Václav Klika

The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation

Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction.

Coupling Effect between Mechanical Loading and Chemical Reactions

This paper offers a theoretical explanation of the coupling effect phenomenon between mechanical loading and chemical reactions based on linear nonequilibrium thermodynamics and also discusses the classical method of obtaining restrictions on the phenomenological coefficients. The question whether static or dynamic loading influences biochemical processes is addressed-the necessity of dynamic loading as a stimulatory mechanism is shown. Further, the presented paper suggests that chemical and mechanical processes do not only facilitate or support one another but they may also play a triggering role for the other coupled process-some biochemical processes may need mechanical stimulation to run and vice versa as well-chemical reactions may provide energy for some mechanical processes. As an example, a detailed analysis of a model for controlled autocatalytic reproduction is presented, where the coupling effect, i.e. the influence of dynamic loading on reaction kinetics, is demonstrated.

New predictive model for monitoring bone remodeling

The aim of this article was to present a new thermodynamic-based model for bone remodeling which is able to predict the functional adaptation of bone in response to changes in both mechanical and biochemical environments. The model was based on chemical kinetics and irreversible thermodynamic principles, in which bone is considered as a self-organizing system that exchanges matter, energy and entropy with its surroundings. The governing equations of the mathematical model have been numerically solved using Matlab software and implemented in ANSYS software using the Finite Element Method. With the aid of this model, the whole inner structure of bone was elucidated. The current model suggested that bone remodeling was a dynamic process which was driven by mechanical loading, metabolic factors and other external contributions. The model clearly indicated that in the absence of mechanical stimulus, the bone was not completely resorbed and reaches a new steady state after about 50% of bone loss. This finding agreed with previous clinical studies. Furthermore, results of virtual computations of bone density in a composite femur showed the development of a dense cortical bone around the medullary canal and a dense trabeculae bone between the femoral head and the calcar region of the medial cortex due to compressive stresses. The comparison of the predicted bone density with the structure of the proximal femur obtained from X-rays and using strain energy density gave credibility to the current model.

A Guide through Available Mixture Theories for Applications

In this article, we discuss the approaches used in the theory of mixtures and provide a critical review from a fresh perspective with the aim to identify limitations and open questions inherent to various versions of the theory. Such a discussion could serve as a guide to the formulation of a model for the problem at hand. We look into the frequently neglected area of kinematic description, drawing from this field criticism of third Truesdells metaphysical principle. Balance laws are carefully formulated for partial quantities with discontinuities for both theory of interacting continua and for averaging theories. Further, we discuss definitions of mixture quantities together with Truesdells metaphysical principles. Finally, we use classical irreversible thermodynamics to derive entropy production for mixture as a whole and thus reaching an extension of its classical form, evolution equations (phenomenological equations), and constitutive relations. As this fundamental step is very much dependent on the use of non equilibrium thermodynamics, we give a brief overview of the theories available.

Hierarchical patterning modes orchestrate hair follicle morphogenesis

Two theories address the origin of repeating patterns, such as hair follicles, limb digits, and intestinal villi, during development. The Turing reaction–diffusion system posits that interacting diffusible signals produced by static cells first define a prepattern that then induces cell rearrangements to produce an anatomical structure. The second theory, that of mesenchymal self-organisation, proposes that mobile cells can form periodic patterns of cell aggregates directly, without reference to any prepattern. Early hair follicle development is characterised by the rapid appearance of periodic arrangements of altered gene expression in the epidermis and prominent clustering of the adjacent dermal mesenchymal cells. We assess the contributions and interplay between reaction–diffusion and mesenchymal self-organisation processes in hair follicle patterning, identifying a network of fibroblast growth factor (FGF), wingless-related integration site (WNT), and bone morphogenetic protein (BMP) signalling interactions capable of spontaneously producing a periodic pattern. Using time-lapse imaging, we find that mesenchymal cell condensation at hair follicles is locally directed by an epidermal prepattern. However, imposing this prepattern’s condition of high FGF and low BMP activity across the entire skin reveals a latent dermal capacity to undergo spatially patterned self-organisation in the absence of epithelial direction. This mesenchymal self-organisation relies on restricted transforming growth factor (TGF) β signalling, which serves to drive chemotactic mesenchymal patterning when reaction–diffusion patterning is suppressed, but, in normal conditions, facilitates cell movement to locally prepatterned sources of FGF. This work illustrates a hierarchy of periodic patterning modes operating in organogenesis.

Investigating stress shielding spanned by biomimetic polymer-composite vs. metallic hip stem: A computational study using mechano-biochemical model.

