In the Classroom edited by
Concepts in Biochemistry
William M. Scovell Bowling Green State University Bowling Green, OH 43403
Protein Unfolding Coupled to Ligand Binding: Differential Scanning Calorimetry Simulation Approach María Soledad Celej and Gerardo Daniel Fidelio* Departamento de Química Biológica-CIQUIBIC, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Córdoba, Argentina; *
[email protected] Sergio Alberto Dassie Unidad de Matemática y Física-INFIQC, Departamento de Fisicoquímica-INFIQC, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Córdoba, Argentina
Protein–ligand interaction is a common event in many cellular processes. It has immediate consequences for protein stability and may involve conformational changes in the macromolecule. Ligand binding to a native protein increases the denaturation temperature of the macromolecule, which, as a result, becomes more resistant to thermally-induced denaturation. Such change can be expected to occur if we consider the thermodynamics of reversible protein unfolding coupled to ligand binding. Pasteurization processes, in which the proteins must be heated at high temperatures for a long time while preserving their native conformation, take advantage of this property (1). An approach similar to the one described in this article has recently been used as a tool for the quick screening of drugs with the potential to increase the denaturation temperature of bound protein relative to unliganded protein (2). From a pedagogical point of view, it is important that graduate and advanced undergraduate chemistry students understand the physicochemical basis of the effect that ligand binding has on protein stability. This article is meant to deepen students’ understanding of the concepts of chemical equilibrium and thermodynamics included in the chemical physics, biochemistry, biophysics, and polymer chemistry curricula.
Differential scanning calorimetry (DSC) is a powerful technique based on direct measurement of heat energy uptake in thermally-induced transitions. It has become a popular method in biophysical chemistry for evaluating protein conformational stability as well as protein–ligand and protein– protein interactions. As it involves model-based assumptions, DSC is a rather indirect technique for studying protein– ligand interactions. Various approaches for describing macromolecular unfolding linked to ligand binding were published by several authors many years ago (3–6). More recently, the application of theory to DSC has been proved to be useful for estimating very tight binding constants (7), as well as for characterizing the energetics of binding and unfolding (8, 9). In this context, it is useful to simulate the signal obtained by DSC in order to: • Understand the thermodynamic basis underlying the observed changes in protein stability when the macromolecule binds to a specific ligand, • Identify the chemical equilibria and modifications that give rise to the observed output signal from the calorimeter, and • Interpret the experimental data by comparing the real and theoretical process, thus confirming or eliminating the assumed model.
This article deals with the thermodynamic basis underlying the changes in protein stability upon ligand binding. It also helps to elucidate the redistribution among the different species (native, unfolded, and liganded protein) involved in the global unfolding process by using the species distribution profile. The simulations are easy to implement and they would be a good exercise for students in a computational practical activity. The article is organized so that the reader can progress from simpler to more complex systems.
Figure 1. Differential scanning calorimeter experiment: (A) scheme of DSC equipment, (B) system perturbation, and (C) DSC output for a typical two-state protein denaturation process. See text for details.
