Behavior and mechanics of dense microgel suspensions.

Suspensions of soft and highly deformable microgels can be concentrated far more than suspensions of hard colloids, leading to their unusual mechanical properties. Microgels can accommodate compression in suspensions in a variety of ways such as interpenetration, deformation, and shrinking. Previous experiments have offered insightful, but somewhat conflicting, accounts of the behavior of individual microgels in compressed suspensions. We develop a mesoscale computational model to probe the behavior of compressed suspensions consisting of microgels with different architectures at a variety of packing fractions and solvent conditions. We find that microgels predominantly change shape and mildly shrink above random close packing. Interpenetration is only appreciable above space filling, remaining small relative to the mean distance between cross-links. At even higher packing fractions, microgels solely shrink. Remarkably, irrespective of the single-microgel properties, and whether the suspension concentration is changed via changing the particle number density or the swelling state of the particles, which can even result in colloidal gelation, the mechanics of the suspension can be quantified in terms of the single-microgel bulk modulus, which thus emerges as the correct mechanical measure for these type of soft-colloidal suspensions. Our results rationalize the many and varied experimental results, providing insights into the relative importance of effects defining the mechanics of suspensions comprising soft particles.

Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic.

In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today's level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than as a powerful scientific method. This position disregards mathematical thinking as having contributed key discoveries in biology for more than a century, e.g., in the connection between genes, inheritance, and evolution or in the mechanisms of enzymatic catalysis. Here, we discuss the role of computational modelling in the arsenal of modern scientific methods in biomedicine. We list frequent misconceptions about mathematical modelling found among biomedical experimentalists and suggest some good practices that can help bridge the cognitive gap between modelers and experimental researchers in biomedicine. This manuscript was written with two readers in mind. Firstly, it is intended for mathematical modelers with a background in physics, mathematics, or engineering who want to jump into biomedicine. We provide them with ideas to motivate the use of mathematical modelling when discussing with experimental partners. Secondly, this is a text for biomedical researchers intrigued with utilizing mathematical modelling to investigate the pathophysiology of human diseases to improve their diagnostics and treatment.

The role of cooperativity in a p53-miR34 dynamical mathematical model.

The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal mathematical model describing the interactions between p53 and miR-34a. The model equations are analyzed for negative, none and normal cooperativity using a specific version of bifurcation theory and they are solved numerically. Special attention is paid to the sign of so-called first Lyapunov value. Interpretations of the results are given, both according to dynamic theory and in biological terms. In terms of cell signaling, we propose the hypothesis that when the outgoing signal of a system spends a physiologically significant amount of time outside of its equilibrium state, then the value of that signal can be sampled at any point along the trajectory towards that equilibrium and indeed, at multiple points. Coupled with non-linear behavior, such as that caused by cooperativity, this feature can account for a complex and varied response, which p53 is known for. From dynamical point of view, we found that when cooperativity is negative, the system has only one stable equilibrium point. In the absence of cooperativity, there is a single unstable equilibrium point with a critical boundary of stability. In the case with normal cooperativity, the system can have one, two, or three steady states with both, bi-stability and bi-instability occurring.

Use of a Real-Time Stress Map for Assessment of Applied Stress for Strain Elastography: Utility in Training and Computation of Strain Ratios.

OBJECTIVES: There is a significant learning curve in strain elastography. Uniform appropriate levels of stress must be applied for accurate elastograms. If the stress is not applied appropriately, inaccurate results will be obtained, particularly when strain ratios are being estimated. This paper describes a new technique which allows the real-time visualization of the applied stress with a color-coded stress map. The potential use of this map is discussed. METHODS: Ten patients (5 breast, 5 thyroid) and phantoms were scanned using the stress map. The stress applied was varied and the resultant change in the strain image evaluated. RESULTS: The stress map was able to document if appropriate stress was applied when performing strain elastography. When inappropriate stress was applied or physiological process effected the strain image the stress map demonstrated the areas of inaccurate measurements in the stress map. CONCLUSIONS: The display of a stress map that depicts the degree and uniformity of applied stress would be helpful both for training of the appropriate technique, for confirming that the elastogram is appropriate for evaluation, and that strain ratio estimates are accurate.

Hierarchical Levels of Biological Systems and their Integration as a Principal Cause for Tumour Occurrence.

