Reaction diffusion model of the enzymatic erosion of insoluble fibrillar matrices

Monitoring the Degradation of Collagen Hydrogels by Collagenase Clostridium histolyticum

Collagen-based hydrogels are investigated extensively in tissue engineering for their tunable physiochemical properties, biocompatibility and biodegradability. However, the effect of the integrity of the collagen triple helical structure on biodegradability is yet to be studied. In this study, we monitored the degradation of intact collagen (C-coll) and hydrolyzed collagen (D-coll) hydrogels in collagenase Clostridium histolyticum to understand their degradation process. Our results show that when peptides are present on the surface of the fibrils of D-coll hydrogels, cleavage of amide bonds occur at a much higher rate. The fibrillar structure of D-coll hydrogel results in a more pronounced breakdown of the gel network and dissolution of collagen peptides. The results from this work will improve the understanding of enzymatic degradation and the resulting bioabsorption of collagen materials used in drug delivery systems and scaffolds.

Competitive effects in bacterial mRNA decay

In living organisms, the same enzyme catalyses the degradation of thousands of different mRNAs, but the possible influence of competing substrates has been largely ignored so far. We develop a simple mechanistic model of the coupled degradation of all cell mRNAs using the total quasi-steady-state approximation of the Michaelis-Menten framework. Numerical simulations of the model using carefully chosen parameters and analyses of rate sensitivity coefficients show how substrate competition alters mRNA decay. The model predictions reproduce and explain a number of experimental observations on mRNA decay following transcription arrest, such as delays before the onset of degradation, the occurrence of variable degradation profiles with increased non linearities and the negative correlation between mRNA half-life and concentration. The competition acts at different levels, through the initial concentration of cell mRNAs and by modifying the enzyme affinity for its targets. The consequence is a global slow down of mRNA decay due to enzyme titration and the amplification of its apparent affinity. Competition happens to stabilize weakly affine mRNAs and to destabilize the most affine ones. We believe that this mechanistic model is an interesting alternative to the exponential models commonly used for the determination of mRNA half-lives. It allows analysing regulatory mechanisms of mRNA degradation and its predictions are directly comparable to experimental data.

Induced Neural Differentiation of MMP-2 Cleaved (RADA)4 Drug Delivery Systems

(RADA)₄ self-assembling peptides (SAPs) are promising for neural nanoscaffolds with on-demand drug delivery capabilities due to their automated synthesis, in-situ assembly, and potential for interaction with and release of biomolecules. Neuroinflammation cued on-demand drug release, due to up-regulated proteases, may well be vital in the treatment of several neurological diseases. In these conditions, releasing neurotrophic growth factors (NTFs) could potentially lead to neuroprotection and neurogenesis. As such, (RADA)₄ was made with the high and low activity matrix metalloproteinase 2 (MMP-2) cleaved sequences, GPQG+IASQ (CP1) and GPQG+PAGQ (CP2), the brain-derived NTF secretion stimulating peptide MVG (DP1) and the ciliary NTF analogue DGGL (DP2). PC-12 cell culture was performed to assess bioactive substrate cell adhesion and NTF specific neuronal differentiation. The laminin-derived IKVAV peptide, known for neural cell attachment and interaction, was tethered to (RADA)₄-IKVAV and mixed in increasing increments with (RADA)₄ for this purpose. With 1 nanomolar MMP-2 treatment, product formation was observed to increase over a three day period, with (RADA)₄/(RADA)₄-CP1/CP2 mixture, however there was little difference between groups. Smaller CP1/CP2 concentrations displayed comparable (RADA)₄ nanoscale morphology to higher concentrations. Acetylcholine esterase and neural differentiation was observed over 3 days with 1 nM MMP-2 treatment according to the following makeup: 8/1/1 (RADA)4/(RADA)4-IKVAV/(RADA)4-CP1/CP2-DP1/DP2. Signalling gradually increased in all groups, and neurite outgrowth was visible after three days.

