New paper on fat

Sex-Associated Differences in Free Fatty Acid Flux of Obese Adolescents.

Diane C Adler-Wailes, Vipul Periwal, Asem H Ali, Sheila M Brady, Jennifer R McDuffie, Gabriel I Uwaifo, Marian Tanofsky-Kraff, Christine G Salaita, Van S Hubbard, James C Reynolds, Carson C Chow, Anne E Sumner, Jack A Yanovski

Section on Growth and Obesity (D.C.A.-W., A.H.A., S.J.R.M., G.I.U., M.T.-K., J.A.Y.), Program in Developmental Endocrinology and Genetics, Eunice Kennedy Shriver National Institute of Child Health and Human Development; Mathematical Cell Modeling Section (V.P., C.C.C.), Division of Extramural Activities (C.G.S.), Division of Nutrition Research Coordination (V.S.H.), and Laboratory of Endocrinology and Receptor Biology (A.E.S.), National Institute of Diabetes and Digestive and Kidney Diseases; and Nuclear Medicine Department (J.C.R.), Hatfield Clinical Research Center, National Institutes of Health, U.S. Department of Health and Human Services, Bethesda, Maryland 20892.

The Journal of clinical endocrinology and metabolism (impact factor: 6.5). 02/2013; DOI:10.1210/jc.2012-3817

ABSTRACT Context: In obesity, increases in free fatty acid (FFA) flux can predict development of insulin resistance. Adult women release more FFA relative to resting energy expenditure (REE) and have greater FFA clearance rates than men. In adolescents, it is unknown whether sex differences in FFA flux occur. Objective: Our objective was to determine the associations of sex, REE, and body composition with FFA kinetics in obese adolescents. Participants: Participants were from a convenience sample of 112 non-Hispanic white and black adolescents (31% male; age range, 12-18 years; body mass index SD score range, 1.6-3.1) studied before initiating obesity treatment. Main Outcome Measures: Glucose, insulin, and FFA were measured during insulin-modified frequently sampled iv glucose tolerance tests. Minimal models for glucose and FFA calculated insulin sensitivity index (SI) and FFA kinetics, including maximum (l0 + l2) and insulin-suppressed (l2) lipolysis rates, clearance rate constant (cf), and insulin concentration for 50% lipolysis suppression (ED50). Relationships of FFA measures to sex, REE, fat mass (FM), lean body mass (LBM) and visceral adipose tissue (VAT) were examined. Results: In models accounting for age, race, pubertal status, height, FM, and LBM, we found sex, pubertal status, age, and REE independently contributed to the prediction of l2 and l0 + l2 (P < .05). Sex and REE independently predicted ED50 (P < .05). Sex, FM/VAT, and LBM were independent predictors of cf. Girls had greater l2, l0 + l2 and ED50 (P < .05, adjusted for REE) and greater cf (P < .05, adjusted for FM or VAT) than boys. Conclusion: Independent of the effects of REE and FM, FFA kinetics differ significantly in obese adolescent girls and boys, suggesting greater FFA flux among girls.

New paper on neural networks

Michael Buice and I have just published a review paper of our work on how to go beyond mean field theory for systems of coupled neurons. The paper can be obtained here. Michael and I actually pursued two lines of thought on how to go beyond mean field theory and we show how the two are related in this review. The first line started in trying to understand how to create a dynamic statistical theory of a high dimensional fully deterministic system. We first applied the method to the Kuramoto system of coupled oscillators but the formalism could apply to any system. Our recent paper in PLoS Computational Biology was an application for a network of synaptically coupled spiking neurons. I’ve written about this work multiple times (e.g. here,  here, and here). In this series of papers, we looked at how you can compute fluctuations around the infinite system size limit, which defines mean field theory for the system, when you have a finite number of neurons. We used the inverse number of neurons as a perturbative expansion parameter but the formalism could be generalized to expand in any small parameter, such as the inverse of a slow time scale.

