Journal of the Royal Society Interface

Chemotaxis, or directed motion in chemical gradients, is critical for various biological processes. Many eukaryotic cells perform spatial sensing, i.e. they detect gradients by comparing spatial differences in binding occupancy of chemosensory receptors across their membrane. In many theoretical models of spatial sensing, it is assumed, for the sake of simplicity, that the receptors concerned do not move. However, in reality, receptors undergo diverse modes of diffusion, and can traverse considerable distances in the time it takes such cells to turn in an external gradient. This sets a physical limit on the accuracy of spatial sensing, which we explore using a model in which receptors diffuse freely over the membrane. We find that the Fisher information carried in binding and unbinding events decreases monotonically with the diffusion constant of the receptors.

Although the influenza A virus has been extensively studied, a quantitative understanding of the infection dynamics is still lacking. To make progress in this direction, we designed several mathematical models and compared them with data from influenza A infections of mice. We find that the immune response (IR) plays an important part in the infection dynamics. Both an innate and an adaptive IR are required to provide adequate explanation of the data. In contrast, regrowth of epithelial cells did not seem to be an important mechanism on the time scale of the infection. We also find that different model variants for both innate and adaptive responses fit the data well, indicating the need for additional data to allow further model discrimination.

Statistical inference for mechanistic models of partially observed dynamic systems is an active area of research. Most existing inference methods place substantial restrictions upon the form of models that can be fitted and hence upon the nature of the scientific hypotheses that can be entertained and the data that can be used to evaluate them. In contrast, the so-calledplug-and-playmethods require only simulations from a model and are thus free of such restrictions. We show the utility of the plug-and-play approach in the context of an investigation of measles transmission dynamics. Our novel methodology enables us to ask and answer questions that previous analyses have been unable to address. Specifically, we demonstrate that plug-and-play methods permit the development of a modelling and inference framework applicable to data from both large and small populations. We thereby obtain novel insights into the nature of heterogeneity in mixing and comment on the importance of including extra-demographic stochasticity as a means of dealing with environmental stochasticity and model misspecification. Our approach is readily applicable to many other epidemiological and ecological systems.

The role of stochasticity and its interplay with nonlinearity are central current issues in studies of the complex population patterns observed in nature, including the pronounced oscillations of wildlife and infectious diseases. The dynamics of childhood diseases have provided influential case studies to develop and test mathematical models with practical application to epidemiology, but are also of general relevance to the central question of whether simple nonlinear systems can explain and predict the complex temporal and spatial patterns observed in nature outside laboratory conditions. Here, we present a stochastic theory for the major dynamical transitions in epidemics from regular to irregular cycles, which relies on the discrete nature of disease transmission and low spatial coupling. The full spectrum of stochastic fluctuations is derived analytically to show how the amplification of noise varies across these transitions. The changes in noise amplification and coherence appear robust to seasonal forcing, questioning the role of seasonality and its interplay with deterministic components of epidemiological models. Childhood diseases are shown to fall into regions of parameter space of high noise amplification. This type of ‘endogenous’ stochastic resonance may be relevant to population oscillations in nonlinear ecological systems in general.

The basic reproduction number ℛ ₀ is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of ℛ ₀ where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the NGM with large domain and the NGM with small domain . The three matrices together reflect the range of possibilities encountered in the literature for the characterization of ℛ ₀ . We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number ℛ ₀ . Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that ℛ ₀ defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r , the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that ℛ ₀ > 1 if and only if r > 0, and ℛ ₀ = 1 if and only if r = 0.

This paper presents a heuristic proof (and simulations of a primordial soup) suggesting that life—or biological self-organization—is an inevitable and emergent property of any (ergodic) random dynamical system that possesses a Markov blanket. This conclusion is based on the following arguments: if the coupling among an ensemble of dynamical systems is mediated by short-range forces, then the states of remote systems must be conditionally independent. These independencies induce a Markov blanket that separates internal and external states in a statistical sense. The existence of a Markov blanket means that internal states will appear to minimize a free energy functional of the states of their Markov blanket. Crucially, this is the same quantity that is optimized in Bayesian inference. Therefore, the internal states (and their blanket) will appear to engage in active Bayesian inference. In other words, they will appear to model—and act on—their world to preserve their functional and structural integrity, leading to homoeostasis and a simple form of autopoiesis.

