## Summary

Time series gene expression (transcriptome) data provide information on global changes in expression patterns occurring through the course of cancer progression. The premise of this work is that cancer can be viewed as a state transition of the transcriptome, and that the transcriptome behaves as a particle in a force field obeying basic physical principles of motion. The implication of this concept is that cancer progression may be understood, and predicted, with mathematical models of motion of the transcriptome in a low-dimensional projection that can be constructed to retain a maximal amount of relevant information in the system. We use a genetic mouse model of acute myeloid leukemia (AML) to demonstrate the concepts of our mathematical model. We show that the transition of the transcriptome from a health state to a leukemia state can be understood in terms of mathematically-derived inflection points which characterize the dynamic probability of leukemia development.

## Introduction

Cancer evolves as a complex dynamic system wherein multilayer interconnected inputs, including genetic and epigenetic alterations, clonal expansion, evolutionary selection, and microenvironmental plasticity, collectively combine to produce a disease state corresponding to a clinical phenotype. Identification of gene mutations, epigenetic changes and gene expression profiles produced by high-throughput sequencing assays are becoming a part of the routine clinical assessment of cancer patients at diagnosis and subsequent time-points. While current theories of cancer evolution conceptually consider changes in the genome as a whole, the predominant focus remains on a handful of specific oncogenic mutations and clonal dynamics (Graham and Sottoriva, 2016; Landau et al., 2014; Michor et al., 2005; Zhao et al., 2016). However, oncogenic mutations are often not mutually exclusive, and associate in a non-random fashion, thereby making it almost impossible to dissect their individual contributions to clinical phenotypes and prioritize them as therapeutic targets. Nevertheless, these combinatorial sets of mutations are often characterized by specific gene expression signatures representing aberrantly activated or inactivated homeostatic pathways that are ultimately responsible for the observed biological and clinical phenotypes of disease (Almassalha et al., 2016). Moreover, epigenetic alterations, clonal dynamics, and microenvironmental inputs are convergently manifested at the level of gene expression. Thus, global changes in gene expression signatures seem to represent ideal genomic biomarker for a complete assessment of disease evolution.

From a clinical perspective of predicting cancer progression, the most pragmatic use of genomic data is to identify subsets of genes or transcripts (a “signature” or “panel”) that are associated with predetermined biological or clinical features (Nabhan et al., 2015; Ng et al., 2016). Unfortunately, the predictive value of these signatures drops off precipitously if all elements of the signature are not apparent, nor do they provide a prediction of how the signatures might change over time (Jo et al., 2014; Sanavia et al., 2015). The exponential number of variations that could be observed from simple changes in a small number of genes in a signature points to a central challenge facing the precision medicine effort, which aims to target individual or sets of genes (Hyman et al., 2017; Lipinski et al., 2016; Tannock and Hickman, 2016). This leads us to agree with the contention that the era of “big data” is in need of “big theory” to guide interpretations of high-dimensional data sets, whose structures and intricate biological meanings are exceedingly complex and change dynamically over time (Coveney et al., 2016). We therefore desire a more holistic, conceptual, and mathematical approach to study the smooth, continual change in configurations of the system that does not suffer from a combinatorial explosion of complexity, while retaining the maximum amount of information in the system. The central hypothesis of our theory is that cancer can be viewed as a state transition of the transcriptome, and that the transcriptome behaves as a particle in a force field obeying basic physical principles of motion.

State transition models have been used to characterize cellular differentiation states (Furchtgott et al., 2017; Hormoz et al., 2016; Li et al., 2016; Mojtahedi et al., 2016; Moris et al., 2016; Rizvi et al., 2017; Zhou et al., 2012), to characterize phenotypes of cells and gene regulatory networks (Wooten and Quaranta, 2017), or to define fitness landscapes in evolutionary models of therapeutic resistance (Nichol et al., 2016). Dynamical systems approaches have been used to study changes in gene expression (Kuwahara and Schwartz, 2012; Mackey et al., 2015), however, these and similar systems biology approaches, are focused on the scale of individual genes and regulatory networks (Zheng et al., 2012). Statistical tools have been developed to analyze time series transcriptomic data (Jo et al., 2014; Spies and Ciaudo, 2015), but these approaches are not predictive theories that hypothesize how the system should- or should-not evolve. To our knowledge, none of these or similar dynamical systems approaches has been applied to define state transition dynamics at a genome wide scale. Here we argue, and demonstrate, that complex processes occurring at the scale of individual or sets of genes, are manifested and represented by simple macroscopic dynamics that may be predictable.

