57,669 research outputs found
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Structurally robust biological networks
Background:
The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation.
Results:
In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature.
Conclusions:
The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters
Partial differential equations for self-organization in cellular and developmental biology
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field
Global convergence of quorum-sensing networks
In many natural synchronization phenomena, communication between individual
elements occurs not directly, but rather through the environment. One of these
instances is bacterial quorum sensing, where bacteria release signaling
molecules in the environment which in turn are sensed and used for population
coordination. Extending this motivation to a general non- linear dynamical
system context, this paper analyzes synchronization phenomena in networks where
communication and coupling between nodes are mediated by shared dynamical quan-
tities, typically provided by the nodes' environment. Our model includes the
case when the dynamics of the shared variables themselves cannot be neglected
or indeed play a central part. Applications to examples from systems biology
illustrate the approach.Comment: Version 2: minor editions, added section on noise. Number of pages:
36
The influence of receptor-mediated interactions on reaction-diffusion mechanisms of cellular self-organisation
Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction
Nanoporous silica-based protocells at multiple scales for designs of life and nanomedicine.
Various protocell models have been constructed de novo with the bottom-up approach. Here we describe a silica-based protocell composed of a nanoporous amorphous silica core encapsulated within a lipid bilayer built by self-assembly that provides for independent definition of cell interior and the surface membrane. In this review, we will first describe the essential features of this architecture and then summarize the current development of silica-based protocells at both micro- and nanoscale with diverse functionalities. As the structure of the silica is relatively static, silica-core protocells do not have the ability to change shape, but their interior structure provides a highly crowded and, in some cases, authentic scaffold upon which biomolecular components and systems could be reconstituted. In basic research, the larger protocells based on precise silica replicas of cells could be developed into geometrically realistic bioreactor platforms to enable cellular functions like coupled biochemical reactions, while in translational research smaller protocells based on mesoporous silica nanoparticles are being developed for targeted nanomedicine. Ultimately we see two different motivations for protocell research and development: (1) to emulate life in order to understand it; and (2) to use biomimicry to engineer desired cellular interactions
Feedback Regulation and its Efficiency in Biochemical Networks
Intracellular biochemical networks fluctuate dynamically due to various
internal and external sources of fluctuation. Dissecting the fluctuation into
biologically relevant components is important for understanding how a cell
controls and harnesses noise and how information is transferred over apparently
noisy intracellular networks. While substantial theoretical and experimental
advancement on the decomposition of fluctuation was achieved for feedforward
networks without any loop, we still lack a theoretical basis that can
consistently extend such advancement to feedback networks. The main obstacle
that hampers is the circulative propagation of fluctuation by feedback loops.
In order to define the relevant quantity for the impact of feedback loops for
fluctuation, disentanglement of the causally interlocked influence between the
components is required. In addition, we also lack an approach that enables us
to infer non-perturbatively the influence of the feedback to fluctuation as the
dual reporter system does in the feedforward network. In this work, we resolve
these problems by extending the work on the fluctuation decomposition and the
dual reporter system. For a single-loop feedback network with two components,
we define feedback loop gain as the feedback efficiency that is consistent with
the fluctuation decomposition for feedforward networks. Then, we clarify the
relation of the feedback efficiency with the fluctuation propagation in an
open-looped FF network. Finally, by extending the dual reporter system, we
propose a conjugate feedback and feedforward system for estimating the feedback
efficiency only from the statistics of the system non-perturbatively
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