www.JCE.DivCHED.org
•
The DSC Experiment and Information Content in DSC Data DSC measures the heat capacity (Cp ) of a system as a function of temperature. We use this technique to study the energetics of protein unfolding. A sensitive DSC instrument is equipped with matched twin cells (Figure 1A). The sample cell (S) is filled, through the stem, with a dilute protein solution and the reference cell (R) with the same buffer used for preparing the sample. When the temperature scan is
Vol. 82 No. 1 January 2005
•
Journal of Chemical Education
85
In the Classroom
started (Figure 1B), electric heaters (Htr) heat both cells. The power supplied to the heaters is adjusted by a thermopile (Thp) placed between the cells that keeps the off-balance temperature close to zero. Additional heaters in the adiabatic jacket and thermopiles between them and the cells hold the overall thermal equilibrium. The ordinate axis receives a signal proportional to the differential heating power applied to the cells. Such signal is a direct measurement of the heat capacity difference between the sample and the reference. The cell temperature is recorded in the abscissa. The reader is referred to work by Plotnikov et al. (10) for a complete description of currently available instruments. A comprehensive work by Chowdhry and Leharne (11) about simulation and analysis of DSC output in protein unfolding without ligands has been published in this Journal. The Cp(T ) output supplies information about the protein conformational state over the temperature range under study. Thus, any change in the protein state is evidenced by a change in the heat capacity profile (12, 13). We will consider the changes induced by temperature for a globular protein undergoing a cooperative and reversible two-state denaturation process, that is, between native and denatured state. The native structure is maintained by a large number of intra and intermolecular forces. When these forces are thermally disrupted, the Cp(T ) follows a bell-shaped curve indicating an intensive heat absorption (Figure 1C). The protein denatures over a temperature interval with a midpoint transition, Tm– , that corresponds to a maximum in the heat capacity (Cpmax). (The superscript “–” indicates absence of ligand.) At temperatures lower and higher than Tm– only slight changes in Cp(T ) are observed and they correspond to the heat capacity of the native and denatured state, CpN and CpU, respectively. The difference between the extrapolated heat capacity of the initial and final states to Tm– is taken as the difference between the heat capacity of the native and of the denatured state of the protein, ∆Cp – (Figure 1C). The higher heat capacity of the denatured state is mainly due to hydration of nonpolar groups, which become exposed to the solvent when the folded conformation is disrupted. The dashed line in Figure 1C represents the shift in baseline resulting from this difference. The calorimetric denaturation enthalpy (∆Hm– ) is evaluated by integrating the area under the curve once the baseline has been subtracted. It is useful to distinguish between the terms “denatured” and “unfolded”. The term denaturation has often been used to refer to a decrease in the activity of a native protein. However, here we use it to refer to reversible conformational changes leading to a highly open and solvated state (14). By “state” we mean the ensemble of many different configurations (microstates) of individual molecules. A macroscopically observable quantity is an average of these microstates and it depends on the system conditions. The denaturation process can be attained by modifying several external conditions such as temperature, pressure, pH, and concentration of denaturant (such as urea or guanidine hydrochloride). The problem of the equivalence of denatured states obtained in these different ways has been discussed for many years (see ref 15 for a detailed review about denatured states). Studies carried out with many globular proteins did not find differences in the enthalpies or in the heat capacity changes between chemically- and thermally-induced conformational 86
Journal of Chemical Education
•
transitions (14). This suggested that, at least from a thermodynamic point of view, the final macroscopic states are indistinguishable from each other, regardless of the denaturing conditions (14). Even so, these final denatured ensembles might be formed by different combinations of denatured chain configurations. On the other hand, the unfolded protein is an idealized state referring to a fully-solvated polypeptide chain, with noninteracting amino acid side chains, that is, a random-coil chain. Its Cp(T ) can be obtained by summing the heat capacity of each amino acid residue and the contribution of the peptide bonds (16). Although in practice the unfolded ideal state is hard to reach, it has been demonstrated that, if aggregation is prevented, denatured proteins can be regarded as completely unfolded polypeptide chains (17). Thus, here we will consider the denatured state of the protein as its completely unfolded state (14). Thermodynamics of Protein Unfolding
General View In a DSC experiment we measure the heat capacity change of the protein as temperature is increased. Disruption of the native structure is evidenced by a cooperative heat absorption proving the endothermic nature of the unfolding process. Therefore, the average enthalpy must be considered (18) as µ ∆H
=
∑ Pi ∆Hi
(1)
i =0
where Pi is the population of molecules in the i state and ∆Hi is the difference in enthalpy between the i state and the reference state (taken as the native form), and the summation is over all relevant conformational states of the protein (µ). The average heat capacity 具∆Cp 典 is obtained by taking the derivative of eq 1: µ
∆C p
=
dP
∑ ∆Hi dTi
i =0
∆Cp
µ
+
∑ Pi
i =0
d ∆Hi dT
= δC C ptrs + δC pbas
(2a)
(2b)
The first term in eq 2b 具δCptrs典 is the transition heat capacity and it is responsible for the characteristic peak(s) of the heat absorption. The second term 具δCpbas典 defines the shift in the baseline associated with the difference in heat capacity between the final and initial states. This theoretical treatment is completely general. If expressions for Pi and ∆Hi for a specific case are known, the calorimetric behavior of the system can be described.