Micromechanical Modeling Study of Mechanical Inhibition of Enzymatic Degradation of Collagen Tissues

This study investigates how the collagen fiber structure influences the enzymatic degradation of collagen tissues. We developed a micromechanical model of a fibrous collagen tissue undergoing enzymatic degradation based on two central hypotheses. The collagen fibers are crimped in the undeformed configuration. Enzymatic degradation is an energy activated process and the activation energy is increased by the axial strain energy density of the fiber. We determined the intrinsic degradation rate and characteristic energy for mechanical inhibition from fibril-level degradation experiments and applied the parameters to predict the effect of the crimped fiber structure and fiber properties on the degradation of bovine cornea and pericardium tissues under controlled tension. We then applied the model to examine the effect of the tissue stress state on the rate of tissue degradation and the anisotropic fiber structures that developed from enzymatic degradation.

Micropatterned sensing hydrogels integrated with reconfigurable microfluidics for detecting protease release from cells

Matrix metalloproteinases (MMPs) play a central role in the breakdown of the extracellular matrix and are typically upregulated in cancer cells. The goal of the present study is to develop microwells suitable for capture of cells and detection of cell-secreted proteases. Hydrogel microwells comprised of poly(ethylene glycol) (PEG) were photopatterned on glass and modified with ligands to promote cell adhesion. To sense protease release, peptides cleavable by MMP9 were designed to contain a donor/acceptor FRET pair (FITC and DABCYL). These sensing molecules were incorporated into the walls of the hydrogel wells to enable a detection scheme where cells captured within the wells secreted protease molecules which diffused into the gel, cleaved the peptide, and caused a fluorescence signal to come on. By challenging sensing hydrogel microstructures to known concentrations of recombinant MMP9, the limit of detection was determined to be 0.625 nM with a linear range extending to 40 nM. To enhance sensitivity and to limit cross-talk between adjacent sensing sites, microwell arrays containing small groups (∼20 cells/well) of lymphoma cells were integrated into reconfigurable PDMS microfluidic devices. Using this combination of sensing hydrogel microwells and reconfigurable microfluidics, detection of MMP9 release from as few as 11 cells was demonstrated. Smart hydrogel microstructures capable of sequestering small groups of cells and sensing cell function have multiple applications ranging from diagnostics to cell/tissue engineering. Further development of this technology will include single-cell analysis and function-based cell sorting capabilities.

A conceptual framework for computational models of Achilles tendon homeostasis

Computational modeling of tendon lags the development of computational models for other tissues. A major bottleneck in the development of realistic computational models for Achilles tendon is the absence of detailed conceptual and theoretical models as to how the tissue actually functions. Without the conceptual models to provide a theoretical framework to guide the development and integration of multiscale computational models, modeling of the Achilles tendon to date has tended to be piecemeal and focused on specific mechanical or biochemical issues. In this paper, we present a new conceptual model of Achilles tendon tissue homeostasis, and discuss this model in terms of existing computational models of tendon. This approach has the benefits of structuring the research on relevant computational modeling to date, while allowing us to identify new computational models requiring development. The critically important functional issue for tendon is that it is continually damaged during use and so has to be repaired. From this follows the centrally important issue of homeostasis of the load carrying collagen fibrils within the collagen fibers of the Achilles tendon. Collagen fibrils may be damaged mechanically-by loading, or damaged biochemically-by proteases. Upon reviewing existing computational models within this conceptual framework of the Achilles tendon structure and function, we demonstrate that a great deal of theoretical and experimental research remains to be done before there are reliably predictive multiscale computational model of Achilles tendon in health and disease.

