Agonist Induced Calcium Oscillations and Waves
In response to agonist simulation, inositol 1,4,5-trisphosphate
is produced within the cell and calcium oscillations and waves result.
A mathematical model has been developed to understand the mechanisms behind
these events as well as the properties of the waves and oscillations.
Cells use calcium waves for
intracellular communication to trigger events such as hormone or enzyme
secretion, gene expression, and contraction in response to certain
neurotransmitters and hormones. In Xenopus laevis oocytes, these
waves sometimes take to form of sprial waves. The movie
shows a simulation of one such spiral.
The model suggested that the level of calcium entry into the cytosol as
well as buffering could control the frequency and amplitude of the oscillations.
The model suggested that if the ER can sustain a membrane potential,
the movement of counterions during ER calcium release actually help to
provide smoother oscillations over a wider set of conditions.
Jafri, M. S. 1993. A theoretical
study of spatial and temporal cytosolic calcium waves. Doctoral Dissertation-The
City University of New York.
Jafri, M. S., S. Vajda, P. Pasik, and
B. Gillo. 1992. A membrane model for cytosolic calcium oscillations: a
Xenopus oocytes. Biophys. J. 63:235-246.
Jafri, M. S. and B. Gillo. 1994. A
membrane potential model with counterions for cytosolic calcium oscillations.
Calcium . 16:9-19.
Jafri, M. S. 1995. A theoretical study
of cytosolic calcium waves in Xenopus oocytes. J. Theor. Biol.
Effects of Calcium Buffering on Calcium Oscillations and Waves
Calcium is highly buffered inside cells.
As a result, the diffusion of calcium is hindered because of its binding
to buffering proteins. With realistic buffering, diffusion becomes
less important in the propagation of calcium waves during agonist stimulation.
Instead, the waves depend on the phase of spatially adjacent oscillators
that are offset in the phase of the oscillation. Hence, calcium waves
are kinematic in nature depending on localized cycle of uptake and release.
The initial phase gradient is set by the rapid diffusion of IP3
at the initiation of the oscillations. As the phase gradient dissipates,
the wave speed increases. The model also suggested that the changes
in oscillation frequency due to the artificial expression of a ER calcium
pump were because the newly expressed pump had different kinetics than
the native pump.
Jafri, M. S. and J. Keizer. 1994. Diffusion
of IP3, but not Ca2+ , is necessary for a class of
IP3-induced Ca2+ wave trains. Proc. Natl. Acad.
Sci. USA 91:9485-9489.
Jafri, M. S. and J. Keizer. 1995. On
the roles of Ca2+ diffusion, Ca2+ buffering, and
the endoplasmic reticulum in IP3-induced Ca2+ release.
Jafri, M. S. and J. Keizer. 1997. Agonist-induced
calcium waves in oscillatory cells: a biological example of Burgers' equation.
Bull. Math. Biol. 59:1125-1144
Further Studies of Calcium Waves
After the application of 2APB, Ca2+
wave can lose up to 80% of their amplitude without slowing down.
This suggests that Ca2+ diffusion might not be siginificant
for Ca2+ wave propagation and supports the suggestion that the
waves might be kinematic in nature.
Jiang, X., W. Xu, M. S. Jafri, and
S. DeLisle. The amplitude of inositol 1,4,5-trisphosphate-induced Ca2+
waves may influence how far but not how fast they propagate. (in submission).
Control of Gene Expression
The Human Genome Project and modern molecular
biology techniques have produced an abundance of data on the genes and
gene products, in particular proteins, that control cell function. On average,
proteins interact with five other proteins to form the complex signaling
and regulatory networks that integrate the input signals to a cell and
orchestrate its response. Pharmaceutical companies are very interested
in understanding how malfunctioning regulatory networks can lead to disease;
indeed, of the 500 different molecular targets at which current drug therapies
are aimed, about half are cell surface receptors, the starting point of
signaling networks. Unlocking the therapeutic potential of the remaining,
downstream components of signaling networks will require more knowledge
of protein-protein interactions, but will also need mathematical and computational
tools for integrating these isolated pieces of data into a single system,
whose overall response can then be studied. The goal of this project is
to develop mathematical techniques and tools for modeling and analyzing
receptor-mediated signaling networks. The project is a part of a multidiscliplinary
effort that involves collaboration with both experimental and theoretical
scientists in both in my research group and at a major pharmaceutical
Cardiac Excitation-Contraction Coupling
Cardiac Calcium Dynamics
A mathematical model for cardiac calcium dynamics
has been developed. It includes a diadic space where the RyRs and
L-type calcium channels can interact, adaptation of the RyRs, calcium-dependent
inactivation of the L-type calcium channels, and the Luo-Rudy phase II
membrane currents. The model produces realistic action potentials
and calcium transients. It suggests that partial depletion of the SR is
necessary for the termination of release. It also suggests that RyR
adaptation plays a role in interval force relations. The model also
suggested that the L-type current was important in the shortening of action
potential duration during increased pacing. A stochastic model of
the cardiac functional unit (basic unit of EC coupling) was also developed
based on the pervious model. It showed that the stochastic gating
of independent functional units were necessary produce graded release.
