Ellman's procedure has been used to study the oxidation rates of cysteine (CSH) and glutathione (GSH) in aqueous solutions, and it was reported that, for CSH, the number of sulfhydryl molecules not oxidized became zero at a specific time, called tc, where it was reported to be finite. We point out that under very general considerations, we should observe tc to be unbounded, and it becomes infinite. The reason is that as the process of forming a disulfide bond proceeds, the probability of two CSH molecules finding each other eventually becomes vanishingly small so that the number of unoxidized molecules approach zero only as tc becomes infinite. We used a Smoluchowski equation to model the process of disulfide bond formation in order to understand how a finite tc can be observed. In addition, atomic scale molecular dynamics simulations were carried out in order to study the spatial distributions of CSH and GSH in aqueous solutions. It was found that electrostatic interactions bring about aggregation of these molecules, and we conclude that this aggregation “hides” unoxidized sufhydryl moieties from interacting with (5,5′-dithiobis-(2-nitrobenzoic acid) DTNB of Ellman's reagent, thereby remaining undetected. It will thus appear as if the number of unoxidized moieties has become zero. In order that all sulfhydryl moieties be detected, it is necessary to disrupt the aggregate, as has been carried out for proteins, so as to expose those moieties to be oxidized and be detected.

Colloidal gliadin particles show promise for use as interface stabilizers and for the encapsulation and delivery of bioactive molecules in food systems. Gliadin particles can be produced with a simple liquid anti-solvent precipitation (LAS) technique. The dynamics of the protein interactions and conformational changes due to changes in solvent quality during LAS have yet to be fully unravelled. In this study, ultra-small- and small-angle x-ray scattering (USAXS/SAXS) were used to investigate the assembly of gliadin proteins into particles and aggregates throughout LAS. Three regimes of gliadin assembly were identified at high (50-70 v/v%), intermediate (30-40 v/v%), and low (12-20 v/v%) ethanol concentrations. At high ethanol concentrations, primary structural units were identified in the high-q region (q > 2 x 10(-2) & Aring;(-1)), believed to be gliadin molecules with coiled structures (R-g1 = 6-7 nm, P-1 approximate to 2). At intermediate ethanol concentrations, polydisperse protein structures were formed. At low ethanol concentrations, two hierarchical structural levels were identified, with gliadin particles (R-g2 approximate to 200-500 nm, 3.5 < P-2 < 4) identified at low-q (q < 2 x 10(-2) & Aring;(-1)) believed to be formed by the assembly of primary structural units which had similar size and shape to those identified in high ethanol samples. Analysis with Fourier-transform infrared spectroscopy indicated that gliadin underwent secondary structural changes, with an increase in intermolecular beta-sheets as the solvent quality was reduced during particle formation. This multi-scale investigation provides insight into the structural changes and interactions that occur during gliadin particle production with LAS.

A classic statistical mechanical model of surface adsorption of an object that interacts with another component present in a medium was developed in this work. The effective Hamiltonian for the process is proposed and developed here, which takes into consideration the interactions between one of the objects with a surface and the interaction with another object in the medium. This model allowed for the prediction of the binding isotherm for the object. Monte Carlo computer simulations were employed to model the behavior of the system, which was in good agreement with the theory. This model was complemented with an equilibrium kinetic model of the same system and simulations. Qualitative agreement between the two approaches was achieved by introducing a degeneracy in the cooperative interaction between the object and the component, namely simultaneous positive and negative binding cooperativity of the same process. The model developed and the results obtained will help explain the variability in the foamability of barista milk, where free fatty acids are known to inhibit the adsorption of proteins to the air bubble surface. Here, we suggest that the variability observed could be due to the ratio of free fatty acids to protein, which was never considered before.

The molecular structure of a crystalline monolayer of hydrocarbon chains was modeled and studied via computer simulation using the Metropolis Monte Carlo algorithm at a temperature T = 300 K. The only interactions in this system occur through Lennard-Jones dispersion forces and short-range atom-atom repulsion. The intent was to establish whether the chains were either rigidly extended or twisted via the thermal formation of gauche bonds and apply the results to understand observations made on two possible oleogelators: triacontane and stearic acid. Specifically, we aimed to understand if their observed crystalline monolayer thicknesses are due to gauche-bond-shortened hydrocarbon chains oriented perpendicular to the monolayer surface, or to fully extended rigid chains oriented at a tilt angle with respect to the surface. The results showed that crystals of hydrocarbon chains did not include significant gauche bonds, so that all molecules were rigidly extended, thus explaining the experimental data previously reported. Accordingly, TC and SA dimer molecules are packed in crystalline multilayers with tilt angles in relation to the methyl group plane.

