Non-biological Applications Research Articles

Demulsification of Pickering emulsions: advances in understanding mechanisms to applications.

Pickering emulsions are ultra-stable dispersions of two immiscible fluids stabilized by solid or microgel particles rather than molecular surfactants. Although their ultra-stability is a signature performance indicator, often such high stability hinders their demulsification, i.e., prevents the droplet coalescence that is needed for phase separation on demand, or release of the active ingredients encapsulated within droplets and/or to recover the particles themselves, which may be catalysts, for example. This review aims to provide theoretical and experimental insights on demulsification of Pickering emulsions, in particular identifying the mechanisms of particle dislodgment from the interface in biological and non-biological applications. Even though the adhesion of particles to the interface can appear irreversible, it is possible to detach particles via (1) alteration of particle wettability, and/or (2) particle dissolution, affecting the particle radius by introducing a range of physical conditions: pH, temperature, heat, shear, or magnetic fields; or via treatment with chemical/biochemical additives, including surfactants, enzymes, salts, or bacteria. Many of these changes ultimately influence the interfacial rheology of the particle-laden interface, which is sometimes underestimated. There is increasing momentum to create responsive Pickering particles such that they offer switchable wettability (demulsification and re-emulsification) when these conditions are changed. Demulsification via wettability alteration seems like the modus operandi whilst particle dissolution remains only partially explored, largely dominated by food digestion-related studies where Pickering particles are digested using gastrointestinal enzymes. Overall, this review aims to stimulate new thinking about the control of demulsification of Pickering emulsions for release of active ingredients associated with these ultra-stable emulsions.

Luminescence Thermometry Beyond the Biological Realm.

As the field of luminescence thermometry has matured, practical applications of luminescence thermometry techniques have grown in both frequency and scope. Due to the biocompatibility of most luminescent thermometers, many of these applications fall within the realm of biology. However, luminescence thermometry is increasingly employed beyond the biological realm, with expanding applications in areas such as thermal characterization of microelectronics, catalysis, and plasmonics. Here, we review the motivations, methodologies, and advances linked to nonbiological applications of luminescence thermometry. We begin with a brief overview of luminescence thermometry probes and techniques, focusing on those most commonly used for nonbiological applications. We then address measurement capabilities that are particularly relevant for these applications and provide a detailed survey of results across various application categories. Throughout the review, we highlight measurement challenges and requirements that are distinct from those of biological applications. Finally, we discuss emerging areas and future directions that present opportunities for continued research.

Development of Multivalent Conjugates with a Single Non-Canonical Amino Acid.

Proteins represent powerful biomacromolecules due to their unique functionality and broad utility both in the cell and in non-biological applications. The genetic encoding of non-canonical amino acids (ncAAs) facilitates functional diversification of these already powerful proteins. Specifically, ncAAs have been demonstrated to provide unique functional handles to bioorthogonally introduce novel functionality via conjugation reactions. Herein we examine the ability of a single ncAA to serve as a handle to generate multivalent bioconjugates to introduce two or more additional components to a protein, yielding a multivalent conjugate. To accomplish this aim, p-bromopropargyloxyphenyalanine (pBrPrF) was genetically encoded into both superfolder green fluorescent protein (sfGFP) and ubiquitin model proteins to serve as a conjugation handle. A sequential bioconjugation sequence involving a copper-assisted cycloaddition reaction coupled with a subsequent Sonogashira cross-coupling was then optimized. The linkage of two additional molecules to the model protein via these reactions yielded the desired multivalent bioconjugate. This domino approach using a single ncAA has a plethora of applications in both therapeutics and diagnostics as multiple unique moieties can be introduced into proteins in a highly controlled fashion.

Quintessential commence of three-dimensional printing in periodontal regeneration-A review.

The prime focus of regenerative periodontal therapy is to reconstruct or regenerate the lost periodontium, including both hard and soft tissues. Over the years, periodontics has witnessed different regenerative modalities, such as bone grafts, guided tissue membranes, growth factors, stem cell technology, 3D printing, etc. 3D printing is a newly emerging manufacturing technology that finds applications in diverse fields, including aerospace, defense, art and design, medical and dental field. Originally developed for non-biological applications, 3D printing has undergone modifications to print biocompatible materials and living cells to minimize any potential compromise on cell viability. Thus, the utilisation of 3D printing in the regeneration of lost periodontal tissues represents a novel approach that facilitates optimal cell interactions and promotes the successful regeneration of biological tissues.