Conformational dynamics accompanying the proteolytic degradation of trimeric collagen I by collagenases

Collagenases are the principal enzymes responsible for the degradation of collagens during embryonic development, wound healing, and cancer metastasis. However, the mechanism by which these enzymes disrupt the highly chemically and structurally stable collagen triple helix remains incompletely understood. We used a single-molecule magnetic tweezers assay to characterize the cleavage of heterotrimeric collagen I by both the human collagenase matrix metalloproteinase-1 (MMP-1) and collagenase from Clostridium histolyticum. We observe that the application of 16 pN of force causes an 8-fold increase in collagen proteolysis rates by MMP-1 but does not affect cleavage rates by Clostridium collagenase. Quantitative analysis of these data allows us to infer the structural changes in collagen associated with proteolytic cleavage by both enzymes. Our data support a model in which MMP-1 cuts a transient, stretched conformation of its recognition site. In contrast, our findings suggest that Clostridium collagenase is able to cleave the fully wound collagen triple helix, accounting for its lack of force sensitivity and low sequence specificity. We observe that the cleavage of heterotrimeric collagen is less force sensitive than the proteolysis of a homotrimeric collagen model peptide, consistent with studies suggesting that the MMP-1 recognition site in heterotrimeric collagen I is partially unwound at equilibrium.

Highly sensitive single-fibril erosion assay demonstrates mechanochemical switch in native collagen fibrils

It has been established that the enzyme susceptibility of collagen, the predominant load-bearing protein in vertebrates, is altered by applied tension. However, whether tensile force increases or decreases the susceptibility to enzyme is a matter of contention. It is critical to establish a definitive understanding of the direction and magnitude of the force versus catalysis rate (k C ) relationship if we are to properly interpret connective tissue development, growth, remodeling, repair, and degeneration. In this investigation, we examine collagen/enzyme mechanochemistry at the smallest scale structurally relevant to connective tissue: the native collagen fibril. A single-fibril mechanochemical erosion assay with nN force resolution was developed which permits detection of the loss of a few layers of monomer from the fibril surface. Native type I fibrils (bovine) held at three levels of tension were exposed to Clostridium histolyticum collagenase A. Fibrils held at zero-load failed rapidly and consistently (20 min) while fibrils at 1.8 pN/monomer failed more slowly (35-55 min). Strikingly, fibrils at 23.9 pN/monomer did not exhibit detectable degradation. The extracted force versus k C data were combined with previous single-molecule results to produce a "master curve" which suggests that collagen degradation is governed by an extremely sensitive mechanochemical switch.

Molecular mechanism of force induced stabilization of collagen against enzymatic breakdown

Collagen cleavage, facilitated by collagenases of the matrix metalloproteinase (MMP) family, is crucial for many physiological and pathological processes such as wound healing, tissue remodeling, cancer invasion and organ morphogenesis. Earlier work has shown that mechanical force alters the cleavage rate of collagen. However, experimental results yielded conflicting data on whether applying force accelerates or slows down the degradation rate. Here we explain these discrepancies and propose a molecular mechanism by which mechanical force might change the rate of collagen cleavage. We find that a type I collagen heterotrimer is unfolded in its equilibrium state and loses its triple helical structure at the cleavage site without applied force, possibly enhancing enzymatic breakdown as each chain is exposed and can directly undergo hydrolysis. Under application of force, the naturally unfolded region refolds into a triple helical structure, potentially protecting the molecule against enzymatic breakdown. In contrast, a type I collagen homotrimer retains a triple helical structure even without applied force, making it more resistant to enzyme cleavage. In the case of the homotrimer, the application of force may directly lead to molecular unwinding, resulting in a destabilization of the molecule under increased mechanical loading. Our study explains the molecular mechanism by which force may regulate the formation and breakdown of collagenous tissue.

In vivo and in vitro tracking of erosion in biodegradable materials using non-invasive fluorescence imaging

The design of erodible biomaterials relies on the ability to program the in vivo retention time, which necessitates real-time monitoring of erosion. However, in vivo performance cannot always be predicted by traditional determination of in vitro erosion, and standard methods sacrifice samples or animals, preventing sequential measures of the same specimen. We harnessed non-invasive fluorescence imaging to sequentially follow in vivo material-mass loss to model the degradation of materials hydrolytically (PEG:dextran hydrogel) and enzymatically (collagen). Hydrogel erosion rates in vivo and in vitro correlated, enabling the prediction of in vivo erosion of new material formulations from in vitro data. Collagen in vivo erosion was used to infer physiologic in vitro conditions that mimic erosive in vivo environments. This approach enables rapid in vitro screening of materials, and can be extended to simultaneously determine drug release and material erosion from a drug-eluting scaffold, or cell viability and material fate in tissue-engineering formulations.

