remain still unclear (Donato & Guyomarc'h, 2009). Shearing at 1000 s⁻¹ promotes the formation of thiol/disulphide interactions between WPs and caseins during heat treatment, by reducing the heat stability of β-Lg and alpha-lactalbumin (α-La) (Bogahawaththa & Vasiljevic, 2020). The irreversible thermal denaturation/aggregation of β-Lg and α-La depends on the milk composition. It is enhanced at higher WP concentration, while it decreases with more non-protein soluble components or lactose in the soluble phase of milk (Anema et al., 2006).

The effects of heating on rennet and acid gelation of milk have been the objects of two reviews (Donato & Guyomarc'h, 2009; Li & Zhao, 2019). They agree that milk heating improves the properties of the acid gel (gel strength, water holding capacity) but slows down the spontaneous whey draining from the acid curd while it impairs the enzymatic coagulation (milk clotting time, kinetics of gel firming) and the strength of the rennet gel. The variation in milk gel properties is linked to both WP complexes bound on the surface of the CMs and of soluble WP complexes in the serum of milk.

## 3.2. Impacts of *in situ* WP aggregates on enzymatic gelation

Once hydrolysed, CMs are coated with WP/κ-casein complexes formed during heating, enabling WP retention within the gel network during draining. This is confirmed as soluble WP/κ-casein complexes isolated from heated milk were shown to interact with unheated CMs during milk renneting (Kethireddipalli et al., 2011). This helps to increase the cheese yield, both in terms of protein content, as protein recovery increases, and total mass, as the curd also retains more water. WP complexes on the surface of CMs interfere with the secondary phase of enzymatic milk gelation, by limiting the enzyme-induced aggregation and fusion of the CMs, while the primary phase of enzymatic hydrolysis is barely affected (Vasbinder et al., 2003). Consequently, the gel formation and contraction are negatively affected.
Identifying the origin of the different ability of heat-treated and unheated milk to be processed into cheese is crucial to reduce the deleterious effects of milk heating. Britten and Giroux (2022) recently reviewed the enzyme-induced coagulation of heated milk and reported a better understanding of the effects of heat treatment on proteins, mineral equilibrium, and coagulation properties of milk. To limit the drawbacks of heat treatment on cheese production, they suggest adapting the cheese-making parameters and correct the mineral balance which shifted during heating, by adding ionic calcium or acidifying the milk through the dissolution of colloidal calcium phosphate from the CM. Other technologies, such as the high hydrostatic pressure processing, may help to achieve this goal: the fragmentation of CMs increases their reactive areas and promotes their aggregation (Corredig & Salvatore, 2016), while preventing the simultaneous denaturation of WPs.

### 3.3. Impacts of *in situ* WP aggregates on acid gelation

High heat treatment of reconstituted skim milk, in the range 80–90 °C between 15–30 min, influenced both microstructure and appearance of acid gels at pH 4.5, producing gels which are more branched with rougher surfaces than those formed from unheated milk. Denatured WPs may take part in the gel formation, altering its microstructure, and then forming a stiffer gel with less syneresis. Heated milk exhibits a higher gelation pH and forms stronger acid gels with higher elastic modulus, G', than unheated milks (Lucey et al., 1998). But the exact mechanisms explaining the improvement of the gel properties are still a matter of debate, as both WPs bound to surface of the CMs and those in the serum phase were reported to take part in the gel structuration (Li & Zhao, 2019). Still, Lucey (2017) reports conflicting results in the literature regarding the relative importance of soluble and micelle-bound denatured WP fractions on the texture of acid milk gels.

The gelation pH and water holding capacity of acid gels increased with higher heating temperature and pH (Qi et al., 2022). Heating milk also impacts the drainage ability of acid milk gels. Depending on the type of product, whey separation may be undesirable as for yogurts, or part of the process as for Cream cheese. For the latter, spontaneous syneresis of the gel is not sufficient to remove the desired amount of whey, requiring centrifugation to raise solid content through external force. Famelart et al. (2025) investigated both spontaneous and centrifugal whey drainage of acid heat-treated milk gels and showed that high heat treatment (95 °C, 120 s) of milk slowed down the whey drainage, leading to a lower final drainage compared to the low heat treatment (72 °C, 20 s). They explain this by the reduced ability of network contraction and whey release, as these gels display smaller pores and smaller network strands. The thermal co-precipitation of milk proteins from milk or blends of milk and whey is also reported by Hill et al. (1982) in the case of the manufacture of Queso Blanco and ricotta type cheese, as an easy method to recover whey proteins.

To conclude, milk heating is therefore recommended to improve fresh cheese characteristics, mainly driven by lactic acidification as classified by Almena-Aliste and Mietton (2014). Their acid gelation
206
207

prevails over rennet gelation characteristic. Unlike soft or hard cheeses, an extensive drainage is not required (Donato & Guyomarc'h, 2009).

208

# 4. Milk gelation in the presence of ex situ aggregates

209

## 4.1. Formation of ex situ WP aggregates

210

Ex situ aggregates are formed by heat treating WPs without casein in an aqueous solution (Figure 1).

211

WP aggregates present a wide range of shapes and properties depending on the chemical characteristics of the solution (pH, ionic strength, etc.) and the operating conditions of heating (temperature gradient, heating time, shearing). WP aggregates are typically classified by their morphology with each category regrouping in reality aggregates of different structures and sizes, which need to be fully assessed when studying their uses and properties. The mechanism of WP aggregation and the conditions to achieve specific types of aggregates have already been extensively studied (Bouhallab & Croguennec, 2014; Guyomarc'h & et al., 2015; Nicolai et al., 2011; Nicolai & Durand, 2013; Ramos et al., 2017). They are briefly described below (Figure 2).

212

213

214

215

216

217

218

219

Amyloids and fibrils are formed from native globular proteins such as β-Lg and whey protein isolate (WPI) (Hoppenreijs et al., 2022; Kroes-Nijboer et al., 2012). They are typically formed at pH 2 (Loveday, Su, et al., 2012). Fibril formation includes acid-hydrolysed peptides identified in the β-Lg amino acid sequence, resulting in a low conversion of WPs (28 % wt). α-La and BSA alone do not form fibrils under the same conditions, but some of their peptides can be part of the fibrils made from β-Lg fragments (Akkermans et al., 2008; Kroes-Nijboer et al., 2012). Fibrils exhibit rigidity and interesting rheological properties influenced by their length, shape and individual mechanical properties (Loveday, Wang, et al., 2012). According to Chen et al. (2022), neutralised preformed fibrils denature gradually under heating time and temperature, limiting their potential use in food applications.

220

221

222

223

224

225

226

227

228

Flexible strands are either known as “amyloid-like”, based on their mechanism of formation, or worm-like primary aggregates, based on their shape (Jung et al., 2008). In comparison to “amyloid,” “amyloid-like” refers to structurally similar fibrils in which β-sheets are less tightly stacked, resulting in shorter and more flexible fibrils (Hoppenreijs et al., 2022). They are built from unfolded non-hydrolysed β-Lg molecules (Heyn et al., 2019) and their apparent D~f~ is 2.1 (Loiseleux et al., 2018). Amyloid-like structures are formed around neutral pH above pH 6, and under pH 3.5–4. They even coexist with fibrils under pH 3.5 (Figure 2) at intermediate ionic strength (33–80 mM CaCl~2~ or > 60 mM NaCl) (Loveday et al., 2010).

229

230

231

232

233

234

235

236

Above the isoelectric point (pI) of WPs (pH 5.8–6.2), nano- and micro-gels form, depending on their size, exhibiting spherical or ellipsoidal shape with high swelling ability that provide them gel-like features (Schmitt et al., 2010). They display an apparent D~f~ of 3.1 (Loiseleux et al., 2018). The microgels are dense and do not interpenetrate each other (Inthavong et al., 2016). Increasing the heating temperature or rate of heating decreases the size of these aggregates (Bromley et al., 2006). Closer to

237

238

239

240
241

pI, near pH 5.3–5.7, β-Lg microgels further aggregate into large particles that precipitate over time (Donato & Guyomarc’h, 2009). It is possible to form microgels at higher pH, up to 7.5 by adjusting the Ca²⁺/β-Lg molar ratio. This suggests that the crucial parameter for microgel formation may be the net charge density of the native proteins (Phan-Xuan *et al.*, 2014).

242

243

244

245

At pH 7 and low ionic strength, curved strands with a diameter of 10 nm are formed. At low protein concentration and low ionic strength, these primary aggregates are stable and do not associate. But increasing the protein concentration triggers the association of the primary aggregates up to a critical protein concentration (9-10% w/w) where β-Lg aggregates percolate into a continuous gel network. Higher ionic strength (>100 mM NaCl) increases the density of the aggregates at small length scales, probably by increasing their degree of branching (Pouzot *et al.*, 2005), thus forming less flexible aggregates (Baussay *et al.*, 2004).

