Note: Descriptions are shown in the official language in which they were submitted.
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COMPUTATIONAL SYSTEM FOR MODELING
PROTEIN EXPRESSION IN AN ORGAN
CROSS REFERENCE TO RELATED APPLICATIONS
s The present invention claims the benefit of provisional application
60/140416, filed 6/2211999 with the same title. The application incorporates
by
reference the disclosure of co pending U.S. Patent Application Serial No.
09/305,188
filed May 04, 1999 in its entirety.
io FIELD OF THE INVENTION
The present invention relates to computer models of organs implemented
in software and more particularly to an organ model that enables one to study
the
effects of protein expression on organ performance and biofunctionality.
is BACKGROUND OF THE INVENTION
U.S Patent 5,947,899 shows how to create a computational model of a
complete organ. That disclosure is set forth in the context of a whole heart
model
where the anatomic relationships between cardiac cells are modeled by a set of
coupling relationships between nodes of a network. Each node represents a
physical
2o subunit of tissue. A separate set of equations define the electrophysiology
of the
individual cardiac cells and these equations are used to compute an action
potential
(AP) at each node. The time course of the action potential may be represented
graphically and compared with physical measurements made experimentally.
In this architecture, each node of the model has two computationally
2s separate types of information associated with it. A distinct advantage of
the model is
the ability to compute the local and global portions of the model
simultaneously and
independently while allowing the local and global processes to interact.
Since the network itself reflects the global anatomic relationships between
cells or groups of cells and the nodes represent the metabolic actions at the
local level
3o the model paradigm allows for the integration of interaction between the
local
physiological data and the global coupling relationships. As a consequence the
cellular activity is propagated in a realistic way over the whole organ and
whole organ
behavior flow directly from the model.
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T"
This methodology allows one to compute the gross macroscopic
biofunctionality at the organ level arising out of discrete populations of
single cell
models. The gross behavior of the model can be compared with physical
experiments
for verification and the detailed cellular modeling can be compared with
electrophysiologic experiments as well.
However, in spite of these advances, there is a continuing need to expand
the generality of the model to other organs and systems, and to extend the
model to
simulate the impact of other cellular, subcellular, genetic and molecular
processes.
to SUMMARY OF THE INVENTION.
In the present invention, a partial organ model is described which can be
used to explore and model the impact of genetic and sex linked cellular
changes on the
organ. Genetic differences in the model are modeled by noting and modeling the
changes in protein function or distribution or transportation associated with
genetic
mutations, sex differences, disease or allele based variations in the pattern
of gene
expression.
In general, experimental measurements of molecular properties, single cell
activity or protein function in normal or genetically altered cellular systems
are
gathered and expressed as equations which describe the observed action
potential of
2o isolated cells or tissues.
This information is combined with anatomic data in the model. In general,
virtual "cells" are constructed and then assembled together into the network.
Each
node location in the network reflects a different physical location. The
virtual cells
that occupy various sections of the model network will typically differ in the
node
2s equations that describe the action potential. It is also common that the
coupling
relationships differ between regions of the network.
The protein computations impact the action potential of all cells but
depending on the actual location in the network the actual time course of an
individuals cells action potential may vary dramatically from its neighbors.
3o This technique is useful for determining the impact of a mutation or sex on
the performance of an otherwise equivalent organ. The ability to model some
sex
based changes and to ignore others within the model domain is a very useful
and a
feature not easily available in physical models.
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The utility of this modeling process is the ability to determine mutation
induced changes in response to disease, drugs, or other perturbations in
transmembrane potential. The organ model is also useful for determining
differences
in the response to drugs, genetic mutations, or disease expression related to
sex and
s allelic variations in cellular background.
The invention is illustrated in the context of a heart wedge model and the
node computations take into account sex based differences in protein
expression as
well as variations in cell type. At the organ level the model simulates sex
based
reactions to drugs. In this model the initial conditions are perturbed by a
simulated
io stimulus which is propagated at the network level and which influences the
time
course of the action potentials computed at each node.