Finite Element Implementation of Computational Fluid Dynamics With Reactive Neutral and Charged Solute Transport in FEBio.

The objective of this study was to implement a novel fluid-solutes solver into the open-source finite element software FEBio, that extended available modeling capabilities for biological fluids and fluid-solute mixtures. Using a reactive mixture framework, this solver accommodates diffusion, convection, chemical reactions, electrical charge effects, and external body forces, without requiring stabilization methods that were deemed necessary in previous computational implementations of the convection-diffusion-reaction equation at high Peclet numbers. Verification and validation problems demonstrated the ability of this solver to produce solutions for Peclet numbers as high as 1011, spanning the range of physiological conditions for convection-dominated solute transport. This outcome was facilitated by the use of a formulation that accommodates realistic values for solvent compressibility, and by expressing the solute mass balance such that it properly captured convective transport by the solvent and produced a natural boundary condition of zero diffusive solute flux at outflow boundaries. Since this numerical scheme was not necessarily foolproof, guidelines were included to achieve better outcomes that minimize or eliminate the potential occurrence of numerical artifacts. The fluid-solutes solver presented in this study represents an important and novel advancement in the modeling capabilities for biomechanics and biophysics as it allows modeling of mechanobiological processes via the incorporation of chemical reactions involving neutral or charged solutes within dynamic fluid flow. The incorporation of charged solutes in a reactive framework represents a significant novelty of this solver. This framework also applies to a broader range of nonbiological applications.

A method for non-destructive microwave focusing for deep brain and tissue stimulation.

Non-invasive stimulation of biological tissue is highly desirable for several biomedical applications. Of specific interest are methods for tumor treatment, endometrial ablation, and neuro-modulation. In traditional neuro-modulation, single- and multi-coil transcranial stimulation techniques in low oscillation frequencies are utilized to non-invasively penetrate the skull and elicit action potentials in cortical neurons. Although these methods have been proven effective, tightly focusing these signals to localized regions is difficult. In recent years, microwave (MW) methods have seen an increase usage as a minimally invasive treatment modality for ablation and neuro-stimulation. Unlike low frequency signals, MW signals can be focused to localized sub-centimeter regions. In this work we demonstrate that a three-dimensional array of MW antennas can be used to tightly focus signals to a localized region in space within the human body with MW frequencies. Assuming an array of small MW loop antennas are placed around the body, the optimal amplitude and phase of each array element can be accurately determined to match an arbitrary desired field profile. The major innovation of the presented method is that the fields that penetrate the biological region are determined via computing numerical Green's functions (NGF) that are then used to drive an optimization algorithm. Using simplified models of regions in the human body, it is shown that the MW fields at 1 GHz can be focused to sub-centimeter sized "hot spots" at depths of several centimeters. The algorithm can be easily extended to more realistic models of the human body or for non-biological applications.

MonoNet: enhancing interpretability in neural networks via monotonic features.

Being able to interpret and explain the predictions made by a machine learning model is of fundamental importance. Unfortunately, a trade-off between accuracy and interpretability is often observed. As a result, the interest in developing more transparent yet powerful models has grown considerably over the past few years. Interpretable models are especially needed in high-stake scenarios, such as computational biology and medical informatics, where erroneous or biased models' predictions can have deleterious consequences for a patient. Furthermore, understanding the inner workings of a model can help increase the trust in the model. We introduce a novel structurally constrained neural network, MonoNet, which is more transparent, while still retaining the same learning capabilities of traditional neural models. MonoNet contains monotonically connected layers that ensure monotonic relationships between (high-level) features and outputs. We show how, by leveraging the monotonic constraint in conjunction with other post hoc strategies, we can interpret our model. To demonstrate our model's capabilities, we train MonoNet to classify cellular populations in a single-cell proteomic dataset. We also demonstrate MonoNet's performance in other benchmark datasets in different domains, including non-biological applications (in the Supplementary Material). Our experiments show how our model can achieve good performance, while providing at the same time useful biological insights about the most important biomarkers. We finally carry out an information-theoretical analysis to show how the monotonic constraint actively contributes to the learning process of the model. Code and sample data are available at https://github.com/phineasng/mononet. Supplementary data are available at Bioinformatics Advances online.

