228 research outputs found
Efficient parametric inference for stochastic biological systems with measured variability
Stochastic systems in biology often exhibit substantial variability within
and between cells. This variability, as well as having dramatic functional
consequences, provides information about the underlying details of the system's
behaviour. It is often desirable to infer properties of the parameters
governing such systems given experimental observations of the mean and variance
of observed quantities. In some circumstances, analytic forms for the
likelihood of these observations allow very efficient inference: we present
these forms and demonstrate their usage. When likelihood functions are
unavailable or difficult to calculate, we show that an implementation of
approximate Bayesian computation (ABC) is a powerful tool for parametric
inference in these systems. However, the calculations required to apply ABC to
these systems can also be computationally expensive, relying on repeated
stochastic simulations. We propose an ABC approach that cheaply eliminates
unimportant regions of parameter space, by addressing computationally simple
mean behaviour before explicitly simulating the more computationally demanding
variance behaviour. We show that this approach leads to a substantial increase
in speed when applied to synthetic and experimental datasets.Comment: 11 pages, 4 fig
Endless love: On the termination of a playground number game
A simple and popular childhood game, `LOVES' or the `Love Calculator',
involves an iterated rule applied to a string of digits and gives rise to
surprisingly rich behaviour. Traditionally, players' names are used to set the
initial conditions for an instance of the game: its behaviour for an exhaustive
set of pairings of popular UK childrens' names, and for more general initial
conditions, is examined. Convergence to a fixed outcome (the desired result) is
not guaranteed, even for some plausible first name pairings. No pairs of top-50
common first names exhibit non-convergence, suggesting that it is rare in the
playground; however, including surnames makes non-convergence more likely due
to higher letter counts (for example, `Reese Witherspoon LOVES Calvin Harris').
Different game keywords (including from different languages) are also
considered. An estimate for non-convergence propensity is derived: if the sum
of digits in a string of length obeys , convergence
is less likely. Pairs of top UK names with pairs of `O's and several `L's (for
example, Chloe and Joseph, or Brooke and Scarlett) often attain high scores.
When considering individual names playing with a range of partners, those with
no `LOVES' letters score lowest, and names with intermediate (not simply the
highest) letter counts often perform best, with Connor and Evie averaging the
highest scores when played with other UK top names.Comment: 12 pages, 9 figure
Efficient vasculature investment in tissues can be determined without global information
Cells are the fundamental building blocks of organs and tissues. Information and mass flow through cellular contacts in these structures is vital for the orchestration of organ function. Constraints imposed by packing and cell immobility limit intercellular communication, particularly as organs and organisms scale up to greater sizes. In order to transcend transport limitations, delivery systems including vascular and respiratory systems evolved to facilitate the movement of matter and information. The construction of these delivery systems has an associated cost, as vascular elements do not perform the metabolic functions of the organs they are part of. This study investigates a fundamental trade-off in vascularization in multicellular tissues: the reduction of path lengths for communication versus the cost associated with producing vasculature. Biologically realistic generative models, using multicellular templates of different dimensionalities, revealed a limited advantage to the vascularization of two-dimensional tissues. Strikingly, scale-free improvements in transport efficiency can be achieved even in the absence of global knowledge of tissue organization. A point of diminishing returns in the investment of additional vascular tissue to the increased reduction of path length in 2.5- and three-dimensional tissues was identified. Applying this theory to experimentally determined biological tissue structures, we show the possibility of a co-dependency between the method used to limit path length and the organization of cells it acts upon. These results provide insight as to why tissues are or are not vascularized in nature, the robustness of developmental generative mechanisms and the extent to which vasculature is advantageous in the support of organ function
Explicit tracking of uncertainty increases the power of quantitative rule-of-thumb reasoning in cell biology
"Back-of-the-envelope" or "rule-of-thumb" calculations involving rough
estimates of quantities play a central scientific role in developing intuition
about the structure and behaviour of physical systems, for example in so-called
`Fermi problems' in the physical sciences. Such calculations can be used to
