Biomedical implications from a morphoelastic continuum model for the simulation of contracture formation in skin grafts that cover excised burns

A continuum hypothesis-based model is developed for the simulation of the (long term) contraction of skin grafts that cover excised burns in order to obtain suggestions regarding the ideal length of splinting therapy and when to start with this therapy such that the therapy is effective optimally. Tissue is modeled as an isotropic, heterogeneous, morphoelastic solid. With respect to the constituents of the tissue, we selected the following constituents as primary model components: fibroblasts, myofibroblasts, collagen molecules, and a generic signaling molecule. Good agreement is demonstrated with respect to the evolution over time of the surface area of unmeshed skin grafts that cover excised burns between outcomes of computer simulations obtained in this study and scar assessment data gathered previously in a clinical study. Based on the simulation results, we suggest that the optimal point in time to start with splinting therapy is directly after placement of the skin graft on its recipient bed. Furthermore, we suggest that it is desirable to continue with splinting therapy until the concentration of the signaling molecules in the grafted area has become negligible such that the formation of contractures can be prevented. We conclude this study with a presentation of some alternative ideas on how to diminish the degree of contracture formation that are not based on a mechanical intervention, and a discussion about how the presented model can be adjusted.     

Colonization factors of diarrheagenicE. coli and their intestinal receptors

WhileEscherichia coli is common as a commensal organism in the distal ileum and colon, the presence of colonization factors (CF) on pathogenic strains ofE. coli facilitates attachment of the organism to intestinal receptor molecules in a species- and tissue-specific fashion. After the initial adherence, colonization occurs, and the involvement of additional virulence determinants leads to illness. EnterotoxigenicE. coli (ETEC) is the most extensively studied of the five categories ofE. coli that cause diarrheal disease, and has the greatest impact on health worldwide. ETEC can be isolated from domestic animals and humans. The biochemistry, genetics, epidemiology, antigenic characteristics, and cell and receptor binding properties of ETEC have been extensively described. Another major category, enteropathogenicE. coli (EPEC), has virulence mechanisms, primarily effacement and cytoskeletal rearrangement of intestinal brush borders, that are distinct from ETEC. An EPEC CF receptor has been purified and characterized as a sialidated transmembrane glycoprotein complex directly attached to actin, thereby associating CF-binding with host-cell response. Three, additional categories ofE. coli diarrheal disease, their colonization factors and their host cell receptors are discussed. It appears that biofilms exist in the intestine in a manner similar to oral bacterial biofilms, and thatE. coli is part of these biofilms as both commensals and pathogens.Abbreviations CF colonization factor - CFA Colonization Factor Antigen - CS coli-surface-associated antigen - EAggEC enteroaggregativeE. coli - ECDD E. coli diarrheal disease - EHEC enterohemorrhagicE. coli - EIEC enteroinvasiveE. coli - EPEC enteropathogenicE. coli - ETEC enterotoxigenicE. coli - Gal galactose - GalNAc N-acetyl galactosamine - LT heat-labile toxin - NeuAc N-acetyl neuraminic acid - PCF Putative colonization factor - RBC red blood cells - SLT Shiga-like toxin - ST heat-stable toxin     

Molecular drift of the bride of sevenless (boss) gene in Drosophila

DNA sequences were determined for three to five alleles of the bride-of- sevenless (boss) gene in each of four species of Drosophila. The product of boss is a transmembrane receptor for a ligand coded by the sevenless gene that triggers differentiation of the R7 photoreceptor cell in the compound eye. Population parameters affecting the rate and pattern of molecular evolution of boss were estimated from the multinomial configurations of nucleotide polymorphisms of synonymous codons. The time of divergence between D. melanogaster and D. simulans was estimated as approximately 1 Myr, that between D. teissieri and D. yakuba as approximately 0.75 Myr, and that between the two pairs of sibling species as approximately 2 Myr. (The boss genes themselves have estimated divergence times approximately 50% greater than the species divergence times.) The effective size of the species was estimated as approximately 5 x 10(6), and the average mutation rate was estimated as 1-2 x 10(-9)/nucleotide/generation. The ratio of amino acid polymorphisms within species to fixed differences between species suggests that approximately 25% of all possible single-step amino acid replacements in the boss gene product may be selectively neutral or nearly neutral. The data also imply that random genetic drift has been responsible for virtually all of the observed differences in the portion of the boss gene analyzed among the four species.      