Arteries exhibit a remarkable ability to adapt to sustained alterations in biomechanical loading, probably via mechanisms that are similarly involved in many arterial pathologies and responses to treatment. Of particular note, diverse data suggest that cell and matrix turnover within vasoaltered states enables arteries to adapt to sustained changes in blood flow and pressure. The goal herein is to show explicitly how altered smooth muscle contractility and matrix growth and remodelling work together to adapt the geometry, structure, stiffness and function of a representative basilar artery. Towards this end, we employ a continuum theory of constrained mixtures to model evolving changes in the wall, which depend on both wall shear stress-induced changes in vasoactive molecules (which alter smooth muscle proliferation and synthesis of matrix) and intramural stress-induced changes in growth factors (which alter cell and matrix turnover). Simulations show, for example, that such considerations help explain the different rates of experimentally observed adaptations to increased versus decreased flows as well as differences in rates of change in response to increased flows or pressures.

Clonal reproduction characterizes a wide range of species including clonal plants in terrestrial and aquatic ecosystems, and clonal microbes such as bacteria and parasitic protozoa, with a key role in human health and ecosystem processes. Clonal organisms present a particular challenge in population genetics because, in addition to the possible existence of replicates of the same genotype in a given sample, some of the hypotheses and concepts underlying classical population genetics models are irreconcilable with clonality. The genetic structure and diversity of clonal populations were examined using a combination of new tools to analyse microsatellite data in the marine angiospermPosidonia oceanica. These tools were based on examination of the frequency distribution of the genetic distance among ramets, termed the spectrum of genetic diversity (GDS), and of networks built on the basis of pairwise genetic distances among genets. Clonal growth and outcrossing are apparently dominant processes, whereas selfing and somatic mutations appear to be marginal, and the contribution of immigration seems to play a small role in adding genetic diversity to populations. The properties and topology of networks based on genetic distances showed a ‘small-world’ topology, characterized by a high degree of connectivity among nodes, and a substantial amount of substructure, revealing organization in subfamilies of closely related individuals. The combination of GDS and network tools proposed here helped in dissecting the influence of various evolutionary processes in shaping the intra-population genetic structure of the clonal organism investigated; these therefore represent promising analytical tools in population genetics.

Bệnh lý động mạch chủ là một nguyên nhân quan trọng gây tử vong ở các quốc gia phát triển. Các hình thức phổ biến nhất của bệnh lý động mạch chủ bao gồm phình động mạch, bóc tách, tắc nghẽn do xơ vữa động mạch và sự cứng lại do lão hóa. Cấu trúc vi mô của mô động mạch chủ đã được nghiên cứu với sự quan tâm lớn, vì việc thay đổi số lượng và/hoặc kiến trúc của các sợi kết nối (elastin và collagen) trong thành động mạch chủ, trực tiếp ảnh hưởng đến tính đàn hồi và sức mạnh, có thể dẫn đến những thay đổi cơ học và chức năng liên quan đến những tình trạng này. Bài viết tổng quan này tóm tắt những tiến bộ trong việc đặc trưng hóa cấu trúc vi mô của các sợi kết nối trong thành động mạch chủ người trong quá trình lão hóa và bệnh lý, đặc biệt nhấn mạnh đến động mạch chủ ngực lên và động mạch chủ bụng, nơi mà các hình thức bệnh lý động mạch chủ phổ biến nhất thường xảy ra.

Tỷ lệ sinh sản,R₀, là một đại lượng cơ bản trong dịch tễ học, xác định sự gia tăng ban đầu của một bệnh truyền nhiễm trong một quần thể vật chủ nhạy cảm. Trong hầu hết các mô hình dịch tễ, có một giá trị cụ thể củaR₀, được gọi là ngưỡng dịch tễ, trên đó các dịch bệnh có thể xảy ra, nhưng dưới ngưỡng đó các dịch bệnh không thể xảy ra. Khi độ phức tạp của một mô hình dịch tễ tăng lên, độ khó tính toán ngưỡng dịch tễ cũng tăng theo. Ở đây, chúng tôi tính toán tỷ lệ sinh sản và ngưỡng dịch tễ cho các dịch bệnh nhạy cảm – nhiễm – hồi phục (SIR) trong một lớp mạng ngẫu nhiên động đơn giản. Như trong hầu hết các mô hình dịch tễ học,R₀ phụ thuộc vào hai tham số dịch tễ cơ bản, đó là tỷ lệ truyền và tỷ lệ hồi phục. Chúng tôi nhận thấy rằngR₀ cũng phụ thuộc vào các tham số xã hội, cụ thể là phân phối bậc mô tả sự không đồng nhất trong số lượng tiếp xúc đồng thời và tham số trộn lẫn chỉ ra tốc độ mà các tiếp xúc được bắt đầu và kết thúc. Chúng tôi chỉ ra rằng sự trộn lẫn xã hội làm thay đổi cơ bản cảnh quan dịch tễ học và do đó, các xấp xỉ mạng tĩnh của các mạng động có thể không đủ.