Nano-engineered particles are a promising tool for medical diagnostics, biomedical imaging and targeted drug delivery. Fundamental to the assessment of particle performance are in vitro particle-cell interaction experiments. These experiments can be summarized with key parameters that facilitate objective comparisons across various cell and particle pairs, such as the particle-cell association rate. Previous studies often focus on point estimates of such parameters and neglect heterogeneity in routine measurements. In this study, we develop an ordinary differential equation-based mechanistic mathematical model that incorporates and exploits the heterogeneity in routine measurements. Connecting this model to data using approximate Bayesian computation parameter inference and prediction tools, we reveal the significant role of heterogeneity in parameters that characterize particle-cell interactions. We then generate predictions for key quantities, such as the time evolution of the number of particles per cell. Finally, by systematically exploring how the choice of experimental time points influences estimates of key quantities, we identify optimal experimental time points that maximize the information that is gained from particle-cell interaction experiments.

We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models of flat epithelia to investigate the influence of curvature for mechanical relaxation. We represent the mechanics of a cell body either by straight springs, or by curved springs that follow the curve’s shape. To understand the collective dynamics of the cells, we devise an appropriate continuum limit in which the number of cells and the length of the substrate are constant but the number of springs tends to infinity. In this limit, cell density is governed by a diffusion equation in arc length coordinates, where diffusion may be linear or nonlinear depending on the choice of the spring restoring force law. Our results have important implications about modelling cells on curved geometries: (i) curved and straight springs can lead to different dynamics when there is a finite number of springs, but they both converge quadratically to the dynamics governed by the diffusion equation; (ii) in the continuum limit, the curvature of the tissue does not affect the mechanical relaxation of cells within the layer nor their tangential stress; (iii) a cell’s normal stress depends on curvature due to surface tension induced by the tangential forces. Normal stress enables cells to sense substrate curvature at length scales much larger than their cell body, and could induce curvature dependences in experiments.

Rheological, electrochemical, and microstructural properties of graphene oxide suspensions as flowable electrodes for energy storage.

This paper introduces an inverse design framework for the precise tailoring of desired nonlinear mechanical responses in periodic microstructures, with particular focus on prescribed nonlinear stress–strain relationships. The topology optimization hinges on minimizing the error between the target and realized properties of the microstructures. A deformation-driven homogenization framework is setup. The periodic constraints needed for the microscale equilibrium equation are imposed through strongly enforced periodic boundary conditions and the removal of the translational nullspace, avoiding the need for Lagrange multipliers, greatly simplifying the implementation. Automatic differentiation is leveraged to efficiently calculate the necessary sensitivities for the gradient-based optimization. To further aid the design of discrete designs a intermediate density penalty constraint is proposed. Numerical examples underscore the efficacy of our methodology, showcasing microstructures that demonstrate targeted softening and stiffening as well as distinctive directional behaviour.

Adeno-associated virus (AAV) vectors are used to deliver therapeutic transgenes, but host immune responses may interfere with transduction and transgene expression. We evaluated prophylactic corticosteroid treatment on AAV5-mediated expression in liver tissue. Wild-type C57BL/6 mice received 6 × 1013 vg/kg AAV5-HLP-hA1AT, an AAV5 vector carrying a human α1-antitrypsin (hA1AT) gene with a hepatocyte-specific promoter. Mice received 4 weeks of daily 2 mg/kg prednisolone or water starting day -1 or 0 before vector dosing. Mice that received prophylactic corticosteroids had significantly higher serum hA1AT protein than mice that did not, starting at 6 weeks and persisting to the study end at 12 weeks, potentially through a decrease in the number of low responders. RNAseq and proteomic analyses investigating mechanisms mediating the improvement of transgene expression found that prophylactic corticosteroid treatment upregulated the AAV5 coreceptor platelet-derived growth factor receptor alpha (PDGFRα) on hepatocytes and downregulated its competitive ligand PDGFα, thus increasing the uptake of AAV5 vectors. Evidently, prophylactic corticosteroid treatment also suppressed acute immune responses to AAV. Together, these mechanisms resulted in increased uptake and preservation of the transgene, allowing more vector genomes to be available to assemble into stable, full-length structures mediating long-term transgene expression. Prophylactic corticosteroids represent a potential actionable strategy to improve AAV5-mediated transgene expression and decrease intersubject variability.

Aberrant cell cycle progression is a hallmark of solid tumors. Therefore, cell cycle analysis is an invaluable technique to study cancer cell biology. However, cell cycle progression has been most commonly assessed by methods that are limited to temporal snapshots or that lack spatial information. In this chapter, we describe a technique that allows spatiotemporal real-time tracking of cell cycle progression of individual cells in a multicellular context. The power of this system lies in the use of 3D melanoma spheroids generated from melanoma cells engineered with the fluorescent ubiquitination-based cell cycle indicator (FUCCI). This technique, combined with mathematical modeling, allows us to gain further and more detailed insight into several relevant aspects of solid cancer cell biology, such as tumor growth, proliferation, invasion, and drug sensitivity.

