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259:S1-S3, 1990.Advan in Physiol EduW. F. Nolanelectrochemical driving force to undergraduatesA problem-solving approach to teaching

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http://www.the-aps.org/.Copyright 1990 by the American Physiological Society. ISSN: 1043-4046, ESSN: 1522-1229. Visit our website atSeptember and December by the American Physiological Society, 9650 Rockville Pike, Bethesda MD 20814-3991.specialized courses and in the broader context of general biology education. It is published four times a year in March, June,

is dedicated to the improvement of teaching and learning physiology, both inAdvances in Physiology Education

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A problem-solving approach to teaching electrochemicaldriving force to undergraduatesWILLIAM F. NOLANDepartment of Biology, University of Hartford, --- -- * 1 - -- - --est Hartford, Connecticut Ml 17

NOLAN, WILLIAM F. A problem-solving approach to teachingelectrochemical driving force to undergraduates. Am. J. Physiol.259 (Adv. Physiol. Educ. 4): Sl-S3, 1990.-The diversity ofstudents in the typical undergraduate general physiology coursedemands consideration of several important educational objec-tives: the instructor seeks to provide students with a soundunderstanding of basic physiological concepts, sharpen theiranalytical skills, and demonstrate how universal physicochem-ical laws determine function within living systems. These ob-jectives converge in a problem-solving approach to electrochem-ical driving force and ion flux across biological membranes.undergraduate physiology; analytical skills

problem-solving approach to ECDF and have found thisto be an effective tool in developing students reasoningability while guiding them to a more complete under-standing of the forces that determine the movement ofions. My objective here is to describe this problem-solving method of teaching ECDF. It is not my intentionto present an exhaustive treatment of membrane poten-tial or bioelectrical signal generation; yet I will beginwith a brief description of these phenomena to providethe context within which ECDF is developed in theundergraduate general physiology course. More exhaus-tive treatments of these topics are available (l-5).BACKGROUNDMATERIAL

PART OF THE CHALLENGE of teaching physiology to un-dergraduates resides in the diversity of the abilities andcareer objectives of the students. It is likely that somestudents in each class will pursue careers in physiologyor medicine but most will not. Many will pursue careersunrelated to science. Because effective teaching demandsa clear perception of educational objectives and becauseeducational objectives must address student needs, theheterogeneity of the typical undergraduate physiologyclass in the typical liberal arts institution challenges theinstructor with several important teaching goals. Theseinclude providing the students with a firm understandingof the basic physiological concepts on which higher orderlife processes are based, enhancing their awareness ofunifying concepts, e.g., the dependence of living sys-tems on fundamental physicochemical laws, and improv-ing their problem-solving skills.

Membrane potential ( Vm) is the separation of chargeacross a cell membrane and is established by the selectivepermeability of the membrane and the active transportof ions across it. The result is a differential distributionof ions and an excess of negative charge on the mem-branes inner surface.

When teaching electrochemical driving force (ECDF),the instructor has the opportunity to accomplish all threeof these educational objectives: ECDF is a basic butimportant physiological concept because of its centralrole in bioelectrical signal generation. It also illustrateshow essential processes within organisms, e.g., actionpotential generation and intercellular communication,rely on the same laws that rule the nonliving universe.Finally, if the instructor takes a problem-solving ap-proach to teaching ECDF, the students analytical skillscan be enhanced. Although a quantitative treatment ofECDF is often seen in neurobiology textbooks designedfor graduate students (5), it is only occasionally found inintroductory physiology texts (1). Thus supplementalmaterial may be needed if the instructor wishes to includesome quantitative aspects of the subject in an undergrad-uate general physiology course.