Two-State Protein Unfolding Consider a two-state protein unfolding process represented by the following equilibrium N
U
K u (T ) =
[U ] [N]
(3)
where Ku – (T ) is the unfolding equilibrium constant and [U] and [N] represent the concentration of unfolded and native protein, respectively.
Vol. 82 No. 1 January 2005
•
www.JCE.DivCHED.org
In the Classroom
ation can be represented by the following equilibria:
The mass balance of the system is
[P]tot [P]tot
= [ N ] + [U ]
(4a)
= [ N ] 1 + K u (T )
(4b)
K u (T ) =
where [P]tot is the total protein concentration. The population of the unfolded state, PU , will be
[U ] [ N ] + [U ]
PU =
(5a)
K bN(T ) =
[U ] [N]
N
U
+
+
L
L
[ NL] [N ][L ]
K bU(T ) =
K u (T ) 1 + K u (T )
(5b)
Due to the ∆Cp– , the enthalpy of the protein unfolding is temperature-dependent and it is expressed by, ∆ H (T ) = ∆Hm + ∆C p · (T − Tm )
(6)
where Tm– is the midpoint temperature transition, that is, the temperature at which the free energy of unfolding, ∆Gu– = 0, and ∆Hm– denotes the enthalpy of protein denaturation. Using this expression to integrate the van’t Hoff equation between T – and T, the equilibrium constant as a function of temperature is obtained:
Here, Kb N(T ) and Kb U(T ) are the binding constants for the native and unfolded form, respectively. By assuming that the binding enthalpy is linear-dependent with respect to temperature we obtain,
( )
∆ H bN (T ) = ∆ H bN Tr N
(
+ ∆CpNb · T − TrN
(11)
( )
× exp
1 − ∆H bN Tr N − ∆CpNb TrN R
1 1 − N T Tr
( )
(12) +
1 × exp − ∆H m − ∆C p Tm R
(
1 1 − Tm T
)
(7)
T + ∆C p ln Tm
The preexponential factor in eq 7 corresponds to the equilibrium constant at the midpoint transition where [N] = [U] and, therefore it is equal to 1. Equations 6 and 7 are used to obtain analytical expressions for 具δCp trs典 and 具δCp bas典. =
)
K bN(T ) = K bN Tr N
K u (T ) = K u (Tm )
δCptrs
[ UL ] [U ][L ]
UL
NL
PU =
(10)
∆H (T ) RT
2
2
K u (T ) 1 + K u (T )
K u (T )
2
(8)
N ∆C pb
ln
T TrN
where TrN is a reference temperature at which the binding constant has been measured, and ∆CpbN is the heat capacity difference between the liganded and free native protein. The expressions for the ligand binding to the unfolded protein, ∆HbU(T ) and KbU(T ), have the same form. The law of mass action for the reaction scheme represented in eq 10 is,
[P]tot
= [ N ] + [ U ] + [ NL ] + [UL ]
[P]tot
= [ N ] 1 + K u (T )
(13a)
{
(13b)
}
+ K bN (T ) + K u (T ) K bU(T ) [L ] (9)
[L ]tot
= [ L ] + [ NL ] + [UL ]
In eq 9 the heat capacity term for the native form has been taken as the reference state and thus considered to equal zero.