Sensitivity of a two-dimensional biomorphoelastic model for post-burn contraction

We consider a two-dimensional biomorphoelastic model describing post-burn scar contraction. This model describes skin displacement and the development of the effective Eulerian strain in the tissue. Besides these mechanical components, signaling molecules, fibroblasts, myofibroblasts, and collagen also play a significant role in the model. We perform a sensitivity analysis for the independent parameters of the model and focus on the effects on features of the relative surface area and the total strain energy density. We conclude that the most sensitive parameters are the Poisson’s ratio, the equilibrium collagen concentration, the contraction inhibitor constant, and the myofibroblast apoptosis rate. Next to these insights, we perform a sensitivity analysis where the proliferation rates of fibroblasts and myofibroblasts are not the same. The impact of this model adaptation is significant.

     

Evolutionary origin of human and primate malarias: evidence from the circumsporozoite protein gene

We have analyzed the conserved regions of the gene coding for the circumsporozoite protein (CSP) in 12 species of Plasmodium, the malaria parasite. The closest evolutionary relative of P. falciparum, the agent of malignant human malaria, is P. reichenowi, a chimpanzee parasite. This is consistent with the hypothesis that P. falciparum is an ancient human parasite, associated with humans since the divergence of the hominids from their closest hominoid relatives. Three other human Plasmodium species are each genetically indistinguishable from species parasitic to nonhuman primates; that is, for the DNA sequences included in our analysis, the differences between species are not greater than the differences between strains of the human species. The human P. malariae is indistinguishable from P. brasilianum, and P. vivax is indistinguishable from P. simium; P. brasilianum and P. simium are parasitic to New World monkeys. The human P. vivax-like is indistinguishable from P. simiovale, a parasite of Old World macaques. We conjecture that P. malariae, P. vivax, and P. vivax-like are evolutionarily recent human parasites, the first two at least acquired only within the last several thousand years, and perhaps within the last few hundred years, after the expansion of human populations in South America following the European colonizations. We estimate the rate of evolution of the conserved regions of the CSP gene as 2.46 x 10(-9) per site per year. The divergence between the P. falciparum and P. reichenowi lineages is accordingly dated 8.9 Myr ago. The divergence between the three lineages leading to the human parasites is very ancient, about 100 Myr old between P. malariae and P. vivax (and P. vivax-like) and about 165 Myr old between P. falciparum and the other two.      

Oligomeric forms of the membrane-bound acetylcholine receptor disclosed upon extraction of the M(r) 43,000 nonreceptor peptide