Scalable large-area mesh-structured microfluidic gradient generator for drug testing applications.

Microfluidic concentration gradient generators are useful in drug testing, drug screening, and other cellular applications to avoid manual errors, save time, and labor. However, expensive fabrication techniques make such devices prohibitively costly. Here, in the present work, we developed a microfluidic concentration gradient generator (μCGG) using a recently proposed non-conventional photolithography-less method. In this method, ceramic suspension fluid was shaped into a square mesh by controlling Saffman Taylor instability in a multiport lifted Hele-Shaw cell (MLHSC). Using the shaped ceramic structure as the template, μCGG was prepared by soft lithography. The concentration gradient was characterized and effect of the flow rates was studied using COMSOL simulations. The simulation result was further validated by creating a fluorescein dye (fluorescein isothiocanate) gradient in the fabricated μCGG. To demonstrate the use of this device for drug testing, we created various concentrations of an anticancer drug-curcumin-using the device and determined its inhibitory concentration on cervical cancer cell-line HeLa. We found that the IC50 of curcumin for HeLa matched well with the conventional multi-well drug testing method. This method of μCGG fabrication has multiple advantages over conventional photolithography such as: (i) the channel layout and inlet-outlet arrangements can be changed by simply wiping the ceramic fluid before it solidifies, (ii) it is cost effective, (iii) large area patterning is easily achievable, and (iv) the method is scalable. This technique can be utilized to achieve a broad range of concentration gradient to be used for various biological and non-biological applications.

Using Artificial Neural Networks to Model Errors in Biochemical Manipulation of DNA Molecules.

In recent years, the non-biological applications of DNA molecules have made considerable progress; most of these applications were performed in vitro, involving biochemical operations such as synthesis, amplification and sequencing. Because errors may occur with specific sequence patterns or experimental instruments, these biochemical operations are not completely reliable. Modeling errors in these biochemical procedures is an interesting research topic. For example, researchers have proposed several methods to avoid the known vulnerable sequence patterns in the study of storing binary information in DNA molecules. However, there are few end-to-end methods to evaluate these biochemical errors with regard to the DNA sequences. In this article, based on the data generated by a DNA storage research, we use artificial neural networks to predict whether a DNA sequence tends to cause errors in biochemical operations. Through comparative experiments and hyperparameter optimization, we analyze the known and potential problems in the research process. As a result, an end-to-end method to model the biochemical errors of DNA molecules in vitro through a computer system is proposed.

Fabrication of Micro Optical Ring Electrodes for Scanning Photoelectrochemical Microscopy Applications

Micro-Optical-Ring electrodes (MOREs) have shown their usefulness in nonbiological applications in the past, but their application to biological samples for diagnostic purposes has yet to be explored. Herein, a simple and cost effective fabrication method of MOREs with a defined geometry is presented. These microelectrodes were characterized by electrochemistry, numerical modeling and Scanning Electron Microscopy (SEM). The integration of MOREs into scanning probe techniques, such as Scanning Electrochemical/Photoelectrochemical Microscopy (SECM/SPECM) enables the sensitive detection and quantification of cell metabolites at the micro- and nanoscopic level. The applicability of the fabricated MOREs was tested by monitoring oxygen production in the biological model systems of Chlorella kessleri and Eremosphaera viridis. A variation in oxygen production levels by the algae was observed in the presence and absence of light, emitted through the MORE-integrated optical fiber. This proof-of-concept study demonstrates the applicability of MOREs to biological systems.

Diffusive Dynamic Modes of Recombinant Squid Ring Teeth Proteins by Neutron Spectroscopy.

Stimuli-responsive structural proteins are emerging as promising biocompatible materials for a wide range of biological and nonbiological applications. To understand the physical properties of structural proteins and to replicate their performance in biosynthetic systems, there is a need to understand the molecular mechanisms and relationships that regulate their structure, dynamics, and properties. Here, we study the dynamics of a recombinant squid-inspired protein from Loligo vulgaris (Lv18) by elastic and quasielastic neutron scattering (QENS) to understand the connection between nanostructure, chain dynamics, and mechanical properties. Lv18 is a semicrystalline structural protein, which is plasticized by water above its glass transition temperature at 35 °C. Elastic scans revealed an increased protein chain mobility upon hydration, superimposed dynamic processes, and a decrease in dynamic transition temperatures. Further analysis by QENS revealed that while dry Lv18 protein dynamics are dominated by localized methyl group rotations, hydrated Lv18 dynamics are dominated by the confined diffusion of flexible chains within a β-sheet nanocrystalline network (8 Å of confinement radius). Our findings establish a relationship between the segment block architecture of Lv18, the diffusive motions within the protein structure, and the mechanical properties of recombinant squid proteins, which will advance the molecular design of novel high-performance protein-inspired materials with tailored dynamics and mechanical properties.