The second line of thought was with regards to the question of how to generalize the Wilson-Cowan equation, which is a phenomenological population activity equation for a set of neurons, which I summarized here. That paper built upon the work that Michael had started in his PhD thesis with Jack Cowan. The Wilson-Cowan equation is a mean field theory of some system but it does not specify what that system is. Michael considered the variable in the Wilson-Cowan equation to be the rate (stochastic intensity) of a Poisson process and prescribed a microscopic stochastic system, dubbed the spike model, that was consistent with the Wilson-Cowan equation. He then considered deviations away from pure Poisson statistics. The expansion parameter in this case was more obscure. Away from a bifurcation (i.e. critical point) the statistics of firing would be pure Poisson but they would deviate near the critical point, so the small parameter was the inverse distance to criticality. Michael, Jack and I then derived a set of self-consistent set of equations for the mean rate and rate correlations that generalized the Wilson-Cowan equation.

The unifying theme of both approaches is that these systems can be described by either a hierarchy of moment equations or equivalently as a functional or path integral. This all boils down to the fact that any stochastic system is equivalently described by a distribution function or the moments of the distribution. Generally, it is impossible to explicitly calculate or compute these quantities but one can apply perturbation theory to extract meaningful quantities. For a path integral, this involves using Laplace’s method or the method of steepest descents to approximate an integral and in the moment hierarchy method it involves finding ways to truncate or close the system. These methods are also directly related to WKB expansion, but I’ll leave that connection to another post.

New paper on finite size effects in spiking neural networks

Michael Buice and I have finally published our paper entitled “Dynamic finite size effects in spiking neural networks” in PLoS Computational Biology (link here). Finishing this paper seemed like a Sisyphean ordeal and it is only the first of a series of papers that we hope to eventually publish. This paper outlines a systematic perturbative formalism to compute fluctuations and correlations in a coupled network of a finite but large number of spiking neurons. The formalism borrows heavily from the kinetic theory of plasmas and statistical field theory and is similar to what we used in our previous work on the Kuramoto model (see here and  here) and the “Spike model” (see here).  Our heuristic paper on path integral methods is  here.  Some recent talks and summaries can be found here and here.

Two New Papers

I have two new papers in the Journal of Biological Chemistry:

Z Zhang, Y Sun, YW Cho, CC Chow, SS Simons. PA1 Protein, a New Competitive Decelerator Acting at More than One Step to Impede Glucocorticoid Receptor-mediated Transactivation. J Biol Chem:42-58 (2012). [PDF]

JA Blackford, C Guo, R Zhu, EJ Dourgherty, CC Chow and SS Simons. Identification of Location and Kinetically Defined Mechanism of Cofactors and Reporter Genes in the Cascade of Steroid-regulated Transactivation. J Biol Chem:40982-95 (2012). [PDF]

Both are applications of our theory for steroid-mediated gene induction.  The theory is applicable for any biochemical system where the dose response curve strictly follows a Michaelis-Menten curve.  A summary of the theory can be found here and here.  Slides for talks on the topic can be found here.  In Zhang et al, we use the theory to predict a mechanism for a protein called PA1.  In Blackford et al, we show that DNA is the effective rate limiting step for gene transcription in steady state, which we dub concentration limiting step, since there are really no rates at steady state.

Revised SDE and path integral paper

At the MBI last week, I gave a tutorial on using path integrals to compute moments of stochastic differential equations perturbatively.  The slides are the same as the tutorial I gave a few years ago (see here).  I slightly modified the review paper that goes with the talk. I added the explicit computation for the generating functional of the complex Gaussian PDF. The new version can be found here.

New paper on repetition priming and suppression

A new paper by Steve Gotts, myself, and Alex Martin has officially been published in the journal Cognitive Neuroscience:

Stephen J. Gotts, Carson C. Chow & Alex Martin (2012): Repetition priming and repetition suppression: Multiple mechanisms in need of testing, Cognitive Neuroscience, 3:3-4, 250-259 [PDF]

This paper is a review of the topic but is partially based on the PhD thesis work of Steve Gotts when we were both in Pittsburgh over a decade ago. Steve was a CNBC graduate student at Carnegie Mellon University and came to visit me one day to tell me about his research project to reconcile the psychological phenomenon of repetition priming with a neurophysiological phenomenon called repetition suppression. It is well known that performance improves when you repeat a task. For example, you will respond faster to words on a random list if you have seen the word before. This is called repetition priming. The priming effect can occur over time scales as short as a few seconds to your life time. Steve was focused on the short time effect. A naive explanation for why you would respond faster to priming is that the pool of neurons that code for the word become slightly more active so when the word reappears they fire more readily. This hypothesis could only be tested  when electrophysiological recordings of cells in awake behaving monkeys and functional magnetic resonance imaging data in humans finally became available in the mid-nineties.  As is often the case in science, the opposite was observed. Neural responses actually decreased and this was called repetition suppression.  So an interesting question arose: How do you get priming with suppression?  Steve had a hypothesis and it involved work I had done so he came to see if I wanted to collaborate.

