Biomarkers.

Background: A generative model of tau PET was applied to multiple cohorts across the Alzheimer's disease (AD) spectrum, revealing longitudinal changes in tau production and transport. A generalisation of the model accounts for amyloid, tau and neurodegeneration (ATN) interactions and accurately explains longitudinal ATN biomarker data, adding potential for region specific and individualized tracking of ATN biomarkers.

Method: A model of tau spreading and production as measured through PET was developed and applied to longitudinal data from amyloid negative (A-), amyloid positive tau negative (A+T-) and amyloid positive tau positive (A+T+) cohorts from the Alzheimer's disease neuroimaging iniative (ADNI; N = 159) and BioFINDER-2 (BF2; N = 135) datasets.

Uncovering the mechanical secrets of the squirting cucumber.

Rapid movement is rare in the plant kingdom, but a prerequisite for ballistic seed dispersal. A particularly dramatic example of rapid motion in plants is the squirting cucumber () which launches its seeds explosively via a high-pressure jet. Despite intriguing scientists for centuries, the exact mechanism of seed dispersal and its effect on subsequent generations remain poorly understood.

Broken detailed balance and entropy production in directed networks.

The structure of a complex network plays a crucial role in determining its dynamical properties. In this paper , we show that the the degree to which a network is directed and hierarchically organized is closely associated with the degree to which its dynamics break detailed balance and produce entropy. We consider a range of dynamical processes and show how different directed network features affect their entropy production rate.

Soft cells and the geometry of seashells.

A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. However, many tilings in Nature are characterized by shapes with curved edges, nonflat faces, and few, if any, sharp corners.

Active shape control by plants in dynamic environments.

Plants are a paradigm for active shape control in response to stimuli. For instance, it is well known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimulus, proprioception. These effects can be modulated when a potted plant is additionally rotated along the plant's axis, as in a rotating clinostat, leading to intricate shapes.

Minimal Design of the Elephant Trunk as an Active Filament.

One of the key problems in active materials is the control of shape through actuation. A fascinating example of such control is the elephant trunk, a long, muscular, and extremely dexterous organ with multiple vital functions. The elephant trunk is an object of fascination for biologists, physicists, and children alike.

Neuronal activity induces symmetry breaking in neurodegenerative disease spreading.

Dynamical systems on networks typically involve several dynamical processes evolving at different timescales. For instance, in Alzheimer's disease, the spread of toxic protein throughout the brain not only disrupts neuronal activity but is also influenced by neuronal activity itself, establishing a feedback loop between the fast neuronal activity and the slow protein spreading. Motivated by the case of Alzheimer's disease, we study the multiple-timescale dynamics of a heterodimer spreading process on an adaptive network of Kuramoto oscillators.

Correction to: Mathematical models of neuronal growth.

Correction to: Biomechanics and Modeling in Mechanobiology (2022) 21:89-118 https://doi.org/10.1007/s10237-021-01539-0.

A simple Turing reaction-diffusion model explains how PLK4 breaks symmetry during centriole duplication and assembly.

Centrioles duplicate when a mother centriole gives birth to a daughter that grows from its side. Polo-like-kinase 4 (PLK4), the master regulator of centriole duplication, is recruited symmetrically around the mother centriole, but it then concentrates at a single focus that defines the daughter centriole assembly site. How PLK4 breaks symmetry is unclear.

Mechanics reveals the role of peristome geometry in prey capture in carnivorous pitcher plants ().

Carnivorous pitcher plants () are a striking example of a natural pitfall trap. The trap's slippery rim, or peristome, plays a critical role in insect capture via an aquaplaning mechanism that is well documented. While the peristome has received significant research attention, the conspicuous variation in peristome geometry across the genus remains unexplored.

Cooperative melting in double-stranded peptide chains through local mechanical interactions.

The separation of double-stranded peptide chains can occur in two ways: cooperatively or non-cooperatively. These two regimes can be driven either by chemical or thermal effects, or through non-local mechanical interactions. Here, we show explicitly that local mechanical interactions in biological systems may regulate the stability, the reversibility, and the cooperative/non-cooperative character of the debonding transition.

Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial.

