An articular cartilage contact model based on real surface geometry

Abnormal, excessive stresses acting on articular joint surfaces are speculated to be one of the causes for joint degeneration. However, articular surface stresses have not been studied systematically, since it is technically difficult to measure in vivo contact areas and pressures in dynamic situations. Therefore, we implemented a numerical model of articular surface contact using accurate surface geometries. The model was developed for the cat patellofemoral joint. We demonstrated that small misalignments of the patella relative to the femur change the joint contact mechanics substantially for a given external load. These results suggest that misalignment might be studied as one of the factors causing articular cartilage disorder and joint degeneration.     

A model of bacterial DNA segregation based upon helical geometry

A new mechanism to segregate daughter genomes in bacterial cells is suggested that is based upon the rules of geometry governing the helix clock (Mendelson, 1982a). The reorientation of cell surface string arrays used as a timing reference in the helix clock is capable of drawing apart the initial products of DNA replication. Physically linking the sister DNA replication origins to the ends of the initial cell surface string inserted into the cell surface at the start of a helix clock cycle, and linking the DNA terminus to a point along the length of the same string provides a means to mark the locations to which the genomes will segregate as well as the place where cell division will occur. The parallel packing of additional cell surface strings into an array which includes the string to which DNA is attached provides the necessary spatial rearrangements. The helical segregation model can account for the precise registration of cell divisions with the completion of replication forks in a multifork replication system, provides a basis for determining the relationship of sister cell sizes at division, and can also accommodate the asymmetrical divisions associated with minicell production and sporulation. Examination of the helical segregation theory under multifork DNA replication conditions moreover reveals that adjacent helical clocks are physically linked to one another although totally independent in terms of their progression through the clock cycle. A relationship between the initiation of DNA replication forks and the insertion of the first cell surface string associated with the start of a helix clock cycle is predicted by the model.     

ASPDock: protein-protein docking algorithm using atomic solvation parameters model

Background  

Atomic Solvation Parameters (ASP) model has been proven to be a very successful method of calculating the binding free energy of protein complexes. This suggests that incorporating it into docking algorithms should improve the accuracy of prediction. In this paper we propose an FFT-based algorithm to calculate ASP scores of protein complexes and develop an ASP-based protein-protein docking method (ASPDock).     

A predictive model of cell traction forces based on cell geometry

Recent work has indicated that the shape and size of a cell can influence how a cell spreads, develops focal adhesions, and exerts forces on the substrate. However, it is unclear how cell shape regulates these events. Here we present a computational model that uses cell shape to predict the magnitude and direction of forces generated by cells. The predicted results are compared to experimentally measured traction forces, and show that the model can predict traction force direction, relative magnitude, and force distribution within the cell using only cell shape as an input. Analysis of the model shows that the magnitude and direction of the traction force at a given point is proportional to the first moment of area about that point in the cell, suggesting that contractile forces within the cell act on the entire cytoskeletal network as a single cohesive unit. Through this model, we demonstrate that intrinsic properties of cell shape can facilitate changes in traction force patterns, independently of heterogeneous mechanical properties or signaling events within the cell.     

Efficient electrostatic solvation model for protein-fragment docking

A method is presented for the fast evaluation of the binding energy of a protein-small molecule complex with electrostatic solvation. It makes use of a fast preprocessing step based on the assumption that the main contribution to electrostatic desolvation upon ligand binding originates from the displacement of the first shell of water molecules. For a rigid protein, the precomputation of the energy contributions on a set of grids allows the estimation of the energy in solution of about 300 protein-fragment binding modes per second on a personal computer. The docking procedure is applied to five rigid binding sites whose size ranges from 17 residues to a whole protein of 107 amino acids. Using a library of 70 mainly rigid molecules, known micromolar inhibitors or close analogs are docked and prioritized correctly. The docking based rank-ordering of the library requires about 5 h and is proposed as a complementary approach to structure-activity relationships by nuclear magnetic resonance. Proteins 2001;42:256-268.     

Landscape as a model: the importance of geometry

In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking.     

