We consider the lifetime of a T cell clonotype, the set of T cells with the same T cell receptor, from its thymic origin to its extinction in a multiclonal repertoire. Using published estimates of total cell numbers and thymic production rates, we calculate the mean number of cells per TCR clonotype, and the total number of clonotypes, in mice and humans. When there is little peripheral division, as in a mouse, the number of cells per clonotype is small and governed by the number of cells with identical TCR that exit the thymus. In humans, peripheral division is important and a clonotype may survive for decades, during which it expands to comprise many cells. We therefore devise and analyse a computational model of homeostasis of a multiclonal population. Each T cell in the model competes for self pMHC stimuli, cells of any one clonotype only recognising a small fraction of the many subsets of stimuli. A constant mean total number of cells is maintained by a balance between cell division and death, and a stable number of clonotypes by a balance between thymic production of new clonotypes and extinction of existing ones. The number of distinct clonotypes in a human body may be smaller than the total number of naive T cells by only one order of magnitude.

DNA has enormous potential as a programmable material for creating artificial nanoscale structures and devices. For more complex systems, however, rational design and optimization can become difficult. We have recently proposed a coarse-grained model of DNA that captures the basic thermodynamic, structural and mechanical changes associated with the fundamental process in much of DNA nanotechnology, the formation of duplexes from single strands.In this article we demonstrate that the model can provide powerful insight into the operation of complex nanotechnological systems through a detailed investigation of a two-footed DNA

Pharmacokinetic/pharmacodynamic (PKPD) modelling is used to describe and quantify dose–concentration–effect relationships. Within paediatric studies in infectious diseases and immunology these methods are often applied to developing guidance on appropriate dosing. In this paper, an introduction to the field of PKPD modelling is given, followed by a review of the PKPD studies that have been undertaken in paediatric infectious diseases and immunology. The main focus is on identifying the methodological approaches used to define the PKPD relationship in these studies. The major findings were that most studies of infectious diseases have developed a PK model and then used simulations to define a dose recommendation based on a pre-defined PD target, which may have been defined in adults or in vitro. For immunological studies much of the modelling has focused on either PK or PD, and since multiple drugs are usually used, delineating the relative contributions of each is challenging. The use of dynamical modelling of in vitro antibacterial studies, and paediatric HIV mechanistic PD models linked with the PK of all drugs, are emerging methods that should enhance PKPD-based recommendations in the future.

Hematopoietic stem cell transplantation (HSCT) is an increasingly common treatment for children with a range of hematological disorders. Conditioning with cytotoxic chemotherapy and total body irradiation leaves patients severely immunocompromised. T‐cell reconstitution can take several years due to delayed restoration of thymic output. Understanding T‐cell reconstitution in children is complicated by normal immune system maturation, heterogeneous diagnoses, and sparse uneven sampling due to the long time spans involved. We describe here a mechanistic mathematical model for CD4 T‐cell immune reconstitution following pediatric transplantation. Including relevant biology and using mixed‐effects modeling allowed the factors affecting reconstitution to be identified. Bayesian predictions for the long‐term reconstitution trajectories of individual children were then obtained using early post‐transplant data. The model was developed using data from 288 children; its predictive ability validated on data from a further 75 children, with long‐term reconstitution predicted accurately in 81% of the patients.