Oleogelators are molecules that, when combined with edible oils can form semi-solid materials. Although many molecules have been tried as oleogelators in the last 20 years, much is still unknown. Here, the molecular structure of two possible oleogelators: triacontane (TC) and behenyl lignocerate (BL) were studied using a mathematical model for each molecule and carrying out computer simulation using the Metropolis Monte Carlo (MMC) algorithm in which the only interaction is via Lennard-Jones dispersion forces. The computer simulation explored the possibility of having either rigidly-extended molecules or twisted ones via the formation of gauche bonds. The results showed that both TL and BL molecules create a monolayer that did not include any gauche bond so that all molecules were effectively rigidly extended. The effective thickness of the monolayer was compared with experimental data and with the predictions of Peyronel et al. (in review) which assumed that the molecules were rigidly-extended. The work reported here justified that assumption. The conclusion was that the TC and BL molecules must be packed with a tilt angle in relation to the methyl group plane to match the experimental data. The angle of TC tilt was calculated to be ~27° which essentially confirms that reported by Peyronel et al. (in review).

Three oleogeletors molecules (Triacontane (TC), Stearic acid (SA), and Behenyl Lignocerate (BL)) were studied individually, in pairs, or all together to make an oleogel using triolein as the oil. WAXS, SAXS and USAXS were used to elucidate the solid structures from angstroms to a few micrometers. A two-dimensional mapping of atomic positions for each molecule was carried out to understand the crystalline multilayer structures formed. We assumed that the molecules were rigidly extended and that they underwent no significant (hindered) rotations so that the free energy is determined by the Lennard-Jones interactions of closely-packed multilayers. TC molecules were predicted to form a tilt angle of θ ≈ 33°, yielding a SAXS line at q≈ 0.194 Å, in acceptable agreement with the measured q=0.181 Å.For SA crystals θ ≈ 33° (predicted) yielding a SAXS line at q=0.150 Å compared to q=0.159 Å (observed). No mixed crystals were observed for any pair of molecules or when all three were used. USAXS data showed that SA forms large nanocrystals compared to TC and BL. All three combinations of molecular pairs showed basic scatterers smaller or similar to those of individual molecules. The theory presented here, together with the experimental results, showed why no mixed crystals are formed from two or all three molecules. Data from the USAXS region suggested that, when using all three molecules, a more compact fractal structure was obtained, compared with those if one or two of the molecules were used.

USAXS and SAXS data were collected at 20°C for Triacontane (TC, C30H62), Stearic Acid (SA, C18H36O2), and Behenyl Lignocerate (BL, C46H92O2) in their solid state in 84% w/w of triolein (OOO) in its liquid state. Samples were prepared using (i) every single molecule, (16% w/w), (ii) pairs of molecules (8% w/w of each molecule), and (iii) 5.33% w/w of all three molecules. The Unified Fit Model was used to fit the scattering intensity data in the USAXS region. The SAXS data exhibited well-defined Bragg peaks. The q value at the Bragg peak maximum was used in the relationship, L = 2π/q, to identify repeat distances L along the local z-axis. A value of L = 34.9 Å, L = 39.3 Å, and L = 52.4 Å were obtained for the case of TC, SA, and BL, respectively, which were interpreted as indicating two dimensional layers. We shall report on hydrocarbon chain organization in terms of gauche conformers and alkyl chain axis tilt, the detailed results of which shall be reported elsewhere. USAXS data for I(q) extended over approximately two orders of magnitude of q. The data exhibited at approximately qknee ≈ 10-3 Å-1. For q > qknee the value of P1 from the slope of I(q) for the single-molecule solids was 4.0 (SA and BL) and 4.2 (TC), while for q less than qknee the value of P2 was 3.6 (TC), 3.8 (SA) and 4.1 (BL). We shall report on, and interpret, the values for pairs of the three molecules and the mix of all three molecules. We shall comment on the extent to which the molecules form single crystals involving one, two, or three of them.

Triacontane (C30H62, TC), Stearic acid (C18H36O2, SA) and Behenyl Lignocerate (C46H92O2, BL) form crystals at temperatures, T, lower than T = TTC* = 64-67 °C (TC), TSA* = 70 °C (SA) and TBL* >80 °C (BL) respectively. In the region, T less than T* these systems undergo other phase transitions. Small angle X-ray scattering at T = 20 °C, showed narrow principal lines and their reflections for q-values. Thus, TC exhibited a sequence for q = 0.18, 0.36 and 0.53 Å─1. This yielded a repeat distance for TC monolayers of LTC = 2π/q = 34.9 Å. In addition, values of LSA = 39.3 Å and LBL = 52.4 Å were obtained for the cases of SA and BL. The length of a TC hydrocarbon chain, the distance between the carbons of the CH3 groups, in its all-trans conformation is 38.6 Å and two parallel such monolayers will exhibit a repeat distance of LTC = 39.9 Å corresponding to a q-value of qTC = 2π/LTC = 0.16 Å─1. The difference between this value and the observation of 0.18 Å─1 cannot be accounted for by appealing to experimental confidence limits. There are at least two possible resolutions of this disagreement: (a) that at T = 20 °C, trans-gauche excitations from the all-trans ground state reduces the effective length of the hydrocarbon chains, and (b) the chains are tilted with respect to the plane of the monolayer. Computer simulations of hydrocarbon chains for TC, SA and BL in a crystal, using the Metropolis Monte Carlo algorithm will be presented. The average distribution of trans-gauche excitations in thermal equilibrium will be computed as will the average tilt angle of the chain axis. Simulations and comparisons with experimental data will be made for TC, SA and BL.