The development of new theories, mathematical methods and models for effective control of complex systems is one of the main problems for modern science. Biological systems are complex and hierarchically organized, with the behaviour of higher levels influencing the dynamics of the lower ones and vice versa. Hierarchical organization can be observed from subcellular to supercellular levels. When biological systems are far from their steady states, then nonlinear dependences take place, and a slight external impact can cause unexpected and unpredictable (chaotic, irregular) behaviour in these systems, resulting in fractal hierarchical structures. By examining tumours as strange (chaotic) attractors, we define in this article the hypothesis that the cause of their occurrence, development and spread (metastasis) is due to disorders in the hierarchical structure and integration of cell signalling pathways in tumour cells. An essential point in this article is the thesis (contrary to the view that the only causality in hierarchical systems is physical causality, i.e. there is no "top-down,' "holistic causality,' "intelligent causality,' etc.) that hierarchical systems are built on the principle of communication. Intelligent systems (in particular biological) that do not interact as mechanical objects, but on the basis of different meanings of biochemical signals obtained after their interpretation, participate in this communication.

Model-Based Phenotypic Signatures Governing the Dynamics of the Stem and Semi-differentiated Cell Populations in Dysplastic Colonic Crypts.

Mathematical modeling of cell differentiated in colonic crypts can contribute to a better understanding of basic mechanisms underlying colonic tissue organization, but also its deregulation during carcinogenesis and tumor progression. Here, we combined bifurcation analysis to assess the effect that time delay has in the complex interplay of stem cells and semi-differentiated cells at the niche of colonic crypts, and systematic model perturbation and simulation to find model-based phenotypes linked to cancer progression. The models suggest that stem cell and semi-differentiated cell population dynamics in colonic crypts can display chaotic behavior. In addition, we found that clinical profiling of colorectal cancer correlates with the in silico phenotypes proposed by the mathematical model. Further, potential therapeutic targets for chemotherapy resistant phenotypes are proposed, which in any case will require experimental validation.

Hybrid modeling of the crosstalk between signaling and transcriptional networks using ordinary differential equations and multi-valued logic.

A decade of successful results indicates that systems biology is the appropriate approach to investigate the regulation of complex biochemical networks involving transcriptional and post-transcriptional regulations. It becomes mandatory when dealing with highly interconnected biochemical networks, composed of hundreds of compounds, or when networks are enriched in non-linear motifs like feedback and feedforward loops. An emerging dilemma is to conciliate models of massive networks and the adequate description of non-linear dynamics in a suitable modeling framework. Boolean networks are an ideal representation of massive networks that are humble in terms of computational complexity and data demand. However, they are inappropriate when dealing with nested feedback/feedforward loops, structural motifs common in biochemical networks. On the other hand, models of ordinary differential equations (ODEs) cope well with these loops, but they require enormous amounts of quantitative data for a full characterization of the model. Here we propose hybrid models, composed of ODE and logical sub-modules, as a strategy to handle large scale, non-linear biochemical networks that include transcriptional and post-transcriptional regulations. We illustrate the construction of this kind of models using as example a regulatory network centered on E2F1, a transcription factor involved in cancer. The hybrid modeling approach proposed is a good compromise between quantitative/qualitative accuracy and scalability when considering large biochemical networks with a small highly interconnected core, and module of transcriptionally regulated genes that are not part of critical regulatory loops. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai.

Self-(Un)rolling Biopolymer Microstructures: Rings, Tubules, and Helical Tubules from the Same Material.

We have demonstrated the facile formation of reversible and fast self-rolling biopolymer microstructures from sandwiched active-passive, silk-on-silk materials. Both experimental and modeling results confirmed that the shape of individual sheets effectively controls biaxial stresses within these sheets, which can self-roll into distinct 3D structures including microscopic rings, tubules, and helical tubules. This is a unique example of tailoring self-rolled 3D geometries through shape design without changing the inner morphology of active bimorph biomaterials. In contrast to traditional organic-soluble synthetic materials, we utilized a biocompatible and biodegradable biopolymer that underwent a facile aqueous layer-by-layer (LbL) assembly process for the fabrication of 2D films. The resulting films can undergo reversible pH-triggered rolling/unrolling, with a variety of 3D structures forming from biopolymer structures that have identical morphology and composition.

Long-living periodic solutions of complex cubic-quintic Ginzburg-Landau equation in the presence of intrapulse Raman scattering: A bifurcation and numerical study.