Molecular mechanochemistry: low force switch slows enzymatic cleavage of human type I collagen monomer

In vertebrate animals, fibrillar collagen accumulates, organizes, and persists in structures which resist mechanical force. This antidissipative behavior is possibly due to a mechanochemical force-switch which converts collagen from enzyme-susceptible to enzyme-resistant. Degradation experiments on native tissue and reconstituted fibrils suggest that collagen/enzyme kinetics favor the retention of loaded collagen. We used a massively parallel, single molecule, mechanochemical reaction assay to demonstrate that the effect is derivative of molecular mechanics. Tensile loads higher than 3 pN dramatically reduced (10×) the enzymatic degradation rate of recombinant human type I collagen monomers by Clostridium histolyticum compared to unloaded controls. Because bacterial collagenase accesses collagen at multiple sites and is an aggressive cleaver of the collagen triple helical domain, the results suggest that collagen molecular architecture is generally more stable when mechanically strained in tension. Thus the tensile mechanical state of collagen monomers is likely to be correlated to their longevity in tissues. Further, strain-actuated molecular stability of collagen may constitute the fundamental basis of a smart structural mechanism which enhances the ability of animals to place, retain, and load-optimize material in the path of mechanical forces.

Mechanical strain stabilizes reconstituted collagen fibrils against enzymatic degradation by mammalian collagenase matrix metalloproteinase 8 (MMP-8)

BACKGROUND

Collagen, a triple-helical, self-organizing protein, is the predominant structural protein in mammals. It is found in bone, ligament, tendon, cartilage, intervertebral disc, skin, blood vessel, and cornea. We have recently postulated that fibrillar collagens (and their complementary enzymes) comprise the basis of a smart structural system which appears to support the retention of molecules in fibrils which are under tensile mechanical strain. The theory suggests that the mechanisms which drive the preferential accumulation of collagen in loaded tissue operate at the molecular level and are not solely cell-driven. The concept reduces control of matrix morphology to an interaction between molecules and the most relevant, physical, and persistent signal: mechanical strain.

METHODOLOGY/PRINCIPAL FINDINGS

The investigation was carried out in an environmentally-controlled microbioreactor in which reconstituted type I collagen micronetworks were gently strained between micropipettes. The strained micronetworks were exposed to active matrix metalloproteinase 8 (MMP-8) and relative degradation rates for loaded and unloaded fibrils were tracked simultaneously using label-free differential interference contrast (DIC) imaging. It was found that applied tensile mechanical strain significantly increased degradation time of loaded fibrils compared to unloaded, paired controls. In many cases, strained fibrils were detectable long after unstrained fibrils were degraded.

CONCLUSIONS/SIGNIFICANCE

In this investigation we demonstrate for the first time that applied mechanical strain preferentially preserves collagen fibrils in the presence of a physiologically-important mammalian enzyme: MMP-8. These results have the potential to contribute to our understanding of many collagen matrix phenomena including development, adaptation, remodeling and disease. Additionally, tissue engineering could benefit from the ability to sculpt desired structures from physiologically compatible and mutable collagen.

Mechanical strain enhances survivability of collagen micronetworks in the presence of collagenase: implications for load-bearing matrix growth and stability

