118 research outputs found
Effect of Dedifferentiation on Time to Mutation Acquisition in Stem Cell-Driven Cancers
Accumulating evidence suggests that many tumors have a hierarchical
organization, with the bulk of the tumor composed of relatively differentiated
short-lived progenitor cells that are maintained by a small population of
undifferentiated long-lived cancer stem cells. It is unclear, however, whether
cancer stem cells originate from normal stem cells or from dedifferentiated
progenitor cells. To address this, we mathematically modeled the effect of
dedifferentiation on carcinogenesis. We considered a hybrid
stochastic-deterministic model of mutation accumulation in both stem cells and
progenitors, including dedifferentiation of progenitor cells to a stem
cell-like state. We performed exact computer simulations of the emergence of
tumor subpopulations with two mutations, and we derived semi-analytical
estimates for the waiting time distribution to fixation. Our results suggest
that dedifferentiation may play an important role in carcinogenesis, depending
on how stem cell homeostasis is maintained. If the stem cell population size is
held strictly constant (due to all divisions being asymmetric), we found that
dedifferentiation acts like a positive selective force in the stem cell
population and thus speeds carcinogenesis. If the stem cell population size is
allowed to vary stochastically with density-dependent reproduction rates
(allowing both symmetric and asymmetric divisions), we found that
dedifferentiation beyond a critical threshold leads to exponential growth of
the stem cell population. Thus, dedifferentiation may play a crucial role, the
common modeling assumption of constant stem cell population size may not be
adequate, and further progress in understanding carcinogenesis demands a more
detailed mechanistic understanding of stem cell homeostasis
Diffusion Approximations for Demographic Inference: DaDi
Models of demographic history (population sizes, migration rates, and divergence times) inferred from genetic data complement archeology and serve as null models in genome scans for selection. Most current inference methods are computationally limited to considering simple models or non-recombining data. We introduce a method based on a diffusion approximation to the joint frequency spectrum of genetic variation between populations. Our implementation, DaDi, can model up to three interacting populations and scales well to genome-wide data. We have applied DaDi to human data from Africa, Europe, and East Asia, building the most complex statistically well-characterized model of human migration out of Africa to date
Sloppiness, Modeling, and Evolution in Biochemical Networks
The wonderful complexity of livings cells cannot be understood solely by studying one gene or protein at a time. Instead, we must consider their interactions and study the complex biochemical networks they function in.
Quantitative computational models are important tools for understanding the dynamics of such biochemical networks, and we begin in Chapter 2 by showing that the sensitivities of such models to parameter changes are generically `sloppy', with eigenvalues roughly evenly spaced over many decades. This sloppiness has practical consequences for the modeling process. In particular, we argue that if one's goal is to make experimentally testable predictions, sloppiness suggests that collectively fitting model parameters to system-level data will often be much more efficient that directly measuring them.
In Chapter 3 we apply some of the lessons of sloppiness to a specific modeling project involving in vitro experiments on the activation of the heterotrimeric G protein transducin. We explore how well time-series activation experiments can constrain model parameters, and we show quantitatively that the T177A mutant of transducin exhibits a much slower rate of rhodopsin-mediated activation than the wild-type.
All the preceding biochemical modeling work is performed using the SloppyCell modeling environment, and Chapter 4 briefly introduces SloppyCell and some of the analyses it implements. Additionally, the two appendices of this thesis contain preliminary user and developer documentation for SloppyCell.
Modelers tweak network parameters with their computers, and nature tweaks such parameters through evolution. We study evolution in Chapter 5 using a version of Fisher's geometrical model with minimal pleiotropy, appropriate for the evolution of biochemical parameters. The model predicts a striking pattern of cusps in the distribution of fitness effects of fixed mutations, and using extreme value theory we show that the consequences of these cusps should be observable in feasible experiments.
Finally, this thesis closes in Chapter 6 by briefly considering several topics: sloppiness in two non-biochemical models, two technical issues with building models, and the effect of sloppiness on evolution beyond the first fixed mutation
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Inferring the Joint Demographic History of Multiple Populations from Multidimensional SNP Frequency Data
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic variants within and between populations. For candidate models we numerically compute the expected spectrum using a diffusion approximation to the one-locus, two-allele Wright-Fisher process, involving up to three simultaneous populations. Our approach is a composite likelihood scheme, since linkage between neutral loci alters the variance but not the expectation of the frequency spectrum. We thus use bootstraps incorporating linkage to estimate uncertainties for parameters and significance values for hypothesis tests. Our method can also incorporate selection on single sites, predicting the joint distribution of selected alleles among populations experiencing a bevy of evolutionary forces, including expansions, contractions, migrations, and admixture. We model human expansion out of Africa and the settlement of the New World, using 5 Mb of noncoding DNA resequenced in 68 individuals from 4 populations (YRI, CHB, CEU, and MXL) by the Environmental Genome Project. We infer divergence between West African and Eurasian populations 140 thousand years ago (95% confidence interval: 40–270 kya). This is earlier than other genetic studies, in part because we incorporate migration. We estimate the European (CEU) and East Asian (CHB) divergence time to be 23 kya (95% c.i.: 17–43 kya), long after archeological evidence places modern humans in Europe. Finally, we estimate divergence between East Asians (CHB) and Mexican-Americans (MXL) of 22 kya (95% c.i.: 16.3–26.9 kya), and our analysis yields no evidence for subsequent migration. Furthermore, combining our demographic model with a previously estimated distribution of selective effects among newly arising amino acid mutations accurately predicts the frequency spectrum of nonsynonymous variants across three continental populations (YRI, CHB, CEU).</p
Universally Sloppy Parameter Sensitivities in Systems Biology
Quantitative computational models play an increasingly important role in
modern biology. Such models typically involve many free parameters, and
assigning their values is often a substantial obstacle to model development.
Directly measuring \emph{in vivo} biochemical parameters is difficult, and
collectively fitting them to other data often yields large parameter
uncertainties. Nevertheless, in earlier work we showed in a
growth-factor-signaling model that collective fitting could yield
well-constrained predictions, even when it left individual parameters very
poorly constrained. We also showed that the model had a `sloppy' spectrum of
parameter sensitivities, with eigenvalues roughly evenly distributed over many
decades. Here we use a collection of models from the literature to test whether
such sloppy spectra are common in systems biology. Strikingly, we find that
every model we examine has a sloppy spectrum of sensitivities. We also test
several consequences of this sloppiness for building predictive models. In
particular, sloppiness suggests that collective fits to even large amounts of
ideal time-series data will often leave many parameters poorly constrained.
Tests over our model collection are consistent with this suggestion. This
difficulty with collective fits may seem to argue for direct parameter
measurements, but sloppiness also implies that such measurements must be
formidably precise and complete to usefully constrain many model predictions.
We confirm this implication in our signaling model. Our results suggest that
sloppy sensitivity spectra are universal in systems biology models. The
prevalence of sloppiness highlights the power of collective fits and suggests
that modelers should focus on predictions rather than on parameters.Comment: Submitted to PLoS Computational Biology. Supplementary Information
available in "Other Formats" bundle. Discussion slightly revised to add
historical contex
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