Instead of tracking hundreds to tens of thousands of changes in specific sets of genes, we consider the state of the genome as a configuration and study the smooth continual change of gene expression (i.e., transcriptome) as a whole over the course of cancer progression. Here we propose a mathematical model, and more generally a theory, of cancer as a state transition of the transcriptome. We present this theory and model as a method to describe and predict the evolution of cancer with a long-term goal of application in clinical settings where whole genome gene expression data over time is available. We use acute myeloid leukemia (AML) (Dohner et al., 2015) as a model system for this endeavor because of the close resemblance of mouse models to human disease and the easy access to blood samples *in vivo* over time. Herein we report on the dynamics of state transition from health to leukemia in a 2-dimensional “state-space” constructed with time series gene expression profiles derived from peripheral blood mononuclear cells (PBMC) from a genetic mouse model of AML. Our mathematical model provides a tool to interpret and predict changes in gene expression over time as well as introduces the novel concept of an leukemogenic (oncogenic) force which determines the dynamics of state transition from health to leukemia.

## Methods

### Inv(16) driven acute myeloid leukemia

**Acute myeloid leukemia (AML)** is a genetically and epigenetically heterogeneous malignant disease of the bone marrow (BM) comprising multiple entities characterized by gene mutations and chromosomal abnormalities. Recurrent chromosomal abnormalities in AML frequently and often result in leukemogenic fusion genes encoding chimeric proteins that contribute to the unique etiology and prognosis of distinct subsets of AML. One of the most common recurrent cytogenetic aberrations found in approximately 5-12% of AML patients is inv(16)(p13.1q22) or t(16;16)(p13.1;q22) [henceforth inv(16)]. At the molecular level, inv(16) disrupts the core-binding factor (CBF) transcription complex fusing *CBFB* with the *MYH11* gene and creates a leukemogenic fusion gene *CBFB-MYH11* (CM), which encodes a leukemogenic chimeric protein. We have established a *CM* knock-in mouse model (*Cbfb ^{+/56M}*/

*Mx1-Cre*), in which conditional expression of

*CM*fusion transcript drives AML development (Cai et al., 2016; Kuo et al., 2006).

To test our state-space mathematical model in which changes of the transcriptome can be modeled over time, we conducted a longitudinal study of conditional *CM* knock-in mice (*Cbfb ^{+/56M}*/

*Mx1-Cre*; C57BL/6; n=9) and littermate controls lacking the transgene (n=7). All mice were injected with a synthetic double-stranded RNA polyinosinic–polycytidylic acid [poly (I:C)]. In

*CM*mice, poly(I:C) induced Cre-mediated recombination and in turn

*CM*expression. Peripheral blood (PB) samples were collected before induction (“0” time point) and at 1, 2, 3, 4.5, 5.5 and 6.5 months after induction, or when

*CM*mice became moribund (Fig. 2a). By 6.5 months (“end” time point), six

*CM*mice developed leukemia, defined by the presence of 20% or more leukemic blasts in the PB and BM (“

*CM*sick”) while three

*CM*mice had not (“

*CM*not sick”) but showed expansion of phenotypic hematopoietic stem and progenitor cell subpopulations in the bone marrow (BM) (Fig. S1), consistent with previous descriptions of

*CM*expression in this mouse strain (Cai et al., 2016). PBMC whole genome RNA-Seq was performed in both

*CM*and control mice. In

*CM*mice, the

*CM*fusion transcript levels were measured based on human

*MYH11*sequencing reads originating from the

*Cbfb*allele and reported in counts per million reads (cpm) at each sequential time point (Fig. 2b).