Photobioreactors for microalgal cultures: A Lagrangian model coupling hydrodynamics and kinetics

Closed photobioreactors have to be optimized in terms of light utilization and overall photosynthesis rate. A simple model coupling the hydrodynamics and the photosynthesis kinetics has been proposed to analyze the photosynthesis dynamics due to the continuous shuttle of microalgae between dark and lighted zones of the photobioreactor. Microalgal motion has been described according to a stochastic Lagrangian approach adopting the turbulence model suitable for the photobioreactor configuration (single vs. two‐phase flows). Effects of light path, biomass concentration, turbulence level and irradiance have been reported in terms of overall photosynthesis rate. Different irradiation strategies (internal, lateral and rounding) and several photobioreactor configurations (flat, tubular, bubble column, airlift) have been investigated. Photobioreactor configurations and the operating conditions to maximize the photosynthesis rate have been pointed out. Results confirmed and explained the common experimental observation that high concentrated cultures are not photoinhibited at high irradiance level. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:1259–1272, 2015     

The finite polygenic mixed model: An alternative formulation for the mixed model of inheritance

This paper presents a mixed model of inheritance with a finite number of polygenic loci. This model leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, likelihood profiles were obtained for the finite polygenic mixed model, the usual mixed model, with exact and approximate calculations, and for a class D regressive model. The profiles for the finite polygenic mixed model were closest to the profiles for the usual mixed model with exact calculations.     

Kinetic model of the action of oligomeric enzymes using phosphofructokinase as an example. II. General formulation of the hierarchical model

A general approach is suggested to describe the steady-state kinetics of the oligomeric enzymes on the base of the generalized statistical Ising model. Detailed analysis is given for the case of a oligomeric enzyme with a hierarchical supramolecular organization. A protomer of this enzyme composed of several equivalent subunits represents the quarternary level of structure. In their turn the finite or infinite number of protomers is associated into a oligomer thus creating a new "quinternary" level of the enzyme organization. The model accounts for the ligand-induced homotrophic cooperative interactions: firstly, between the neighbouring protomers and secondly, between the subunits of the same protomer. The influence of protomer conformation on the subunit state and the cooperativity induction caused by two-ligand binding are also taken into consideration. Monod-Wyman-Changeux's and Koshland's models are shown to be special limit cases of the suggested general theory.     

An improved formulation of SYPRO Ruby protein gel stain: comparison with the original formulation and with a ruthenium II tris (bathophenanthroline disulfonate) formulation

SYPRO Ruby protein gel stain is compatible with a variety of imaging platforms since it absorbs maximally in the ultraviolet (280 nm) and visible (470 nm) regions of the spectrum. Dye localization is achieved by noncovalent, electrostatic and hydrophobic binding to proteins, with signal being detected at 610 nm. Since proteins are not covalently modified by the dye, compatibility with downstream proteomics techniques such as matrix-assisted laser desorption/ionisation-time of flight mass spectrometry is assured. The principal limitation of the original formulation of SYPRO Ruby protein gel stain, is that it was only compatible with a limited number of gel fixation procedures. Too aggressive a fixation protocol led to diminished signal intensity and poor detection sensitivity. This is particularly apparent when post-staining gels subjected to labeling with other fluorophores such as Schiff's base staining of glycoproteins with fluorescent hydrazides. Consequently, we have developed an improved formulation of SYPRO Ruby protein gel stain that is fully compatible with commonly implemented protein fixation procedures and is suitable for post-staining gels after detection of glycoproteins using the green fluorescent Pro-Q Emerald 300 glycoprotein stain or detection of beta-glucuronidase using the green fluorescent ELF 97 beta-D-glucuronide. The new stain formulation is brighter, making it easier to manually excise spots for peptide mass profiling. An additional benefit of the improved formulation is that it permits staining of proteins in isoelectric focusing gels, without the requirement for caustic acids.     

