Algorithm for Mesoscopic Advection-Diffusion

On predicting heterogeneity in nanoparticle dosage

Nanoparticles are increasingly employed as a vehicle for the targeted delivery of therapeutics to specific cell types. However, much remains to be discovered about the fundamental biology that dictates the interactions between nanoparticles and cells. Accordingly, few nanoparticle-based targeted therapeutics have succeeded in clinical trials. One element that hinders our understanding of nanoparticle-cell interactions is the presence of heterogeneity in nanoparticle dosage data obtained from standard experiments. It is difficult to distinguish between heterogeneity that arises from stochasticity in nanoparticle-cell interactions, and that which arises from heterogeneity in the cell population. Mathematical investigations have revealed that both sources of heterogeneity contribute meaningfully to the heterogeneity in nanoparticle dosage. However, these investigations have relied on simplified models of nanoparticle internalisation. Here we present a stochastic mathematical model of nanoparticle internalisation that incorporates a suite of relevant biological phenomena such as multistage internalisation, cell division, asymmetric nanoparticle inheritance and nanoparticle saturation. Critically, our model provides information about nanoparticle dosage at an individual cell level. We perform model simulations to examine the influence of specific biological phenomena on the heterogeneity in nanoparticle dosage in the absence of heterogeneity in the cell population. Under certain modelling assumptions, we derive analytic approximations of the nanoparticle dosage distribution. We demonstrate that the analytic approximations are accurate, and show that nanoparticle dosage can be described by a Poisson mixture distribution with rate parameters that are a function of Beta-distributed random variables. We discuss the implications of the analytic results with respect to parameter estimation and model identifiability from standard experimental data. Finally, we highlight extensions and directions for future research.

A Simple Queuing Model for Molecular Communications Receivers

The complexity of molecular communications system, involving a massive number of interacting entities, makes scalability a fundamental property of simulators and modeling tools. A typical scenario is that of targeted drug delivery systems, which makes use of biological nanomachines close to a biological target, able to release molecules in the diseased area. In this paper, we propose a simple but reliable receiver model for diffusion-based molecular communication systems tackling the time needed for analyzing such a system. The proposed model consists of using an equivalent markovian queuing model, which reproduces the aggregate behavior of thousands of receptors spread over the receiver surface. It takes into account not only the fact that the absorption of molecules can occur only through receptors, but also that absorption is not an instantaneous process and may require a significant time during which the receptor is not available to bind to other molecules. Our results, expressed in terms of number of absorbed molecules and average number of busy receptors, demonstrate that the proposed approach is in good agreement with results obtained through particle-based simulations of a large number of receptors, although the time taken for obtaining the results with the proposed model is an order of magnitudes lower than the simulation time. We believe that this model can be the precursor of novel class of models based on similar principles that allow realizing reliable simulations of much larger systems.

On Gradient Descent Optimization in Diffusion-Advection Based 3-D Molecular Cooperative Communication

This work considers a cooperative communication system in 3-D fluid medium in which the flow of molecules is supported by the drift and the diffusion phenomena. To enhance the system performance, the equal gain combining is used at the destination nanomachine (DN) where the molecular signals arriving from the direct and the cooperative paths are combined together by employing equal weights. Using the gradient descent algorithm, the optimum threshold at DN, and the optimal number of molecules transmitted from source and cooperative nanomachines are obtained. For this purpose, the convex constraints are determined using the closed-form expression for the average probability of error at DN. Finally, the accuracy of the analytical results is validated through the particle/ Monte Carlo-based simulations.

Isolating the sources of heterogeneity in nano-engineered particle-cell interactions

Nano-engineered particles have the potential to enhance therapeutic success and reduce toxicity-based treatment side effects via the targeted delivery of drugs to cells. This delivery relies on complex interactions between numerous biological, chemical and physical processes. The intertwined nature of these processes has thus far hindered attempts to understand their individual impact. Variation in experimental data, such as the number of particles inside each cell, further inhibits understanding. Here, we present a mathematical framework that is capable of examining the impact of individual processes during particle delivery. We demonstrate that variation in experimental particle uptake data can be explained by three factors: random particle motion; variation in particle-cell interactions; and variation in the maximum particle uptake per cell. Without all three factors, the experimental data cannot be explained. This work provides insight into biological mechanisms that cause heterogeneous responses to treatment, and enables precise identification of treatment-resistant cell subpopulations.