246

247

248

249

250

251

252

Although β-Lg and α-La have different sensitivities to temperature (> 80°C) (Dannenberg & Kessler, 1988; Kiesner *et al.*, 2000) and pH during heating (Tolkach *et al.*, 2005), this seems to have negligible impact on the structure of WP aggregates. β-Lg is considered to drive WP aggregation (Schokker *et al.*, 2000). However, while isolated β-Lg and WPI display similar behaviours when heated, WP concentrate and cheese whey produce aggregates with a large degree of variability (Triani & Foegeding, 2019; Kruchinin *et al.*, 2022), which is an important parameter to consider when the aim is to use *ex situ* WP aggregates in cheesemaking. Also, the stability of WP aggregates subjected to environmental changes during cheesemaking is worth considering. The following section synthetises the influence of adding these WP *ex situ* aggregates on rennet kinetics and derived functionalities in cheese products. Then, the impact of WP *ex situ* aggregates on acid gelation formation and on acid gel properties is described.

253

254

255

256

257

258

259

260

261

262

## 4.2. Impacts of *ex situ* WP aggregates on enzymatic gelation.

263

Hinrichs (2001) reviewed the incorporation of WPs in several types of cheese, in an attempt to retain their nutritional value, as they would be otherwise expelled in the whey. Using cheese milk at 2.1% caseins with or without added WPs to reach a casein/WPs ratio of 1, Gamlath *et al.* (2020) show that the WPs impaired the enzymatic milk gelation, though the impact of WP aggregates was less pronounced compared to native WPs. They attributed this difference to the lower number of WP aggregates compared to native WPs surrounding the CMs in the serum phase of milk. Larger WP aggregates (60–600 µm) in cheese milk reduced the steric barrier for para-CM aggregation and led to faster kinetics of milk gelation compared to cheese milk containing smaller WP aggregates, that were more numerous.

264

265

266

267

268

269

270

271

272

Perreault *et al.* (2016) investigated the impact of two distinct fractions from the same WP aggregates preparation on enzymatic milk gelation and showed that heat-treated WP solutions contained different types of aggregates that distinctly interfered with the enzymatic milk gel formation and contraction. Sedimentable particles (WP aggregates recovered in the pellet and re-dispersed in the serum phase of

273

274

275
milk) acted as inert fillers. They decreased the maximum coagulation rate, G' at 60 min, and the contraction capacity of the casein network, probably due to their water-holding capacity. Non-sedimentable soluble particles (WP aggregates in the supernatant after centrifugation) also had a negative impact on enzymatic-milk gel formation and curd contraction by interacting with para-CMs and hindering the crosslinking of caseins. Smaller WP aggregates that were characterised by a higher surface hydrophobicity than larger WP aggregates (Gamlath et al., 2020) could have a stronger impact.

Perreault et al. (2017) suggested a two-step mechanism for WP aggregates during cheese manufacture, depending on their hydration layer and ability to interact with the casein network. First, in a loose enzymatic gel (before gel cutting and draining), WP aggregates are surrounded by a thick hydration layer, and they behave as inert fillers. Second, after curd draining and pressing, WP aggregates are concentrated in the matrix, where they interact with the casein network as active fillers and help increase its rigidity. The WP aggregates that exhibit a larger surface hydrophobicity interacted more strongly with the casein network, reducing their release in the draining whey (Giroux et al., 2015). Accordingly, Barden et al. (2015) observed a reinforcement of the cheese structure when the volume fraction of filler particles (i.e., non-melted fat globules or Sephadex beads) was increased. Therefore, the behaviour of WP aggregates during cheese manufacture seems to depend on the cheese processing step.

The incorporation of denatured WPs as relatively large particles reduces the gel firmness before draining and enhances the meltability of the resulting cheese. The incorporated WPs did not contribute to the protein matrix structure of the cheese and may have even disrupted its structure (inactive filler particles). This contrasts with native WPs, which contribute to the network formation after milk heating (Lee et al., 2013). In Gouda-type low-fat cheese, the presence of inert WP aggregates in the casein network may lead to fewer casein crosslinks and therefore a softer texture (Schenkel et al., 2013). Larger WP aggregates (60–600 µm) gave a more open cheese microstructure and lessened the hardness of low-fat cheeses (Gamlath et al., 2020), while for the same amount of denatured WPs added to milk, Giroux et al. (2018) indicated smaller WP aggregates (0.38–2.68 µm) decreased the curd firmness.

The addition of WP aggregates to cow milk increases both moisture content and protein retention in the curd, but the increased yield (defined as the ratio of curd mass to starting milk mass) could not be related to the protein retention alone, given the simultaneous increase in the moisture content (Giroux et al., 2018). Indeed, much of the cheese yield increase was attributed to an increased cheese moisture content resulting from the enhanced water binding capacity of the denatured WPs (Stankey et al., 2017). Still, Schenkel et al. (2013) showed no significant improvement in the protein retention in Gouda-type low-fat cheese after adding microparticulated WPs to cheese milk.

Cheeses made from milk containing added WP aggregates exhibited lower fat retention, as the less structured curd shattered under agitation. This was attributed to the steric disturbance of the casein matrix by the WP aggregates resulting in higher amounts of fat released in whey (Mead & Roupas,
2001). The negative effect of WP aggregates on fat retention disappears when the casein concentration in milk is increased. Fat globules and large WP aggregates (6 µm) both act as fillers, but differently (Perreault *et al.*, 2015). Microparticulated WPs act as inert fillers that could be used to replace fat, on the contrary to *in situ* denatured WPs. However, microparticulated WPs act similarly to fat globules at temperatures where milk fat is partially crystallised but does not melt when cheese is heated (Stankey *et al.*, 2017). In Italian Caciotta cheese, increasing microparticulated WP to fat ratio in high and standard fat cheeses did not have an effect on the yield. But a higher yield in low-fat cheese may be obtained by increasing microparticulated WP concentration (3 to 4%) (Sturaro *et al.*, 2015). On a sensory aspect, Stankey *et al.* (2017) showed that the use of microparticulated WPs in low-fat Cheddar cheese gives a softer texture and lessens the meltability without developing off-flavours.

Guyomarc'h (2006) compared the enzymatic milk gelation of milk containing WP aggregates prepared *in situ* and microparticulated WPs prepared *ex situ*. Milk containing *ex situ* microparticulated aggregates led to a shorter enzymatic coagulation time than *in situ* aggregates, by several minutes. Microparticulated WPs decreased the rate of aggregation of CMs during curd formation, explaining the increasing rennet coagulation time. To optimise the retention of microparticulated WPs in low-fat products, Sturaro *et al.* (2014) suggested extending the enzymatic phase before cutting the curd as a way to account for the slower milk gelation.

The above section suggests that a distinction can be made between nanoparticulated WP aggregates, that are closer to the size ranges of CMs (50–200 nm) and microparticulated aggregates that are closer to the size ranges of the fat globules (0.1–15 µm) with regard to their influence on milk gelation and gel properties. The studies dealing with the use of nanoparticulated WP aggregates in rennet cheese-making remain scarce. Furthermore, their structural characterisation is often omitted and the mechanism by which WP added in milk affect the functional properties of cheeses remain unclear. To our knowledge, no study precisely related the structuration kinetics of the enzymatic milk gel (second and third phase of the enzymatic gelation of milk, see 2.1.) to the amount of WP aggregates added to cheese milk.

### 4.3. Impacts of *ex situ* WP aggregates on acid gelation

Unlike enzymatic milk coagulation, the effects of the shapes and sizes of WP aggregates on acid-milk gel formation have been more largely studied using various types of matrices, from model acid milk gels to real products such as fresh cheeses or yogurts.

Gélébart *et al.* (2019) introduced native WPs or different types of milk protein aggregates in milk which was then heated and acidified at pH 4.6 and compared the effects of the added proteins on the characteristics of the obtained acid gels. Native WPs and fractal WP aggregates increased the strength of the acid gels, while WP microgels and *in situ* WP aggregates had no impact on the measured properties. The fractal WP aggregates seemed to play an important role in the acid gel structure formation through efficient thiol/disulphide interchange reactions and the establishment of non-covalent
interactions, such as hydrophobic interactions, with the other proteins present in milk. Particle size measurement after milk heating indicated that the nanoparticulated WPs were able to bind to CMs, with particle diameters ranging from 0.3 to almost 100 µm (Liu et al., 2016). The addition of either mono- or polydisperse nanoparticulated WPs in milk increased the gel strength and firmness. But polydisperse fractal aggregates formed a weaker acid gel, with lower firmness and protein network density in comparison with monodisperse fractal aggregates. The presence of a population of large aggregates in the polydisperse fractal aggregates might be the reason why acid gels enriched with polydisperse fractal aggregates had a lower storage modulus, yield stress, firmness, and thickness (Lesme et al., 2019).