I joined the math department at Pitt in the fall of 1998 (the webpage has a nice picture of Bard Ermentrout, Rodica Curtu and Pranay Goel standing at a white board). I had just come from doing a post doc with Nancy Kopell at BU.   At that time, the computational neuroscience community was interested in how a population of spiking neurons would become synchronous.  The history of synchrony and coupled oscillators is long with many threads but I got into the game because of the weekly meetings Nancy organized at BU, which we dubbed “N-group”. People from all over the Boston area would participate.  It was quite exciting at that time. One day Xiao Jing Wang, who was at Brandeis at the time, came to give a seminar on his joint work with Gyorgy Buzsaki on gamma oscillations in the hippocampus, which resulted in this highly cited paper. What the paper was really about was how inhibition could induce synchrony in a network with heterogeneous connections.  It had already been shown by a number of people that a network with inhibitory synapses could synchronize a network of spiking neurons. This was somewhat counter intuitive because the conventional wisdom was that inhibition would lead to anti-synchrony.  The key ingredient was that the inhibition had to be slow. Xiao Jing argued from his simulations that the hippocampus had a sweet spot for synchronization for the gamma band (i.e. frequencies around 40Hz). I was highly intrigued by his result and spent the next two years trying to understand the simulations mathematically. This resulted in four papers:

C.C. Chow, J.A. White, J. Ritt, and N. Kopell, `Frequency control in synchronized networks of inhibitory neurons’, J. Comp. Neurosci. 5, 407-420 (1998). [PDF]

J.A. White, C.C. Chow, J. Ritt, C. Soto-Trevino, and N. Kopell, `Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons’, J. Comp. Neurosci. 5, 5-16 (1998). [PDF]

C.C. Chow, `Phase-locking in weakly heterogeneous neuronal networks’, Physica D 118, 343-370 (1998). [PDF]

C.C. Chow and N. Kopell, `Dynamics of spiking neurons with electrical coupling’, Neural Comp. 12, 1643-1678 (2000). [PDF]

In a nutshell, these papers showed that in a heterogeneous network, neurons will tend to synchronize around the time scale of the synaptic inhibition, which in the case of the inhibitory neurotransmitter receptor GABA_A is around 25 ms or 40 Hz. When the firing frequency is too high the neurons tend to fire asynchronously and when the frequency is too slow, neurons tend to stop firing all together.

Steve read my papers (and practically everything else) and thought  that this might be the resolution of his question.  Now, it had also been known for a while that when neurons fire they tend to slow down. This is due to both spike-frequency adaptation and synaptic depression, so repetition suppression is not entirely surprising since when neurons are stimulated they will tend to fire slower. What is surprising is that slowing down makes you respond faster.  Steve thought that maybe suppression synchronized neurons and made them more effective in getting downstream neurons to fire. In essence, what he needed to find was a mechanism that increases the gain of a neuron for a decrease in input and synchrony was a solution. I helped him work out some technical details and he wrote a very nice thesis showing how this could work and match the data. He then went on to work with Bob Desimone and Alex Martin at NIH. However, we never wrote the theoretical paper from his thesis because of a critique that we never got around to answering. The issue was that if a lowering of network frequency can elicit priming then why does a reduction in contrast in the primed stimulus, which also reduces network frequency, not do the same? This came up after Steve had left and I turned my attention to other things. The answer is probably because not all frequency reductions are equal. A reduction in contrast lowers the total input to the early part of the visual system while synaptic depression will have the largest effect on the most active neurons.  The ensuing dynamics will likely be different but we never had the time to fully flesh this out. Although, I always wanted to get back to this, the project sat idle for me for about eight years until Steve sent me an email one day saying that he’s writing a review with Alex on the topic and wanted to know if I wanted to be included. I was delighted.  The paper covers all the current theories for priming and suppression and is accompanied by commentaries from many of the key players in the field. I’ve just covered a small part of the many interesting issues brought up in the review.