Ellman's procedure for detecting thiol moieties has been used to quantify the formation of disulfide bonds. The philosophy here is that DTNB used by Ellman will detect the development of oxidation as a function of time as per temporal decrease of the SH moieties. Recently (Lauwers et al 2016, Cao et al 2021) this technique was used to quantify the oxidation of cysteine and glutathione as function of time. It was reported that, at pH = 6.5, for all cases of cysteine and one case of glutathione studied, the number of thiols became zero in a finite time, tc. Using Smoluchowski equations (a) we pointed out that in milliQ water with cysteine molecules searching randomly to form disulfide bonds, we should find that tc → ∞, and (b) we proposed that cysteine molecules, carrying zero net charge at pH = 6.5, aggregated so that SH groups were ‘hidden’ in the interior thus preventing the detection of thiols by DTNB thus erroneously reporting the number of thiols to be zero after a finite time. This is analogous to the necessity to disrupt the structure of a protein before using Ellman's procedure. We have used atomic scale molecular dynamics to simulate both cysteine and glutathione in milliQ water. The results showed that, instead of being randomly distributed, cysteine does indeed form aggregates as the Smoluchowski equations indicated. We shall present results for glutathione to (i) establish whether this molecule, which is charged at pH = 6.5, forms aggregates, (ii) if aggregates are formed, whether DTNB will be unable to access thiols hidden inside them.

Chocolate is a manufactured product enjoyed worldwide. Over the years, manufacturers have learned how to appeal to humans using this rich-fat food that arouses all the senses. Good quality chocolate is recognized by its smoothness, a slow melt in the mouth, and a snap when bitten, and described as well-tempered. This work compares dark chocolate samples manufactured to obtain under- and well-tempered chocolate, where undertempered does not show all the physical properties desired by consumers. The microstructure was studied using the ultra small angle X-ray scattering (USAXS) technique, complemented by small and wide angle X-ray scattering to identify the polymorphs. It was observed that under- and well-tempered chocolates exhibited differences in the q-region - 2 x 10-5 angstrom-1 < q < -1.5 x 10-4 angstrom- 1, which correspond to spatial length scales from 32 mu m to 3.2 mu m. The differences are manifested in the value of the mass fractal dimension, D, obtained when the USAXS data were fitted using the Unified Fit model (Irena software). The characteristic length scale at which these differences were observed falls in length scales detected by humans in the oral cavity. This work proposes that a D = 2.1 characterizes an under-tempered 70% dark chocolate while a D = 2.3 characterizes a welltempered 70% dark chocolate. This work also presents a simple model that describes the disintegration of those aggregates formed by the basic scatter units for under- and well-tempered chocolate. The model proposes that aggregates formed in under-tempered chocolate persist after the bulk chocolate has melted, which can be perceived as grittiness. However, the model proposes that the aggregates for well-tempered chocolate melt at the same or lower temperatures than the bulk chocolate melting temperature; hence no grittiness is perceived. The model is supported by the observation that the heat of transition for the under-tempered chocolate is smaller than that of the well-tempered case.

Coagulation of milk is a fundamental process in the manufacture of dairy products. Under the enzymatic action of rennet, casein micelles form aggregates resulting in a fractal gel network. There are few studies of microstructures using scattering techniques resulting from rennet coagulation in commercial milk in its native state. Here we employ ultra-small angle neutron scattering (USANS) and. small angle neutron scattering (SANS) covering the scattering q-vector range of 5 x 10(-5) < q < 2 x 10(-2) angstrom(-1) and the fractal cylinder model to study fractal structures and sizes resulting from calf and fungal rennet-induced coagulation of commercial skim and whole milk. We report evidence of aggregation with fractal properties analogous to that of swollen, randomly-branched polymers. Calf rennet resulted in a larger fractal dimension in skim compared to whole milk. In milk coagulated by fungal M. miehei, the randomly-branched polymer-like structures had a slightly larger fractal dimension of 2.5 and the structural unit was smaller. These measurements provide an important foundation for continuing study of the structure of commercial cheese with scattering techniques.

