Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

A point electric dipole: From basic optical properties to the fluctuation–dissipation theorem

We comprehensively review the deceptively simple concept of dipole scattering in order to uncover and resolve all ambiguities and controversies existing in the literature. First, we consider a point electric dipole in a non-magnetic environment as a singular point in space whose sole ability is to be polarized due to the external electric field. We show that the postulation of the Green’s dyadic of the specific form provides the unified description of the contribution of the dipole into the electromagnetic properties of the whole space. This is the most complete, concise, and unambiguous definition of a point dipole and its polarizability. All optical properties, including the fluctuation–dissipation theorem for a fluctuating dipole, are derived from this definition. Second, we obtain the same results for a small homogeneous sphere by taking a small-size limit of the Lorenz–Mie theory. Third, and most interestingly, we generalize this microscopic description to small particles of arbitrary shape. Both bare (static) and dressed (dynamic) polarizabilities are defined as the double integrals of the corresponding dyadic transition operator over the particle’s volume. While many derivations and some results are novel, all of them follow from or are connected with the existing literature, which we review throughout the paper

Method for the simulation of blood platelet shape and its evolution during activation

<div><p>We present a simple physically based quantitative model of blood platelet shape and its evolution during agonist-induced activation. The model is based on the consideration of two major cytoskeletal elements: the marginal band of microtubules and the submembrane cortex. Mathematically, we consider the problem of minimization of surface area constrained to confine the marginal band and a certain cellular volume. For resting platelets, the marginal band appears as a peripheral ring, allowing for the analytical solution of the minimization problem. Upon activation, the marginal band coils out of plane and forms 3D convoluted structure. We show that its shape is well approximated by an overcurved circle, a mathematical concept of closed curve with constant excessive curvature. Possible mechanisms leading to such marginal band coiling are discussed, resulting in simple parametric expression for the marginal band shape during platelet activation. The excessive curvature of marginal band is a convenient state variable which tracks the progress of activation. The cell surface is determined using numerical optimization. The shapes are strictly mathematically defined by only three parameters and show good agreement with literature data. They can be utilized in simulation of platelets interaction with different physical fields, e.g. for the description of hydrodynamic and mechanical properties of platelets, leading to better understanding of platelets margination and adhesion and thrombus formation in blood flow. It would also facilitate precise characterization of platelets in clinical diagnosis, where a novel optical model is needed for the correct solution of inverse light-scattering problem.</p></div

Overcurvature (<i>O</i>_p)–Dimensionless volume (<i>v</i>) phase diagram of platelets model morphologies.

<p>Area I corresponds to resting platelets with overcurvature = 1; Area II stands for activated platelets (hypothetically reversible activation); Area III is where platelets become sphered (irreversible activation).</p

All possible axisymmetric profiles of resting platelets as obtained by the solution of variational problem (4).

<p>Black circles correspond to the marginal band cross-sections. Volume increases from top to bottom, curvature increases when going from the first to the fifth row, but decreases for the last row.</p

Possible mechanism of the overcurvature formation.

<p>Molecular motors induce relative sliding of microtubules, which are additionally cross-linked by bridge proteins. This leads to the formation of excessive curvature in the microtubules bundle, which manifests itself by the out-of-plane coiling of marginal band.</p

Illustration of platelet surface optimization problem.

<p>The surface is made by the revolution of profile {<i>x</i>(<i>t</i>), <i>y</i>(<i>t</i>)} (thick line) around the ordinate axis. It consists of two parts: free (light red) and attached to the marginal band (green). Point <i>t</i> = <i>u</i> corresponds to the contact between one of the mobile subdomain and the fixed part, and points <i>t</i> = 0 and <i>t</i> = <i>T</i> are where the the surface intersects the axis <i>x</i> = 0.</p

Scheme of the construction of blood platelet shape model (A–E) and the soap bubble supported by the overcurved wire ring (F), which presents the real-world approximation of the optimization problem solution for the mobile surface parts.

<p>Scheme of the construction of blood platelet shape model (A–E) and the soap bubble supported by the overcurved wire ring (F), which presents the real-world approximation of the optimization problem solution for the mobile surface parts.</p