Obesity references

I’ve been asked about references to papers on which my New York Times interview is based so I’ve listed them below.  You can find summaries for some of them as well as the slides for my talks and posts related to obesity here.

K.D. Hall, G.Sacks, D. Chandramohan, C.C Chow, C. Wang; S. Gortmaker; B. Swinburn, `Quantifying the effect of energy imbalance on body weight change.’ The Lancet 378:826-37 (2011).

K.D. Hall and C.C. Chow, `Estimating changes of free-living energy intake and its confidence interval,’ Am J Clin Nutr 94:66-74 (2011).

K.D. Hall, M. Dore, J. Guo, and C.C. Chow, ‘The progressive increase of food waste in America’, PLoS ONE 4(11): e7940 (2009).

C.C. Chow and K.D. Hall, `The dynamics of human body weight change’, PLoS Computational Biology 4 , e1000045 (2008).

K.D. Hall, H.L. Bain and C.C. Chow, `How adaptations of substrate utilization regulate body composition’, International Journal of Obesity, 31 , 1378-83 (2007). [PDF]

V. Periwal and C.C. Chow, ‘Patterns in food intake correlate with body mass index’, American Journal of Physiology: Endocrinology and Metabolism, 291 929-936 (2006) [PDF]

Errata recap

I want to stress that there is nothing wrong with the results in the paper. The mistakes are typographical in the sense that the formulas in the methods were transcribed incorrectly from our code.  This was just pointed out to me that the errata could be misinterpreted.  What happened was that MS Word kept turning our equations into pictures so we couldn’t edit them so we retyped them over and over again.  Transcription errors then started to creep in and we were so adapted to the equations that we didn’t notice anymore.  Not a good excuse but unfortunately that is what happened.

Errata for PLoS Genetics paper

I just discovered some glaring typographical errors in the Methods Section of our recent paper: Heritability and genetic correlations explained by common SNPS for metabolic syndrome traits.  The corrected Methods can be obtained here.  I will see if I can include an errata on the PLoS Genetics website as well. The results in the paper are fine.

edited on May 9 to clear up possible misconception.

Heritability and GWAS

Here is the backstory for the paper in the previous post.  Immediately after the  human genome project was completed a decade ago, people set out to discover the genes responsible for diseases. Traditionally, genes had been discovered by tracing the incidence in families that exhibit the disease. This was a painstaking process – a classic example being the discovery of the gene for Huntington’s disease.  The  completion of the  human genome project provided a simpler approach.  The first thing was to create what is known as a haplotype map or HapMap. This is a catalog of all the common genome differences between people.  The genome between humans only differ by about 0.1%. These differences include  Single Nucleotide Variations (SNPs) where a given base (A,C,G,T) is changed and  Copy Number Variations (CNV) where there are differences in the number of copies of segments of DNA.   There are about 10 million common SNPs.

The Genome Wide Association Study (GWAS) usually looks for differences in SNPs between people with and without diseases.  The working hypothesis at that time was that common diseases like Alzheimer’s disease or Type II diabetes should be due to differences in common SNPs (i.e. common disease, common variant). People thought that the genes for many of these diseases would be found within a decade. Towards this end, companies like Affymetrics and Illumina began making microarray chips, which consist of tiny wells with snippets of complement DNA (cDNA) of a small segment of the sequence around each SNP.  SNP variants are found by seeing what types of DNA fragments in genetic samples (e.g. saliva) get bound to the complement strands in the  array. A classic GWAS study then considers the differences in SNP variants observed in disease and control groups. For any finite sample, there will always be fluctuations  so a statistical criterion must be established to evaluate whether a variant is significant. This is done by computing the probability or p-value of the occurrence of a variant due to random chance.  However, in a set of a million SNPS, which is standard for a chip, the probability of one SNP being randomly associated with a disease is a million fold higher if the SNPs are all independent (i.e. it’s just the sum of the probabilities of each event (see Bonferonni correction)). However, since SNPs are not always independent, this is a very conservative criterion.