[L ]tot
= [ L ] 1 + K bN(T ) + K u (T ) K bU(T ) [ N ] (14b)
Two-State Protein Unfolding Coupled to Ligand Binding We will describe the general case where a ligand binds to both the native and the unfolded forms of the protein (7– 9). We will assume that all processes are two-state. This situ-
where [L]tot denotes the total ligand concentration and [L] is the free ligand concentration. Due to the coupling between the unfolding and binding equilibrium the effective equilibrium constant between the total unfolded form, [U]tot, and the total folded form,
δCpbas =
1 + K u (T )
∆C p
www.JCE.DivCHED.org
•
Vol. 82 No. 1 January 2005
{
(14a)
}
•
Journal of Chemical Education
87
In the Classroom
13b and 14,
[N]tot, is
K u (T ) =
K u (T ) = K u (T )
[ U ]tot [ N]tot 1+ 1+
(T ) [ L ] (T ) [L ]
b2 − 4 a c 2a
−b +
(19)
(15b) Simulations
PU =
[ U ] + [UL ] [P ] tot
(16a)
PU =
K u (T ) 1 + K u (T )
(16b)
During unfolding the ligand is released by the native protein and taken by the unfolded protein. This ligand redistribution contributes to the total enthalpy ∆H(T ) and can be expressed as ∆ H (T ) = ∆ H (T ) − υN ∆ H bN(T ) + υU ∆ H bU(T ) (17) where υN is the extent of saturation of the native protein with ligand and is defined by
υN =
=
where a = Kb N(T ) + Kb U(T )Ku– (T ), b = 1 + Ku – (T ) + ([P]tot − [L]tot)[Kb N(T ) + Kb U(T )Ku – (T )] and c = [L]tot[1 + Ku – (T )].
K bU K bN
The population of the unfolded state is
υN =
[L ]
(15a)
[ NL ] [ N ] + [ NL ]
(18a)
K bN(T ) [ L ]
(18b)
1 + K bN(T ) [ L ]
and υU is the extent of saturation of the unfolded protein with ligand and has the same form as υN. It is impossible to obtain an analytical expression for 具δCp trs典 and 具δCp bas典. Thus the free ligand concentration must be calculated in order to evaluate Ku(T ) and ∆H(T ). A quadratic equation in [L] is obtained by solving the mass eqs
For each simulation it is necessary to define a finite number of thermodynamic parameters that characterize the system (Table 1). Also, the analytical concentrations of ligand and protein have to be fixed. The simulation consists of calculating the population of the denatured state, PU, as the temperature is increased. The process ends when PU ≈ 1, that is, when all the protein is denatured.
Simulation for Two-State Protein Unfolding The required parameters are [P]tot, Tm– , ∆Hm– , and – ∆Cp . During the temperature scan, the enthalpy and the equilibrium constant are calculated for each point (eqs 6 and 7, respectively). The average heat capacity change is obtained by adding eqs 8 and 9. Furthermore, the species concentration profile can be evaluated during unfolding using eqs 3 and 4b. Simulation for Two-State Protein Unfolding Coupled to Ligand Binding The required parameters are [P]tot, Tm– , ∆Hm– , ∆Cp– , [L]tot, KbN(TrN), TrN, ∆HbN(TrN), ∆CpbN, KbU(TrN), TrU, ∆HbU(TrN), and ∆CpbU. During the temperature scan, the enthalpies and the constants for the unfolding transition (eqs 6 and 7) and ligand binding (eqs 11 and 12) are evaluated for each point and so are the equivalent equations for the ligand binding to the unfolded protein. The free ligand concentration is obtained from eq 19. This allows computation of the values of Ku(T ), PU, and ∆H(T )(eqs 15b–17). The heat capacity change for the transition and the baseline are obtained through eq 2a. Furthermore, the species concentration profile can be evaluated during the unfolding by solving the mass balance for each species.
Table 1. Simulation Parameters for the Figures Parameter
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
[P]tot/mM – Tm/C ∆H –/(kJ mol1)
0.2
0.2
0.2
0.2
0.2
0.1 or 1
62
62
62
62
62
62
460
460
460
460
460
460 6.3
m
88
– ∆Cp/(kJ mol1 K1)
6.3
6.3
6.3
6.3
6.3
KbN(TrN)/M1
---
1 x 10 5
---
1 x 105
1 x 107
1 x 104
TrN/C
---
---
25 84
25 84 0.8
∆HbN(TrN)/(kJ mol1)
---
25 84
---
25 84
∆CpbN/(kJ mol1 K1)
---
0.8
---
0.8
0.8
KbU(TrU)/M1
---
---
1 x 105
1 x 103
---
---
TrU/C
---
---
25
---
---
42
---
---
0.4
---
---
∆HbU(TrU)/(kJ mol1)
---
---
25 84
∆CpbU/(kJ mol1 K1)
---
---
0.8
Journal of Chemical Education
•
Vol. 82 No. 1 January 2005
•
www.JCE.DivCHED.org
In the Classroom
The guidance described in this section is useful for simulating thermograms in the absence and presence of ligands. The complete computer code is available on request (mcelej@ dqb.fcq.unc.edu.ar). A method of minimization of multidimensional functions (e.g., Simplex) can be used to obtain the characteristic parameters of the system from direct fitting of DSC data. Through this procedure it is possible to perform a global analysis and to explore the phase space defined by the n-parameters (19).