There has been great interest in understanding the methods by which collagen-based load-bearing tissue is constructed, grown and maintained in vertebrate animals. To date, the responsibility for this process has largely been placed with mesenchymal fibroblastic cells that are thought to fully control the morphology of load-bearing extracellular matrix (ECM). However, given clear limitations in the ability of fibroblastic cells to precisely place or remove single collagen molecules to sculpt tissue, we have hypothesized that the material itself must play a critical role in the determination of the form of structural ECM. We here demonstrate directly, using live, dynamic, differential interference contrast imaging, that mechanically strained networks of collagen fibrils, exposed to collagenase (Clostridium histolyticum), degrade preferentially. Specifically, unstrained fibrils are removed 'quickly', while strained fibrils persist significantly longer. The demonstration supports the idea that collagen networks are mechanosensitive in that they are stabilized by mechanical strain. Thus, collagen molecules (together with their complement enzymes) may comprise the basis of a smart, load-adaptive, structural material system. This concept has the potential to drastically simplify the assumed role of the fibroblast, which would need only to provide ECM molecules and mechanical force to sculpt collagenous tissue.

Deformation-dependent enzyme mechanokinetic cleavage of type I collagen

Collagen is a key structural protein in the extracellular matrix of many tissues. It provides biological tissues with tensile mechanical strength and is enzymatically cleaved by a class of matrix metalloproteinases known as collagenases. Collagen enzymatic kinetics has been well characterized in solubilized, gel, and reconstituted forms. However, limited information exists on enzyme degradation of structurally intact collagen fibers and, more importantly, on the effect of mechanical deformation on collagen cleavage. We studied the degradation of native rat tail tendon fibers by collagenase after the fibers were mechanically elongated to strains of epsilon=1-10%. After the fibers were elongated and the stress was allowed to relax, the fiber was immersed in Clostridium histolyticum collagenase and the decrease in stress (sigma) was monitored as a means of calculating the rate of enzyme cleavage of the fiber. An enzyme mechanokinetic (EMK) relaxation function T(E)(epsilon) in s(-1) was calculated from the linear stress-time response during fiber cleavage, where T(E)(epsilon) corresponds to the zero order Michaelis-Menten enzyme-substrate kinetic response. The EMK relaxation function T(E)(epsilon) was found to decrease with applied strain at a rate of approximately 9% per percent strain, with complete inhibition of collagen cleavage predicted to occur at a strain of approximately 11%. However, comparison of the EMK response (T(E) versus epsilon) to collagen's stress-strain response (sigma versus epsilon) suggested the possibility of three different EMK responses: (1) constant T(E)(epsilon) within the toe region (epsilon<3%), (2) a rapid decrease ( approximately 50%) in the transition of the toe-to-heel region (epsilon congruent with3%) followed by (3) a constant value throughout the heel (epsilon=3-5%) and linear (epsilon=5-10%) regions. This observation suggests that the mechanism for the strain-dependent inhibition of enzyme cleavage of the collagen triple helix may be by a conformational change in the triple helix since the decrease in T(E)(epsilon) appeared concomitant with stretching of the collagen molecule.

Human neutrophil elastase responsive delivery from poly(ethylene glycol) hydrogels

A novel enzyme-responsive hydrogel drug delivery system was developed with the potential to treat inflammation locally. Human neutrophil elastase (HNE) is a serine protease secreted by neutrophils which are the first cells recruited to inflammatory sites. We exploited this cell-secreted enzyme as a biological cue for controlled release. HNE sensitive peptide linkers were immobilized within poly(ethylene glycol) hydrogels using photopolymerization techniques. The kinetics of the enzyme reaction within the gel was tailored by varying the amino acid residues present in the P1 and P1' substrate positions (immediately adjacent to cleavage location). A novel FRET-based hydrogel platform was designed to characterize the accessibility of the substrate within the cross-linked, macroscopic hydrogel. Lastly, a diffusion-reaction mathematical model with Michaelis-Menten kinetics was developed to predict the overall release profile and captured the initial 80% of the experimentally observed release. The hydrogel platform presented shows highly controlled release kinetics with potential applications in cellular responsive drug delivery.

Diffusion-limited binding explains binary dose response for local arterial and tumour drug delivery

BACKGROUND

Local drug delivery has transformed medicine, yet it remains unclear how drug efficacy depends on physicochemical properties and delivery kinetics. Most therapies seek to prolong release, yet recent studies demonstrate sustained clinical benefit following local bolus endovascular delivery.