Oligomeric forms of the acetylcholine receptor are directly visualized by electron microscopy in receptor-rich membranes from torpedo marmorata. The receptor structures are quantitatively correlated with the molecular species so far identified only after detergent solubilization, and further related to the polypeptide composition of the membranes and changes thereof. The structural identification is made possibly by the increased fragility of the membranes after extraction of nonreceptor peptides and their subsequent disruption upon drying onto hydrophilic carbon supports. Receptor particles in native membranes depleted of nonreceptor peptides appear as single units of 7-8 nm, and double and multiple aggregates thereof. Particle doublets having a main-axis diameter of 19 +/- 3 nm predominate in these membranes. Linear aggregates of particles similar to those observed in rotary replicas of quick-frozen fresh electrolytes (Heuser, J.E. and S. R. Salpeter. 1979, J. Cell Biol. 82: 150-173) are also present in the alkaline-extracted membranes. Chemical modifications of the thiol groups shift the distribution of structural species. Dithiothreitol reduction, which renders almost exclusively the 9S, monomeric receptor form, results in the observation of the 7-8 nm particle in isolated form. The proportion of doublets increases in membranes alkylated with N-ethylmaleimide. Treatment with 5,5’-dithiobis-(nitrobenzoic acid) increases the proportion of higher oligomeric species, and particle aggregates (n=oligo) predominate. The nonreceptor v-peptide (doublet of M(r) 43,000) appears to play a role in the receptor monomer-polymer equilibria. Receptor protein and v-peptide co-aggregate upon reduction and reoxidation of native membranes. In membranes protected ab initio with N- ethylmaleimide, only the receptor appears to self-aggregate. The v-peptide cannot be extracted from these alkylated membranes, though it is easily released from normal, subsequently alkylated or reduced membranes. A stabilization of the dimeric species by the nonreceptor v-peptide is suggested by these experiments. Monospecific antibodies against the v-peptide are used in conjunction with rhodamine- labeled anti-bodies in an indirect immunoflourescence assay to map the vectorial exposure of the v-peptide. When intact membranes, v-peptide depleted and “holey” native membranes (treated with 0.3 percent saponin) are compared, maximal labeling is obtained with the latter type of membranes, suggesting a predominantly cytoplasmic exposure of the antigenic determinants of the v-peptide in the membrane. The influence of the v-peptide in the thiol-dependent interconversions of the receptor protein and the putative topography of the peptide are analyzed in the light of the present results.     

A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes

The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429–1450, 2018), Vermolen and Gefen (BMM 12:301–323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340–348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.

     

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a ‘wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This ‘wave-like’ profile contradicts experimental observations. In our study we investigate the conditions, under which such profile appears in the solution. Those conditions are determined in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system. The stability analysis was carried out for the reduced system of PDE’s, of which we prove, that it is equivalent to the original system of equations, with respect to the stability properties of constant solutions. The conclusions, derived from the linear stability analysis, are extended for the case of large perturbations. If the constant solution is unstable, then the solution of the system never converges to this constant solution. The analytical results are validated with finite element simulations. The simulations show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.     

A finite-element model for healing of cutaneous wounds combining contraction, angiogenesis and closure

A simplified finite-element model for wound healing is proposed. The model takes into account the sequential steps of dermal regeneration, wound contraction, angiogenesis and wound closure. An innovation in the present study is the combination of the aforementioned partially overlapping processes, which can be used to deliver novel insights into the process of wound healing, such as geometry related influences, as well as the influence of coupling between the various existing subprocesses on the actual healing behavior. The model confirms the clinical observation that epidermal closure proceeds by a crawling and climbing mechanism at the early stages, and by a stratification process in layers parallel to the skin surface at the later stages. The local epidermal oxygen content may play an important role here. The model can also be used to investigate the influence of local injection of hormones that stimulate partial processes occurring during wound healing. These insights can be used to improve wound healing treatments.     

A biomechanical mathematical model for the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds

A continuum hypothesis-based, biomechanical model is presented for the simulation of the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds that cover a large surface area. Since wound contraction mainly takes place in the dermal layer of the skin, solely a portion of this layer is included explicitly into the model. This portion of dermal layer is modeled as a heterogeneous, orthotropic continuous solid with bulk mechanical properties that are locally dependent on both the local concentration and the local geometrical arrangement of the collagen bundles. With respect to the dynamic regulation of the geometrical arrangement of the collagen bundles, it is assumed that a portion of the collagen molecules are deposited and reoriented in the direction of movement of (myo)fibroblasts. The remainder of the newly secreted collagen molecules are deposited by ratio in the direction of the present collagen bundles. Simulation results show that the distribution of the collagen bundles influences the evolution over time of both the shape of the wounded area and the degree of overall contraction of the wounded area. Interestingly, these effects are solely a consequence of alterations in the initial overall distribution of the collagen bundles, and not a consequence of alterations in the evolution over time of the different cell densities and concentrations of the modeled constituents. In accordance with experimental observations, simulation results show furthermore that ultimately the majority of the collagen molecules ends up permanently oriented toward the center of the wound and in the plane that runs parallel to the surface of the skin.