The first set of results from GWAS  started to be published shortly after I arrived at the NIH in 2004 and they weren’t very promising. A small number of SNPs were found for some common diseases but they only conferred a very small increase in  risk even when the disease were thought to be highly heritable. Heritability is a measure of the proportion of phenotypic variation between people explained by genetic variation.  (I’ll give a primer on heritability in a following post.) The one notable exception was age-related macular degeneration for which five SNPs were found to be associated with a 2 to 3 fold increase in risk. The difference between the heritability of a disease as measured by classical genetic methods and what was found to be explained by SNPs came to be known as the “Missing heritability” problem. I thought this was an interesting puzzle but didn’t think much about it until I saw the results from this paper (summarized on Steve Hsu’s blog), which showed that different European subpopulations could be separated by just projecting onto two principal components of 300,000 SNPS of 6000 people. (Principle components are the eigenvectors of the 6000 by 6000 correlation matrix of the 300,000 dimensional SNP vectors of each person.)  This was a revelation to me because it implied that although single genes did not carry much weight, the collection of all the genes certainly did.  I decided right then that I would show that the missing heritability for obesity was contained in the “pattern” of SNPs rather than in single SNPs. I did this without really knowing anything at all about genetics or heritability.

New paper on heritability from GWAS

Heritability and genetic correlations explained by common SNPS in metabolic syndrome traits

PLoS Genet 8(3): e1002637. doi:10.1371/journal.pgen.1002637

Shashaank Vattikuti, Juen Guo, and Carson C. Chow

Abstract: We used a bivariate (multivariate) linear mixed-effects model to estimate the narrow-sense heritability (h²) and heritability explained by the common SNPs (h_g²) for several metabolic syndrome (MetS) traits and the genetic correlation between pairs of traits for the Atherosclerosis Risk in Communities (ARIC) genome-wide association study (GWAS) population. MetS traits included body-mass index (BMI), waist-to-hip ratio (WHR), systolic blood pressure (SBP), fasting glucose (GLU), fasting insulin (INS), fasting trigylcerides (TG), and fasting high-density lipoprotein (HDL). We found the percentage of h² accounted for by common SNPs to be 58% of h² for height, 41% for BMI, 46% for WHR, 30% for GLU, 39% for INS, 34% for TG, 25% for HDL, and 80% for SBP. We confirmed prior reports for height and BMI using the ARIC population and independently in the Framingham Heart Study (FHS) population. We demonstrated that the multivariate model supported large genetic correlations between BMI and WHR and between TG and HDL. We also showed that the genetic correlations between the MetS traits are directly proportional to the phenotypic correlations.

Author Summary: The narrow-sense heritability of a trait such as body-mass index is a measure of the variability of the trait between people that is accounted for by their additive genetic differences. Knowledge of these genetic differences provides insight into biological mechanisms and hence treatments for diseases. Genome-wide association studies (GWAS) survey a large set of genetic markers common to the population. They have identified several single markers that are associated with traits and diseases. However, these markers do not seem to account for all of the known narrow-sense heritability. Here we used a recently developed model to quantify the genetic information contained in GWAS for single traits and shared between traits. We specifically investigated metabolic syndrome traits that are associated with type 2 diabetes and heart disease, and we found that for the majority of these traits much of the previously unaccounted for heritability is contained within common markers surveyed in GWAS. We also computed the genetic correlation between traits, which is a measure of the genetic components shared by traits. We found that the genetic correlation between these traits could be predicted from their phenotypic correlation.

I am very happy that this paper is finally out.  It has been a three year long ordeal.  I’ll write about the story and background for this paper later.

New paper in Biophysical Journal

Bayesian Functional Integral Method for Inferring Continuous Data from Discrete Measurements

Biophysical Journal, Volume 102, Issue 3, 399-406, 8 February 2012

doi:10.1016/j.bpj.2011.12.046

William J. Heuett, Bernard V. Miller, Susan B. Racette, John O. Holloszy, Carson C. Chow, and Vipul Periwal

Abstract: Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a “model”. An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models.

