64 research outputs found
Nonequilibrium Statistical Mechanics of Dividing Cell Populations
We present and study a model for the nonequilibrium statistical mechanics of protein distributions in a proliferating cell population. Our model describes how the total protein variation is shaped by two processes: variation in protein production internal to the cells and variation in division and inheritance at the population level. It enables us to assess the contribution of each of these components separately. We find that, even if production is deterministic, cell division can generate a large variation in protein distribution. In this limit we solve exactly a special case and draw an analogy between protein distribution along cell generations and stress distribution in layers of granular material. At the other limit of extremely noisy protein production, we find that the population structure restrains variation and that the details of division do not affect the tail of the distribution
From cellular properties to population asymptotics in the Population Balance Equation
Proliferating cell populations at steady state growth often exhibit broad
protein distributions with exponential tails. The sources of this variation and
its universality are of much theoretical interest. Here we address the problem
by asymptotic analysis of the Population Balance Equation. We show that the
steady state distribution tail is determined by a combination of protein
production and cell division and is insensitive to other model details. Under
general conditions this tail is exponential with a dependence on parameters
consistent with experiment. We discuss the conditions for this effect to be
dominant over other sources of variation and the relation to experiments.Comment: Exact solution of Eq. 9 is adde
Identifying Dynamic Regulation with Adversarial Surrogates
Homeostasis, the ability to maintain a stable internal environment in the
face of perturbations, is essential for the functioning of living systems.
Given observations of a system, or even a detailed model of one, it is both
valuable and extremely challenging to extract the control objectives of the
homeostatic mechanisms. Lacking a clear separation between plant and
controller, frameworks such as inverse optimal control and inverse
reinforcement learning are unable to identify the homeostatic mechanisms. A
recently developed data-driven algorithm, Identifying Regulation with
Adversarial Surrogates (IRAS), detects highly regulated or conserved quantities
as the solution of a min-max optimization scheme that automates classical
surrogate data methods. Yet, the definition of homeostasis as regulation within
narrow limits is too strict for biological systems which show sustained
oscillations such as circadian rhythms. In this work, we introduce Identifying
Dynamic Regulation with Adversarial Surrogates (IDRAS), a generalization of the
IRAS algorithm, capable of identifying control objectives that are regulated
with respect to a dynamical reference value. We test the algorithm on
simulation data from realistic biological models and benchmark physical
systems, demonstrating excellent empirical results
Visual detection of time-varying signals: opposing biases and their timescales
Human visual perception is a complex, dynamic and fluctuating process. In
addition to the incoming visual stimulus, it is affected by many other factors
including temporal context, both external and internal to the observer. In this
study we investigate the dynamic properties of psychophysical responses to a
continuous stream of visual near-threshold detection tasks. We manipulate the
incoming signals to have temporal structures with various characteristic
timescales. Responses of human observers to these signals are analyzed using
tools that highlight their dynamical features as well.
We find that two opposing biases shape perception, and operate over distinct
timescales. Positive recency appears over short times, e.g. consecutive trials.
Adaptation, entailing an increased probability of changed response, reflects
trends over longer times. Analysis of psychometric curves conditioned on
various temporal events reveals that the balance between the two biases can
shift depending on their interplay with the temporal properties of the input
signal. A simple mathematical model reproduces the experimental data in all
stimulus regimes. Taken together, our results support the view that visual
response fluctuations reflect complex internal dynamics, possibly related to
higher cognitive processes.Comment: Number of pages: 31 Number of figures: 2
Single-cell protein dynamics reproduce universal fluctuations in cell populations
Protein variability in single cells has been studied extensively in
populations, but little is known about temporal protein fluctuations in a
single cell over extended times. We present here traces of protein copy number
measured in individual bacteria over multiple generations and investigate their
statistical properties, comparing them to previously measured population
snapshots. We find that temporal fluctuations in individual traces exhibit the
same universal features as those previously observed in populations. Scaled
fluctuations around the mean of each trace exhibit the same universal
distribution shape as found in populations measured under a wide range of
conditions and in two distinct microorganisms. Additionally, the mean and
variance of the traces over time obey the same quadratic relation. Analyzing
the temporal features of the protein traces in individual cells, reveals that
within a cell cycle protein content increases as an exponential function with a
rate that varies from cycle to cycle. This leads to a compact description of
the protein trace as a 3-variable stochastic process - the exponential rate,
the cell-cycle duration and the value at the cycle start - sampled once each
cell cycle. This compact description is sufficient to preserve the universal
statistical properties of the protein fluctuations, namely, the protein
distribution shape and the quadratic relationship between variance and mean.
Our results show that the protein distribution shape is insensitive to
sub-cycle intracellular microscopic details and reflects global cellular
properties that fluctuate between generations
Excitability Constraints on Voltage-Gated Sodium Channels
We study how functional constraints bound and shape evolution through an analysis of mammalian voltage-gated sodium channels. The primary function of sodium channels is to allow the propagation of action potentials. Since Hodgkin and Huxley, mathematical models have suggested that sodium channel properties need to be tightly constrained for an action potential to propagate. There are nine mammalian genes encoding voltage-gated sodium channels, many of which are more than ≈90% identical by sequence. This sequence similarity presumably corresponds to similarity of function, consistent with the idea that these properties must be tightly constrained. However, the multiplicity of genes encoding sodium channels raises the question: why are there so many? We demonstrate that the simplest theoretical constraints bounding sodium channel diversity—the requirements of membrane excitability and the uniqueness of the resting potential—act directly on constraining sodium channel properties. We compare the predicted constraints with functional data on mammalian sodium channel properties collected from the literature, including 172 different sets of measurements from 40 publications, wild-type and mutant, under a variety of conditions. The data from all channel types, including mutants, obeys the excitability constraint; on the other hand, channels expressed in muscle tend to obey the constraint of a unique resting potential, while channels expressed in neuronal tissue do not. The excitability properties alone distinguish the nine sodium channels into four different groups that are consistent with phylogenetic analysis. Our calculations suggest interpretations for the functional differences between these groups
Individuality and slow dynamics in bacterial growth homeostasis
Microbial growth and division are fundamental processes relevant to many
areas of life science. Of particular interest are homeostasis mechanisms, which
buffer growth and division from accumulating fluctuations over multiple cycles.
These mechanisms operate within single cells, possibly extending over several
division cycles. However, all experimental studies to date have relied on
measurements pooled from many distinct cells. Here, we disentangle long-term
measured traces of individual cells from one another, revealing subtle
differences between temporal and pooled statistics. By analyzing correlations
along up to hundreds of generations, we find that the parameter describing
effective cell-size homeostasis strength varies significantly among cells. At
the same time, we find an invariant cell size which acts as an attractor to all
individual traces, albeit with different effective attractive forces. Despite
the common attractor, each cell maintains a distinct average size over its
finite lifetime with suppressed temporal fluctuations around it, and
equilibration to the global average size is surprisingly slow (> 150 cell
cycles). To demonstrate a possible source of variable homeostasis strength, we
construct a mathematical model relying on intracellular interactions, which
integrates measured properties of cell size with those of highly expressed
proteins. Effective homeostasis strength is then influenced by interactions and
by noise levels, and generally varies among cells. A predictable and measurable
consequence of variable homeostasis strength appears as distinct oscillatory
patterns in cell size and protein content over many generations. We discuss the
implications of our results to understanding mechanisms controlling division in
single cells and their characteristic timescalesComment: In press with PNAS. 50 pages, including supplementary informatio
- …