Applications of second harmonic generation (SHG)/sum-frequency generation (SFG) imaging for biophysical characterization of the plasma membrane

The plasma membrane is a lipid bilayer of < 10 nm width that separates intra- and extra-cellular environments and serves as the site of cell-cell communication, as well as communication between cells and the extracellular environment. As such, biophysical phenomena at and around the plasma membrane play key roles in determining cellular physiology and pathophysiology. Thus, the selective visualization and characterization of the plasma membrane are crucial aspects of research in wide areas of biology and medicine. However, the specific characterization of the plasma membrane has been a challenge using conventional imaging techniques, which are unable to effectively distinguish between signals arising from the plasma membrane and those from intracellular lipid structures. In this regard, interface-specific second harmonic generation (SHG) and sum-frequency generation (SFG) imaging demonstrate great potential. When combined with exogenous SHG/SFG active dyes, SHG/SFG can specifically highlight the plasma membrane as the most prominent interface associated with cells. Furthermore, SHG/SFG imaging can be readily extended to multimodal multiphoton microscopy with simultaneous occurrence of other multiphoton phenomena, including multiphoton excitation and coherent Raman scattering, which shed light on the biophysical properties of the plasma membrane from different perspectives. Here, we review traditional and current applications, as well as the prospects of long-known but unexplored SHG/SFG imaging techniques in biophysics, with special focus on their use in the biophysical characterization of the plasma membrane.     

Non-identifiability of the Rayleigh damping material model in Magnetic Resonance Elastography

Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Magnetic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, _μI${\mu }_I$ and _ρI${\rho }_I$.     

Dynamic stability of a human standing on a balance board

The neuromuscular system used to stabilize upright posture in humans is a nonlinear dynamical system with time delays. The analysis of this system is important for improving balance and for early diagnosis of neuromuscular disease. In this work, we study the dynamic coupling between the neuromuscular system and a balance board—an unstable platform often used to improve balance in young athletes, and older or neurologically impaired patients. Using a simple inverted pendulum model of human posture on a balance board, we describe a surprisingly broad range of divergent and oscillatory CoP/CoM responses associated with instabilities of the upright equilibrium. The analysis predicts that a variety of sudden changes in the stability of upright postural equilibrium occurs with slow continuous deterioration in balance board stiffness, neuromuscular gain, and time delay associated with the changes in proprioceptive/vestibular/visual-neuromuscular feedback. The analysis also provides deeper insight into changes in the control of posture that enable stable upright posture on otherwise unstable platforms.     

Voice disorders assessed by (cross-) Sample Entropy of electroglottogram and microphone signals

The quantitative analysis of vocal disorders by nonlinear signal processing methods has been extensively used in the last two decades. In this work, two algorithms for nonlinear time-series analysis, Sample Entropy and cross-Sample Entropy, are used on electroglottogram (EGG) and microphone (MIC) signals recorded from 51 normal and 80 dysphonic subjects, to obtain summary measures of voice disorders through SampEn and cross-SampEn indices. Such parameters quantify, respectively, the degree of irregularity (in the sense of self-dissimilarity) within a time-series and of asynchrony (in the sense of cross-dissimilarity) between two distinct time-series. The aims of this work are: to determine if statistically significant differences in terms of signal irregularity quantified by SampEn occur between normal and pathological subjects, investigating whether or not such differences can be equally seen in EGG and MIC; to assess if cross-SampEn reveals different degrees of asynchrony between EGG and MIC signals in the two groups. Results show that SampEn in pathological subjects is higher than in normal subjects for both EGG and MIC time-series, with a statistically significant difference detectable from both signals (Pe < 10^?4 for EGG and Pe < 10^?7 for MIC). Cross-SampEn exhibits a statistically significant difference too, showing a higher degree of cross-dissimilarity between EGG and MIC time-series for pathological subjects (Pe < 10^?4). In conclusion, SampEn and cross-SampEn well quantify the increase of complexity of both EGG and MIC signals and the decrease of their cross-similarity in presence of vocal disorders. Thanks to the complementarity of nonlinear indicators to the traditionally considered linear ones, SampEn and cross-SampEn appear as suitable candidates to enter the pool of approaches to investigate speech pathologies and to obtain potentially new insights on their nature.     