^{+/56M}We constructed a matrix ** X**, consisting of all time series gene expression data in units TPM (see supplementary methods) with dimension [

*M*×

*N*] where

*M*is the number of genes, and

*N*=

*nτ*is the number of mice (

*n*) multiplied by the number of observations (

*τ*) across all mice (Fig. 2c). To simplify the complexity of the state-space and the state transition analysis, we elected to project the high-dimensional space of gene expression onto a 2-dimensional (2D) plane, which we defined to be the health-leukemia state-space, by factoring the data matrix

**X**with the singular value decomposition (SVD) (Fig. 2d). The SVD is a matrix factorization method previously used to decompose gene expression data (Aiello and Alter, 2016; Ponnapalli et al., 2011). We selected the first two components of the SVD to define a 2D state-space, consisting of two basis vectors

*ν*

_{0},

*ν*

_{1}in the canonical Cartesian coordinate system which we label (

*s,s*

_{1}), so that each point in the state-space is a linear combination of all genes in the transcriptome. Of note, the 2D state-space constructed with gene expression data using the SVD approach results in a coordinate space without physical units.

### Mathematical model of gene expression state transition

An essential concept of our state transition theory is that of a “state-space:” a low dimensional projection of the transcriptomic space, where states are defined geometrically and energetically by potential energy functions. To develop a mathematical model of cancer–and here we show for AML–as a state transition of the transcriptome, we postulate that the macroscopic dynamics of the transcriptome may be represented as a particle with unit mass moving in a potential energy field in a transcriptomic state-space. In healthy conditions, we suggest the transcriptome behaves as a stochastically varying homeostatic process where relatively large fluctuations in gene expression are prevented by feedback mechanisms. Thus, we represent the net force acting on a healthy transcriptome as a gradient of a homeostatic potential , where is a Brownian stochastic process that is uncorrelated in time with zero mean and variance *σ* > 0 (Fig. 1A). The Brownian process represents stochastic fluctuations in gene expression and the internal energy of the system to move in the space. Homeostasis is modeled as an Ornstein-Uhlenbeck process (Rohlfs et al., 2014; Uhlenbeck and Ornstein, 1930) which is a stochastic process that reverts to a mean state located at *M* = [*μ*_{0}, *μ*_{1}] given by where in general, *S* is an ordered n-tuple in Cartesian coordinates, with n=2 we have *S* = (*s*_{0}, *s*_{1}), with homeostatic reversion rate constants given by the elements in the parameter matrix *Θ* = [*θ*_{0,0} *θ*_{0,1}; *θ*_{1,0} *θ*_{1,1}].

Next, we hypothesize that the expression of an oncogene (here we will use the AML transgene *CM* as an example) can create a singularity in the health potential and generate a “oncogenic” force that drives the system towards the singularity (Fig. 1B). Thus, we hypothesize the net force exerted on the particle (i.e. transcriptome) upon expression of *CM* would consist of a normal homeostatic health potential *U _{H}*, and a leukemic potential

*U*

_{L}as follows, with ∇

*U*and ∇

_{L}*U*given by

_{H}Here *A* = [*α*_{0,0} *α*_{0,1}; *α*_{1,0} *α*_{1,1}] is a 2×2 matrix of parameters which determine the rate of transition to leukemia and *N* is a parameter that determines the magnitude of the *CM* leukemogenic force. Due to the stochastic component of the net force, the creation of the singularity and presence of the leukemogenic force does not guarantee or predetermine the transition to a leukemic state. We postulate that the equation of motion in the potential energy space is given by the Langevin equation where *λ* is the damping constant in an overdamped motion on the potential and may be taken to be unity (Bezuglyy et al., 2006; Zhou et al., 2012).

### Structure and construction of a transcriptome state-space

A key concept of our theory is that the transcriptome contains essential information necessary to describe the dynamical process of leukemia development. However, given the high dimensional nature of the transcriptome (order of 10^{6}) and the fact that not all the information present in the transcriptome is equally important, we desire a projection of the transcriptome information into a lower dimensional space that can preserve a maximum amount of information in the system relevant to the process of interest. Ideally, in a 2-dimensional representation, the leukemic and non-leukemic components should also be orthogonal, and therefore their contributions to the overall dynamics should be separable. The orthogonality property will be particularly useful in the modeling of the two processes (i.e., health and leukemia) independently.