During dough making wheat flour is mixed with (tap) water containing low anion/cation levels. Research indicated that thiol oxidation kinetics and possibly the final bread product quality are affected by these low ion concentrations. Accordingly, the aim of this work was to understand the effect of (low concentrations of) different ions commonly found in tap water (Ca2+, Mg2+, Na+, Cl− and SO42−) on thiol oxidation in a model and dough system, and batter and dough properties. Solutions of selected salts (CaCl2, CaSO4, NaCl and MgCl2) and tap water promoted thiol oxidation in both model and dough systems relative to what was observed for MilliQ water. Even at these low concentrations, ions affect protein properties, impacting dough stability and rheology and potentially the associated bread quality. This work provides a better conceptual understanding of the role (different) ions play in the formation of a protein network and the rheological properties of a viscoelastic dough.

It is proposed that "crystal memory", observed in a discontinuous solid-liquid phase transition of saturated triacylglycerol (TAG) molecules, is due to the coexistence of solid TAG crystalline phases and a liquid TAG phase, in a superheated metastable regime. Such a coexistence has been detected. Solid crystals can act as heterogeneous nuclei onto which molecules can condense as the temperature is lowered. We outlined a mathematical model, with a single phase transition, that shows how the time-temperature observations can be explained, makes predictions, and relates them to recent experimental data. A modified Vogel-Fulcher-Tammann (VFT) equation is used to predict time-temperature relations for the observation of "crystal memory" and to show boundaries beyond which "crystal memory" is not observed. A plot of the lifetime of a metastable state versus temperature, using the modified VFT equation, agrees with recent time-temperature data. The model can be falsified through its predictions: the model possesses a critical point and we outline a procedure describing how it could be observed by changing the hydrocarbon chain length. We make predictions about how thermodynamic functions will change as the critical point is reached and as the system enters a crossover regime. The model predicts that the phenomenon of "crystal memory" will not be observed unless the system is cooled from a superheated metastable regime associated with a discontinuous phase transition.

We have used Ultra Small Angle X-ray Scattering (USAXS) and mathematical models to study seemingly-spontaneous aggregation structures in two pasteurized bovine milks. Although extensive studies of casein micelles and their aggregation have been carried out, few have been done to numerically characterize submicron structures to micron-scale structures. We measured the USAXS intensity, I(q), as a function of the scattering vector magnitude, q, for commercial pasteurized skim milk and nonhomogenized whole milk at two temperatures, 7 °C and 45 °C. We observed broad peaks, reported previously to be related to casein micelles, centered at q ≈ 2 × 10−2 Å−1 and at q ≈ 9 × 10−2 Å−1. At lower q values, log I(q) displayed a behavior characteristic of aggregation manifested for a slope in the region 3–7 × 10−4 Å−1 < q < 4 × 10−3 Å−1. This behavior appeared in the absence of (a) chymosin, (b) any change in pH or CaCl2 concentration, and (c) temperature changes. We introduced a model of milk and used computer simulations to investigate consequences of casein micelles possessing surface areas lacking the water-soluble components of κ-casein proteins. These components exist to provide stability against aggregation to the casein micelles. We propose that bovine casein micelles spontaneously formed 1-dimensional aggregates.

Milk and milk products are an essential part of global nutrition and the world-wide food industry. Studies of milk components using scattering techniques are well documented in the literature. However, those studies focused on the q scattering wavevector region 10(-3) < q < 2 angstrom(-1). This manuscript presents scattering results in the region 3 x 10(-5) < q < 2 x 10(-2) angstrom(-1), a region that allows the simultaneous study of fat globules and proteins found in commercial food-grade milk. The small and ultra-small angle neutron scattering (SANS and USANS) measurements show that a model based on the Schulz distribution function using uniform spheres was a reasonable choice to successfully fit the scattering features below q = 0.007 angstrom(-1). Contrast measurements using D2O on whole milk were carried out to distinguish fat from protein signals. Casein micelles were found to have mean diameters of 96 +/- 10 nm with 33% polydispersity. The average scattering length density of the micelles varied from -0.04 x 10(-6) angstrom(-2) in homogenized, pasteurized commercial milk to 2.8 x 10(-6) angstrom(-2) with 50% dilution by D2O, with a match point of 43 +/- 3%, as seen in previous studies. It was found that the average diameter of fat globules in homogenized whole milk was 0.47 +/- 0.04 mu m with a polydispersity of 45 +/- 5%, and a volume fraction of 0.034 +/- 0.002 when the scattering length density is fixed at 0.20 x 10(-6) angstrom(-2). These USANS measurements provide an important foundation as similar techniques are employed to study cheese varieties and cheese formation.