The cells types illustrated are excitable cells which signal by changing
their transmembrane potentials. The invention may be utilized to model other
system
with excitable cells and the heart wedge illustration is exemplary and not
intended to
~s be limiting.
BRIEF DESCRIPTION OF THE DRAWINGS
Throughout the various figures of the drawing identical reference numerals
indicate identical structures or processes. The embodiments of the invention
shown
2o are illustrative and should not be taken as limiting the scope of the
invention, wherein:
FIG. 1 has a panel 1A that is a simplified flow chart describing the
creation and computation of the model, panel 1B is an alternate schematic
representation of the model and the model building process;
FIG. 2 includes panel 2A which is a schematic representation of an organ,
2s and panel 2B which is a schematic representation of a network model showing
a lattice
of nodes and relationships between nodes;
FIG. 3 is graphic representation of action potentials presented as panel 3A
and panel 3B;
FIG. 4 includes panels 4A, panel 4B, and panel 4C, which are computed
so action potentials related to sex;
FIG. 5 is a computed action potential related to sex based differences in
the effect of a drug;
FIG. 6 is presented as panel 6A that shows experimental data and panel 6B
that represents simulation; and
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FIG. 7 is a series of panels that represent in panel 7A and panel 7B action
potentials of mutation based variations in protein expression, panels 7C and
7D show
the variation of action potential as a function of cell type.
DETAILED DESCRIPTION
Overview
The invention is both a computation model and related methods for
modeling a biologic organ, the steps of the process are carried out on a
general
purpose computer. The computer is not shown in the figures explicitly. However
the
to figures are the result of the computations carried out according to the
software
processes described.
The method.of the invention begins with the collection of experimental
data related to the molecular properties and physiology of cells with normal
and
mutant gene expression. The most interesting interactions are the protein
interactions
t5 that involve the transmembrane ionic currents. In the case of gene
mutations
specifically, the impact of mutation on protein function, and secondarily, the
impact on
the transmembrane potentials and other features of cell activity are explored
in detail,
including biophysical changes in the ion pumps, transmembrane channels,
receptors
and signaling pathways. Experimental data provide the parameters needed to
model a
2o single cell containing proteins having both "normal" and "aberrant"
functionality. The
profile of cellular functionality is thus developed and the general set of
equations is
extended to model complex behaviors of the cell.
In this step of the process, molecular properties of the gene or protein are
measured and alterations in expression levels or patterns of expression for a
particular
25 gene or protein are noted. For example certain proteins appear to increase
the number
of channels that are open. Other proteins are responsible for the magnitude of
the
current across the membrane.
The resulting physiological properties of the mutation are characterized by
alterations in the time course of the membrane current, transmembrane
potential, ion
so flux, or biochemical reaction rate. At the conclusion of this data
collection and
representation step the impact of protein function on the action potential can
be shown
graphically and used computationally.
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These data and information are used to create or modify single cell models.
The network model is an ensemble of the single cell models that integrates
these
changes in the biofunctionality of the cells into a whole organ or portion of
an organ.
Gender may be modeled in a similar fashion in that sex-specific differences
associated
s with protein type, location, and other molecular and physiological
properties are used
to modify the cellular models.
The anatomic detail is required to model disease accurately and the
incorporated organ model is required to allow this spatial distribution of
cells into
nodes and subsequently intact tissue. W tn the noae iocanons anu m~:al
~~ua~1~11J
to defined, the model is solved and results displayed. It is a convenient
property of the
model methodology that the node computations can be performed simultaneously
and
independently of each other, thus allowing the model to be implemented
effectively on
parallel computers. Heterogeneity in the spatial distribution of the mutation
or
mutations can also be modeled, as well as altered gene or protein expression
patterns
is in the organ, by specifying different cellular, subcellular, and molecular
properties at
individual nodes within the complex model. Various aspects of the modeling
process
are also presented in U.S. Patent 5,947,899.