are equimolecular and at this particular temperature T = Tm– and Ku – (T ) = 1. In the next sections we will illustrate the changes induced by the presence of a ligand that binds either to N, to U, or to both conformations. We emphasize how the different chemical equilibria are affected by the presence of a ligand and how the thermogram can be deduced from the concentration-temperature course for each species.
Case I: Two-State Protein Unfolding By using eqs 3–9 it is possible to calculate the thermogram trace for a two-state protein denaturation process. Figure 2 shows the theoretical thermogram and the fractions of species during heating. As it can easily be seen, at T > Tm– the predominant species is U. It is important to note that at Cpmax the quantities of N and U
Case II: Two-State Protein Unfolding Coupled to Ligand Binding to the Native Protein The case of a ligand binding only to the N conformation with a given affinity is analyzed first. For a constant quantity of protein, the thermograms shift to higher temperatures as the ligand concentration increases (Figure 3A). This indicates that, as the ligand兾protein mole ratio increases, higher energy is required to change from the liganded native state into the free unfolded state. The increase in protein thermal stability is a consequence of the coupling of binding and unfolding equilibria. The total unfolding free energy (∆Gu ) of the liganded state can be
Figure 2. Two-state protein unfolding: (A) simulated thermogram for a two-state protein unfolding process and (B) species distribution profile. Concentration normalization was carried out on total protein concentration, [X]tot = [P]tot. See Table 1 for simulation parameters.
Figure 3. Effect on protein stability of ligand binding to native protein: (A) simulated thermograms as a function of ligand concentration and (B) species distribution profile at [L]tot/[P]tot = 2. Concentration normalization was carried out on total protein concentration for all species of protein [X]tot = [P]tot and on total ligand concentration for the free ligand species [X]tot = [L]tot. See Table 1 for parameters.
Results and Discussion
www.JCE.DivCHED.org
•
Vol. 82 No. 1 January 2005
•
Journal of Chemical Education
89
In the Classroom
separated into the following additive free energy terms: NL
N
N
U
NL
U
+ L
−∆G bN ∆G u
+ L
∆G u = ∆G u − ∆G bN
Figure 3B shows the concentration–temperature profile of the different species in equilibrium corresponding to the thermogram obtained at a mole ratio of [L]tot兾[P]tot = 2 and a Kb N(T ) of 105 M1. In this specific condition the denaturation occurs at T > 55 C, which is evidenced by the further increase in U as temperature increases. The redistribution of both native species N and NL at lower temperatures should be noted. A decline in the complex (NL) occurs with a corresponding increase in the free native protein (N) and free ligand (L) as a consequence of a reduction in the affinity as temperature increases (since we used a negative ∆Hb N(T ) in the simulation). However, at temperatures below 55 C the redistribution of native species does not contribute to the unfolding, since U remains almost constant. From this temperature point and over a range of about 5 C there is an increase in N, even when this is consumed by the unfolding process (conversion to U species). Such increase is due to a higher contribution from the dissociation of NL. From 60 C both native protein species (free and liganded) drop abruptly contributing to the unfolding (Figure 3B).
