59 research outputs found
Monod-Wyman-Changeux Analysis of Ligand-Gated Ion Channel Mutants
We present a framework for computing the gating properties of ligand-gated
ion channel mutants using the Monod-Wyman-Changeux (MWC) model of allostery. We
derive simple analytic formulas for key functional properties such as the
leakiness, dynamic range, half-maximal effective concentration, and effective
Hill coefficient, and explore the full spectrum of phenotypes that are
accessible through mutations. Specifically, we consider mutations in the
channel pore of nicotinic acetylcholine receptor (nAChR) and the ligand binding
domain of a cyclic nucleotide-gated (CNG) ion channel, demonstrating how each
mutation can be characterized as only affecting a subset of the biophysical
parameters. In addition, we show how the unifying perspective offered by the
MWC model allows us, perhaps surprisingly, to collapse the plethora of
dose-response data from different classes of ion channels into a universal
family of curves
Combinatorial Control through Allostery
Many instances of cellular signaling and transcriptional regulation involve
switch-like molecular responses to the presence or absence of input ligands. To
understand how these responses come about and how they can be harnessed, we
develop a statistical mechanical model to characterize the types of Boolean
logic that can arise from allosteric molecules following the
Monod-Wyman-Changeux (MWC) model. Building upon previous work, we show how an
allosteric molecule regulated by two inputs can elicit AND, OR, NAND and NOR
responses, but is unable to realize XOR or XNOR gates. Next, we demonstrate the
ability of an MWC molecule to perform ratiometric sensing - a response behavior
where activity depends monotonically on the ratio of ligand concentrations. We
then extend our analysis to more general schemes of combinatorial control
involving either additional binding sites for the two ligands or an additional
third ligand and show how these additions can cause a switch in the logic
behavior of the molecule. Overall, our results demonstrate the wide variety of
control schemes that biological systems can implement using simple mechanisms
How the avidity of polymerase binding to the –35/–10 promoter sites affects gene expression
Although the key promoter elements necessary to drive transcription in Escherichia coli have long been understood, we still cannot predict the behavior of arbitrary novel promoters, hampering our ability to characterize the myriad sequenced regulatory architectures as well as to design new synthetic circuits. This work builds upon a beautiful recent experiment by Urtecho et al. [G. Urtecho, et al., Biochemistry, 68, 1539–1551 (2019)] who measured the gene expression of over 10,000 promoters spanning all possible combinations of a small set of regulatory elements. Using these data, we demonstrate that a central claim in energy matrix models of gene expression—that each promoter element contributes independently and additively to gene expression—contradicts experimental measurements. We propose that a key missing ingredient from such models is the avidity between the –35 and –10 RNA polymerase binding sites and develop what we call a multivalent model that incorporates this effect and can successfully characterize the full suite of gene expression data. We explore several applications of this framework, namely, how multivalent binding at the –35 and –10 sites can buffer RNA polymerase (RNAP) kinetics against mutations and how promoters that bind overly tightly to RNA polymerase can inhibit gene expression. The success of our approach suggests that avidity represents a key physical principle governing the interaction of RNA polymerase to its promoter
Taming the Molecular Dance: Harnessing Statistical Mechanics to Quantitatively Characterize Allosteric Systems
The pace of biological research continues to grow at a staggering pace as high-throughput experimental techniques rapidly increase our ability to sequence DNA, quantify cell behavior, and image molecules of all types within the cellular milieu. Given this surge in experimental prowess, the time is ripe to examine how well our conceptual cartoons of biological phenomena can not only recapitulate the data but also successfully predict the outcomes of future experiments.
One of the fundamental challenges in biology is that the space of possible molecules is overwhelmingly large. The number of variants of a moderately-sized protein (20^300) is larger than the number of atoms in the universe, as is the space of possible bacterial genomes, protein interaction networks, and effector functions; progress in any of these fronts requires a theory-experiment dialogue that can extrapolate our small drop of data to explain large swaths of parameter space.
My thesis strives towards this goal by analyzing a number of central molecular players in biology including enzymes (biological catalysts that accelerate chemical reactions), transcription factors (proteins that bind to DNA and regulate its expression), and ion channels (signaling proteins that regulate ion transport). I develop a quantitative description in each context by harnessing the statistical mechanical Monod-Wyman-Changeux model of allostery which coarse-grains the behavior of a multi-state system into two effective states, demonstrating that these seemingly diverse molecules are all governed by the same fundamental equation.