We have found long-living periodic solutions of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) perturbed with intrapulse Raman scattering. To achieve this we have applied a model system of ordinary differential equations (SODE). A set of the fixed points of the system has been described. A complete phase portrait as well as phase portraits near the fixed points have been built for a proper choice of parameters. The behavior of the model system near the fixed points has been determined. We have presented a detailed description of the subcritical Poincaré-Andronov-Hopf bifurcation due to the intrapulse Raman scattering that appears at one of the fixed points. We have established that there appears an unstable limit cycle in the SODE. To check the validity of the obtained results from the model system we have compared them with the results of the numerical solution of the CCQGLE perturbed with intrapulse Raman scattering. There has been found a remarkable correspondence between the obtained numerical results for the amplitude and frequency of the soliton pulses and the results for these parameters of the bifurcation theory. We have observed that the numerical characteristics of the propagating solitonlike pulses-amplitude, frequency, width, and position-periodically change if we change the distance with a period determined by the bifurcation analysis.

Can DNA barcoding be used to identify closely related Clunio Haliday, 1855 species (Diptera: Chironomidae, Orthocladiinae)?

DNA barcoding based on a fragment of mitochondrial Cytochrome C Oxidase subunit 1 gene (COI) was applied to the two chironomids Clunio balticus Heimbach (690 base pairs) and C. ponticus Michailova (691 base pairs). The two species differed by one deletion in the nucleotide sequence Adenine. However, the 658-nucleotide long sequences of DNA from the mitochondrial Cytochrome C Oxidase subunit 1 gene (COI) of C. balticus and C. ponticus were identical upon comparison. Further, they compared with homologous sequences for C. marinus Holiday and C. tsushimensis Tokunaga from the Barcode of Life (BOLD) database and the results plotted as a weighted graph, where C. tsushimensis, C. marinus and C. balticus C. ponticus formed three almost equidistant groups. From this, we established that the genetic distance between the respective COI sequences of C. balticus and C. ponticus is minimal, indicating a close relationship between the species indicative of recent common origin. However, the comparative analysis between C. tsushimensis, C. marinus, C. balticus and C. ponticus showed a wider divergence in their respective nucleotide sequences. Overall, our results emphasized that the COI region does not work well as a DNA barcode to identify species within the Clunio genus. Either longer sequences or a multifaceted methodological approach, including morphology, cytogenetic and ecology is needed to distinguish some members of Clunio genus.

Platelet heterogeneity enhances blood clot volumetric contraction: An example of asynchrono-mechanical amplification.

Physiological processes such as blood clotting and wound healing as well as pathologies such as fibroses and musculoskeletal contractures, all involve biological materials composed of a contracting cellular population within a fibrous matrix, yet how the microscale interactions among the cells and the matrix lead to the resultant emergent behavior at the macroscale tissue level remains poorly understood. Platelets, the anucleate cell fragments that do not divide nor synthesize extracellular matrix, represent an ideal model to study such systems. During blood clot contraction, microscopic platelets actively pull fibers to shrink the macroscale clot to less than 10% of its initial volume. We discovered that platelets utilize a new emergent behavior, asynchrono-mechanical amplification, to enhanced volumetric material contraction and to magnify contractile forces. This behavior is triggered by the heterogeneity in the timing of a population of actuators. This result indicates that cell heterogeneity, often attributed to stochastic cell-to-cell variability, can carry an essential biophysical function, thereby highlighting the importance of considering 4 dimensions (space + time) in cell-matrix biomaterials. This concept of amplification via heterogeneity can be harnessed to increase mechanical efficiency in diverse systems including implantable biomaterials, swarm robotics, and active polymer composites.

Absolute Monocyte and Platelet Counts May Provide Additional Prognostic Information in Primary Gastric Diffuse Large B-cell Lymphoma Patients Treated with Rituximab and CHOP.