In an acid-milk gel, the CMs form the backbone of the gel network. The WP aggregates only seem to affect the range of the elastic modulus of the resulting gel, probably through the strength of the bonds stabilizing the protein network (Andoyo et al., 2015). Andoyo et al. (2014) showed that coating around only 8% of the surface of CM with WP aggregates yields acid gels with significantly higher storage modulus than those composed only of CMs. Liu et al. (2016) also showed that WP nanoparticles at the surface of the CM contributed to the strength of the acid gel. The surface area of CMs covered with WP aggregates decreased when the casein/WP ratio increased but the acid-induced casein-casein interactions also contributed to the strength of the milk gel containing WP aggregates. Morand et al. (2012) modified the charge (pI) of model WP aggregates through their methylation and succinylation. The authors showed that the net charge of the WP aggregates determined the onset of acid gelation of heated model milk, but it had no effect on maximal G' value of the acid gel which probably depended primarily on the ability of the proteins to establish attractive interactions. Recently, Famelart et al. (2025) submitted a comprehensive work on the use of nanoparticulated WP aggregates (40–300 nm) in substitution of a part of the milk proteins. They compared it to the use of in situ aggregates formed during heat treatment for fresh acid cheese making. A scheme of putative mechanisms of interactions between CM and such aggregates was proposed, based on the literature and their own observations. In their case, WP aggregates would interact with CMs during gelation via hydrophobic interactions, while reducing the gel firmness without hindering the gel syneresis.

Microparticulated WP aggregates were used for the manufacture of acid milk gel (Silva & O'Mahony, 2018). They display diameters closer to fat globules than CMs. Compared to the acid-milk gel without microparticulated WPs, those containing microparticulated WPs were less elastic, less firm with a more porous and open structure. The greater pore connectivity would explain the lower water holding capacity of the acid-milk gel with microparticulated WPs. The added microparticulated WPs were not efficiently integrated as part of the gel network in the model systems. They limited the casein aggregation and created new serum channels in the acid milk gel (Silva & O'Mahony, 2018). Due to their large particle size and restricted bonding ability with other milk proteins, microparticulated WPs may prevent formation of a dense protein network, which also explains the softer acid milk gel (Liu et al., 2016). Sensory evaluation revealed no significant difference between control and petit-Suisse
cheese with a substitution of 10–40% wt of fat by microparticulated WPs. This confirms the microparticulated WPs are suitable to replace a part of the fat content in fat-reduced dairy products, in terms of sensory acceptability (Sánchez-Obando *et al.*, 2020).

## 5. Physics-based approach to milk gelation.

### 5.1. Casein micelle gels as gel-forming particles.

The self-assembly of food proteins exhibits hybrid characteristics between colloidal and polymeric objects, depending on whether they are respectively globular or (naturally) unfolded. These complementary physical approaches may help elucidate the complex interplay of phenomena occurring during milk gelation and curd aging. Several models through different length scales, from nanoscale molecular interactions to macroscopic properties of protein-based materials, have been developed to understand the underlying mechanisms responsible of the structural and functional changes during food product manufacture (Boire *et al.*, 2019). Several theoretical models, have been applied to describe milk gelation, including fractal aggregation, adhesive hard spheres, and the percolation models, as reviewed by Salvador *et al.* (2022) and Lucey (2017). Still, it is the fractal aggregation model that has been most widely used to date to describe the mechanism of CMs gelation.

Lazzari *et al.* (2016) reviewed colloidal gels that follow a fractal scaling, meaning they are composed of repetitive, self-similar structural units and remain invariant at different length scales. This approach has been adopted to understand various food gelation mechanisms, such as the heat-set gelation of β-Lg (Hagiwara *et al.*, 1997) or the cold-set gelation of fractal WPI aggregates (Marangoni *et al.*, 2000). The Df is a practical structural parameter, quantifying individual aggregate morphology on a continuum from 1 (linear aggregates) to 3 (spherical aggregates). Furthermore, the fractal concept may extend to describe the entire structure of a space filling gel, where the storage modulus (G') follows a power-law relationship (Df) with the particle volume fraction (φ) (Mezzenga & Fischer, 2013) as follow [1]:

$$G' \propto \phi^{Df} \quad [1]$$

To relate the elastic properties of a gel to its network structure, this theory assumes that the structure of a colloidal gel is analogous to that of a polymer gel, with self-similar fractal clusters of a correlation length ξ, without interpenetration. The number and the interaction strength between the particles in the clusters are responsible for the gel properties (Pantina & Furst, 2006). More specifically, some strands are assumed to support and transmit the stress from cluster to cluster and are responsible for the rheological properties of the colloidal gel while other strands are inactive (Gravelle & Marangoni, 2021). Shih *et al.* (1990) distinguishes a strong-link, weak-link, and in-between regime, whether the intercluster links are stronger than the clusters themselves.

Colloidal gels are open structures with typically Df values ranging from 1.8 for diffusion-limited cluster aggregation (DLCA) to 2.1 for reaction-limited cluster aggregation (RLCA) (Dickinson, 2000). The
enzyme-induced aggregation of CMs has been described as a diffusion-controlled mechanism delayed by a long-range repulsive barrier. This results in gels with a higher fractal dimensionality compared to those formed through pure diffusion-limited colloidal aggregation (Mellema *et al.*, 1999). At the microscopic scale, CM clusters grow by progressive incorporation of smaller clusters until forming a space filling network. The resulting gel represents a kinetically "arrested" phase separation between the CMs (clusters) and the serum phase. Despite their disordered structure, these milk gels are able to support small external stresses and therefore behave macroscopically like solids. Their mechanical and rheological properties are determined by both their structure and the number and strength of the interactions between mechanically-active tensors (Del Gado & Kob, 2010). In milk gels, these mechanically active tensors are not completely clear-cut: they may correspond to clusters of CMs, supporting strands, CMs, or substructure of CMs such as the hard regions defined by Bouchoux *et al.* (2010).

The stress distribution in the colloidal network is heterogenous and increases over time due to the increased contact surface area between CMs. This leads to slow rearrangements at different length scales (CM fusion, strand breaking, pore enlargement), leading to a progressive loss of the gel fractal structure (Bauland *et al.*, 2024). Overall, the number of bonds between proteins in the gel increases and the supporting strands become thicker as a result of the integration of loose end of snapped strands. Therefore, rearrangements progressively increase gel structure stability, causing the rate of the gel structure rearrangement to slow down over time, a universal feature in colloidal systems (Cipelletti *et al.*, 2000).

Mellema, van Opheusden *et al.* (2002) developed models based on the number of deformable links in a gel strand and their bendability to establish correlations between the rheology of rennet-induced milk gels and five types of gel structures: random, curved, hinged, straight and rigid. These rheology-structure relations are based on scaling laws of $G'$ (storage modulus), $\gamma_0$ (maximum linear strain) and $\sigma_y$ (macroscopic yield stress) with $\varphi$ (volume fraction of particles in the whole system), to understand what information the $D_f$ conveys. When applied to rennet-induced casein gels from skim milk, these models confirmed the fractal nature of casein aggregation, leading to the formation of straight strands requiring stretching prior to rupture. But applying this model to milk at lower pH (≤ 5.3) and higher temperatures (≥ 30 °C) needs further assumptions during the aging stage, which may differ from theory, because of the increased gel matrix rearrangement.

However, none of these models fully describe the complexity of milk gelation. Indeed, casein gels do not follow the same rules of a classical particle gel model. Enzymatic milk gels differ from ideal fractal gels by their characteristics: intermediate concentration and range of repulsive interactions (Horne & Lucey, 2014). For acidified milk gels, Horne (1999) points the inability of the fractal model to predict the gelation kinetics, and the absence of theoretised link between the fractal dimension and the
451
452

rearrangement during the gel aging. Based on this previous work, Andoyo *et al.* (2015) notice three limitations when applying the self-similarity approach of the fractal theory to acid milk gels:

453
454
455
456

- estimating the fractal dimension for high volume fractions of CMs (above 15 g.L⁻¹);

- compromise to be found between the protein concentration needed for length scales studies and for rheological measurements;

- CM rearrangements should be limited compared to position shifts.

457
458
459
460
461
462
463

To go further, Bouthier and Gibaud (2022) refined the fractal model by proposing a three-length scales model to compare two hypothesised mechanisms of gelation: i) clusters of clusters (hierarchical aggregation) and ii) interpenetrating clusters (mutually penetrating networks). The clusters of clusters model better described gelation in the weak link regime where inter-cluster interactions are weaker than intra-cluster ones, which corresponds to acid milk gels (Famelart *et al.*, 2025). Otherwise, likelihood for colloidal clusters to interpenetrate and behave on several length scales is not hypothesised in the standard fractal model and may help enhancing it for milk gels.