Periprosthetic bone loss in response to total hip arthroplasty is a serious complication compromising patients life quality as it may cause the premature failure of the implant. Stress shielding as a result of an uneven load sharing between the hip implant and the bone is a key factor leading to bone density decrease. A number of composite hip implants have been designed so far to improve load sharing characteristics. However, they have rarely been investigated from the bone remodeling point of view to predict a long-term response. This is the first study that employed a mechano-biochemical model, which considers the coupling effect between mechanical loading and bone biochemistry, to investigate bone remodeling after composite hip implantation. In this study, periprosthetic bone remodeling in the presence of Carbon fiber polyamide 12 (CF/PA12), CoCrMo and Ti alloy implants was predicted and compared. Our findings revealed that the most significant periprosthetic bone loss in response to metallic implants occurs in Gruen zone 7 (-43% with CoCrMo; -35% with Ti) and 6 (-40% with CoCrMo; -29% with Ti), while zone 4 has the lowest bone density decrease with all three implants (-9%). Also, the results showed that in terms of bone remodeling, the composite hip implant is more advantageous over the metallic ones as it provides a more uniform density change across the bone and induces less stress shielding which consequently results in a lower post-operative bone loss (-9% with CF/PA12 implant compared to -27% and -21% with CoCrMo and Ti alloy implants, respectively).

Investigating the Turing conditions for diffusion-driven instability in the presence of a binding immobile substrate

Turings diffusion-driven instability for the standard two species reaction-diffusion system is only achievable under well-known and rather restrictive conditions on both the diffusion rates and the kinetic parameters, which necessitates the pairing of a self-activator with a self-inhibitor. In this study we generalize the standard two-species model by considering the case where the reactants can bind to an immobile substrate, for instance extra-cellular matrix, and investigate the influence of this dynamics on Turings diffusion-driven instability. Such systems have been previously studied on the grounds that binding of the self-activator to a substrate may effectively reduce its diffusion rate and thus induce a Turing instability for species with equal diffusion coefficients, as originally demonstrated by Lengyel and Epstein (1992) under the assumption that the bound state dynamics occurs on a fast timescale. We, however, analyse the full system without any separation of timescales and demonstrate that the full system also allows a relaxation of the standard constraints on the reaction kinetics for the Turing instability, increasing the type of interactions that could give rise to spatial patterning. In particular, we show that two self-activators can undertake a diffusively driven instability in the presence of a binding immobile substrate, highlighting that the interactions required of a putative biological Turing instability need not be associated with a self-activator-self-inhibitor morphogen pair.

Predicting Bone Remodeling in Response to Total Hip Arthroplasty: Computational Study Using Mechanobiochemical Model

Periprosthetic bone loss following total hip arthroplasty (THA) is a serious concern leading to the premature failure of prosthetic implant. Therefore, investigating bone remodeling in response to hip arthroplasty is of paramount for the purpose of designing long lasting prostheses. In this study, a thermodynamic-based theory, which considers the coupling between the mechanical loading and biochemical affinity as stimulus for bone formation and resorption, was used to simulate the femoral density change in response to THA. The results of the numerical simulations using 3D finite element analysis revealed that in Gruen zone 7, after remarkable postoperative bone loss, the bone density started recovering and got stabilized after 9% increase. The most significant periprosthetic bone loss was found in Gruen zone 7 (-17.93%) followed by zone 1 (-13.77%). Conversely, in zone 4, bone densification was observed (+4.63%). The results have also shown that the bone density loss in the posterior region of the proximal metaphysis was greater than that in the anterior side. This study provided a quantitative figure for monitoring the distribution variation of density throughout the femoral bone. The predicted bone density distribution before and after THA agree well with the bone morphology and previous results from the literature.

An overview of multiphase cartilage mechanical modelling and its role in understanding function and pathology.

There is a long history of mathematical and computational modelling with the objective of understanding the mechanisms governing cartilage׳s remarkable mechanical performance. Nonetheless, despite sophisticated modelling development, simulations of cartilage have consistently lagged behind structural knowledge and thus the relationship between structure and function in cartilage is not fully understood. However, in the most recent generation of studies, there is an emerging confluence between our structural knowledge and the structure represented in cartilage modelling. This raises the prospect of further refinement in our understanding of cartilage function and also the initiation of an engineering-level understanding for how structural degradation and ageing relates to cartilage dysfunction and pathology, as well as informing the potential design of prospective interventions. Aimed at researchers entering the field of cartilage modelling, we thus review the basic principles of cartilage models, discussing the underlying physics and assumptions in relatively simple settings, whilst presenting the derivation of relatively parsimonious multiphase cartilage models consistent with our discussions. We proceed to consider modern developments that start aligning the structure captured in the models with observed complexities. This emphasises the challenges associated with constitutive relations, boundary conditions, parameter estimation and validation in cartilage modelling programmes. Consequently, we further detail how both experimental interrogations and modelling developments can be utilised to investigate and reduce such difficulties before summarising how cartilage modelling initiatives may improve our understanding of cartilage ageing, pathology and intervention.

Reductions and extensions in mesoscopic dynamics.

Reduction of a mesoscopic level to a level with fewer details is made by the time evolution during which the entropy increases. An extension of a mesoscopic level is a construction of a level with more details. In particular, we discuss extensions in which extra state variables are found in the vector fields appearing on the level that we want to extend. Reductions, extensions, and compatibility relations among them are formulated first in an abstract setting and then illustrated in specific mesoscopic theories.