Analysis of multitemperature isothermal titration calorimetry data at very low c: Global beats van't Hoff

Isothermal titration calorimetry data for very low c (≡K[M]₀) must normally be analyzed with the stoichiometry parameter n fixed — at its known value or at any reasonable value if the system is not well characterized. In the latter case, ΔH° (and hence n) can be estimated from the T-dependence of the binding constant K, using the van't Hoff (vH) relation. An alternative is global or simultaneous fitting of data at multiple temperatures. In this Note, global analysis of low-c data at two temperatures is shown to estimate ΔH° and n with double the precision of the vH method.     

Algebraic structures generating reaction-diffusion models: The activator-substrate system

We shall construct a class of nonlinear reaction-diffusion equations starting from an infinitesimal algebraic skeleton. Our aim is to explore the possibility of an algebraic foundation of integrability properties and of stability of equilibrium states associated with nonlinear models describing patterns formation.     

Nonlinear modelling of renal vasoaction

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions are useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus, modelling of such physiological systems can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the influence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood flow rates. This paper proposes a number of nonlinear mathematical models for the relationship between neural influences (sympathetic nerve activity (SNA)) and renal blood flow, using a feedback path to model the predominantly nonlinear effect of local vasoactive modulators such as nitric oxide, which oppose the action of SNA. The model structures are motivated by basic physiological principles, while the model parameters are determined using numerical optimisation techniques using open-loop data collected from rabbits. The models were verified by demonstrating correlation between experimental results and model outputs.     

Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting

Objective functions that arise when fitting nonlinear models often contain local minima that are of little significance except for their propensity to trap minimization algorithms. The standard methods for attempting to deal with this problem treat the objective function as fixed and employ stochastic minimization approaches in the hope of randomly jumping out of local minima. This article suggests a simple trick for performing such minimizations that can be employed in conjunction with most conventional nonstochastic fitting methods. The trick is to stochastically perturb the objective function by bootstrapping the data to be fit. Each bootstrap objective shares the large-scale structure of the original objective but has different small-scale structure. Minimizations of bootstrap objective functions are alternated with minimizations of the original objective function starting from the parameter values with which minimization of the previous bootstrap objective terminated. An example is presented, fitting a nonlinear population dynamic model to population dynamic data and including a comparison of the suggested method with simulated annealing. Convergence diagnostics are discussed.     

A model for thermograms

Thermograms are curves resulting from thermal analysis and are of great interest in the study of various food and biological products physical properties. A method to separate underlying peaks is proposed, and statistical properties of estimates for some characteristic parameters are derived. The total number of peaks can be estimated with a sequential analysis of the residual plots. For each new peak, a statistical criterion is proposed to check whether it is significantly different from the noise of the recording. As an example, the method is applied to a summer milk fat fusion thermogram.     

Stochastic models for cell motion and taxis

Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using stochastic differential equations. These models suggest statistics for quantifying experimental results and testing relevant hypotheses, and carry implications for the qualitative behavior of cells and for underlying biophysical mechanisms. Directional cell motion in response to a stimulus, termed taxis, has previously been modeled at a phenomenological level using the Keller-Segel diffusion equation. The Keller-Segel model cannot distinguish certain modes of taxis, and this motivates the introduction of a richer class of models which is nevertheless still amenable to statistical analysis. A state space model formulation is used to link models proposed for cell velocity to observed data. Sequential Monte Carlo methods enable parameter estimation via maximum likelihood for a range of applicable models. One particular experimental situation, involving the effect of an electric field on cell behavior, is considered in detail. In this case, an Ornstein- Uhlenbeck model for cell velocity is found to compare favorably with a nonlinear diffusion model.