INTRODUCTION: Primary gastric diffuse large B cell lymphoma (PG-DLBCL) is the most common histological subtype of primary gastric lymphoma. The standard of care of PG-DLBCL patients is the combination rituximab-based immunochemotherapy (R-CHOP). Re-cently, different host-related factors have been shown to have significant prognostic significance in non-Hodgkin lymphoma. However, data regarding their prognostic contribution to PG-DLBCL are limited. AIM: To assess the prognostic impact of a panel of simple, cost-effective laboratory variables which are easy to apply in routine labora-tory use for R-CHOP-treated PG-DLBCL patients in an attempt to identify those among them that are high-risk category. MATERIALS AND METHODS: We retrospectively assessed the possible prognostic impact of different laboratory markers in 42 R-CHOP treated PG-DLBCL patients treated between 2004 and 2014 and followed at a single institution. RESULTS: The estimated 5-year overall (OS) and progression-free survival (PFS) of the whole group were 80.9% and 78%, respectively. The absolute monocyte and platelet counts in univariate analysis predicted PFS and OS when analyzed as continuous and dichotomized variables. On multivariate analysis performed with factors included in the stage-modified International Prognostic Index (m-IPI), the absolute monocyte and platelet counts remained independent predictors of PFS and OS. Therefore, the absolute monocyte and platelet counts were combined to generate a prognostic index that identified patients with an especially poor overall survival. CONCLUSIONS: This prognostic index was independent of the m-IPI and could provide additional prognostic information for better stratification of these patients.

Phagocyte-Inspired Smart Microcapsules.

Phagocytes protect the organism by ingesting harmful foreign particles and cells. We use mesoscale computer simulations to design a phagocyte-inspired active microcapsule that is capable of selectively capturing nanoparticles dispersed in solvent. Our fully synthetic microdevice is actuated by a temperature-sensitive microgel enclosed inside a perforated spherical shell. The shell pores are decorated with a copolymer brush that regulates the transport of solutes into the capsule interior. When exposed to an external stimulus, the microgel swells, expanding through the shell pores to make contact with the nanoparticle-rich solution surrounding the capsule. Upon removal of the external stimulus, the gel retracts back into the shell, bringing along with it captured nanoparticles. We probe how periodic application of the stimulus combined with nanoparticle-microgel adhesion enable selectivity and enhance capturing efficiency of our nature-inspired microdevice.

Imaging Performance for Two Row-Column Arrays.

This study evaluates the volumetric imaging performance of two prototyped 62 + 62 row-column-addressed (RCA) 2-D array transducer probes using three synthetic aperture imaging (SAI) emission sequences and two different beamformers. The probes are fabricated using capacitive micromachined ultrasonic transducer (CMUT) and piezoelectric transducer (PZT) technology. Both have integrated apodization to reduce ghost echoes and are designed with similar acoustical features, i.e., 3-MHz center frequency, λ /2 pitch, and [Formula: see text] active footprint. Raw RF data are obtained using an experimental research ultrasound scanner, SARUS. The SAI sequences are designed for imaging down to 14 cm at a volume rate of 88 Hz. Two beamforming methods, spatial matched filtering and row-column adapted delay-and-sum, are used for beamforming the RF data. The imaging quality is investigated through simulations and phantom measurements. Both probes on average have similar lateral full-width at half-maximum (FWHM) values, but the PZT probe has 20% smaller cystic resolution values and 70% larger contrast-to-noise ratio (CNR) compared to the capacitive micromachined ultrasonic transducer (CMUT) probe. The CMUT probe can penetrate down to 15 cm, and the PZT probe down to 30 cm. The CMUT probe has 17% smaller axial FWHM values. The matched filter focusing shows an improved B-mode image for measurements on a cyst phantom with an improved speckle pattern and better visualization of deeper lying cysts. The results of this study demonstrate the potentials of RCA 2-D arrays against fully addressed 2-D arrays, which are low channel count (e.g., 124 instead of 3844), low acoustic intensity mechanical index (MI ≤ 0.88 and spatial-peak-temporal-average intensity [Formula: see text]), and high penetration depth (down to 30 cm), which makes 3-D imaging at high volume rates possible with equipment in the price range of conventional 2-D imaging.

Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization.

We model the elastic properties of bone at the level of mineralized collagen fibrils via step-by-step homogenization from the staggered arrangement of collagen molecules up to an array of parallel mineralized fibrils. A new model for extrafibrillar mineralization is proposed, assuming that the extrafibrillar minerals are mechanically equivalent to reinforcing rings coating each individual fibril. Our modeling suggests that no more than 30% of the total mineral content is extrafibrillar and the fraction of extrafibrillar minerals grows linearly with the overall degree of mineralization. It is shown that the extrafibrillar mineralization considerably reinforces the fibrils' mechanical properties in the transverse directions and the fibrils' shear moduli. The model predictions for the elastic moduli and constants are found to be in a good agreement with the experimental data reported in the literature.

