Research Summary

Calcium Signaling

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 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 study using Xenopus oocytes. Biophys. J. 63:235-246.

Jafri, M. S. and B. Gillo. 1994. A membrane potential model with counterions for cytosolic calcium oscillations. Cell Calcium . 16:9-19.

Jafri, M. S. 1995. A theoretical study of cytosolic calcium waves in Xenopus oocytes. J. Theor. Biol. 172:209-216.

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. Biophys. J. 69:2139-2153.

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 company.

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. J. 77:1871-1884.

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. Circ. Res. 84:571-586.

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. Eng. 2:119-155.

Rice, J. J. and M. S. Jafri. 2001. Modeling calcium handling in cardiac cells. Phil. Trans. Roy. Soc. A. 359:1143-1157.

Heart Failure

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)

Newborn Heart

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 unaccounted for.

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

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).

Energy Metabolism

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.

Sodium Channel

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.

Protein Folding

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. 33:173-192.

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. 2:41-54.