For any ion, X, present in unequal concentrationsacross the membrane, there are two forces acting on it.First, there is a chemical driving force (CDF) resultingfrom the concentration gradient. Second, there is anelectrical driving force (EDF) resulting from the inter-action between the charge of the ion and Vm. If theseforces are equal in magnitude but opposite in direction,there will be no net, or electrochemical, driving forceacting on that ion (Fig. 1A). Under these conditions, ionX will be in electrochemical equilibrium and will exhibitno net flux in either direction across the membrane. Themembrane potential that exactly balances the CDF, thusestablishing electrochemical equilibrium, is obtainedfrom the Nernst equation

Ex = (RT/zF)ln(X,/XJwhere E, is the equilibrium potential for ion X, R is thegas constant, T is the absolute temperature, z is thevalance of ion X, F is the Faraday constant, Xe theextracellular concentration of X, and Xi the intracellularconcentration of X. Converting to log base 10 for amonovalent ion at 18OC, he Nernst equation reduces toc

Ex = 58 lOg(XJXi)If Vm does not equal E,, then X will be out of electro-chemical equilibrium and there will exist an ECDF equalin magnitude to the difference between Vm and E,

I have been using as an instructional aid a simple (ECDF), = Vm - E,1043-4046/90 $1.50 Copyright 0 1990 the American Physio logical Society Sl

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s2 TEACHING ELECTROCHEMICAL DRIVING FORCE

1\ EDFI=) CDF -

NET DF=CDF-EDFr\This will result in a net passive flux of X across themembrane in the same direction as the ECDF (Fig. lI3).Thus X will carry current, Ix, across the membrane inaccordance with a modified version of Ohms law

I x = gxwn - Ex)where g, is the membrane conductance for ion X.In the steady state, when the cell is not signaling (i.e.,at resting Vm), the concentrat ion gradients of ions thatare not in electrochemical equilibrium and that, there-fore, exhibit net passive flux across the membrane, aremaintained by active transport. Thus the passive flux ofan ion in one direction will be offset by active transportin the opposite direction. The end result for all ions isno net movement of charge across the membrane and astable, resting Vm.

The deflection of Vm from rest is the basis of bioelectri-cal signal generation. This is accomplished by changingmembrane conductance to an ion (or ions) that is (are)out of electrochemical equilibrium, resulting in a netmembrane current and, therefore, a change in Vm. Themembrane conductance for specific ions is altered byopening or closing specific gated ion channels. Achange in membrane conductance for any ion X, whichis not in electrochemical equilibrium, will cause a changein Ix

Ar, = 4Lu4n - Ex)Thus the balance between active and passive fluxes willbe transiently disrupted, a net movement of charge acrossthe membrane will occur, Vm will deflect from its restingvalue, and a bioelectrical signal will be generated. Forany given change in g,, the direction of the resultingchange in 1x and its magnitude, i.e., the nature of thesignal, will be determined by the direction and magnitudeof the electrochemical driving force acting on X.I have found that most students easily grasp the con-cept and mechanism of changes in membrane conduct-ance. Computing the numerical value of electrochemicaldriving force is also simple. However, understanding themechanistic basis of ECDF and, in particular, determin-ing its direction for a particular ion under a given set ofconditions are often considerably more difficult. Notethat this last determinat ion is critical because for anyion the direction of its electrochemical driving force willdetermine the direction of its passive flux and, therefore,

FI G. 1. A: example of a neuron whereelectrical and chem ical driving forces(EDF and CDF, respectively) acting oncation X are equal a nd in oppos ite direc-tions, resulting in no net, or electro-chem ical, driving force (DF) for X, i.e.,electroche mical equilibrium with respectto X. B: example of a neuron whereoutward CDF for cation X exceeds in-ward EDF, resulting in outward net driv-ing force acting on X. Vm, membranepote ntial; [x+]i, [x+1,, intra- and extra-cellular concen trations of cation X, re-spectively.

whether the membrane current it carries is depolarizing(excitatory) or hyperpolarizing (inhibitory).GRAPHIC AND NUMERICAL ANALYSISOF ELECTRO CHEMICA L DRIVING FORCE