It also suggested that termination of release required partial depletion
of the SR. The models of EC coupling during heart failure shows that
the changes in calcium handling were crucial for the increase action potential
duration seen in heart failure.
Jafri, M. S., J. J. Rice and R. L. Winslow. 1998.
Cardiac calcium dynamics: the roles of ryanodine receptor adaptation and
sarcoplasmic reticulum Ca2+ load. Biophys. J. 74:1149-1168.
Rice, J. J., M. S. Jafri
and R. L. Winslow. 1999. Modeling gain and gradedness of Ca2+
release in the functional unit of the cardiac diadic space. Biophys.
Winslow, R. L., J. J. Rice, M. S. Jafri,
E. Marban, and B. O'Rourke. 1999. Mechanisms of altered excitation-contraction
coupling in canine tachycardia-induced heart failure II. model studies.
Winslow, R. L., J. J. Rice, and M.
S. Jafri. 1998. Modeling the cellular basis of altered excitation-contraction
coupling in heart failure. Prog. Biphys. Mol. Biol. 69:497-514.
Winslow, R. L., D. F. Scollan, A. Holmes,
L. Irvine, C. Y. Yung, and M. S. Jafri. 2000. Electrophysiological modeling
of cardiac ventricular function: from cell to organ. Ann. Rev. Biomed.
Rice, J. J. and M. S. Jafri. 2001.
Modeling calcium handling in cardiac cells. Phil. Trans. Roy. Soc. A.
During heart failure there are clinically observed
changes in cardiac output, skeletal muscle function, and hemodynamics.These
changes are directly linked to changes on the cellular level in the heart,
skeletal muscle, and vascular system.This study explores these correlations.Future
work will look at correlations for the effects of drugs on both on the
cellular and clinical levels.
Jafri, M. S. and S. H. Ellahham. Chronic heart
failure and exercise: the correlation between cellular changes and clinical
symptoms. (in preparation).
Cardiac Interval-Force Relations
In the heart, as the interval between beats changes,
so does the amount of force generated.This study analyzes these interval-force
relations using a model of the cardiac ventricular myocyte.The study suggests
that mechanical restitution results from the recovery of the RyRs from
adaptation/inactivation.As the interbeat interval increases, there is more
time for the RyRs to recover. The model also suggests that potentiation
results from increased SR load resulting from less calcium released during
the previous beat, and more calcium entry through the L-type channel because
of reduction in the calcium-dependent inactivation in the previous beat.
Rice, J. J., M. S. Jafri, and R. L. Winslow.
1998. Modeling short-term interval force relations in cardiac muscle. Ann.
N. Y. Acad. Sci. 853:345-349.
Rice, J. J., M. S. Jafri, and R. L.
Winslow. 2000. Modeling short-term interval-force relations in cardiac
muscle. Am. J. Physiol. 278:H913-H931.
Jafri, M. S. and J. J. Rice. Cardiac
Ca2+ dynamics: the role of SR lumenal Ca2+ in interval
force relations. (in preparation)
The physiology of the newborn heart differs greatly
from the adult.Hence adult theraputics are not ideal for the newborn mathematical
model of newborn calcium calcium handling that includes diffusion, increase
sodium-calcium exchange, decreased, L-type current, reduced size, no T-tubules,
and reduced buffering. The model suggests that calcium entry from sodium-calcium
exchange and diffusion are sufficient to account for the calcium transient
seen in newborn heart. Internal uptake of calcium is also necessary
to account for the spatio-temporal profiles observed experimentally.
Other studies examined the changes to the membrane currents seen in newborns.
In corporation of these changes into a model of the newborn ventricular
myocyte suggest that there might be additional changes that are as of yet
Haddock, P. S., W. A. Coetzee, E. Cho,
H. Katoh, D. M. Bers, M. S. Jafri, and M. Artman. 1999. Sub-cellular [Ca2+]
gradients during excitation-contraction coupling in newborn rabbit ventricular
myocytes. Circ. Res. 84:571-586.