Differential evolution for protein folding optimization based on a three-dimensional AB off-lattice model

This paper presents a differential evolution algorithm that is adapted for the protein folding optimization on a three-dimensional AB off-lattice model. The proposed algorithm is based on a self-adaptive differential evolution that improves the algorithm efficiency and reduces the number of control parameters. A mutation strategy for the fast convergence is used inside the algorithm. A temporal locality is used in order to speed up the algorithm convergence additionally and to find amino-acid conformations with the lowest free energy values. Within this mechanism a new vector is calculated when the trial vector is better than the corresponding vector from the population. This new vector is likely better than the trial vector and this accelerates convergence speed. Because of the fast convergence the algorithm has some chance to be trapped into the local optima. To mitigate this problem the algorithm includes reinitialization. The proposed algorithm was tested on amino-acid sequences that are used frequently in literature. The obtained results show that the proposed algorithm is superior to the algorithms from the literature and the obtained amino-acid sequences have significantly lower free energy values.

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Graphical Abstract Protein folding optimization on a three-dimensional AB off-lattice model using the differential evolution algorithm.

     

Control of whole heart geometry by intramyocardial mechano-feedback: a model study

Geometry of the heart adapts to mechanical load, imposed by pressures and volumes of the cavities. We regarded preservation of cardiac geometry as a homeostatic control system. The control loop was simulated by a chain of models, starting with geometry of the cardiac walls, sequentially simulating circulation hemodynamics, myofiber stress and strain in the walls, transfer of mechano-sensed signals to structural changes of the myocardium, and finalized by calculation of resulting changes in cardiac wall geometry. Instead of modeling detailed mechano-transductive pathways and their interconnections, we used principles of control theory to find optimal transfer functions, representing the overall biological responses to mechanical signals. As biological responses we regarded tissue mass, extent of contractile myocyte structure and extent of the extra-cellular matrix. Mechano-structural stimulus-response characteristics were considered to be the same for atrial and ventricular tissue. Simulation of adaptation to self-generated hemodynamic load rendered physiologic geometry of all cardiac cavities automatically. Adaptation of geometry to chronic hypertension and volume load appeared also physiologic. Different combinations of mechano-sensors satisfied the condition that control of geometry is stable. Thus, we expect that for various species, evolution may have selected different solutions for mechano-adaptation.     

A cell cycle model for somitogenesis: mathematical formulation and numerical simulation

After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems in developmental biology. Here we present a mathematical formulation of the cell cycle model for somitogenesis proposed in Development105 (1989), 119-130. Somite precursor cells in the node are asynchronous, and therefore, as a population, generate continuously pre-somite cells which enter the segmental plate. The model makes the hypothesis that there exists a time window within the cell cycle, making up one-seventh of the cycle, which gates the pre-somite cells so that they make somites discretely, seven per cycle. We show that the model can indeed account for the spatiotemporal patterning of somite formation during normal development as well as the periodic abnormalities produced by heat shock treatment. We also relate the model to recent molecular data on the process of somite formation.     

A model for the human cornea: constitutive formulation and numerical analysis

The human cornea (the external lens of the eye) has the macroscopic structure of a thin shell, originated by the organization of collagen lamellae parallel to the middle surface of the shell. The lamellae, composed of bundles of collagen fibrils, are responsible for the experimentally observed anisotropy of the cornea. Anomalies in the fibril structure may explain the changes in the mechanical behavior of the tissue observed in pathologies such as keratoconus. We employ a fiber-matrix constitutive model and propose a numerical model for the human cornea that is able to account for its mechanical behavior in healthy conditions or in the presence of keratoconus under increasing values of the intraocular pressure. The ability of our model to reproduce the behavior of the human cornea opens a promising perspective for the numerical simulation of refractive surgery.     

The resource-constrained project scheduling model of Bianco and Caramia: clarifications and an alternative model formulation

Recently, Bianco and Caramia (Flex Serv Manuf J 25(1–2), 6–24, 2013) proposed a new model for the resource-constrained project scheduling problem. Despite its potential, the presentation of the mixed-integer programming model contains some ambiguity which may create misunderstanding in the implementation phase. Here, we clarify the definitions of the decision variables and illustrate their corresponding values using a numerical example. Furthermore, we propose a different interpretation of two decision variables which gives rise to an alternative model formulation also presented using the same numerical example.