New paper on steroid-mediated gene induction

A follow-up  to our PNAS paper on a new theory of steroid-mediated gene induction is now available on PLoS One here.  The title and abstract is below.  In the first paper, we proposed a general mathematical framework to compute how much protein will be produced from a steroid-mediated gene.  It had been noted in the past that the dose response curve of product given steroid amount follows a Michaelis-Menten curve or first order Hill function (e.g. Product = Amax [S]/(EC50+[S], where [S] is the added steroid concentration)..  In our previous work, we exploited this fact and showed that a complete closed form expression for the dose response curve could be written down for an arbitrary number of linked reactions.  The formula also indicates how added cofactors could increase or decrease the Amax or EC50.  What we do in this paper is to show how this expression can be used to predict the mechanism and order in the sequence of reactions a given cofactor will act by analyzing how two cofactors affect the Amax and EC50.

Deducing the Temporal Order of Cofactor Function in Ligand-Regulated Gene Transcription: Theory and Experimental Verification

Edward J. Dougherty, Chunhua Guo, S. Stoney Simons Jr, Carson C. Chow

Abstract: Cofactors are intimately involved in steroid-regulated gene expression. Two critical questions are (1) the steps at which cofactors exert their biological activities and (2) the nature of that activity. Here we show that a new mathematical theory of steroid hormone action can be used to deduce the kinetic properties and reaction sequence position for the functioning of any two cofactors relative to a concentration limiting step (CLS) and to each other. The predictions of the theory, which can be applied using graphical methods similar to those of enzyme kinetics, are validated by obtaining internally consistent data for pair-wise analyses of three cofactors (TIF2, sSMRT, and NCoR) in U2OS cells. The analysis of TIF2 and sSMRT actions on GR-induction of an endogenous gene gave results identical to those with an exogenous reporter. Thus new tools to determine previously unobtainable information about the nature and position of cofactor action in any process displaying first-order Hill plot kinetics are now available.

New paper on GPCRs

New paper in PloS One:

Fatakia SN, Costanzi S, Chow CC (2011) Molecular Evolution of the Transmembrane Domains of G Protein-Coupled Receptors. PLoS ONE 6(11): e27813. doi:10.1371/journal.pone.0027813

Abstract

G protein-coupled receptors (GPCRs) are a superfamily of integral membrane proteins vital for signaling and are important targets for pharmaceutical intervention in humans. Previously, we identified a group of ten amino acid positions (called key positions), within the seven transmembrane domain (7TM) interhelical region, which had high mutual information with each other and many other positions in the 7TM. Here, we estimated the evolutionary selection pressure at those key positions. We found that the key positions of receptors for small molecule natural ligands were under strong negative selection. Receptors naturally activated by lipids had weaker negative selection in general when compared to small molecule-activated receptors. Selection pressure varied widely in peptide-activated receptors. We used this observation to predict that a subgroup of orphan GPCRs not under strong selection may not possess a natural small-molecule ligand. In the subgroup of MRGX1-type GPCRs, we identified a key position, along with two non-key positions, under statistically significant positive selection.

New paper

A new paper in Physical Review E is now available on line here.  In this paper Michael Buice and I show how you can derive an effective stochastic differential (Langevin) equation for a single element (e.g. neuron) embedded in a network by averaging over the unknown dynamics of the other elements. This then implies that given measurements from a single neuron, one might be able to infer properties of the network that it lives in.  We hope to show this in the future. In this paper, we perform the calculation explicitly for the Kuramoto model of coupled oscillators (e.g. see here) but it can be generalized to any network of coupled elements.  The calculation relies on the path or functional integral formalism Michael developed in his thesis and generalized at the NIH.  It is a nice application of what is called “effective field theory”, where new dynamics (i.e. action) are obtained by marginalizing or integrating out unwanted degrees of freedom.  The path integral formalism gives a nice platform to perform this averaging.  The resulting Langevin equation has a noise term that is nonwhite, non-Gaussian and multiplicative.  It is probably not something you would have guessed a priori.

