Experimental characterization and computational modeling of hydrogel cross-linking for bioprinting applications

2019 ◽  
Vol 42 (10) ◽  
pp. 548-557 ◽  
Author(s):  
Aidin Hajikhani ◽  
Franca Scocozza ◽  
Michele Conti ◽  
Michele Marino ◽  
Ferdinando Auricchio ◽  
...  
Keyword(s):  
Calcium Chloride ◽  
Reaction Diffusion ◽  
Chloride Diffusion ◽  
Chemical System ◽  
Cross Linking ◽  
Modeling Framework ◽  
Reaction Diffusion Model ◽  
Constant Diffusivity ◽  
Low Toxicity ◽  
Element Discretizations

Alginate-based hydrogels are extensively used to create bioinks for bioprinting, due to their biocompatibility, low toxicity, low costs, and slight gelling. Modeling of bioprinting process can boost experimental design reducing trial-and-error tests. To this aim, the cross-linking kinetics for the chemical gelation of sodium alginate hydrogels via calcium chloride diffusion is analyzed. Experimental measurements on the absorbed volume of calcium chloride in the hydrogel are obtained at different times. Moreover, a reaction-diffusion model is developed, accounting for the dependence of diffusive properties on the gelation degree. The coupled chemical system is solved using finite element discretizations which include the inhomogeneous evolution of hydrogel state in time and space. Experimental results are fitted within the proposed modeling framework, which is thereby calibrated and validated. Moreover, the importance of accounting for cross-linking-dependent diffusive properties is highlighted, showing that, if a constant diffusivity property is employed, the model does not properly capture the experimental evidence. Since the analyzed mechanisms highly affect the evolution of the front of the solidified gel in the final bioprinted structure, the present study is a step towards the development of reliable computational tools for the in silico optimization of protocols and post-printing treatments for bioprinting applications.

scholarly journals Dynamic partitioning of mitotic kinesin-5 cross-linkers between microtubule-bound and freely diffusing states

2008 ◽  
Vol 182 (3) ◽  
pp. 429-436 ◽  
Author(s):  
Dhanya K. Cheerambathur ◽  
Ingrid Brust-Mascher ◽  
Gul Civelekoglu-Scholey ◽  
Jonathan M. Scholey
Keyword(s):  
Fluorescence Recovery After Photobleaching ◽  
Reaction Diffusion ◽  
Cross Linking ◽  
Spindle Matrix ◽  
Dynamic Partitioning ◽  
Spindle Poles ◽  
Reaction Diffusion Model ◽  
Dynamic Mobility ◽  
Spindle Microtubules ◽  
Transgenic Drosophila

The dynamic behavior of homotetrameric kinesin-5 during mitosis is poorly understood. Kinesin-5 may function only by binding, cross-linking, and sliding adjacent spindle microtubules (MTs), or, alternatively, it may bind to a stable “spindle matrix” to generate mitotic movements. We created transgenic Drosophila melanogaster expressing fluorescent kinesin-5, KLP61F-GFP, in a klp61f mutant background, where it rescues mitosis and viability. KLP61F-GFP localizes to interpolar MT bundles, half spindles, and asters, and is enriched around spindle poles. In fluorescence recovery after photobleaching experiments, KLP61F-GFP displays dynamic mobility similar to tubulin, which is inconsistent with a substantial static pool of kinesin-5. The data conform to a reaction–diffusion model in which most KLP61F is bound to spindle MTs, with the remainder diffusing freely. KLP61F appears to transiently bind MTs, moving short distances along them before detaching. Thus, kinesin-5 motors can function by cross-linking and sliding adjacent spindle MTs without the need for a static spindle matrix.

Curvature and spiral geometry in aggregation patterns of Dictyostelium discoideum

Development ◽  
1990 ◽  
Vol 109 (1) ◽  
pp. 11-16
Author(s):  
P. Foerster ◽  
S.C. Muller ◽  
B. Hess
Keyword(s):  
Dictyostelium Discoideum ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Dark Field ◽  
Chemical System ◽  
Geometrical Parameters ◽  
Normal Velocity ◽  
Field Equipment ◽  
Reaction Diffusion Model ◽  
Spiral Geometry

Aggregation patterns of the slime mould Dictyostelium discoideum were recorded using dark-field equipment combined with video techniques. Computerized image processing allowed the analysis of wave collision structures, expanding concentric circles and rotating spirals in terms of wave velocity and front geometry, as previously done in the Belousov-Zhabotinskii reaction, a chemical system showing similar patterns. We verified the linear relationship between the normal velocity and the curvature of wave fronts predicted by a reaction-diffusion model. The proportionality factor, which in this case is the diffusion coefficient of the chemical signal transmitter cAMP establishing communication between the cells, was determined to be 0.66×10-5cm2s-1. From measurements of positively curved circular waves, we could roughly estimate the critical radius of wave propagation Rcrit (approximately 200_m); which means that up to 500 cells are necessary to form a center of an aggregation structure. Furthermore, we analyzed the geometrical parameters of spiral wave patterns and estimated the core radius ro to be approximately equal to 300_m.

scholarly journals Intrinsic Dynamic Behavior of Fascin in Filopodia

2007 ◽  
Vol 18 (10) ◽  
pp. 3928-3940 ◽  
Author(s):  
Yvonne S. Aratyn ◽  
Thomas E. Schaus ◽  
Edwin W. Taylor ◽  
Gary G. Borisy
Keyword(s):  
Dynamic Behavior ◽  
Fluorescence Recovery After Photobleaching ◽  
Reaction Diffusion ◽  
Computational Approach ◽  
Cross Linking ◽  
Rapid Cycling ◽  
Reaction Diffusion Model ◽  
Cross Linker ◽  
Intrinsic Dynamic

Recent studies showed that the actin cross-linking protein, fascin, undergoes rapid cycling between filopodial filaments. Here, we used an experimental and computational approach to dissect features of fascin exchange and incorporation in filopodia. Using expression of phosphomimetic fascin mutants, we determined that fascin in the phosphorylated state is primarily freely diffusing, whereas actin bundling in filopodia is accomplished by fascin dephosphorylated at serine 39. Fluorescence recovery after photobleaching analysis revealed that fascin rapidly dissociates from filopodial filaments with a kinetic off-rate of 0.12 s−1 and that it undergoes diffusion at moderate rates with a coefficient of 6 μm2s−1. This kinetic off-rate was recapitulated in vitro, indicating that dynamic behavior is intrinsic to the fascin cross-linker. A computational reaction–diffusion model showed that reversible cross-linking is required for the delivery of fascin to growing filopodial tips at sufficient rates. Analysis of fascin bundling indicated that filopodia are semiordered bundles with one bound fascin per 25–60 actin monomers.

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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