OBJECTIVES

The purpose of the current study was to examine interplay between drug dose, diffusion and binding in determining tissue penetration and effect.

METHODS

We introduce a quantitative framework that balances dose, saturable binding and diffusion, and measured the specific binding parameters of drugs to target tissues.

RESULTS

Model reduction techniques augmented by numerical simulations revealed that impact of saturable binding on drug transport and retention is determined by the magnitude of a binding potential, B(p), ratio of binding capacity to product of equilibrium dissociation constant and accessible tissue volume fraction. At low B(p) (< 1), drugs are predominantly free and transport scales linearly with concentration. At high B(p) (> 40), drug transport exhibits threshold dependence on applied surface concentration.

CONCLUSIONS

In this paradigm, drugs and antibodies with large B(p) penetrate faster and deeper into tissues when presented at high concentrations. Threshold dependence of tissue transport on applied surface concentration of paclitaxel and rapamycin may explain threshold dose dependence of in vivo biological efficacy of these drugs.

A model describing the effect of enzymatic degradation on drug release from collagen minirods

A drug delivery system, named minirod, containing insoluble non-cross-linked collagen was prepared to investigate the release of model drug compounds. To characterise the complete drug release process properly, a mathematical model was developed. Previously, a mathematical model describing water penetration, matrix swelling and drug release by diffusion from dense collagen matrices has been introduced and tested. However, enzymatic matrix degradation influences the drug release as well. Based on experimental data, a model was developed which describes drug release by collagenolytic matrix degradation based on enzyme diffusion, adsorption and cleavage. Data for swelling, collagen degradation and FITC dextran release from insoluble equine collagen type I minirods were collected. Sorption studies demonstrated a tight sorption of collagenase on collagen surfaces that follows a Freundlich sorption isotherm and results in a degradation constant of 3.8x10(-5) mol/l for the minirods. The diffusion coefficients of FITC dextran 20 and 70 (3x10(-3) and 2.4x10(-3) cm2/h) in water were analyzed by fluorescence correlation spectroscopy (FCS). Using these data, the mathematical model was verified by two-dimensional simulations. The numerical results agreed well with the measurements.

Quasi-steady-state kinetics at enzyme and substrate concentrations in excess of the Michaelis-Menten constant

In vitro enzyme reactions are traditionally conducted under conditions of pronounced substrate excess since this guarantees that the bound enzyme is at quasi-steady-state (QSS) with respect to the free substrate, thereby justifying the Briggs-Haldane approximation (BHA). In contrast, intracellular reactions, amplification assays, allergen digestion assays and industrial applications span a range of enzyme-to-substrate ratios for which the BHA is invalid, including the extreme of enzyme excess. The quasi-equilibrium approximation (QEA) is valid for a subset of enzyme excess states. Previously, we showed that the total QSSA (tQSSA) overlaps and extends the validity of the BHA and the QEA, and that it is at least roughly valid for any total substrate and enzyme concentrations. The analysis of the tQSSA is hampered by square root nonlinearity. Previous simplifications of the tQSSA rate law are valid in a parameter domain that overlaps the validity domains of the BHA and the QEA and only slightly extends them. We now integrate the tQSSA rate equation in closed form, without resorting to further approximations. Moreover, we introduce a complimentary simplification of the tQSSA rate law that is valid in states of enzyme excess when the absolute difference between total enzyme and substrate concentrations greatly exceeds the Michaelis-Menten constant. This includes a wide range of enzyme and substrate concentrations where both the BHA and the QEA are invalid and allows us to define precisely the conditions for zero-order and first-order product formation. Remarkably, analytical approximations provided by the tQSSA closely match the expected stochastic kinetics for as few as 15 reactant molecules, suggesting that the conditions for the validity of the tQSSA and for its various simplifications are also of relevance at low molecule numbers.