464
465
466
467
468
469

Milk gels exhibit continuous structural evolution during both rennet-induced (Mellema, Walstra *et al.*, 2002) and acid-induced gelation (Horne, 2003). Consequently, this dynamic behaviour requires considering several models which may overlap and follow successively according to the i) evolution of the interaction potentials between individual CMs as well as their structural modifications, ii) rearrangement of the gel strands and iii) other macroscopic phenomena such as syneresis and gel contraction.

470

## 5.2. Whey protein aggregates as filler particles in milk gels

471
472
473
474
475

When added in a milk gel, WP aggregates may be considered as filler particles, with varying sizes and interaction properties with the initial CMs gelled matrix (Fig. 3A). Noninteracting particles during the gel network formation are considered as inert fillers, although their presence may still modify gel structure and properties (Fig. 3B–3C). Interacting particles contribute actively to the structure and properties of the colloidal gel and are considered as active fillers (Fig. 3D–3E).

476
477
478
479
480
481

At filler particle volume fraction <0.5, noninteracting filler microparticles decrease the elastic modulus of the gel matrix (van Vliet, 1988). The gel organisation is perturbated around the filled particle, so that a zone of gel matrix depletion is observed around the particles (Fig. 3C). The mechanical forces exerted on the gel network at low strain do not interfere with the filled particles, that could be considered as void filled of aqueous solution. For noninteracting filler nanoparticles, no explicit model has been described, though this case may correspond to the hypothesis of Gamlath *et al.*, 2020. (Fig. 3B).

482
483
484

The elastic modulus of the acid milk gel containing interactive filler microparticles increases with the volume fraction of the filler particle (Van Vliet, 1988). The interactions between the gel matrix and the filler particles add cross-linking sites in the gel network (Fig. 3E), but this is often not enough to explain
485

486

487

the reinforcement of the filled gel matrix. These interactions also induce a densification of the gel network around the filled particles reducing the microscopic dynamics of the gel that add to the reinforcement of its elastic properties (Dellatolas et al, 2023).

488

489

490

491

492

493

494

495

Gravelle and Marangoni (2021) used a modified fractal model to capture fractal characteristics of casein gels, by adding rigid and strongly bound filler particles to a fully connected colloidal network. The filler particles were considered the same size as the self-repeating clusters of particles of the colloidal network. Instead of the usual assumption of homogenous stress translation, they introduced a heterogeneity at scales exceeding the cluster size: some strands held the mechanical stress through “load-bearing links”, while others did not and were mechanically inefficient. The scaling relation modification could be observed on experimental data, whether the filler particles participated in the stress bearing network, or not.

496

497

498

499

500

501

502

503

504

505

Barden *et al.* (2015) studied the rheological properties of Cheddar cheeses filled with Sephadex beads, that are larger than CMs. Composed of cross-linked polydextrans, Sephadex beads are perfectly spherical, thermally stable, and can be used as micrometric scale models (20 - 150 µm diameter) for simplified milkfat globules or microparticulated aggregates. They reported the contribution of the filler particles to the rheological properties of cheese, using the filled gel theory. Their model accounts only for the volume of spherical filler, and not their shape or size. Using the filled gel model and considering the fillers are active (Fig. 3E), they confirmed the simultaneous contribution of the gel matrix and filler particle volume fraction, for predicting the mechanical properties of the cheese. Moreover, the filler particles are sites for stress concentration and therefore lower the strain required for initiating gel fracture.

506

507

508

509

510

511

512

513

514

515

516

In the case of interacting filler nanoparticles (Fig. 3D1–2), no model has been described explicitly. One could imagine nanoscale fillers to actively take part in the structure of the gel matrix as part of the load-bearing strands (Fig. 3D1). If the interspecific bonds between filler particles and the gelled colloidal particles are stronger than the intraspecific bonds among the gelled colloidal particles, this would lead to an overall stronger structure. This is in agreement with Andoyo *et al.* (2015), who reported stronger acid gels with added WP aggregates smaller than CMs (respectively 132 nm and 208 nm hydrodynamic diameters), acting as active filler on bonds stabilising the acid milk gel (see 4.3.). On the contrary, a weak bonding between the nanoscale fillers and the gelled colloidal particles constitutes a poor elastic stress transmitter resulting in a softer structure. Finally, WP aggregates could also be located around the load-bearing strands (Fig. 3D2), and have no active role in the tension distribution, while still interacting with the matrix.

517

518

519

Another model may be observed when two types of colloidal particles are interpenetrated, with each forming an independent gel: bigels (Fig. 3D3). They are bicontinuous structure obtained from the arrested phase separation of a colloidal mixture of two components and have been explicitly theorised
by (Varrato et al., 2012). In their model, the two components have the same size, but different intra- and interparticle interactions. A bigel is observed above a critical volume fraction for the two components when they have similar intraparticle interactions and the interparticle interaction are zero. A bigel model with colloidal particles having distinct size ratios and asymmetrical attractions for both subgels is still needed.

Although CMs act differently from ideal particles usually considered in the fractal theory, as described previously, simplified models remain useful to describe isolated mechanisms. Progressively increasing model complexity to get closer to real food systems is possible; while challenging, this approach is rewarding in understanding the links between molecular mechanisms and macroscale observations (Boire et al., 2019). For instance, in the case of casein gels with WP aggregates, it would be interesting to i) apply the scaling model by Mellema, van Opheusden et al. (2002) to study casein gels and ii) to compare the results to casein gels with WP aggregates. In colloidal science, the effects of nanofillers on colloidal composites in the rubbery state is well explored, both in terms of filler size and volume fraction. But nanofiller size effects on the creep and fracture properties is not fully studied, as reported by Makepeace et al. (2018), who hypothesise the strong influence of the size ratio between filler and the colloid on the material properties. Moreover, the matrices studied in these fields vary greatly from casein gels. To our knowledge, no nano-filled colloidal gelation model applied to dairy gels has been published.

## 6. Conclusions

Milk gelation, whether induced by rennet or acidification, is governed by the destabilisation and restructuring of CMs into a continuous colloidal network. The incorporation of WP aggregates, formed either *in situ* (during milk heating) or *ex situ* (pre-formed in solutions), notably alters gelation dynamics and final properties.

*In situ* WP aggregates are mainly attached to k-casein either onto the surface of CM and/or in the serum phase of milk in proportions that depend on the physicochemical conditions of milk at heating. They are smaller than CM and impair enzyme-induced CM aggregation and milk gel contraction. In contrast, they reinforce the structure of acid-induced milk gels. In both cases, *in situ* WP aggregates enhance water retention in the gel matrix and reduce whey drainage.

The structure and size of *ex situ* aggregates may be controlled by adjusting the physicochemical and heating conditions of the WP solution. Apart from microparticulated WP aggregates that mimic fat globules, only a limited number of studies have dealt with smaller aggregates in cheesemaking. When added to milk, *ex situ* WP aggregates affect milk gelation and curd properties differently than *in situ* aggregates. Still, there remains a lack of studies correlating the fine characteristics of *ex situ* WP
553

aggregates (structure, size, and reactivity) - especially their interaction with the (hydrolysed) CMs -
with their influence on i) the kinetics of gel formation and ii) the properties of both enzymatic- and
acid-induced milk gels.

554

555

556

Empirical models, such as fractal theory, have been developed to describe the structure of colloidal gels based on their rheological properties. Recent advances, such as the “clusters of clusters” model, offer insights into gelation mechanisms under flow. While these models provide valuable insights, the unique properties of CMs and their dynamic evolution during gelation requires more specific and complex models. Moreover, while models exist for both interactive and inert filler particles larger than the colloidal particles forming the gel, no models address nano-fillers to date. Thus, considering the complex interplay of WP aggregates, casein networks, and environmental factors requires more research to achieve refined modelling.

557

558

559

560

561

562

563

564

Future research should prioritise elucidating the detailed mechanisms by which WP aggregates interact
with CMs. By analysing empirical findings with physics-based modelling, the dairy industry could
make better use of *ex situ* WP aggregates to renew or innovate cheese making practices to meet evolving
consumer demands for texture and nutrition while maximizing the yield.

565

566

567

568

Author contributions

569

Erik Juste: Conceptualisation; Visualisation; Writing – original draft; Writing – review and editing.

570

**Jeehyun Lee**: Conceptualisation; Visualisation; Writing – original draft; Writing – review and editing; Supervision. **Thomas Croguennec**: Conceptualisation; Writing – review and editing; Supervision, Funding acquisition, Project administration.

571

572

573

Funding sources

574

This work was supported by the Association Nationale de la Recherche et de la Technologie.
575 References

576 Akkermans, C., Venema, P., van der Goot, A. J., Gruppen, H., Bakx, E. J., Boom, R. M., & van der

577 Linden, E. (2008). Peptides are building blocks of heat-induced fibrillar protein aggregates of β-

578 lactoglobulin formed at pH 2. *Biomacromolecules*, *9*(5), 1474–1479.

