Diffusion Equation-Assisted Markov Chain Monte Carlo Methods for the Inverse Radiative Transfer Equation

Optical tomography is the process of reconstructing the optical properties of biological tissue using measurements of incoming and outgoing light intensity at the tissue boundary. Mathematically, light propagation is modeled by the radiative transfer equation (RTE), and optical tomography amounts to reconstructing the scattering coefficient in the RTE using the boundary measurements. In the strong scattering regime, the RTE is asymptotically equivalent to the diffusion equation (DE), and the inverse problem becomes reconstructing the diffusion coefficient using Dirichlet and Neumann data on the boundary. We study this problem in the Bayesian framework, meaning that we examine the posterior distribution of the scattering coefficient after the measurements have been taken. However, sampling from this distribution is computationally expensive, since to evaluate each Markov Chain Monte Carlo (MCMC) sample, one needs to run the RTE solvers multiple times. We therefore propose the DE-assisted two-level MCMC technique, in which bad samples are filtered out using DE solvers that are significantly cheaper than RTE solvers. This allows us to make sampling from the RTE posterior distribution computationally feasible.

Long-Range Capture and Delivery of Water-Dispersed Nano-objects by Microbubbles Generated on 3D Plasmonic Surfaces

The possibility of investigating small amounts of molecules, moieties, or nano-objects dispersed in solution constitutes a central step for various application areas in which high sensitivity is necessary. Here, we show that the rapid expansion of a water bubble can act as a fast-moving net for molecules or nano-objects, collecting the floating objects in the surrounding medium in a range up to 100 μm. Thanks to an engineered 3D patterning of the substrate, the collapse of the bubble could be guided toward a designed area of the surface with micrometric precision. Thus, a locally confined high density of particles is obtained, ready for evaluation by most optical/spectroscopic detection schemes. One of the main relevant strengths of the long-range capture and delivery method is the ability to increase, by a few orders of magnitude, the local density of particles with no changes in their physiological environment. The bubble is generated by an ultrafast IR laser pulse train focused on a resonant plasmonic antenna; due to the excitation process, the technique is trustworthy and applicable to biological samples. We have tested the reliabilities of the process by concentrating highly dispersed fluorescence molecules and fluorescent beads. Lastly, as an ultimate test, we have applied the bubble clustering method on nanosized exosome vesicles dispersed in water; due to the clustering effect, we were able to effectively perform Raman spectroscopy on specimens that were otherwise extremely difficult to measure.

Birth-jump processes and application to forest fire spotting

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Rate Dynamics of Leaky Integrate-and-Fire Neurons with Strong Synapses

Firing-rate models provide a practical tool for studying the dynamics of trial- or population-averaged neuronal signals. A wealth of theoretical and experimental studies has been dedicated to the derivation or extraction of such models by investigating the firing-rate response characteristics of ensembles of neurons. The majority of these studies assumes that neurons receive input spikes at a high rate through weak synapses (diffusion approximation). For many biological neural systems, however, this assumption cannot be justified. So far, it is unclear how time-varying presynaptic firing rates are transmitted by a population of neurons if the diffusion assumption is dropped. Here, we numerically investigate the stationary and non-stationary firing-rate response properties of leaky integrate-and-fire neurons receiving input spikes through excitatory synapses with alpha-function shaped postsynaptic currents for strong synaptic weights. Input spike trains are modeled by inhomogeneous Poisson point processes with sinusoidal rate. Average rates, modulation amplitudes, and phases of the period-averaged spike responses are measured for a broad range of stimulus, synapse, and neuron parameters. Across wide parameter regions, the resulting transfer functions can be approximated by a linear first-order low-pass filter. Below a critical synaptic weight, the cutoff frequencies are approximately constant and determined by the synaptic time constants. Only for synapses with unrealistically strong weights are the cutoff frequencies significantly increased. To account for stimuli with larger modulation depths, we combine the measured linear transfer function with the nonlinear response characteristics obtained for stationary inputs. The resulting linear-nonlinear model accurately predicts the population response for a variety of non-sinusoidal stimuli.

Carbon dioxide hydration activity of carbonic anhydrase: paradoxical consequences of the unusually rapid catalysis

The kinetic parameters for carbon dioxide hydration catalysis by carbonic anhydrase (EC 4.2.1.1) present an apparent paradox. The assumption of H(2)CO(3) as the hydration product requires the rate of recombination of H(2)CO(3) with enzyme to be faster than the diffusion limit. The alternative assumption of HCO(3) (-) as the product of hydration likewise requires active-site ionization rates to exceed the diffusion limit. We previously postulated the presence of special means for rapid active-site ionization. It is shown here that when proton transfer between enzyme and buffer species is taken into account, there is no need to invoke rates exceeding the diffusion limit. Bicarbonate ion thus appears as the most probable hydration product and dehydration substrate.