The reasoning that is applied in analyzing ECDF bythis method may be summarized as follows.1) The electrical and chemical driving forces acting onan ion may be in the same or in opposite directions. Ifthey are in the same direction (e.g., from inside to outsidethe cell), then the direction of the ECDF acting on thation will be in that direction as well, and its magnitudewill equal the sum of EDF and CDF. If EDF and CDFare in opposite directions, then the direction of thegreater of these forces will determine the direction of theECDF. The magnitude of the ECDF in this situation willequal the difference between the EDF and the CDF (Fig.1B)2) In cases where the directions of the EDF and CDFare opposite, their magnitudes must be compared todetermine the direction of the ECDF. The strength ofthe EDF acting on an ion is equal to the membranepotential. Because the equilibrium potential for any ionis the membrane potential required to balance its CDF,the Nernst equation can be used to calculate the millivoltequivalent of its CDF. Thus the equilibrium (i.e., Nernst)potential can be compared with the given Vm (also inmV), and the direction of the ECDF for any ion can bedetermined.Sample problem 1. Consider a situation where K ionhas an intracellular fluid (ICF) concentration of 350 mMand an extracellular fluid (ECF) concentration of 50 mM.What will be the direction and magnitude of the ECDFacting on K at Vm = -60 mV?Solution: the magnitude of the EDF is 60 mV (thegiven membrane potential) and is directed toward thecell interior because of electrostatic attraction. The mag-nitude of the CDF, computed from the Nernst equation,is 49 mV. Its direction is from the region to higher tolower concentration or, in this case, toward the ECF.The magnitude of the ECDF is equal to 60 - 49, or 11mV. Its direction is the same as that of the EDF. Solvingthis problem is facilitated by the graphic representationof the given conditions (Fig. 2). Once the direction andrelative magnitude (indicated by arrow length) of theEDF and CDF are drawn, the direction and relative

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TEACHING ELECTROCHEMICAL DRIVING FORCE s3

~ EDF (6OmWCDF (49mV)Net DF (1lmV)

to carry their analysis one step further and determinewhether a given change in conductance will result in adepolarization or a hyperpolarization of the cell mem-brane. Thus the importance of ECDF in signal genera-tion is emphasized.\ [K 1. =35O mMI [K le =50 mM CONCLUSION

This approach to teaching electrochemical drivingFIG. 2. Example of a case where potassium ion is out of electro- force helps students comprehend the forces that governchem ical equilibrium. See SampZe probZem I and Fig. 1 for abbrevia-tions. ion flux across biological membranes and sets the stagefor more elaborate analysis of bioelectrical signals. It alsomagnitude of the ECDF becomes apparent. Althoughclassroom discussion should certainly emphasize actualneuron structure and membrane differentia tion with re-spect to ion channels, the use of a simple circle diagram,as in Fig. 2, provides a quick way of representing intra-and extracellular fluid compartments for directionalanalysis of driving force.

Sample problem 2. If ICF K ion concentration is 350mM, what ECF K concentration is required for thecondition of no net passive flux of K across the mem-brane at Vm = -60 mV?

challenges their reasoning abi lity and sharpens theirproblem-solving skills. For the students who will notpursue a career in science, perhaps the major benefit ofa thorough understanding of ECDF and ion flux is itscontribution to the development of an expensive world-view that places living systems within the domain ofuniversal laws.Received 2 November 1989; accepted in final form 14 June 1990.REFERENCES

Solution: because K must be in electrochemical equi- 1.librium for it to exhibit no net passive transmembraneflux, the problem reduces to one of determining the ECF 2.concentration of K needed to yield a K Nernst potentia lof -60 mV given that ICF K concentration is 350 mM. 3.Solving the Nernst potential for ECF K after makingappropriate substitutions yields a value of 29.2 mM. 4.I generally assign several of these problems dealingwith both anions and cations under various conditions 5.of Vm and concentration gradient. I also ask my students

ECKER T, R., D. RANDALL, AND G. AUGUSTINE. AnimaZ Physiology:Mechan isms and Adaptations (3rd ed.). New York: Freeman, 1988.HODGKIN, A. L. The ionic basis of electrical activity in nerve andmus cle. BioZ. Reu. 26: 339-409, 1951.HODGKIN, A. L., AND A. F. HUXLEY. Currents carried by sodiumand potass ium ions through the membrane of the giant axon ofLoZigo. J. PhysioZ. Lond. 116: 449-472, 1952.HODGKIN, A. L., AND A. F. HUXLEY. The components of themembrane condu ctance in the giant axon of Loligo. J. Physiol.Lond. 116: 473-496,1952.KANDEL, E. R., AND J. H. SCHWARTZ. PrincipZes ofNeural Science.New York: Elsevier, 1983.

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