Distinct modes of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell: insights from a computational model

Matrix metalloproteinases (MMPs) are a family of enzymes responsible for the proteolytic processing of extracellular matrix (ECM) structural proteins under physiological and pathological conditions. During sprouting angiogenesis, the MMPs expressed by a single "tip" endothelial cell exhibit proteolytic activity that allows the cells of the sprouting vessel bud to migrate into the ECM. Membrane type I matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase MMP2, in the presence of the tissue inhibitor of metalloproteinases TIMP2, constitute a system of proteins that play an important role during the proteolysis of collagen type I matrices. Here, we have formulated a computational model to investigate the proteolytic potential of such a tip endothelial cell. The cell expresses MMP2 in its proenzyme form, pro-MMP2, as well as MT1-MMP and TIMP2. The interactions of the proteins are described by a biochemically detailed reaction network. Assuming that the rate-limiting step of the migration is the ability of the tip cell to carry out proteolysis, we have estimated cell velocities for matrices of different collagen content. The estimated velocities of a few microns per hour are in agreement with experimental data. At high collagen content, proteolysis was carried out primarily by MT1-MMP and localized to the cell leading edge, whereas at lower concentrations, MT1-MMP and MMP2 were found to act in parallel, causing proteolysis in the vicinity of the leading edge. TIMP2 is a regulator of the proteolysis localization because it can shift the activity of MT1-MMP from its enzymatic toward its activatory mode, suggesting a tight mechanosensitive regulation of the enzymes and inhibitor expression. The model described here provides a foundation for quantitative studies of angiogenesis in extracellular matrices of different compositions, both in vitro and in vivo. It also identifies critical parameters whose values are not presently available and which should be determined in future experiments.

Analysis of compartmental models of ligand-induced endocytosis

Kinetic models have played a pivotal role in the study of ligand-induced endocytosis. However, an analysis that suggests a systematic way to validate such models is lacking. The current work analyses the base model of ligand-induced endocytosis for three widely used experimental protocols. In protocol I cells initially devoid of ligand are incubated in ligand solution, whereas protocols II and III are desorption experiments in which an initial pool of surface or internalized ligand-receptor complexes, respectively, are released into an elution medium that is initially devoid of ligand. A short-time analysis of protocol I using successive substitutions yielded a corrected pre-factor for the In/Sur plot introduced by Wiley and Cunningham (Cell 25 (1981) 433). In contrast, neglecting the variation in receptor numbers yielded an approximation of protocol I that is valid for long times (e.g. tens of minutes). Similarly, the low cell-concentration limits of protocols II and III are derived by neglecting the concentration of free ligand. The simplicity of these approximations provides a simple and reliable method for estimating the parameters governing ligand kinetics, while their definitive nature implies that they can be used to verify the validity of the base model. This analysis also provides insight on the fast endocytosis and recycling limit of protocol III.

The total quasi-steady-state approximation is valid for reversible enzyme kinetics

The Briggs-Haldane approximation of the irreversible Michaelis-Menten scheme of enzyme kinetics is cited in virtually every biochemistry textbook and is widely considered the classic example of a quasi-steady-state approximation. Though of similar importance, the reversible Michaelis-Menten scheme is not as well characterized. This is a serious limitation since even enzymatic reactions that go to completion may be reversible. The current work derives a total quasi-steady-state approximation (tQSSA) for the reversible Michaelis-Menten and delineates its validity domain. The tQSSA allows the derivation of uniformly valid approximations for the limit of low enzyme concentrations, ET<<ST+KM, and under certain more restrictive conditions also for high enzyme concentrations such that ST<<ET+KM. Using these simple analytical approximations, a sequential experimental-theoretical method is suggested for unambiguously estimating all the kinetic parameters of the reversible Michaelis-Menten scheme.

The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery

We combine the physics of gels with the hydrodynamics of two-phase fluids to construct a set of equations that describe the hydration dynamics of polyelectrolyte gels. We use the model to address three problems. First, we express the effective diffusion constants for neutral and charged spherically distributed gels in terms of microscopic parameters. Second, we use the model to describe the locomotion of nematode sperm cells. Finally, we describe the swelling dynamics of polyelectrolyte gels used for drug release.