Universal Strategy for Designing Shape Memory Hydrogels.

Smart polymeric biomaterials have been the focus of many recent biomedical studies, especially those with adaptability to defects and potential to be implanted in the human body. Herein we report a versatile and straightforward method to convert non-thermoresponsive hydrogels into thermoresponsive systems with shape memory ability. As a proof of concept, a thermoresponsive polyurethane mesh was embedded within a methacrylated chitosan (CHTMA), gelatin (GELMA), laminarin (LAMMA) or hyaluronic acid (HAMA) hydrogel network, which afforded hydrogel composites with shape memory ability. With this system, we achieved good to excellent shape fixity ratios (50-90%) and excellent shape recovery ratios (∼100%, almost instantaneously) at body temperature (37 °C). Cytocompatibility tests demonstrated good viability either with cells on top or encapsulated during all shape memory processes. This straightforward approach opens a broad range of possibilities to convey shape memory properties to virtually any synthetic or natural-based hydrogel for several biological and nonbiological applications.

Inertial Self-Assembly Dynamics of Interacting Droplet Ensembles in Microfluidic Flows.

The multiphase flow of droplets is widespread and used for both biological and nonbiological applications alike. However, the ensemble interactions of such systems are inherently nonlinear and complex, compounded by interfacial effects, making it a difficult many-body problem. In comparison, the self-assembly dynamics of solid particles in flow have long been studied and exploited in the field of inertial microfluidics. Here, we report novel self-assembly dynamics of liquid drops in microfluidic channels that contrast starkly with the established paradigm of inertial microfluidics, which stipulates that higher inertia leads to better spatial ordering. Instead, we find that ordering can be negatively correlated with inertia, while Dean flow can achieve long-range spatial periodicity on length scales at least 3 orders of magnitude greater than the drop diameter. Experimentally, we decouple droplet generation from ordering, enabling independent and systematic variation of key parameters, especially in ranges practical to droplet microfluidics. We find the inertia-dependent emergence of preferred drop separations and show that surfactant effects can influence the longitudinal ordering of multidrop arrays. The dynamics we describe have immediate utility to droplet microfluidics, where the ability to order drops is key to the streamlined integration of on-chip incubation with deterministic drop manipulation downstream─two important functions for biological assays. To this end, we demonstrate the use of passive inertial drop self-assembly to combine a delay line with picoinjection. These results not only present a largely unexplored direction for inertial microfluidics but also show the practical benefit of its unification with the versatile field of droplet microfluidics.

Acoustic focusing of microplastics in microfabricated and steel tube devices: An experimental study on the effects from particle size and medium density

The contamination of aquatic systems with microplastics is becoming a severe threat to living organisms. Microplastics found in the environment consist of a wide range of particle sizes thus give rise to several challenges to current purification methods. Acoustic focusing has been utilized as a particle concentrating method in biological and non-biological applications. In this study, we investigate the feasibility of using acoustic focusing technology to isolate microplastics in aqueous samples and find that a two-stage mechanism is essential to concentrate microplastics of wide size ranges of the same material. We demonstrate for the first time experimentally that when the particle size is comparable to the resonance wavelength, they deviate from typical pressure nodal focusing and show pressure antinodal focusing. Further, we have expanded microplastics isolation beyond microfluidic systems and demonstrate their extraction capabilities relatively at higher flow rates using microplastics of polystyrene, polyethylene, and polymethyl methacrylate ranging from 6 µm to 300 µm diameter and in devices fabricated with cylindrical steel tubes. We could extract 70% of microplastics smaller than 180 µm and 82% of microplastics greater than 180 µm in diameter from an aqueous sample at a flow rate of 12 mL/min. We demonstrate that small microplastics focus on acoustic pressure nodes regardless of the medium density. However, focusing of large microplastics of the same material depends on the medium density.