Data Collection
2o FIG. 1 is a flowchart that shows a stepwise sequence for both a single cell
model and an organ level model. In general, processes 10 through 16 represent
the
data collection and construction of a single cell model. Processes 24 through
28
involve the creation of the network model of the organ or a part of the organ,
while
process 20 reflects the computation of a single cell model. Process 30
reflects the
2s output of either simulation and typically both graphic data and data in
tabular form are
created. Although process 18 represents a choice between single cell and multi
cell
models it should be understood that simulations at the cellular level may be
used to
validate the single cell model against experimental data while network level
organ
simulations can be used to validate the organ level description against
experimental
so tissue experiments.
In process 10 experimental data concerning the behavior of the altered cell
type, and the specific functional properties of the, target protein are
collected. This is a
very labor intensive step because the data are presented in various formats
and may
require substantial searching to uncover the appropriate literature or source
for the
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experimental data. It is common for wet lab experiments to be reported both on
line
and in paper journals. In any given instance the investigator or author may
show a
measured action potential from an isolated cell or group of cells. Gene
sequencing
may show which proteins are active at the time of the electrophysiologic
measurement.
s The data may be available to other investigators in the form of computer
files
representing raw measurements and the protein expression data may be
accompanied
with a wealth of ancillary data. However, the quality of the data is always
problematic. A generalized set of acceptance criteria may be developed. At
present
"in specie" as opposed to "outside specie" work is preferred. Although many
protein
to interactions are similar across cell lines there is no way to determine a
priori whether
this is true for a particular study. Nominal data taken in "usual"
circumstances is
preferred to data taken. during "unusual" metabolic conditions. It is likely
that
"trusted" sources of data taken in accord with a defined protocol will be
preferred.
is Model Building
In process 12 those data collected in step 10 are used to modify the system
of nonlinear ordinary differential equations (ODES) defined at each node of
the lattice,
and to modify the ionic currents of the cellular model. These equations define
the
biophysical processes giving rise to the unique properties of cardiac tissue
and the
2o various cardiac cells. In general, this system includes: a) equations
defining properties
of nonlinear, voltage-gated transmembrane currents; b) equations describing
properties
of ion pumps, exchangers and other features in the cell; c) equations
describing the
buffering, uptake, storage, transfer, and release of calcium ions by
intracellular
organelles; d) equations describing time-varying changes of intracellular ion
2s concentration, and e) equations describing the effects of
neurotransmitters, hormones
and second messengers on these components.
A useful paradigm for modeling cellular dynamics is a
battery/resistor/capacitor model where the membrane currents are the sum of a
set of
voltage sources in parallel with a capacitancence. The voltage sources are
modeled as
3o a battery in series with a resistor. The battery represents the driving
force for ionic
flux through the channel provided by the ionic gradient across the membrane.
The
resistor represents the resistance to ionic flow through the pore of the
channel.
Mathematical models for most ionic currents can be taken directly from data
collected
in step 10. The general form of the equation is I~hannel=Iopenchanel(V~~Popen
where the
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desired channel current is a function of a voltage dependant open channel
current and
the state of the pore as opened or closed. Various methodologies known in the
literature including Hodgkin-Huxley and Markov state modeling can be used to
estimate the open channel and closed channel currents. The simple electrical
model
allows easy accommodation of additional current values and estimates. This
electrical
circuit analogy mates easily with the network node portion of the model used
to
represent anatomy. It is important to note that this methodology models each
ionic
current separately and independently. This means that the ionic currents may
be added
to the model without revising other portions of the model. This independence
allows
to modularity in construction and facilitates model refinement. In general
mutation or
sex based expression will result in differing amounts of protein available for
modulation of transmembrane currents. The cell level model computes action
potentials based on the availability of the requisite proteins.
Another significant value of this methodology is the ability to validate the
~s cellular model alone. In essence, predictions based upon data and modeled
currents
can be compared to experimental data to verify the predictive value of the
cell model
before inclusion into the organ and system model. Fine tuning of the model can
be
accomplished more easily because of this partitioning and architecture.