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this tutorial, we formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability.

A multi-scale model explains oscillatory slowing and neuronal hyperactivity in Alzheimer's disease.

Alzheimer's disease is the most common cause of dementia and is linked to the spreading of pathological amyloid- and tau proteins throughout the brain. Recent studies have highlighted stark differences in how amyloid- and tau affect neurons at the cellular scale. On a larger scale, Alzheimer's patients are observed to undergo a period of early-stage neuronal hyperactivation followed by neurodegeneration and frequency slowing of neuronal oscillations.

Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK.

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits.

A mathematical model for the auxetic response of liquid crystal elastomers.

We develop a mathematical model that builds on the surprising nonlinear mechanical response observed in recent experiments on nematic liquid crystal elastomers. Namely, under uniaxial tensile loads, the material, rather than thinning in the perpendicular directions, becomes thicker in one direction for a sufficiently large strain, while its volume remains unchanged. Motivated by this unusual large-strain auxetic behaviour, we model the material using an Ogden-type strain-energy function and calibrate its parameters to available datasets.

Centrioles generate a local pulse of Polo/PLK1 activity to initiate mitotic centrosome assembly.

Mitotic centrosomes are formed when centrioles start to recruit large amounts of pericentriolar material (PCM) around themselves in preparation for mitosis. This centrosome "maturation" requires the centrioles and also Polo/PLK1 protein kinase. The PCM comprises several hundred proteins and, in Drosophila, Polo cooperates with the conserved centrosome proteins Spd-2/CEP192 and Cnn/CDK5RAP2 to assemble a PCM scaffold around the mother centriole that then recruits other PCM client proteins.

Nematic liquid crystalline elastomers are aeolotropic materials.

Continuum models describing ideal nematic solids are widely used in theoretical studies of liquid crystal elastomers. However, experiments on nematic elastomers show a type of anisotropic response that is not predicted by the ideal models. Therefore, their description requires an additional term coupling elastic and nematic responses, to account for aeolotropic effects.

Braiding Braak and Braak: Staging patterns and model selection in network neurodegeneration.

A hallmark of Alzheimer's disease is the aggregation of insoluble amyloid-beta plaques and tau protein neurofibrillary tangles. A key histopathological observation is that tau protein aggregates follow a structured progression pattern through the brain. Mathematical network models of prion-like propagation have the ability to capture such patterns, but a number of factors impact the observed staging result, thus introducing questions regarding model selection.

Mathematical models of neuronal growth.

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites-axons and dendrites-to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment.

The physical basis of mollusk shell chiral coiling.

Snails are model organisms for studying the genetic, molecular, and developmental bases of left-right asymmetry in Bilateria. However, the development of their typical helicospiral shell, present for the last 540 million years in environments as different as the abyss or our gardens, remains poorly understood. Conversely, ammonites typically have a bilaterally symmetric, planispiraly coiled shell, with only 1% of 3,000 genera displaying either a helicospiral or a meandering asymmetric shell.

Effects of B.1.1.7 and B.1.351 on COVID-19 Dynamics: A Campus Reopening Study.

The timing and sequence of safe campus reopening has remained the most controversial topic in higher education since the outbreak of the COVID-19 pandemic. By the end of March 2020, almost all colleges and universities in the United States had transitioned to an all online education and many institutions have not yet fully reopened to date. For a residential campus like Stanford University, the major challenge of reopening is to estimate the number of incoming infectious students at the first day of class.

Theory for Durotactic Axon Guidance.

During the development of the nervous system, neurons extend bundles of axons that grow and meet other neurons to form the neuronal network. Robust guidance mechanisms are needed for these bundles to migrate and reach their functional target. Directional information depends on external cues such as chemical or mechanical gradients.

The mathematical foundations of anelasticity: existence of smooth global intermediate configurations.

A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground.

Global and local mobility as a barometer for COVID-19 dynamics.

The spreading of infectious diseases including COVID-19 depends on human interactions. In an environment where behavioral patterns and physical contacts are constantly evolving according to new governmental regulations, measuring these interactions is a major challenge. Mobility has emerged as an indicator for human activity and, implicitly, for human interactions.