3D printing of bioreactors in tissue engineering: A generalised approach.

3D printing is a rapidly evolving field for biological (bioprinting) and non-biological applications. Due to a high degree of freedom for geometrical parameters in 3D printing, prototype printing of bioreactors is a promising approach in the field of Tissue Engineering. The variety of printers, materials, printing parameters and device settings is difficult to overview both for beginners as well as for most professionals. In order to address this problem, we designed a guidance including test bodies to elucidate the real printing performance for a given printer system. Therefore, performance parameters such as accuracy or mechanical stability of the test bodies are systematically analysed. Moreover, post processing steps such as sterilisation or cleaning are considered in the test procedure. The guidance presented here is also applicable to optimise the printer settings for a given printer device. As proof of concept, we compared fused filament fabrication, stereolithography and selective laser sintering as the three most used printing methods. We determined fused filament fabrication printing as the most economical solution, while stereolithography is most accurate and features the highest surface quality. Finally, we tested the applicability of our guidance by identifying a printer solution to manufacture a complex bioreactor for a perfused tissue construct. Due to its design, the manufacture via subtractive mechanical methods would be 21-fold more expensive than additive manufacturing and therefore, would result in three times the number of parts to be assembled subsequently. Using this bioreactor we showed a successful 14-day-culture of a biofabricated collagen-based tissue construct containing human dermal fibroblasts as the stromal part and a perfusable central channel with human microvascular endothelial cells. Our study indicates how the full potential of biofabrication can be exploited, as most printed tissues exhibit individual shapes and require storage under physiological conditions, after the bioprinting process.

In Situ, Noncovalent Labeling and Stimulated Emission Depletion-Based Super-Resolution Imaging of Supramolecular Peptide Nanostructures.

Supramolecular materials have gained substantial interest for a number biological and nonbiological applications. However, for optimum utilization of these dynamic self-assembled materials, it is important to visualize and understand their structures at the nanoscale, in solution and in real time. Previous approaches for imaging these structures have utilized super-resolution optical imaging methods such as STORM, which has provided important insights, but suffers from drawbacks of complex sample preparation and slow acquisition times, thus limiting real-time in situ imaging of dynamic processes. We demonstrate a noncovalent fluorescent labeling design for STED-based super-resolution imaging of self-assembling peptides. This is achieved by in situ, electrostatic binding of anionic sulfonates of Alexa-488 dye to the cationic sites of lysine (or arginine) residues exposed on the peptide nanostructure surface. A direct, multiscale visualization of static structures reveals hierarchical organization of supramolecular fibers with sub-60 nm resolution. In addition, the degradation of nanofibers upon enzymatic hydrolysis of peptide could be directly imaged in real time, and although resolution was compromised in this dynamic process, it provided mechanistic insights into the enzymatic degradation process. Noncovalent Alexa-488 labeling and subsequent imaging of a range of cationic self-assembling peptides and peptide-functionalized gold nanoparticles demonstrated the versatility of the methodology for the imaging of cationic supramolecular structures. Overall, our approach presents a general and simple method for the electrostatic fluorescent labeling of cationic peptide nanostructures for nanoscale imaging under physiological conditions and probe dynamic processes in real time and in situ.

Molecular Modeling and Simulations of Peptide-Polymer Conjugates.

Peptide-polymer conjugates are a class of soft materials composed of covalently linked blocks of protein/polypeptides and synthetic/natural polymers. These materials are practically useful in biological applications, such as drug delivery, DNA/gene delivery, and antimicrobial coatings, as well as nonbiological applications, such as electronics, separations, optics, and sensing. Given their broad applicability, there is motivation to understand the molecular and macroscale structure, dynamics, and thermodynamic behavior exhibited by such materials. We focus on the past and ongoing molecular simulation studies aimed at obtaining such fundamental understanding and predicting molecular design rules for the target function. We describe briefly the experimental work in this field that validates or motivates these computational studies. We also describe the various models (e.g., atomistic, coarse-grained, or hybrid) and simulation methods (e.g., stochastic versus deterministic, enhanced sampling) that have been used and the types of questions that have been answered using these computational approaches.