Writ large, there are two overarching goals encompassed by these projects. The first is to translate our biological knowledge into concrete physical models, enabling us to quantitatively describe how the key molecular components in each system interact to carry out their function. The second goal is to analyze how mutations can be mapped into the fundamental biophysical parameters governing each system. In my opinion, predicting the effects of mutations remains one of the great unsolved problems in biology, and it has been incredibly exciting to make progress on this front.
Looking back at my amazing graduate school experience, one of the most surprising aspects of my PhD was how closely each of my projects revolved around experiments. I entered graduate school as a theoretical physicist expecting to work on esoteric mathematical models, yet the direct connection with data provided a window into the exhilarating world of biology. While I have never physically manipulated these biological systems in the lab, my models allow me to push and prod and examine their behavior from the most mundane to the utterly extreme limits. Through modeling, I test our assumptions of how these systems work and tease out insights into their underlying biophysical mechanism. Most importantly, these models enable me to harness the incredible wealth of hard-won data to weave a few more threads of understanding into our tapestry of how these incredible living systems operate.</p
Statistical Mechanics of Allosteric Enzymes
The concept of allostery in which macromolecules switch between two different conformations is a central theme in biological processes ranging from gene regulation to cell signaling to enzymology. Allosteric enzymes pervade metabolic processes, yet a simple and unified treatment of the effects of allostery in enzymes has been lacking. In this work, we take a step toward this goal by modeling allosteric enzymes and their interaction with two key molecular players—allosteric regulators and competitive inhibitors. We then apply this model to characterize existing data on enzyme activity, comment on how enzyme parameters (such as substrate binding affinity) can be experimentally tuned, and make novel predictions on how to control phenomena such as substrate inhibition
Tuning transcriptional regulation through signaling: A predictive theory of allosteric induction
Allosteric regulation is found across all domains of life, yet we still lack
simple, predictive theories that directly link the experimentally tunable
parameters of a system to its input-output response. To that end, we present a
general theory of allosteric transcriptional regulation using the
Monod-Wyman-Changeux model. We rigorously test this model using the ubiquitous
simple repression motif in bacteria by first predicting the behavior of strains
that span a large range of repressor copy numbers and DNA binding strengths and
then constructing and measuring their response. Our model not only accurately
captures the induction profiles of these strains but also enables us to derive
analytic expressions for key properties such as the dynamic range and
. Finally, we derive an expression for the free energy of allosteric
repressors which enables us to collapse our experimental data onto a single
master curve that captures the diverse phenomenology of the induction profiles.Comment: Substantial revisions for resubmission (3 new figures, significantly
elaborated discussion); added Professor Mitchell Lewis as another author for
his continuing contributions to the projec
The Energetics of Molecular Adaptation in Transcriptional Regulation
Mutation is a critical mechanism by which evolution explores the functional
landscape of proteins. Despite our ability to experimentally inflict mutations
at will, it remains difficult to link sequence-level perturbations to
systems-level responses. Here, we present a framework centered on measuring
changes in the free energy of the system to link individual mutations in an
allosteric transcriptional repressor to the parameters which govern its
response. We find the energetic effects of the mutations can be categorized
into several classes which have characteristic curves as a function of the
inducer concentration. We experimentally test these diagnostic predictions
using the well-characterized LacI repressor of Escherichia coli, probing
several mutations in the DNA binding and inducer binding domains. We find that
the change in gene expression due to a point mutation can be captured by
modifying only a subset of the model parameters that describe the respective
domain of the wild-type protein. These parameters appear to be insulated, with
mutations in the DNA binding domain altering only the DNA affinity and those in
the inducer binding domain altering only the allosteric parameters. Changing
these subsets of parameters tunes the free energy of the system in a way that
is concordant with theoretical expectations. Finally, we show that the
induction profiles and resulting free energies associated with pairwise double
mutants can be predicted with quantitative accuracy given knowledge of the
single mutants, providing an avenue for identifying and quantifying epistatic
interactions.Comment: 11 pages, 6 figures, supplemental info. available via
http://rpgroup.caltech.edu/mwc_mutant
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