1,437 research outputs found
Fundamental Limits to Position Determination by Concentration Gradients
Position determination in biological systems is often achieved through
protein concentration gradients. Measuring the local concentration of such a
protein with a spatially-varying distribution allows the measurement of
position within the system. In order for these systems to work effectively,
position determination must be robust to noise. Here, we calculate fundamental
limits to the precision of position determination by concentration gradients
due to unavoidable biochemical noise perturbing the gradients. We focus on
gradient proteins with first order reaction kinetics. Systems of this type have
been experimentally characterised in both developmental and cell biology
settings. For a single gradient we show that, through time-averaging, great
precision can potentially be achieved even with very low protein copy numbers.
As a second example, we investigate the ability of a system with oppositely
directed gradients to find its centre. With this mechanism, positional
precision close to the centre improves more slowly with increasing averaging
time, and so longer averaging times or higher copy numbers are required for
high precision. For both single and double gradients, we demonstrate the
existence of optimal length scales for the gradients, where precision is
maximized, as well as analyzing how precision depends on the size of the
concentration measuring apparatus. Our results provide fundamental constraints
on the positional precision supplied by concentration gradients in various
contexts, including both in developmental biology and also within a single
cell.Comment: 24 pages, 2 figure
Modeling craniofacial development reveals spatiotemporal constraints on robust patterning of the mandibular arch
How does pattern formation occur accurately when confronted with tissue growth and stochastic fluctuations (noise) in gene expression? Dorso-ventral (D-V) patterning of the mandibular arch specifies upper versus lower jaw skeletal elements through a combination of Bone morphogenetic protein (Bmp), Endothelin-1 (Edn1), and Notch signaling, and this system is highly robust. We combine NanoString experiments of early D-V gene expression with live imaging of arch development in zebrafish to construct a computational model of the D-V mandibular patterning network. The model recapitulates published genetic perturbations in arch development. Patterning is most sensitive to changes in Bmp signaling, and the temporal order of gene expression modulates the response of the patterning network to noise. Thus, our integrated systems biology approach reveals non-intuitive features of the complex signaling system crucial for craniofacial development, including novel insights into roles of gene expression timing and stochasticity in signaling and gene regulation
Analysis of Dynamic Brain Imaging Data
Modern imaging techniques for probing brain function, including functional
Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging,
and magnetoencephalography, generate large data sets with complex content. In
this paper we develop appropriate techniques of analysis and visualization of
such imaging data, in order to separate the signal from the noise, as well as
to characterize the signal. The techniques developed fall into the general
category of multivariate time series analysis, and in particular we extensively
use the multitaper framework of spectral analysis. We develop specific
protocols for the analysis of fMRI, optical imaging and MEG data, and
illustrate the techniques by applications to real data sets generated by these
imaging modalities. In general, the analysis protocols involve two distinct
stages: `noise' characterization and suppression, and `signal' characterization
and visualization. An important general conclusion of our study is the utility
of a frequency-based representation, with short, moving analysis windows to
account for non-stationarity in the data. Of particular note are (a) the
development of a decomposition technique (`space-frequency singular value
decomposition') that is shown to be a useful means of characterizing the image
data, and (b) the development of an algorithm, based on multitaper methods, for
the removal of approximately periodic physiological artifacts arising from
cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9804003
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
Switchable slow cellular conductances determine robustness and tunability of network states.
Neuronal information processing is regulated by fast and localized fluctuations of brain states. Brain states reliably switch between distinct spatiotemporal signatures at a network scale even though they are composed of heterogeneous and variable rhythms at a cellular scale. We investigated the mechanisms of this network control in a conductance-based population model that reliably switches between active and oscillatory mean-fields. Robust control of the mean-field properties relies critically on a switchable negative intrinsic conductance at the cellular level. This conductance endows circuits with a shared cellular positive feedback that can switch population rhythms on and off at a cellular resolution. The switch is largely independent from other intrinsic neuronal properties, network size and synaptic connectivity. It is therefore compatible with the temporal variability and spatial heterogeneity induced by slower regulatory functions such as neuromodulation, synaptic plasticity and homeostasis. Strikingly, the required cellular mechanism is available in all cell types that possess T-type calcium channels but unavailable in computational models that neglect the slow kinetics of their activation
Power spectra methods for a stochastic description of diffusion on deterministically growing domains
A central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity. Generally, the mathematical treatments of biological systems have used continuum, mean-field hypotheses for their constituent parts, which ignores any sources of intrinsic stochastic effects. In this paper we consider a stochastic space-jump process as a description of diffusion, i.e., particles are able to undergo a random walk on a discretized domain. By developing analytical Fourier methods we are able to probe this probabilistic framework, which gives us insight into the patterning potential of diffusive systems. Further, an alternative description of domain growth is introduced, with which we are able to rigorously link the mean-field and stochastic descriptions. Finally, through combining these ideas, it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean-field steady state
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