Investigating the Photochemistry of C7 and C8 Functionalized N(5)-Ethyl-flavinium Cation: A Computational Study

Flavins are a diverse set of compounds with a wide variety of biological and nonbiological applications. Applications of flavins receiving attention recently consist of electro- and photocatalytic oxidation of substrates for organic synthesis, bioengineered nanotechnology, and water splitting catalysts, among others. While there is vast knowledge regarding the structure-property relationships of flavins and their electrochemistry, there is much less work elucidating the structure property relationships as they pertain to flavinium photochemistry. Herein, we report the effect of molecular tailoring on the molecular properties of N(5)-ethyl-flavinium cation (Et-Fl+), a derivative of the biocatalytic coenzyme riboflavin, by incorporating electron withdrawing and donating groups at the C7 and C8 position of the isoalloxazine ring. The presence of electron withdrawing groups at the C8 position caused a red shift in the absorption spectrum, while the electron donating groups caused a blue shift. Functionalization at the C7 position had the opposite effect on the absorption spectrum. The effects of single substitution were relatively negated with simultaneous functionalization at both the C8 and C7 positions. Difference density plots indicate no change in the nature of the S1 excited state, which was confirmed by optimization of the excited state geometries. The results presented in this study indicate that functionalization of the isoalloxazine unit affects the photophysical properties of N(5)-ethyl-flavinium cations.

Preparation of calcium deficient hydroxyapatite on the montmorillonite substrate: Structure and morphology

Ca-deficient hydroxyapatite (CDH) is biocompatible and inexpensive material used for biomedical and non-biological applications. Due to similarity of CDH with human hard tissues is suitable for manufacturing of bone substituents. Clay minerals are natural materials often used as substrate for nanoparticles anchoring. Excellent combination of non-toxic clay minerals and CDH is just right composition for medical or catalytic applications.Aim of the study was to prepare CDH on the surface of monoionic Na- and Mg-form of montmorillonite (Mt) from Czech Republic. The CDH was prepared using precipitation methods under constant mixing or sonication conditions. XRD analysis confirmed successful creation of CDH on the Mt substrate. Bonding interactions between Mt and CDH were not found using FTIR methods. Using scanning electron microscopy, the presence of CDH particles on Mt surface was observed where the CDH creates film-like layer of small particles. The specific surface of nanocomposites is large, which is demanded for medical or catalytic applications. The results revealed that montmorillonite is appropriate as support for CDH particles.

Batch and continuous studies on the removal of heavy metals from aqueous solution using biosynthesised melanin-coated PVDF membranes.

Heavy metals like mercury, chromium, lead and copper present in groundwater at lower concentrations cause severe health issues and can even be fatal when consumed. The biopigment/biopolymer melanin can be reaped from different sources like bacterium, fungus, and human hair. It has excellent heavy metal ion scavenging property and can be exploited for non-biological applications, substantially including water purification. In this work, melanin nanoparticles were derived from the marine bacterium Pseudomonas stutzeri and were coated onto hydrophobic polyvinylidene fluoride (PVDF) membrane as a support, for batch and continuous removal of heavy metal studies. Batch studies on the effect of pH, temperature and adsorbate dose and continuous adsorption studies on the effect of flow rate, adsorbate and adsorbent mass loadings were carried out by using biosynthesised melanin-coated PVDF membranes for the removal of Hg(II), Cr(VI), Pb(II) and Cu(II). Scanning electron microscope (SEM) images revealed the surface morphology, Fourier-transform infrared spectroscopy (FTIR) and energy-dispersive X-ray spectroscopy (EDS) deciphered the chemical characteristics of melanin-coated PVDF membranes before and after adsorption. Contact angle measurement confirmed the improvement in hydrophilicity of PVDF membrane upon coating with melanin. The maximum removal percentages of heavy metals achieved by melanin-coated PVDF membranes under batch mode operation were 87.6%, 88.45%, 91.8% and 95.8% for mercury, chromium, lead and copper, respectively optimised at 318 K and pH of 3 for chromium and 5 for other metals. However, the continuous mode of operation with a flow rate of 0.5 mL/min having 1 mg/L of heavy metal solution concentration exposed to 50 mg of melanin loading with a working volume of 200 mL showed better removal efficiencies compared with batch mode. The dynamic studies using Thomas and Yoon-Nelson models described the transient stage of the breakthrough curve and the model constants were calculated for column design and scale-up.