Jafri, M. S., M. Artman, and W. A.
Coetzee. Modeling subcellular Ca2+ gradients during EC coupling
in newborn ventricular myocytes (in preparation).
Calcium sparks are the fundamental
events that underlie calcium release and excitation contraction coupling.
A novel mechanism for calcium sparks is developed in a stochastic computer
model that includes coupling between the RyRs, RyR dependence on SR lumenal
calcium, and a large number of RyRs. Disruption of the coupling between
RyRs prolongs sparks consistent with experiments. Removal of the
lumenal dependence results in sparks that fail to terminate. The
spark characteristics are relatively insensitive to the number of RyRs.
Future studies are planned that look at spark restitution and the spatial
spread of calcium release throughout the sarcomere.
Sobie, E. A., K. Dilly, J. d. S. Cruz,
W. J. Lederer, and M. S. Jafri. Termination of cardiac Ca2+
sparks: an investigative mathematical model of calcium induced calcium
release. (in revision).
Regulation of the Citric Acid Cycle
The heart consumes large amounts of energy in
is function as a pump. During exercise this demand rises and is fulfilled
in health hearts. Hence, the system for energy production and utilization
in the heart is highly regulated. During ischemia, this regulation
breaks down. model for energy metabolism in the heart
is being developed. Thus far a model for the citric acid cycle has
been developed. The model contains detailed descriptions of the regulatory
enzymes and uses mass action for the remaining enzymes. The model
suggests that the cycle is functionally split by the aspartate aminotransferase
reaction into an upper and lower half that proceed at different rates.
During activation of cycle by calcium, flux through lower span accelerates
greatly while flux through the upper span actually decreases. During
regulation by pH, ADP, and redox potential, all spans of the cycle
are activated in parallel. Future studies are planned with Dean Sherry
(UT-Dallas) and Mark Jeffrey (UT-Southwestern) to test the predictions
of the model. The model will be incorporated into the ventricular
cell model above to study energy production and utilization in the myocyte
during exercise and ischemia.
Jafri, M. S., S. J. Dudycha, and B. O'Rourke.
2001. Cardiac energy metabolism: models of cellular respiration.
Ann. Rev. Biomed. Eng. 3:3:57-81.
Dudycha, S. J., and M. S. Jafri. A kinetic model
for the regulation of the tricarboxylic acid cycle. (in revision).
Dudycha, S. J., and M. S. Jafri. Modeling the highly
regulated enzymes of the TCA cycle. (in revision).
Ion Channel Function
Althought the Hodgkin-Huxley representation of
the ion channel is adequate for understanding excitation of the action
potential, it is inadequate to understand the action of drugs on the sodium
channels. A multi-state markov model for the sodium channel that
produced proper activation and inactivation kinetics at different temperatures
was developed. The model suggested that there were in fact two open
states for the sodium channel. The model was expanded to include
the effects of lidocaine and a mutation that results in long-QT syndrome.
Irvine, L. A., M. S. Jafri, and R. L. Winslow.
1999. Cardiac sodium channel markov model with temperature dependence and
recovery from inactivation. Biophys. J. 76:1868-1885.
This project studied and evaluated commonly used
energy minimization algorithms (ECEPP and CHARMM) used for protein structural
prediction.The studies found that the algorithms predicted conformations
that differed from the native structures and that have lower energies than
the native. This occurs when the assumption of standard bond lengths
and bond angles is relaxed, a small and constant dielectric permittivity
is used, and a hydrophobic folding energyis incorporated into the potential.
Identifying Protein Conformational Structure by Energy Minimization
Vajda, S., M. S. Jafri, O. U. Sezerman, and C.
Delisi. 1993. Necessary conditions for avoiding incorrect polypeptide folds
in conformational search by energy minimization. Biopolymers.
Protein Disulphide Bonding Patterns and Topology
This project examines the topological properties
of protein disulphide bonding patterns for proteins whose structures were
contained in PDB.No examples were found where the loops formed from the
protein backbone and the disulphide bond were topologically linked.There
were no examples topologically knotted loops either. In contrast,
pseudolinking is a relatively common event.The results suggest that
disulphide bonding patterns are the result of a direct process rather than
of a random process.
Benham, C. J. and M. S. Jafri. 1993. Disulphide
bonding patterns and protein topologies. Protein Science.