Process step 14 relates to maictng me ionic c;urrGm val~ula~l~l.~
2o computationally efficient. Many techniques are available to compute sets of
ordinary
differential equations. Process 16 relates to the selection of the particular
simulation
methodology used to analyze the data. For example, some a priori knowledge may
allow the user to ignore some variable or make other simplifying assumptions
for a
particular simulation. In a typical setting a user may have several "single
cell" model
2s available and each will "work". The specific choice for a particular study
may be
simply a user preference.
In process 18 a single cell or network model is selected. Users may begin
with a series of single cell simulations and then select a network model
without
redesigning the single cell model.
so Processes 24 through 28 relate directly to structuring the network model
by defining the location of altered cells in the physical representation of
the organ.
Typically a finite difference lattice work of nodes are preferred to represent
physical
structure of the heart and the physical locations for mutated cells. This
spatial
placement is based upon anatomic knowledge. It is important to note that all
or just
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some cells may have the altered properties. FIG. 2 address this aspect of the
model in
more detail.
The output data from the simulation are available in process 30. Various
figures such as FIG. 2A, FIG. 3, FIG. 4, FIG. 5, and FIG. 7 represent examples
of the
s output from process 30. Both graphic and tabular data is available.
The extension of the model to a specialized tissue preparation and the
operation of the model are facilitated by a brief discussion of FIG. 2. FIG.
2A is
schematic representation of three groups of cells or tissues in a portion of a
"wedge"
40 of cardiac tissues. The tissue group typified by cell 42 (A) is on the
interior of the
o "wedge" and represents an endocardial surface. Cells typified by cell 44 (B)
occupy
the interior of the wedge while cells typified by cell 46 (C) lie on the outer
surface of
the wedge and are representations of the epicardial surface. In general these
autonomous cell layers will have characteristics action potentials depicted in
panel 50
for the corresponding tissue type. The wide variation in the duration of the
action
~s potentials is demonstrating the dynamic behavior of the organ model when
paced at
various rates. The dispersion in duration of action potentials mimics or
models a
similar behavior seen in physical wedge preparations. The longest duration
corresponding to trace 43 are the result of pacing at about 5s intervals and
the shorter
duration typified by trace 41 represents "fatigue" and non linear behaviors at
faster
2o pacing rates corresponding to about 500ms intervals.
The A, B and C types of tissue can depolarize giving rise to a voltage.
Currents associated with this voltage can be communicated to the companion
tissue
groups. This coupling relationship is the fundamental requirement of the organ
model.
The relationship between the tissues is represented in the Figure can give
rise to
2s superficial or surface waveforms that follow the surface of the tissue
wedge. In this
fashion local events in tissue groups are communicated to neighboring tissues.
It is
common to begin the model at time T=0 with a current stimulus to initiate
depolarization of one or more cells. This initial perturbation causes the
dynamic
features of the model presentation seen as the depolarization waveform 47 in
FIG. 2A.
3o The duration of the response is extremely sensitive to the time between
stimuli. Once
the model is running the states of the various virtual cells diverge in a
manner that may
be difficult to predict under some circumstances. The various displayed
durations for
the activation potentials seen in panel 2A "B" for example reflect cycle to
cycle
variations. Each of the different traces of action potential seen in the
figure arises at a
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different cycle length. This figure shows how a simple single cell model
buried in a
dynamic organ model can exhibit realistic cycle to cycle variation in action
potential.
FIG. 2b shows the network model used to model the physical specimen of
FIG. 2a. In FIG. 2b the node 54 is receiving activation from the neighbor node
52.
s However the communication is not symmetrical and the coupling relationship
is diode
like. Symmetrical communication is allowed between node 54 and node 56 as
indicated by the double arrow head configuration of coupling relationship 58.