579 https://doi.org/10.1021/bm7014224

580 Almena-Aliste, M., & Mietton, B. (2014). Cheese classification, characterization, and categorization:

581 A global perspective. *Microbiology Spectrum*, *2*(1). https://doi.org/10.1128/microbiolspec.cm-0003-

582 2012

583 Andoyo, R., Guyomarc’h, F., Burel, A., & Famelart, M.-H. (2015). Spatial arrangement of casein

584 micelles and whey protein aggregate in acid gels: Insight on mechanisms. *Food Hydrocolloids*, *51*,

585 118–128. https://doi.org/10.1016/j.foodhyd.2015.04.031

586 Andoyo, R., Guyomarc’h, F., Cauty, C., & Famelart, M.-H. (2014). Model mixtures evidence the

587 respective roles of whey protein particles and casein micelles during acid gelation. *Food*

588 *Hydrocolloids*, *37*, 203–212. https://doi.org/10.1016/j.foodhyd.2013.10.019

589 Anema, S. G., & Li, Y. (2003). Effect of pH on the association of denatured whey proteins with

590 casein micelles in heated reconstituted skim milk. *Journal of Agricultural and Food Chemistry*, *51*(6),

591 1640–1646. https://doi.org/10.1021/jf025673a

592 Anema, S. G., Lee, S. K., & Klostermeyer, H. (2006). Effect of protein, nonprotein-soluble

593 components, and lactose concentrations on the irreversible thermal denaturation of β-lactoglobulin

594 and α-lactalbumin in skim milk. *Journal of Agricultural and Food Chemistry*, *54*(19), 7339–7348.

595 https://doi.org/10.1021/jf061508

596 Barden, L. M., Osborne, J. A., McMahon, D. J., & Foegeding, E. A. (2015). Investigating the filled

597 gel model in Cheddar cheese through use of Sephadex beads. *Journal of Dairy Science*, *98*(3), 1502–

598 1516. https://doi.org/10.3168/jds.2014-8597

599 Bauland, J., Bouchoux, A., Croguennec, T., Famelart, M.-H., & Guyomarc’h, F. (2022). Atomic

600 Force Microscopy to assess the mechanical properties of individual casein micelles. *Food*

601 *Hydrocolloids*, *128*, 107577. https://doi.org/10.1016/j.foodhyd.2022.107577

602 Bauland, J., Manna, G., Divoux, T., & Gibaud, T. (2024). Two-step aging dynamics in enzymatic

603 milk gels. *Physical Review Materials*, *8*(7), L072601.

604 https://doi.org/10.1103/physrevmaterials.8.1072601

605 Baussay, K., Le Bon, C., Nicolai, T., Durand, D., & Busnel, J.-P. (2004). Influence of the ionic

606 strength on the heat-induced aggregation of the globular protein β-lactoglobulin at pH 7. *International*

607 *Journal of Biological Macromolecules*, *34*(1–2), 21–28.

608 https://doi.org/10.1016/j.ijbiomac.2003.11.003

609 Bogahawaththa, D., & Vasiljevic, T. (2020). Shearing accelerates denaturation of β-lactoglobulin and

610 α-lactalbumin in skim milk during heating. *International Dairy Journal*, *105*, 104674.

611 https://doi.org/10.1016/j.idairyj.2020.104674

612 Boire, A., Renard, D., Bouchoux, A., Pezennec, S., Croguennec, T., Lechevalier, V., Le Floch-

613 Fouéré, C., Bouhallab, S., & Menut, P. (2019). Soft-matter approaches for controlling food protein

614 interactions and assembly. *Annual Review of Food Science and Technology*, *10*(1), 521–539.

615 https://doi.org/10.1146/annurev-food-032818-121907
616 Bouchoux, A., Gésan-Guiziou, G., Pérez, J., & Cabane, B. (2010). How to squeeze a sponge: Casein micelles under osmotic stress, a SAXS study. *Biophysical Journal*, 99(11), 3754–3762.

617 https://doi.org/10.1016/j.bpj.2010.10.019

619 Bouhallab, S., Croguennec, T. (2013). Spontaneous assembly and induced aggregation of food proteins. In Müller, M. (Ed.), *Polyelectrolyte complexes in the dispersed and solid state II* (Advances in Polymer Science, vol. 256, pp. 67–101). Springer. https://doi.org/10.1007/12_2012_201

622 Bouthier, L.-V., & Gibaud, T. (2023). Three length-scales colloidal gels: The clusters of clusters versus the interpenetrating clusters approach. *Journal of Rheology*, 67(3), 621–633.

624 https://doi.org/10.1122/8.0000595

625 Britten, M., & Giroux, H. J. (2022). Rennet coagulation of heated milk: A Review. *International Dairy Journal*, 124, 105179. https://doi.org/10.1016/j.idairyj.2021.105179

627 Bromley, E. H., Krebs, M. R., & Donald, A. M. (2006). Mechanisms of structure formation in particulate gels of β-lactoglobulin formed near the isoelectric point. *The European Physical Journal E*, 21(2), 145–152. https://doi.org/10.1140/epje/i2006-10055-7

630 Castillo, M., Jordán, M. J., Godoy, A., Laencina, J., & López, M. B. (2000). Kinetics of syneresis in fresh goat cheese. *Milchwissenschaft*, 55(10), 566–569.

632 Chen, D., Pinho, L. S., Federici, E., Zuo, X., Ilavsky, J., Kuzmenko, I., Yang, Z., Jones, O. G., & Campanella, O. (2022). Heat accelerates degradation of β-lactoglobulin fibrils at neutral pH. *Food Hydrocolloids*, 124, 107291. https://doi.org/10.1016/j.foodhyd.2021.107291

635 Cipelletti, L., Manley, S., Ball, R. C., & Weitz, D. A. (2000). Universal aging features in the restructuring of fractal colloidal gels. *Physical Review Letters*, 84(10), 2275–2278.

637 https://doi.org/10.1103/physrevlett.84.2275

638 Corredig, M., & Salvatore, E. (2016). Enzymatic coagulation of milk. *Advanced Dairy Chemistry*, 287–307. https://doi.org/10.1007/978-1-4939-2800-2_11

640 Čurlej, J., Zajác, P., Čapla, J., Golian, J., Benešová, L., Partika, A., Fehér, A., & Jakabová, S. (2022). The effect of heat treatment on cow’s milk protein profiles. *Foods*, 11(7), 1023.

642 https://doi.org/10.3390/foods11071023

643 Dalgleish, D. G., & Corredig, M. (2012). The structure of the casein micelle of milk and its changes during processing. *Annual Review of Food Science and Technology*, 3(1), 449–467.

645 https://doi.org/10.1146/annurev-food-022811-101214

646 Dannenberg, F., & Kessler, H.-G. (1988). Reaction kinetics of the denaturation of whey proteins in milk. *Journal of Food Science*, 53(1), 258–263. https://doi.org/10.1111/j.1365-2621.1988.tb10223.x

648 Dejmek, P., & Walstra, P. (2004). The syneresis of rennet-coagulated curd. In Fox, P. F., McSweeney, P. L.H., Cogan, T. M., & Guinee T. P. (Eds), *Cheese: Chemistry, Physics and Microbiology* (3rd ed., vol. 1, pp. 71–103). https://doi.org/10.1016/s1874-558x(04)80063-0

651 Del Gado, E., & Kob, W. (2010). A microscopic model for colloidal gels with directional effective interactions: Network induced glassy dynamics. *Soft Matter*, 6(7), 1547–1558.

653 https://doi.org/10.1039/b916813c

654 Dellatolas, I., Bantawa, M., Damerau, B., Guo, M., Divoux, T., Del Gado, E., & Bischofberger, I. (2023). Local mechanism governs global reinforcement of nanofiller-Hydrogel Composites. *ACS Nano*, 17(21), 20939–20948. https://doi.org/10.1021/acsnano.3c00716
657

Dickinson, E. (2000). Structure and rheology of simulated gels formed from aggregated colloidal particles. *Journal of Colloid and Interface Science*, 225(1), 2–15.

658

659

https://doi.org/10.1006/jcis.1999.6662

660

Donato, L., & Guyomarc'h, F. (2009). Formation and properties of the whey protein/κ-casein complexes in heated skim milk – A review. *Dairy Science and Technology*, 89(1), 3–29.

661

662

https://doi.org/10.1051/dst:2008033

663

Fagan, C. C., O'Callaghan, D. J., Mateo, M. J., & Dejmek, P. (2017). The syneresis of rennet-coagulated curd. In McSweeney, P. L.H., Fox, P. F., Cotter, P. D., & Everett, D. W. (Eds.), *Cheese: Chemistry, Physics and Microbiology* (4th ed., vol. 1, pp. 145–177). Academic press.