We show that it is possible using information content measured by mutual information with respect to state variables, to construct an orthogonalized 2-dimensional state-space coordinate system (*S* = (*s*_{0}, *s*_{1})) that maximizes the amount of information relevant to leukemia development along the ordinate axis (Fig. S2). Therefore, we contend the dynamics of state transition from health to leukemia in the orthogonalized 2-dimensional state-space are determined by stationary points of the equation of motion in one dimension along the leukemia (*s*_{1}) axis. In particular, the dynamics in the ordinate and absicca directions of the state-space are sufficiently decoupled so that we may take off-diagonal elements in the matrices *Θ* and *A* to be zero, so that all entries in the matrix *A* are zero except *α*_{1,1} > 0 and the singularity is located at (*μ*_{0, 0}). This simplification may be relaxed to study the degree of coupling between the homeostatic and leukemogenic dynamics.

### Critical points in the dynamics of state transition in the state-space

The critical points are positions in the state-space where the velocity of movement is zero and are calculated by considering the deterministic terms in the equation of motion in one dimension along the leukemia axis, . There can be zero, one, or two critical points in the system for *s*_{1} > 0 (see Supplementary methods). In the case of two critical points, the critical point *c*_{1} is an attractor point and represents the perturbation of the transcriptome away from the health equilibrium at *μ*_{1}. The movement of point *c*_{1} away from *μ*_{1} is due to a leukemogenic force directed towards the singularity at zero. The critical point *c*_{2} is an unstable critical point and represents a transition point in the dynamics from health to leukemia. When the particle in the state-space crosses the critical point *c*_{2}, the velocity of the particle increases unboundedly, and asymptotically approaches the singularity (Fig. 1C). These dynamics can be interpreted **biologically** as an acceleration of leukemia development after the threshold *c*_{2} is crossed. The boundary of the health and leukemia states in the state-space is located where the magnitude of the leukemogenic potential equals the magnitude of the health potential, *U _{L}* =

*U*denoted

_{H}*c*

_{3}which lies beyond the transition point (Fig. 1D). The parameters (

*α*

_{1,1},

*N*) can be calculated based solely on estimates of the critical points

*c*

_{1}, and

*c*

_{2}in the state-space (see Supplementary methods). The values of the parameters

*θ*

_{1,1},

*μ*

_{1}may be taken to be unity without a change in the qualitative dynamics of the system.

## Results

*CM* leukemogenic force correlates with *CM* expression

Because *CM* fusion transcript is a principle biological determinant in driving AML development, we examined the correlation between the expression level of CM ([*CM*]) and the force exerted on the particle in the state-space by evaluating the force function with the parameters estimated from the data (see Supplementary methods). At each point in the state-space, a force vector is defined by Equation (1), which represents the deterministic dynamics of the movement of the particle representing the transcriptome in the state-space at that position (Fig. 2F,G). At an arbitrary position in the state-space , the magnitude of the leukemic force is computed along the leukemic axis as and the magnitude of the health force is given by (Fig. 3A). Induced CM mice in general develop leukemia between 3 to 6 months within the observation time of our experiment (7 months); we defined these mice as “*CM* sick”. A subset of mice may either take longer time or never develop leukemia; we defined these mice as “*CM* not sick”. The median leukemogenic force in the *CM* sick mice was an order of magnitude higher than that in the *CM* not sick (0.20 vs. 0.08, p < 0.001), with the range of values extending several orders of magnitude higher in *CM* sick mice than *CM* not sick mice (Fig. 3B). The magnitude of the leukemogenic force was able to discriminate *CM* sick from *CM* not sick mice as early as 1 month post induction; however the change in [CM] was not able to distinguish the two groups (Fig. S4A,B). The leukemogenic force and [CM] were not correlated at 1 month post induction (Fig. S4C), however the differences in the expression level of [CM] become more pronounced between the *CM* sick and *CM* not sick mice over time (Fig. S4D). We observed a strong correlation between [*CM*] and the leukemia force exerted on the transcriptome particle as it moved in the state-space, with a stronger correlation for the *CM* sick mice (r^{2}=0.81, p<0.001) than the *CM* not sick mice (r^{2}=0.21, p=0.117) and a weaker correlation between [*CM*] and the healthy force (*CM* sick r^{2}=0.60; *CM* not sick r^{2}=0.35; Fig. 3C).