In this paper, a multiscale structural optimization framework capable of efficiently designing two-scale structures with prescribed displacements in the nonlinear elastic regime is presented. In contrast to previous multiscale structural optimization frameworks, which are founded upon the assumptions of linear elasticity, the present framework is capable of efficiently operating within the nonlinear elastic regime. At the core of the present framework is a parameterized microscale geometry, which through the straightforward manipulation of the microscale parameters provides direct access to both positive and negative Poisson’s ratios. The microscale model is concurrently coupled to the macroscale model such that only the microscale parameter space traversed by the optimizer is resolved during the optimization procedure, leading to a significant reduction in the computational expense of analysis. To demonstrate the capability of this framework, three prescribed deformation profiles are targeted by three distinct optimization procedures. In all instances, the deformation profile is successfully targeted. To verify the accuracy of the optimized structures, high-fidelity single-scale simulations are performed. In each case, excellent agreement is noted between the high-fidelity simulations and the corresponding optimized macroscale displacement fields, with errors of less than 10

Throughout the life sciences, we routinely seek to interpret measurements and observations using parametrized mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis and prediction, called profile-wise analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

Partial differential equation (PDE) models are often used to study biological phenomena involving movementbirth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.

In The Narrow Corridor, Acemoglu and Robinson create a compelling narrative concerning the relationship between the power of states, the power of societies, and economic development, illustrated with a series of historical vignettes. Using a recently constructed historical dataset of state capacity, we provide a series of formal and informal tests of their hypothesis. We first visualise the historical paths of the strength of society and the strength of the state for each country so as to operationalise the claims of Acemoglu and Robinson. We then measure whether the balance of the strength of society and the strength of the state is predictive of improvements in both. We find very little evidence in favour of Acemoglu and Robinson.

Background: Hypertrophic cardiomyopathy (HCM) is a life-threatening inherited heart disease characterized by left ventricular hypertrophy and diastolic dysfunction. The most common cause of HCM is genetic variants in MYBPC3 , encoding cardiac myosin binding protein C (cMyBP-C), a sarcomeric protein with structural and regulatory roles. The majority of MYBPC3 gene variants are truncating leading to protein haploinsufficiency. Hypothesis: Transfer of a functional copy of MYBPC3 to heart muscle deficient in cMyBP-C will lead to sustained improvements in cardiac function. Aims: To determine whether BMN 293 (AAV-hMYBPC3) can restore cMyBP-C levels in the sarcomere and halt and/or reverse disease progression in non-clinical models of genetic HCM due to MYPBC3 deficiency. Methods: BMN 293 is an adeno-associated virus (AAV) vector that encodes wild-type human MYBPC3 under the control of a cardiomyocyte-selective promoter. We transduced human iPSC-derived cardiomyocytes and engineered heart tissues (EHTs) carrying a compound heterozygous truncating MYBPC3 mutation (MYBPC3 -/- ) with BMN 293 and assessed cMyBP-C levels and contractile parameters. We also systemically administered BMN 293 to MYBPC3 -/- mice and assessed cardiac distribution of human cMyBP-C by molecular and histological methods and determined its impact on left ventricular hypertrophy and function by echocardiography and other imaging techniques. Results: BMN 293 transduction of human iPSC MYBPC3 -/- cardiomyocytes and EHTs resulted in high levels of human MYBPC3 mRNA and cMyBP-C protein, correct incorporation of cMyBP-C into the sarcomere, and complete normalization of contractile kinetics. BMN 293 was well tolerated in MYBPC3 -/- mice and resulted in uniform restoration of cMyBP-C expression throughout the heart and significant correction of structural and functional cardiac abnormalities. Conclusions: A single IV infusion of BMN 293 to MYBPC3 -/- mice resulted in early and sustained reduction in left ventricular hypertrophy and durable improvements in diastolic function.

Tumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used to understand cancer progression and develop cancer therapies, have been routinely performed for the past fifty years in constant external environments. Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases.

In this work the resonant properties of a series of structurally optimized, additively manufactured lattices are investigated. The hierarchical cantilever-beams are modelled using a multiscale homogenization-based methodology and optimised for minimum compliance subject to varying constraints on their resonant frequencies. Optimisation is performed by spatially-varying the radii of the underlying seven-member open-truss lattice microstructure. This produces a functionally-graded lattice exhibiting vastly superior resonant and mechanical properties in comparison to a uniform lattice of equal mass. The optimized cantilever-beams are manufactured using a titanium alloy, Ti64, on an EOS M290 printer. A full CT scan is conducted on the specimens to determine the print quality and to identify any manufacturing defects. The resonant frequencies of the cantilever-beams are determined experimentally using a mechanical shaker to excite the specimens through a sinusoidal sweep. The measured resonant frequencies are then compared to the predicted values derived through the multiscale model to determine the accuracy of the underlying lattice surrogate model. A discrepancy of 8.5 % is observed between the predicted and measured responses.

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Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret coculture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan’s seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan’s seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.

Dataset by Country of the Economic Freedom of the World: 2023 Annual Report that measures the degree to which the policies and institutions of countries are supportive of economic freedom. The cornerstones of economic freedom are personal choice, voluntary exchange, freedom to enter markets and compete, and security of the person and privately owned property. Forty-two data points are used to construct a summary index, along with a Gender Legal Rights Adjustment to measure the extent to which women have the same level of economic freedom as men. The degree of economic freedom is measured in five broad areas: Size of Government, Legal System and Property Rights, Sound Money, Freedom to Trade Internationally, and Regulation.