664

665

666

https://doi.org/10.1016/b978-0-12-417012-4.00006-5

667

Famelart, M.-H., Mtibaa, I., Rousseau, F., Perrignon, M., Richoux, R., Rondeau-Mouro, C., & Gaborit, P. (2025). Drainage of acid-rennet gels: Rheological and microstructural study of milk heat treatment and milk proteins/whey protein aggregates ratio effects. *Journal of Food Engineering*, 391, 112457. https://doi.org/10.1016/j.jfoodeng.2024.112457

668

669

670

671

Gamlath, C. J., Leong, T. S. H., Ashokkumar, M., & Martin, G. J. O. (2020). Incorporating whey protein aggregates produced with heat and ultrasound treatment into rennet gels and model non-fat cheese systems. *Food Hydrocolloids*, 109, 106103. https://doi.org/10.1016/j.foodhyd.2020.106103

672

673

674

Gastaldi, E., Lagaude, A., & Tarodo de la Fuente, B. T. (1996). Micellar transition state in casein between pH 5.5 and 5.0. *Journal of Food Science*, 61(1), 59–64. https://doi.org/10.1111/j.1365-2621.1996.tb14725.x

675

676

677

Gélébart, P., Riaublanc, A., Famelart, M.-H., Jonchère, C., Beaumal, V., Anton, M., & Garnier, C. (2019). Protein aggregates modulate the texture of emulsified and acidified acid milk gels. *Food Hydrocolloids*, 93, 176–188. https://doi.org/10.1016/j.foodhyd.2019.02.007

678

679

680

Giroux, H. J., Lanouette, G., & Britten, M. (2015). Effect of whey protein aggregates of various sizes on the formation and properties of rennet-induced milk gels. *Food Hydrocolloids*, 45, 272–278. https://doi.org/10.1016/j.foodhyd.2014.12.004

681

682

683

Giroux, H. J., Veillette, N., & Britten, M. (2018). Use of denatured whey protein in the production of artisanal cheeses from cow, goat and sheep milk. *Small Ruminant Research*, 161, 34–42. https://doi.org/10.1016/j.smallrumres.2018.02.006

684

685

686

Gravelle, A. J., & Marangoni, A. G. (2021). A new fractal structural-mechanical theory of particle-filled colloidal networks with heterogeneous stress translation. *Journal of Colloid and Interface Science*, 598, 56–68. https://doi.org/10.1016/j.jcis.2021.03.180

687

688

689

Guyomarc'h, F., Famelart, M.-H., Henry, G., Gulzar, M., Leonil, J., Hamon, P., Bouhallab, S., & Croguennec, T. (2014). Current ways to modify the structure of whey proteins for specific functionalities—A review. *Dairy Science & Technology*, 95(6), 795–814. https://doi.org/10.1007/s13594-014-0190-5

690

691

692

693

Guyomarc'h, F. (2006). Formation of heat-induced protein aggregates in milk as a means to recover the whey protein fraction in cheese manufacture, and potential of heat-treating milk at alkaline pH values in order to keep its rennet coagulation properties. A review. *Le Lait*, 86(1), 1–20. https://doi.org/10.1051/lait:2005046

694

695

696

697

Hagiwara, T., Kumagai, H., Matsunaga, T., & Nakamura, K. (1997). Analysis of aggregate structure in food protein gels with the concept of fractal. *Bioscience, Biotechnology, and Biochemistry*, 61(10), 1663–1667. https://doi.org/10.1271/bbb.61.1663

698

699
700 Heyn, T. R., Garamus, V. M., Neumann, H. R., Uttinger, M. J., Guckeisen, T., Heuer, M., Selhuber-
701 Unkel, C., Peukert, W., & Keppler, J. K. (2019). Influence of the polydispersity of pH 2 and pH 3.5
702 beta-lactoglobulin amyloid fibril solutions on analytical methods. *European Polymer Journal*, 120,
703 109211. https://doi.org/10.1016/j.eurpolymj.2019.08.038

704 Hill, A. R., Irvine, D. M., & Bullock, D. H. (1982). Precipitation and recovery of whey proteins: A
705 Review. *Canadian Institute of Food Science and Technology Journal*, 15(3), 155-160.
706 https://doi.org/10.1016/s0315-5463(82)72529-5

707 Hinrichs, J. (2001). Incorporation of whey proteins in cheese. *International Dairy Journal*, 11(4-7),
708 495-503. https://doi.org/10.1016/s0958-6946(01)00071-1

709 Hoppenreijs, L. J. G., Fitzner, L., Ruhmlieb, T., Heyn, T. R., Schild, K., van der Goot, A.-J., Boom,
710 R. M., Steffen-Heins, A., Schwarz, K., & Keppler, J. K. (2022). Engineering amyloid and amyloid-
711 like morphologies of β-lactoglobulin. *Food Hydrocolloids*, 124, 107301.
712 https://doi.org/10.1016/j.foodhyd.2021.107301

713 Horne, D. S. (1999). Formation and structure of acidified milk gels. *International Dairy Journal*, 9(3-
714 6), 261-268. https://doi.org/10.1016/s0958-6946(99)00072-2

715 Horne, D. S. (2003). Casein micelles as hard spheres: Limitations of the model in acidified gel
716 formation. *Colloids and Surfaces A: Physicochemical and Engineering Aspects*, 213(2-3), 255-263.
717 https://doi.org/10.1016/s0927-7757(02)00518-6

718 Horne, D.S., & Lucey, J. A. (2014). Revisiting the temperature dependence of the coagulation of
719 renneted bovine casein micelles. *Food Hydrocolloids*, 42, 75-80.
720 https://doi.org/10.1016/j.foodhyd.2013.12.021

721 Horne, D. S., & Lucey, J. A. (2017). Rennet-Induced Coagulation of Milk. In McSweeney, P. L.H.,
722 Fox, P. F., Cotter, P. D., & Everett, D. W. (Eds.), *Cheese: Chemistry, Physics and Microbiology* (4th
723 ed., vol. 1, pp. 115-143). Academic press. https://doi.org/10.1016/B978-0-12-417012-4.00005-3

724 Inthavong, W., Kharlamova, A., Chassenieux, C., & Nicolai, T. (2016). Structure and flow of dense
725 suspensions of protein fractal aggregates in comparison with microgels. *Soft Matter*, 12(10), 2785-
726 2793. https://doi.org/10.1039/c5sm02893k

727 Jung, J.-M., Savin, G., Pouzot, M., Schmitt, C., & Mezzenga, R. (2008). Structure of heat-induced β-
728 lactoglobulin aggregates and their complexes with sodium-dodecyl sulfate. *Biomacromolecules*, 9(9),
729 2477-2486. https://doi.org/10.1021/bm800502j

730 Kethireddipalli, P., Hill, A. R., & Dalgleish, D. G. (2011). Interaction between casein micelles and
731 whey protein/k-casein complexes during renneting of heat-treated reconstituted skim milk powder and
732 casein micelle/serum mixtures. *Journal of Agricultural and Food Chemistry*, 59(4), 1442-1448.
733 https://doi.org/10.1021/jf103943e

734 Kiesner, C., Clawin-Rädecker, I., Meisel, H., & Buchheim, W. (2000). Manufacturing of α-
735 lactalbumin-enriched whey systems by selective thermal treatment in combination with membrane
736 processes. *Le Lait*, 80(1), 99-111. https://doi.org/10.1051/lait:2000111

737 Kroes-Nijboer, A., Venema, P., & van der Linden, E. (2012). Fibrillar structures in food. *Food &
738 Function*, 3(3), 221-227. https://doi.org/10.1039/c1fo10163c

739 Kruchinin, A. G., Bolshakova, E. I., & Bigaeva, A. V. (2022). Kinetics of changes in the
740 granulometric composition of thermodenatured whey proteins. *Carpathian Journal of Food Science
741 and Technology*, 116-127. https://doi.org/10.34302/crpjfst/2022.14.3.10
742 Lazzari, S., Nicoud, L., Jaquet, B., Lattuada, M., & Morbidelli, M. (2016). Fractal-like structures in colloid science. *Advances in Colloid and Interface Science*, 235, 1-13.

744 https://doi.org/10.1016/j.cis.2016.05.002

745 Lee, S. K., Huss, M., Klostermeyer, H., & Anema, S. G. (2013). The effect of pre-denatured whey proteins on the textural and micro-structural properties of model processed cheese spreads.

747 *International Dairy Journal*, 32(2), 79-88. https://doi.org/10.1016/j.idairyj.2013.04.006

748 Lesme, H., Rannou, C., Loisel, C., Famelart, M.-H., Bouhallab, S., & Prost, C. (2019). Controlled whey protein aggregates to modulate the texture of fat-free set-type yoghurts. *International Dairy Journal*, 92, 28-36. https://doi.org/10.1016/j.idairyj.2019.01.004

751 Li, H., Zhao, T., Li, H., & Yu, J. (2021). Effect of heat treatment on the property, structure, and aggregation of skim milk proteins. *Frontiers in Nutrition*, 8, 714869.