Michael A. Buice1,2 and Carson C. Chow11Laboratory of Biological Modeling, NIDDK, NIH, Bethesda, Maryland 20892, USA 2Center for Learning and Memory, University of  Texas at Austin, Austin, Texas, USA Received 25 July 2011; revised 12 September 2011; published 17 November 2011 Complex systems are generally analytically intractable and difficult to simulate. We introduce a method for deriving an effective stochastic equation for a high-dimensional deterministic dynamical system for which some portion of the configuration is not precisely specified. We use a response function path integral to construct an equivalent distribution for the stochastic dynamics from the distribution of the incomplete information. We apply this method to the Kuramoto model of coupled oscillators to derive an effective stochastic equation for a single oscillator interacting with a bath of oscillators and also outline the procedure for other systems. Published by the American Physical Society URL: http://link.aps.org/doi/10.1103/PhysRevE.84.051120 DOI: 10.1103/PhysRevE.84.051120 PACS: 05.40.-a, 05.45.Xt, 05.20.Dd, 05.70.Ln

New paper in The Lancet

The Lancet has just published a series of articles on obesity.  They can be found here.  I am an author on the third paper, which covers the work Kevin Hall and I have been working on for the past seven years.  There was a press conference in London yesterday that Kevin attended and there is a symposium today.  The announcement has since been picked up in the popular press.  Here are some samples:  Science Daily, Mirror, The Australian, and The Chart at CNN.

 

 

New paper on binocular rivalry

J Neurophysiol. 2011 Jul 20. [Epub ahead of print]

The role of mutual inhibition in binocular rivalry.

Seely J, Chow CC.

Binocular rivalry is a phenomenon that occurs when ambiguous images are presented
to each of the eyes. The observer generally perceives just one image at a time,
with perceptual switches occurring every few seconds. A natural assumption is
that this perceptual mutual exclusivity is achieved via mutual inhibition between
populations of neurons that encode for either percept. Theoretical models that
incorporate mutual inhibition have been largely successful at capturing
experimental features of rivalry, including Levelt's propositions, which
characterize perceptual dominance durations as a function of image contrasts.
However, basic mutual inhibition models do not fully comply with Levelt's fourth
proposition, which states that percepts alternate faster as the stimulus
contrasts to both eyes are increased simultaneously. This theory-experiment
discrepancy has been taken as evidence against the role of mutual inhibition for
binocular rivalry. Here, we show how various biophysically plausible
modifications to mutual inhibition models can resolve this problem.

PMID: 21775721  [PubMed - as supplied by publisher]

Paper can be downloaded here.

Review paper on steroid-mediated gene expression

Mol Cell Endocrinol. 2011 Jun 1. [Epub ahead of print]

The road less traveled: New views of steroid receptor action 
from the path of dose-response curves. 
Simons SS Jr, Chow CC.

Steroid Hormones Section, NIDDK/CEB, NIDDK, National Institutes of Health,
Bethesda, MD, United States.

Conventional studies of steroid hormone action proceed via quantitation of the
maximal activity for gene induction at saturating concentrations of agonist
steroid (i.e., A(max)). Less frequently analyzed parameters of receptor-mediated
gene expression are EC(50) and PAA. The EC(50) is the concentration of steroid
required for half-maximal agonist activity and is readily determined from the
dose-response curve. The PAA is the partial agonist activity of an antagonist
steroid, expressed as percent of A(max) under the same conditions. Recent results
demonstrate that new and otherwise inaccessible mechanistic information is
obtained when the EC(50) and/or PAA are examined in addition to the A(max).
Specifically, A(max), EC(50), and PAA can be independently regulated, which
suggests that novel pathways and factors may preferentially modify the EC(50)
and/or PAA with little effect on A(max). Other approaches indicate that the
activity of receptor-bound factors can be altered without changing the binding of
factors to receptor. Finally, a new theoretical model of steroid hormone action
not only permits a mechanistically based definition of factor activity but also
allows the positioning of when a factor acts, as opposed to binds, relative to a
kinetically defined step. These advances illustrate some of the benefits of
expanding the mechanistic studies of steroid hormone action to routinely include
EC(50) and PAA.

PMID: 21664235  [PubMed - as supplied by publisher]

New paper on insulin’s effect on lipolysis

J Clin Endocrinol Metab. 2011 May 18. [Epub ahead of print]

Higher Acute Insulin Response to Glucose May Determine Greater 
Free Fatty Acid Clearance in African-American Women.

Chow CC, Periwal V, Csako G, Ricks M, Courville AB, Miller BV 3rd, Vega GL,
Sumner AE.