The
Loop 55 represents the iterative calculation of the local biophysical
equations used to
model the action potential of the tissues represented by the node 54. It is
the value of
to the model that it can solve local equations and compute the interaction of
the local data
to give rise to overall activity of the organ. The family of coupling
relationships
' shown in FIG. 2b allow the construction of heterogeneous tissue structures
using
identical cell types. Heterogeneity can also be achieved by varying the cell
type in
various locations in the model. Anatomic linkages and pathways can be
accurately
~5 reproduced by selecting the correct coupling relationship.
FIG. 3 shows a first panel 3A that represents the action potential 60 of a
male cell and an action potential 62 of a female cell. In this modeling
experiment the
sex based differences in protein expression, uptake and transport has related
in a
substantially different action potentials waveforms. The female trace 62 shows
an
2o extended repolarization time. Panel 3B is labeled with the name of the
current tracked
for sex based differences in protein expression. There are no uniformly
followed
naming conventions for proteins although the labels in the figure are in
common
usage. The B.Ito current is the transient outward current. The C.IKr current
is the
delayed rectifier current. The D.IKl current is the inward rectifier current.
E.IKs
25 current is the slow delayed rectifier current. The disparity between male
66 and
female 68 in the IKr channel provides an insight into the morphology of the
tissue
electrophysiology seen in panel 3A. This output represents the ability of the
model to
display important electrophysiologic consequences of modest allele or sex
based
variations in protein expression.
3o FIG. 4 illustrates the impact of cell type on the cardiac action potential
for
"male" 71 and "female" 69 cells of various cells within the wedge model. The
wedge
model accurately displays significant variations in action potential duration
and
morphology based on differences in protein to expression in cells which differ
solely
by "sex". This illustration points out that the simulation allows the user to
"fix" a set
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variables and allow only specific sex linked or allele based variation to
drive the
model. In this fashion subtle variations in protein expression can be
revealed.
Figure 5 shows the effects of sex-based differences in the expression of
specific ion channels on the computed action potential for "male" and "female"
s cardiac ventricular cells. In each complex in the figure typified by complex
77 the
"male" duration is the shorter of the two durations as typified by trace 75.
In this
complex 77 the longer trace 73 is "female". The figure shows the differential
impact
of a drug acting on these cells. As the drug dose increases, the percent of
channel
blockage increases, resulting in a proarrhythmic response as indicated by the
o appearance of early depolarizations especially in females. The alternans
exhibited in
the 60% blocked channel shows up in the female model but not the male model.
The
alternans is noted by comparing the sequence~of complexes 79, 81, 83, 85 and
77. The
long potentials followed by short potentials is the hallmark of the
arrhythmia.
Although this illustration is modeled with d-sotol it is likely valid for all
potassium
is blocking drugs. The figure shows multiple events paced at an interval of
approximately 2.5 seconds. The multi-dimensional impact of these gender-based
differences, alone and in combination with drug, can be illustrate using a
simulated
electrocardiogram as the read-out. This illustration shows channel blockages
corresponding to an "overdose" of drug. The computer model is substantially
more
2o tolerant of overdose than an experimental preparation. The results provide
a
mechanistic explanation for the prolonged electrocardiographic QT, and for the
increased incidence of drug-induced proarrhythmia interval typically observed
in
females vs. males.
Figure 6 shows in panel 6A classic data of the type collected in process
2s step 10. The data show variations in myocytes based on location and based
on pacing
rate. The simulations of panel 6B are taken under the same conditions and they
show
good agreement with the experimental data thus validating the model. The
ability to
test the model and various scales in time and space is an important attribute
of the
architecture of the model.
3o Figure 7 has a panel 7A which represents a normal (wild) genotype ECG
96 taken from a network model. Corresponding panel 7C shows the action
potentials
of mycoyte at various levels in the simulated wedge epicardial cells are shown
by trace
90, midmyocardial cells are shown by trace 91 and endocardial cells are shown
at 92.
Panel 7B shows a mutation that impacts the surface ECG 97. The individual
behavior
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of the corresponding myocytes seen in trace 93, 94, and 95 in panel 7D shows
the
corresponding action potentials for the mycoyte locations.