753 https://doi.org/10.3389/fnut.2021.714869

754 Li, Q., & Zhao, Z. (2019). Acid and rennet-induced coagulation behavior of casein micelles with modified structure. *Food Chemistry*, 291, 231-238. https://doi.org/10.1016/j.foodchem.2019.04.028

755 Liu, G., Buldo, P., Greve, M. T., Nielsen, S. B., Nielsen, J. H., & Ipsen, R. (2016). Effects of added whey protein aggregates on textural and microstructural properties of acidified Milk Model Systems. *International Dairy Journal*, 62, 43-52. https://doi.org/10.1016/j.idairyj.2016.07.006

759 Loiseleux, T., Rolland-Sabaté, A., Garnier, C., Croguennec, T., Guilois, S., Anton, M., & Riaublanc, A. (2018). Determination of hydro-colloidal characteristics of milk protein aggregates using Asymmetrical Flow Field-Flow Fractionation coupled with Multiangle Laser Light Scattering and Differential Refractometer (AF4-MALLS-DRi). *Food Hydrocolloids*, 74, 197-206.

763 https://doi.org/10.1016/j.foodhyd.2017.08.012

764 Loveday, S. M., Su, J., Rao, M. A., Anema, S. G., & Singh, H. (2012). Whey protein nanofibrils: Kinetic, rheological and morphological effects of group IA and IIA cations. *International Dairy Journal*, 26(2), 133-140. https://doi.org/10.1016/j.idairyj.2012.03.001

767 Loveday, S. M., Wang, X. L., Rao, M. A., Anema, S. G., Creamer, L. K., & Singh, H. (2010). Tuning the properties of β-lactoglobulin nanofibrils with pH, NaCl and CaCl₂. *International Dairy Journal*, 20(9), 571-579. https://doi.org/10.1016/j.idairyj.2010.02.014

770 Loveday, S. M., Wang, X. L., Rao, M. A., Anema, S. G., & Singh, H. (2012). β-lactoglobulin nanofibrils: Effect of temperature on fibril formation kinetics, fibril morphology and the rheological properties of fibril dispersions. *Food Hydrocolloids*, 27(1), 242-249.

773 https://doi.org/10.1016/j.foodhyd.2011.07.001

774 Lucey, J. A. (2017). Formation, structural properties, and rheology of acid-coagulated milk gels. In McSweeney, P. L.H., Fox, P. F., Cotter, P. D., & Everett, D. W. (Eds.), *Cheese: Chemistry, Physics and Microbiology* (4th ed., vol. 1, pp. 179-197). Academic press. https://doi.org/10.1016/b978-0-12-417012-4.00007-7

778 Lucey, J. A., Teo, C. T., Munro, P. A., & Singh, H. (1998). Microstructure, permeability and appearance of acid gels made from heated skim milk. *Food Hydrocolloids*, 12(2), 159-165.

780 https://doi.org/10.1016/s0268-005x(98)00012-5

781 Makepeace, D. K., Locatelli, P., Lindsay, C., Adams, J. M., & Keddie, J. L. (2018). Colloidal polymer composites: Are nano-fillers always better for improving mechanical properties? *Journal of Colloid and Interface Science*, 523, 45-55. https://doi.org/10.1016/j.jcis.2018.03.067
784 Marangoni, A. G., Barbut, S., McGauley, S. E., Marcone, M., & Narine, S. S. (2000). On the structure of particulate gels—the case of salt-induced cold gelation of heat-denatured whey protein isolate.
*Food Hydrocolloids, 14*(1), 61–74. https://doi.org/10.1016/s0268-005x(99)00046-6

787 Marchin, S., Putaux, J.-L., Pignon, F., & Léonil, J. (2007). Effects of the environmental factors on the casein micelle structure studied by cryo transmission electron microscopy and small-angle X-ray scattering/ultrasmall-angle X-ray scattering. *The Journal of Chemical Physics*, 126(4), 045101.
https://doi.org/10.1063/1.2409933

791 Markoska, T., Huppertz, T., & Vasiljevic, T. (2021). Influence of pH and solids content on heat-induced changes in structural arrangements of proteins in milk. *Mljekarstvo : Journal for Dairy Production and Processing Improvement*, 71(2), 95–105.
https://doi.org/10.15567/mljekarstvo.2021.0202

795 Mead, D., & Roupas, P. (2001). Effect of incorporation of denatured whey proteins on chemical composition and functionality of pizza cheese. *Australian Journal of Dairy Technology*, 56(1), 19–23.

797 Mellema, M., van Opheusden, J. H. J., & van Vliet, T. (1999). Relating colloidal particle interactions to gel structure using Brownian dynamics simulations and the Fuchs stability ratio. *The Journal of Chemical Physics*, 111(13), 6129–6135. https://doi.org/10.1063/1.479956

800 Mellema, M., van Opheusden, J. H. J., & van Vliet, T. (2002). Categorization of rheological scaling models for particle gels applied to casein gels. *Journal of Rheology*, 46(1), 11–29.
https://doi.org/10.1122/1.1423311

803 Mellema, M., Walstra, P., van Opheusden, J. H. J., & van Vliet, T. (2002). Effects of structural rearrangements on the rheology of rennet-induced casein particle gels. *Advances in Colloid and Interface Science*, 98(1), 25–50. https://doi.org/10.1016/s0001-8686(01)00089-6

806 Mezzenga, R., & Fischer, P. (2013). The self-assembly, aggregation and phase transitions of food protein systems in one, two and three dimensions. *Reports on Progress in Physics*, 76(4), 046601.
https://doi.org/10.1088/0034-4885/76/4/046601

809 Morand, M., Guyomarc'h, F., Legland, D., & Famelart, M.-H. (2012). Changing the isoelectric point of the heat-induced whey protein complexes affects the acid gelation of skim milk. *International Dairy Journal*, 23(1), 9–17. https://doi.org/10.1016/j.idairyj.2011.10.006

812 Nicolai, T., Britten, M., & Schmitt, C. (2011). β-lactoglobulin and WPI aggregates: Formation, structure and applications. *Food Hydrocolloids*, 25(8), 1945–1962.
https://doi.org/10.1016/j.foodhyd.2011.02.006

815 Nicolai, T., & Durand, D. (2013). Controlled food protein aggregation for new functionality. *Current Opinion in Colloid & Interface Science*, 18(4), 249–256. https://doi.org/10.1016/j.cocis.2013.03.001

817 Pantina, J. P., & Furst, E. M. (2006). Colloidal aggregate micromechanics in the presence of divalent ions. *Langmuir*, 22(12), 5282–5288. https://doi.org/10.1021/la0534120

819 Perreault, V., Morin, P., Pouliot, Y., & Britten, M. (2017). Effect of denatured whey protein concentrate and its fractions on rennet-induced milk gels. *International Dairy Journal*, 64, 48–55.
https://doi.org/10.1016/j.idairyj.2016.09.005

822 Perreault, V., Rémillard, N., Chabot, D., Morin, P., Pouliot, Y., & Britten, M. (2017). Effect of denatured whey protein concentrate and its fractions on cheese composition and rheological properties. *Journal of Dairy Science*, 100(7), 5139–5152. https://doi.org/10.3168/jds.2016-12473
825 Perreault, V., Turcotte, O., Morin, P., Pouliot, Y., & Britten, M. (2016). Combined effect of denatured whey protein concentrate level and fat level in milk on rennet gel properties. *International Dairy Journal*, 55, 1–9. https://doi.org/10.1016/j.idairyj.2015.11.008

828 Phan-Xuan, T., Durand, D., Nicolai, T., Donato, L., Schmitt, C., & Bovetto, L. (2014). Heat induced formation of beta-lactoglobulin microgels driven by addition of calcium ions. *Food Hydrocolloids*, 34, 227–235. https://doi.org/10.1016/j.foodhyd.2012.09.008

831 Pouzot, M., Nicolai, T., Visschers, R. W., & Weijers, M. (2005). X-ray and light scattering study of the structure of large protein aggregates at neutral pH. *Food Hydrocolloids*, 19(2), 231–238. https://doi.org/10.1016/j.foodhyd.2004.06.003

834 Qi, X., Liu, D., Yuan, J., Regenstein, J. M., & Zhou, P. (2022). Effects of heating temperatures and pH of skim milk fortified with milk protein concentrate on the texture and microstructure of high-protein yoghurts. *International Dairy Journal*, 131, 105395. https://doi.org/10.1016/j.idairyj.2022.105395

838 Ramos, O. L., Pereira, R. N., Martins, A., Rodrigues, R., Fuciños, C., Teixeira, J. A., Pastrana, L., Malcata, F. X., & Vicente, A. A. (2017). Design of whey protein nanostructures for incorporation and release of nutraceutical compounds in food. *Critical Reviews in Food Science and Nutrition*, 57(7), 1377–1393. https://doi.org/10.1080/10408398.2014.993749

842 Roefs, S. P. F. M., & Van Vliet, T. (1990). Structure of acid casein gels 2. dynamic measurements and type of interaction forces. *Colloids and Surfaces*, 50, 161–175. https://doi.org/10.1016/0166-6622(90)80260-b