Laboratory of Biological Modeling (C.C.C., V.P.), National Institute of Diabetes
and Digestive and Kidney Diseases, National Institutes of Health, Bethesda,
Maryland 20892; Departments of Laboratory Medicine (G.C.) and Nutrition (A.B.C.),
Clinical Center, National Institutes of Health, and Clinical Endocrinology Branch
(M.R., B.V.M., A.E.S.), National Institute of Diabetes and Digestive and Kidney
Diseases, National Institutes of Health, Bethesda, Maryland 20892; and Center for
Human Nutrition (G.L.V.), University of Texas Southwestern Medical Center at
Dallas, Dallas, Texas 75235.

Context: Obesity and diabetes are more common in African-Americans than whites.
Because free fatty acids (FFA) participate in the development of these
conditions, studying race differences in the regulation of FFA and glucose by
insulin is essential. Objective: The objective of the study was to determine
whether race differences exist in glucose and FFA response to insulin. Design:
This was a cross-sectional study. Setting: The study was conducted at a clinical
research center. Participants: Thirty-four premenopausal women (17
African-Americans, 17 whites) matched for age [36 ± 10 yr (mean ± sd)] and body
mass index (30.0 ± 6.7 kg/m(2)). Interventions: Insulin-modified frequently
sampled iv glucose tolerance tests were performed with data analyzed by separate
minimal models for glucose and FFA. Main Outcome Measures: Glucose measures were
insulin sensitivity index (S(I)) and acute insulin response to glucose (AIRg).
FFA measures were FFA clearance rate (c(f)). Results: Body mass index was similar
but fat mass was higher in African-Americans than whites (P < 0.01). Compared
with whites, African-Americans had lower S(I) (3.71 ± 1.55 vs. 5.23 ± 2.74
[×10(-4) min(-1)/(microunits per milliliter)] (P = 0.05) and higher AIRg (642 ±
379 vs. 263 ± 206 mU/liter(-1) · min, P < 0.01). Adjusting for fat mass,
African-Americans had higher FFA clearance, c(f) (0.13 ± 0.06 vs. 0.08 ± 0.05
min(-1), P < 0.01). After adjusting for AIRg, the race difference in c(f) was no
longer present (P = 0.51). For all women, the relationship between c(f) and AIRg
was significant (r = 0.64, P < 0.01), but the relationship between c(f) and S(I)
was not (r = -0.07, P = 0.71). The same pattern persisted when the two groups
were studied separately. Conclusion: African-American women were more insulin
resistant than white women, yet they had greater FFA clearance. Acutely higher
insulin concentrations in African-American women accounted for higher FFA
clearance.

PMID: 21593106  [PubMed - as supplied by publisher]

New paper on estimating food intake from body weight

 Am J Clin Nutr. 2011 Jul;94(1):66-74. Epub 2011 May 11.

Estimating changes in free-living energy intake and its confidence interval.

Hall KD, Chow CC.

Laboratory of Biological Modeling, National Institute of Diabetes and Digestive
and Kidney Diseases, Bethesda, MD.

Background: Free-living energy intake in humans is notoriously difficult to
measure but is required to properly assess outpatient weight-control
interventions. Objective: Our objective was to develop a simple methodology that 
uses longitudinal body weight measurements to estimate changes in energy intake
and its 95% CI in individual subjects. Design: We showed how an energy balance
equation with 2 parameters can be derived from any mathematical model of human
metabolism. We solved the energy balance equation for changes in free-living
energy intake as a function of body weight and its rate of change. We tested the 
predicted changes in energy intake by using weight-loss data from controlled
inpatient feeding studies as well as simulated free-living data from a group of
"virtual study subjects" that included realistic fluctuations in body water and
day-to-day variations in energy intake. Results: Our method accurately predicted 
individual energy intake changes with the use of weight-loss data from controlled
inpatient feeding experiments. By applying the method to our simulated
free-living virtual study subjects, we showed that daily weight measurements over
periods >28 d were required to obtain accurate estimates of energy intake change 
with a 95% CI of <300 kcal/d. These estimates were relatively insensitive to
initial body composition or physical activity level. Conclusions: Frequent
measurements of body weight over extended time periods are required to precisely 
estimate changes in energy intake in free-living individuals. Such measurements
are feasible, relatively inexpensive, and can be used to estimate diet adherence 
during clinical weight-management programs.

PMCID: PMC3127505 [Available on 2012/7/1]
PMID: 21562087  [PubMed - in process]