### Energy states

As a novel measure of the state of the transcriptome and its association with either a health or leukemia state, we calculated the potential energy in the state-space for the control and *CM* mice along the leukemic axis. At an arbitrary position in the space, , the potential energy for control mice (denoted *E ^{Ctl}*) is given by evaluating the health potential at that position, . For the

*CM*mice, the potential energy (denoted

*E*) at the position

^{CM}*S*

^{0}is given by evaluating the sum of the health and leukemic potentials, . The potential energy at the boundary of the leukemia (denoted

*E*) and the health states (

_{L}*c*

_{3}) is given by

*E*=

_{L}*E*(

^{CM}*c*

_{3}) ≈ −0.7021. The shift in potential energy at

*c*

_{1}caused by

*CM*expression is

*E*(

^{CM}*c*

_{1}) ≈ −0.5178 vs. that of health equilibrium

*E*(

^{Ctl}*μ*

_{1}) = −0.5. Accordingly, the change in potential energy associated with the leukemogenic alteration is immediately seen at 1 month post induction, with a mean energy of

*CM*sick mice of −0.517±4.6 ×10

^{−4}, a mean energy of control mice of −0.4999±−9.4×10

^{−5}(

*CM*sick vs. control p<0.01), and a mean energy of

*CM*not sick mice of −0.516±−5.5×10

^{−4}(

*CM*sick vs.

*CM*not sick p=0.55). The differences in potential energy between the

*CM*sick,

*CM*not sick, and control mice becomes more pronounced as they transition from health to leukemia states (Fig. 3D).

### Dynamics of leukemia transition in the state-space

The mathematical model predicts the effects of *CM* induction to be immediately observed as a shift in the stable equilibrium *μ*_{1} (translated so that *μ*_{1} = 1) to the critical point *c*_{1} along the leukemia axis as a result of the singularity in the transcriptomic space and the leukemogenic force introduced by the *CM* fusion gene (Fig. 3E). As early as one month post induction, the *CM* sick mice are observed to exhibit a pronounced shift downward in their position in the state-space with *CM* sick mice having a mean position (*s*_{1}) of 0.83±0.04, while the *CM* not sick mice had a mean position of 0.96±0.02 (p<0.01) and controls 0.99±0.01 (*CM* sick vs. control, p<0.01). To use the model to predict the dynamics of transition from health to leukemia, 20,000 Monte Carlo simulations were initialized with the initial (t = 0) positions in the state-space taken from the data using the parameters estimated from the data with control and leukemia trajectories (Fig. 3F). To calculate the probability of transition to leukemia over time, we calculated the mean time to reach the leukemia state (*c*_{3}) from the Monte Carlo simulations and represented the time to transition as a survival curve. The time to leukemia for simulated and observed data were compared using the logrank test in a survival curve analysis and were found to be statistically indistinguishable from each other (p=ns).

Trajectories for control mice are confined to a specific region in the state-space, defined to be *μ*_{1}, compared to *CM* mice. The trajectories of *CM* not sick mice fluctuate around the stationary point *c*_{1} and do not approach the transition point c_{2}. In contrast, the trajectories of the *CM* sick mice are near *c*_{2} and transition to the leukemia state at *c*_{3} (Fig. 4A). Indeed, immunophenotypic analysis by fluorescence activated cell-sorting (FACS) demonstrates that leukemia progression accelerates after crossing the critical point *c*_{2} as evidenced by a sharp emergence of leukemia blast (cKit+) (Fig.4C, D).

## Discussion

The study of state transitions is common in physics, but is virtually nonexistent in biology. A simple example of a state transition is the transition of water from a solid, to a liquid based on changes in temperature and pressure. The theory and mathematics of state transitions is a powerful tool for interpreting and predicting the behavior of complex systems that has yet to be effectively leveraged with genomic data in cancer. Here we report a theory and mathematical model of state transition of the transcriptome from health to leukemia, and demonstrate the mathematical and biological implications of this theory in a mouse model of AML.

The construction of a transcriptomic state-space which defines health and leukemia states geometrically allows a privileged perspective to study leukemia dynamics by isolating as much as possible the processes directly affecting the transition to a leukemia state. Using Langevin dynamics in a state-space defined geometrically and energetically with a mathematical model, we demonstrate our ability to predict state transition from a health state to a leukemia state based on changes in genome-wide gene expression (i.e., transcriptome) over time. Using mathematical methods to project the transcriptome into a 2-dimensional “state-space” representation which maximally preserves relevant information in the system (SVD), we used simple mathematical equations to provide a physical perspective through which to understand progression to leukemia as a continuous change in the configuration of the transcriptome. Movement through this space could be understood in terms of critical points, mathematically-derived inflection points which provides a computational framework to predict the development of leukemia for any point in the space, at any time point in leukemia progression.