Dynamic properties of a delayed protein cross talk model.

In this paper we investigate how the inclusion of time delay alters the dynamical properties of the Jacob-Monod model, describing the control of the beta-galactosidase synthesis by the lac repressor protein in E. coli. The consequences of a time delay on the dynamics of this system are analysed using Hopf's theorem and Lyapunov-Andronov's theory applied to the original mathematical model and to an approximated version. Our analytical calculations predict that time delay acts as a key bifurcation parameter. This is confirmed by numerical simulations. A critical value of time delay, which depends on the values of the model parameters, is analytically established. Around this critical value, the properties of the system change drastically, allowing under certain conditions the emergence of stable limit cycles, that is self-sustained oscillations. In addition, the features of the end product repression play an essential role in the characterisation of these limit cycles: if cooperativity is considered in the end product repression, time delay higher than the mentioned critical value induce differentiated responses during the oscillations, provoking cycles of all-or-nothing response in the concentration of the species.

Curvilinear 3-D Imaging Using Row-Column-Addressed 2-D Arrays With a Diverging Lens: Phantom Study.

A double-curved diverging lens over the flat row-column-addressed (RCA) 2-D array can extend its inherent rectilinear 3-D imaging field of view (FOV) to a curvilinear volume region, which is necessary for applications such as abdominal and cardiac imaging. Two concave lenses with radii of 12.7 and 25.4 mm were manufactured using RTV664 silicone. The diverging properties of the lenses were evaluated based on simulations and measurements on several phantoms. The measured FOV for both lenses in contact with tissue mimicking phantom was less than 15% different from the theoretical predictions, i.e., a curvilinear FOV of and for the 12.7- and 25.4-mm radii lenses. A synthetic aperture imaging sequence with single-element transmissions was designed for imaging down to 140 mm at a volume rate of 88 Hz. The performance was evaluated in terms of signal-to-noise ratio, FOV, and full-width at half-maximum (FWHM) of a focused beam. The penetration depths in a tissue mimicking phantom with 0.5-dB/(cm MHz) attenuation were 100 and 125 mm for the lenses with radii of 12.7 and 25.4 mm. The azimuth, elevation, and radial FWHM at 43-mm depth were (5.8, 5.8, 1) and (6, 6, 1) . The results of this study confirm that the proposed lens approach is an effective method for increasing the FOV, when imaging with RCA 2-D arrays.

Extreme thermodynamics with polymer gel tori: Harnessing thermodynamic instabilities to induce large-scale deformations.

When a swollen, thermoresponsive polymer gel is heated in a solvent bath, it expels solvent and deswells. When this heating is slow, deswelling proceeds homogeneously, as observed in a toroid-shaped gel that changes volume while maintaining its toroidal shape. By contrast, if the gel is heated quickly, an impermeable layer of collapsed polymer forms and traps solvent within the gel, arresting the volume change. The ensuing evolution of the gel then happens at fixed volume, leading to phase separation and the development of inhomogeneous stress that deforms the toroidal shape. We observe that this stress can cause the torus to buckle out of the plane, via a mechanism analogous to the bending of bimetallic strips upon heating. Our results demonstrate that thermodynamic instabilities, i.e., phase transitions, can be used to actuate mechanical deformation in an extreme thermodynamics of materials.

Principal difference between stability and structural stability (robustness) as used in systems biology.

The concepts stability and structural stability (robustness) are used often in systems biology. According to Kitano (2004) robustness is a fundamental property of evolvable complex biological systems. For that reason, the purpose of this review is to clarify: (a) how are strictly formulated concepts, such as stability and robustness of a dynamical system, used in computational systems biology; (b) what is meant by structural stability (robustness) in contemporary biology and how are stability and robustness distinguished from each other; and (c) why is it necessary to investigate whether a cell signal pathway is stable. We formulate the two concepts stability and structural stability (robustness) of a dynamical system with an arbitrary dimensionality, in the way they are known in mathematics and mechanics, and clarify the principal difference between them. We also consider how these two concepts are used in the analysis of a concrete biological system in systems biology. In the last section we formulate when, according to us, in biology (and in systems biology in particular), it should be said that a system (process) is stable, and when it is structurally stable.