powerfully and quantitatively reason about biological systems, particularly at
the interface between physics and biology. However, substantial uncertainties
are often associated with values in cell biology, and performing calculations
without taking this uncertainty into account may limit the extent to which
results can be interpreted for a given problem. We present a means to
facilitate such calculations where uncertainties are explicitly tracked through
the line of reasoning, and introduce a `probabilistic calculator' called
Caladis, a web tool freely available at www.caladis.org, designed to perform
this tracking. This approach allows users to perform more statistically robust
calculations in cell biology despite having uncertain values, and to identify
which quantities need to be measured more precisely in order to make confident
statements, facilitating efficient experimental design. We illustrate the use
of our tool for tracking uncertainty in several example biological
calculations, showing that the results yield powerful and interpretable
statistics on the quantities of interest. We also demonstrate that the outcomes
of calculations may differ from point estimates when uncertainty is accurately
tracked. An integral link between Caladis and the Bionumbers repository of
biological quantities further facilitates the straightforward location,
selection, and use of a wealth of experimental data in cell biological
calculations.Comment: 8 pages, 3 figure
Modelling the Self-Assembly of Virus Capsids
We use computer simulations to study a model, first proposed by Wales [1],
for the reversible and monodisperse self-assembly of simple icosahedral virus
capsid structures. The success and efficiency of assembly as a function of
thermodynamic and geometric factors can be qualitatively related to the
potential energy landscape structure of the assembling system. Even though the
model is strongly coarse-grained, it exhibits a number of features also
observed in experiments, such as sigmoidal assembly dynamics, hysteresis in
capsid formation and numerous kinetic traps. We also investigate the effect of
macromolecular crowding on the assembly dynamics. Crowding agents generally
reduce capsid yields at optimal conditions for non-crowded assembly, but may
increase yields for parameter regimes away from the optimum. Finally, we
generalize the model to a larger triangulation number T = 3, and observe more
complex assembly dynamics than that seen for the original T = 1 model.Comment: 16 pages, 11 figure
A tractable genotype-phenotype map for the self-assembly of protein quaternary structure
The mapping between biological genotypes and phenotypes is central to the
study of biological evolution. Here we introduce a rich, intuitive, and
biologically realistic genotype-phenotype (GP) map, that serves as a model of
self-assembling biological structures, such as protein complexes, and remains
computationally and analytically tractable. Our GP map arises naturally from
the self-assembly of polyomino structures on a 2D lattice and exhibits a number
of properties: (genotypes vastly outnumber phenotypes),
(genotypic redundancy varies greatly between
phenotypes), (phenotypes consist
of disconnected mutational networks) and (most
phenotypes can be reached in a small number of mutations). We also show that
the mutational robustness of phenotypes scales very roughly logarithmically
with phenotype redundancy and is positively correlated with phenotypic
evolvability. Although our GP map describes the assembly of disconnected
objects, it shares many properties with other popular GP maps for connected
units, such as models for RNA secondary structure or the HP lattice model for
protein tertiary structure. The remarkable fact that these important properties
similarly emerge from such different models suggests the possibility that
universal features underlie a much wider class of biologically realistic GP
maps.Comment: 12 pages, 6 figure
Evolutionary Dynamics in a Simple Model of Self-Assembly
We investigate the evolutionary dynamics of an idealised model for the robust
self-assembly of two-dimensional structures called polyominoes. The model
includes rules that encode interactions between sets of square tiles that drive
the self-assembly process. The relationship between the model's rule set and
its resulting self-assembled structure can be viewed as a genotype-phenotype
map and incorporated into a genetic algorithm. The rule sets evolve under
selection for specified target structures. The corresponding, complex fitness
landscape generates rich evolutionary dynamics as a function of parameters such
as the population size, search space size, mutation rate, and method of
recombination. Furthermore, these systems are simple enough that in some cases
the associated model genome space can be completely characterised, shedding
light on how the evolutionary dynamics depends on the detailed structure of the
fitness landscape. Finally, we apply the model to study the emergence of the
preference for dihedral over cyclic symmetry observed for homomeric protein
tetramers
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