This approach permitted us to differentiate, at very early time points (i.e., 1 month), mice that eventually developed leukemia from those that did not upon induction of the leukemogenic transgene, whose expression alone was not able yet to predict which mouse would develop overt leukemia within the observation time (Fig. S4). In addition, we show that the critical points, positions and trajectories in the state-space derived from our model remain valid and apply to an independent gene expression dataset from an independent cohort of mice (Fig. S5). Consistent with the mathematically-derived inflection points predicted by our theory, after crossing the critical point *c*_{2} we observed accelerated trajectories towards a leukemia state based on FACS-based immunophenotypic analysis. Notably, at this point leukemia development is not yet evident based on conventional FACS assays. Thus, a predictive mathematical model of the dynamics of transition to leukemia that may anticipate critical transitions (Scheffer et al., 2012) has many implications and potential uses, including when to monitor disease changes, and as a novel tool to quantify and predict response to therapy.

The concept of a disease space in the context of infection (Torres et al., 2016) and information theoretic potential energy landscapes in the epigenome (Jenkinson et al., 2017), and the Ornstien-Uhlenbeck model has recently been proposed to describe the evolution of gene expression patterns in the mammalian genome (Chen et al., 2017). Although these approaches do not include a mathematical treatment of dynamics or changes over time. The mathematically-derived theory of state transition presented here intuitively contextualizes complex time series gene expression data into a simple conceptual framework that associates a state of disease with an increased state of energy of the gene expression space, and introduces the concept of a leukemogenic force associated with a particular genomic alteration. Our model is an innovative departure from conventional mathematical modeling approaches of cancer that focus on the accumulation of oncogenic mutations and clonal dynamics, and introduces the novel concept of genetic alterations as forces that drive state transitions in gene expression that accompany the evolution of cancer.

Our theory leads to the hypothesis that there exists a necessary and sufficient force exerted on the genome required to initiate state transition, as well as to the conjecture that an equal and opposite therapeutic force could be required to return to a health equilibrium. Furthermore, this work suggests the homeostatic relaxation rate and noise parameters should be measured, perhaps through non-oncogenic perturbations of the system. This approach provides a novel framework to quantify the effects and magnitude of oncogenic alterations on the transcriptome, and ultimately on a disease process.

Analysis of trajectories and dynamics in the state-space of complex time series genes expression data are given context by our mathematical model and theory. We provide a new perspective on AML development at a level of abstraction which to our knowledge, has not been previously demonstrated in a controlled experiment. In principle, the state-space and mathematical model may be applied to other systems (e.g., other subtypes of leukemias or cancers), and to other forms of omics data (e.g., epigenomics, proteomics). Therefore, this work may have a broad impact on understanding cancer development, improving molecular-risk stratification and prognostication, guiding treatment selection, and more generally, studying the evolution of multidimensional changes in biological entities as a state-based dynamical system.

## Author contributions

RCR, SB, Y-HK, GM, designed the experiments; RCR, SB designed the mathematical model; JQ, GJC, W-KH, EC, AM performed the experiments; HW, DM, DO’M, contributed data analysis and model simulations; XW, Y-CY, ZL, DO’M, contributed bioinformatics analysis and processing of raw data; NC, SJF, LDW, Y-HK, GM, RCR, SB, HW, DO’M, contributed to data interpretation and analysis; Y-HK, RCR, GM provided financial support. All authors contributed to manuscript editing. RCR, SB, NC, LDW, Y-HK, GM gave final approval of manuscript.

No competing financial interests

Correspondence and requests for materials should be addressed to Russell Rockne (rrockne{at}coh.org); Ya-Huei Kuo (ykuo{at}coh.org); Guido Marcucci (gmarcucci{at}coh.org).

## Acknowledgments

This study was funded by the Gehr Family Center for Leukemia Research, and in part by the National Institutes of Health under award number R01CA178387 (to Y.-H.K.) and a St. Baldrick’s Foundation Scholar Award (to L.D.W.). Research reported in this publication included work performed in the Analytical Cytometry Core and Animal Resource Center supported by the National Cancer Institute of the National Institutes of Health under award number P30CA33572. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. We thank Art Riggs for his support of this project.