845 Salvador, D., Acosta, Y., Zamora, A., & Castillo, M. (2022). Rennet-induced casein micelle aggregation models: A review. *Foods*, 11(9), 1243. https://doi.org/10.3390/foods11091243

847 Sánchez-Obando, J.-D., Cabrera-Trujillo, M. A., Olivares-Tenorio, M.-L., & Klotz, B. (2020). Use of optimized microparticulated whey protein in the process of reduced-fat spread and petit-suisse cheeses. *LWT*, 120, 108933. https://doi.org/10.1016/j.lwt.2019.108933

850 Schenkel, P., Samudrala, R., & Hinrichs, J. (2013). The effect of adding whey protein particles as inert filler on thermophysical properties of fat-reduced semihard cheese type Gouda. *International Journal of Dairy Technology*, 66(2), 220–230. https://doi.org/10.1111/1471-0307.12036

853 Schmitt, C., Moitzi, C., Bovay, C., Rouvet, M., Bovetto, L., Donato, L., Leser, M. E., Schurtenberger, P., & Stradner, A. (2010). Internal structure and colloidal behaviour of covalent whey protein microgels obtained by heat treatment. *Soft Matter*, 6(19), 4876–4884. https://doi.org/10.1039/c0sm00220h

857 Schokker, E. P., Singh, H., Pinder, D. N., & Creamer, L. K. (2000). Heat-induced aggregation of β-lactoglobulin AB at pH 2.5 as influenced by ionic strength and protein concentration. *International Dairy Journal*, 10(4), 233–240. https://doi.org/10.1016/s0958-6946(00)00047-9

860 Shih, W.-H., Shih, W. Y., Kim, S.-I., Liu, J., & Aksay, I. A. (1990). Scaling behavior of the elastic properties of colloidal gels. *Physical Review A*, 42(8), 4772–4779. https://doi.org/10.1103/physreva.42.4772

863 Silva, J. V. C., & O'Mahony, J. A. (2018). Microparticulated whey protein addition modulates rheological and microstructural properties of high-protein acid milk gels. *International Dairy Journal*, 78, 145–151. https://doi.org/10.1016/j.idairyj.2017.11.013

866 Stankey, J. A., Lu, Y., Abdalla, A., Govindasamy-Lucey, S., Jaeggi, J. J., Mikkelsen, B. Ø., Pedersen, K. T., & Andersen, C. B. (2017). Low-fat Cheddar cheese made using microparticulated whey
868 proteins: Effect on yield and cheese quality. *International Journal of Dairy Technology*, 70(4), 481-
869 491. https://doi.org/10.1111/1471-0307.12413

870 Sturaro, A., De Marchi, M., Zorzi, E., & Cassandro, M. (2015). Effect of microparticulated whey
871 protein concentration and protein-to-fat ratio on Caciotta cheese yield and composition. *International
872 Dairy Journal*, 48, 46–52. https://doi.org/10.1016/j.idairyj.2015.02.003

873 Sturaro, A., Penasa, M., Cassandro, M., Varotto, A., & De Marchi, M. (2014). Effect of
874 microparticulated whey proteins on milk coagulation properties. *Journal of Dairy Science*, 97(11),
875 6729–6736. https://doi.org/10.3168/jds.2014-8157

876 Tolkach, A., Steinle, S., & Kulozik, U. (2006). Optimization of thermal pretreatment conditions for
877 the separation of native α-lactalbumin from whey protein concentrates by means of selective
878 denaturation of β-lactoglobulin. *Journal of Food Science*, 70(9), E557–E566.
879 https://doi.org/10.1111/j.1365-2621.2005.tb08319.x

880 Triani, R., & Foegeding, E. A. (2019). Heat stability of whey protein ingredients based on state
diagrams. *International Dairy Journal*, 91, 25–35. https://doi.org/10.1016/j.idairyj.2018.12.006

882 van Vliet, T. (1988). Rheological properties of filled gels. influence of filler matrix interaction.
*Colloid and Polymer Science*, 266(6), 518–524. https://doi.org/10.1007/bf01420762

884 van Vliet, T., van Dijk, H. J. M., Zoon, P., & Walstra, P. (1991). Relation between syneresis and
885 rheological properties of particle gels. *Colloid and Polymer Science*, 269(6), 620–627.
886 https://doi.org/10.1007/bf00659917

887 van Vliet, T., & Walstra, P. (1994). Water in casein gels; How to get it out or keep it in. *Journal of Food Engineering*, 22(1–4), 75–88. https://doi.org/10.1016/0260-8774(94)90026-4

889 Varrato, F., Di Michele, L., Belushkin, M., Dorsaz, N., Nathan, S. H., Eiser, E., & Foffi, G. (2012).
890 Arrested demixing opens route to bigels. *Proceedings of the National Academy of Sciences*, 109(47),
891 19155–19160. https://doi.org/10.1073/pnas.1214971109

892 Vasbinder, A. J., & de Kruif, C. G. (2003). Casein–whey protein interactions in heated milk: The
893 influence of pH. *International Dairy Journal*, 13(8), 669–677. https://doi.org/10.1016/s0958-6946(03)00120-1
1

**Figure 1:** Two main ways of producing whey protein aggregates before their further use for making dairy products.

2

3

**Figure 2:** Main types of whey protein aggregates formed upon heating, as a function of pH and ionic strength, at a fixed protein concentration of 50 g.L⁻¹. The effects of other factors such as temperature, heating time, and shear are not considered.

4

5

6

**Figure 3:** Schematic representations of filled gels showing the hypothetical interactions between casein micelles gel matrix (grey solid line circles) and whey protein (WP) aggregates (orange solid line circles). A: Single fractal cluster of aggregated casein micelles. Dotted line circles represent the smallest enclosing sphere (diameter ξ) of aggregated particle clusters (individual diameter a). Dashed particles show the load-bearing strands. B: noninteracting nanoscale filler particles (diameter $b_1$ ≈ a). C: noninteracting microscale filler particle (diameter $b_2$ > a). D: interacting nanoscale filler particles (D1: taking part in the load-bearing structure. D2: absent of the load-bearing structure. D3: bigel). E: interacting macroscale filler particle.

10

11

12

13

14
Milk

<figure><img src="image_3.png" /></figure>

Milk
heating

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

Ex situ

Milk

<figure><img src="image_6.png" /></figure>

Whey

<figure><img src="image_7.png" /></figure>

Whey
heating

<figure><img src="image_8.png" /></figure>

Whey protein
aggregates

<figure><img src="image_9.png" /></figure>

Addition
in milk

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

Casein micelle

Native whey protein

Whey protein aggregate

<figure><img src="image_12.png" /></figure>
fine-stranded
gel

stranded
(branched)
aggregates

<figure><img src="image_13.png" /></figure>

fibrils

(1-10 µm)

D<sub>f</sub> = 1

<figure><img src="image_14.png" /></figure>

overlap of stranded aggregates

hydrolysed
peptide
(< nm)

associated
mature fibrils

(1-10 µm)

D<sub>f</sub> = 1

long and rigid
amyoids

particulate gel

hydrogels
(nano- to micro-gels)

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

sol-gel transition

particulate gel

hydrogels
(nano- to micro-gels)

sol-gel transition

(nm to µm)

D<sub>f</sub> ~ 3.1

<figure><img src="image_17.png" /></figure>

(nm to µm)

D<sub>f</sub> ~ 2.7

<figure><img src="image_18.png" /></figure>

fine-stranded
gel

stranded
(branched)
aggregates

(nm to µm)

D<sub>f</sub> ~ 2.1

<figure><img src="image_19.png" /></figure>

unfolded
protein

<figure><img src="image_20.png" /></figure>

primary
worm-like
aggregate
(~ 10 nm)

short and flexible structure
issued from amyloid-like
aggregation

spherical and
ellipsoidal
structure

unfolded
protein

primary
ellipsoidal
aggregate
(~ 10 nm)

<figure><img src="image_21.png" /></figure>

pH = 5.2

pH
With added
WP aggregates

Without
WP aggregates

A

Journal Pre-proof

<figure><img src="image_22.png" /></figure>

Nanoscale
WP aggregates
$b_1 \approx a$

Inert
filler

B

<figure><img src="image_23.png" /></figure>

Microscale
WP aggregates
$b_2 > a$

C

<figure><img src="image_24.png" /></figure>

Active
filler

D1

<figure><img src="image_25.png" /></figure>

D2

<figure><img src="image_26.png" /></figure>

D3

<figure><img src="image_27.png" /></figure>

E

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

Casein micelle

Whey protein aggregate

Smallest enclosing sphere of an aggregated particle cluster

Non load-bearing strand

Load-bearing strand
**Declaration of interests**

☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☒ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Erik Juste reports financial support was provided by Association Nationale de la Recherche et de la Technologie. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.