Case III: Two-State Protein Unfolding Coupled to Ligand Binding to the Denatured Protein Figure 4 shows a case similar to that mentioned in the previous section, but now the ligand has affinity only with the unfolded U species. As the ligand concentration increases, an opposite effect is observed and the protein thermal stability decreases. The binding of L to U favors the unfolding process since it shifts the equilibrium to U. In this case, the decrease in N clearly indicates the progress of the denaturation reaction. At a mole ratio of [L]tot兾[P]tot = 2, N and L are the only species initially present in the system and denaturation begins at 50 C (Figure 4B). As unfolding proceeds, a fraction of free ligand binds to U forming, in turn, the UL complex. Over a 50–70 C temperature range, both unfolded conformations, U and UL, increase but the unfolded liganded state predominates. At temperatures higher than 70 C the unfolding process has fully completed and only redistribution of U and UL occurs (Figure 4B). Case IV: Two-State Protein Unfolding Coupled to Ligand Binding to Both the Native and the Denatured Protein Now we shall analyze the case of a ligand able to bind to both states, native and unfolded, with different affinities. Figure 5A shows the thermogram outputs, including as references the profile observed in the absence of ligand, and when this is bound only to native or to unfolded state. The temperature-course distribution of the species throughout the process is shown in Figure 5B.
90
Journal of Chemical Education
•
Figure 4. Effect on protein stability of ligand binding to unfolded protein. (A) Simulated thermograms as a function of ligand concentration. (B) Species distribution profile at [L]tot/[P]tot = 2. Concentration normalization was carried out as in Figure 3. See Table 1 for simulation parameters.
Given the simulation parameters indicated in Table 1 for Figure 5, the Tm of the system is close to the Tm– observed for the protein in the absence of ligand, but with a higher Cpmax. The shift between these two thermograms is due to the different properties of ligand binding to N compared with U species. The process can be divided into the following steps, NL U
+ L N
+ L
N
−∆G bN
UL
∆G bU
U
∆G u
so the global reaction with its corresponding associated free energy is NL
UL
∆G u = ∆G u − ∆G bN + ∆G bU
If the binding energies to both protein conformational states, N and U, are identical (∆GbN = ∆GbU) the global free energy of unfolding will be the same either in the presence or in the absence of ligands. Thus, the corresponding thermograms will be indistinguishable. On the contrary, if ∆GbN > ∆GbU the binding to U will be favored by shifting the ther-
Vol. 82 No. 1 January 2005
•
www.JCE.DivCHED.org
In the Classroom
Figure 5. Effect on protein stability of ligand binding to native and unfolded protein. (A) Simulated thermograms for (a) free protein unfolding and protein unfolding coupled to (b) ligand binding to native protein, (c) ligand binding to unfolded protein and (d) ligand binding to native and unfolded protein at [L]tot 兾[P]tot = 5. (B) Species distribution profile when the ligand binds to both conformational states of the protein at [L]tot 兾[P]tot = 5. Concentration normalization was carried out as in Figure 3. See Table 1 for simulation parameters.
mogram to lower temperatures. Figure 5 illustrates the opposite case where the binding to N is favored, since ∆GbN < ∆GbU. The redistribution of species can be analyzed in a way similar to that used in the previous cases (Figures 3B and 4B). Here the free ligand concentration is not substantially modified since over the whole range of temperature, the binding occurs to both conformers (Figure 5B). The thermodynamic parameters of binding between a ligand and a protein can be determined by complementary techniques (such as fluorescence spectroscopy, isothermal titration calorimetry, etc.) in conditions of predominance of the native species. Then, these binding parameters can be used to simulate the expected thermogram assuming that the ligand binds only to the N conformer. Any discrepancy in the experimental thermogram may be ascribed to the probable interaction between the ligand and the U conformation.
Case V: Particular Situations A—Biphasic Thermograms All previously shown thermograms display a bellshaped trace. However, this is not always the case. Figure
www.JCE.DivCHED.org
•
Figure 6. Effect on thermogram shape of ligand binding constant. (A) Simulated thermograms as a function of ligand concentration. (B) Species distribution profile at [L]tot 兾[P]tot = 0.5. Concentration normalization was carried out as in Figure 3. See Table 1 for simulation parameters.
6 shows several thermograms for a protein interacting with a ligand only in its N conformer with an affinity constant, KbN(Tr) = 1 × 107 M1. In case II, the binding constant used was K bN(Tr) = 1 × 105 M1. The higher binding constant brings about further stabilization of NL species as compared with case II. In both cases, the thermograms show the same trend towards shifting to higher temperature as free-ligand concentration increases. However, the profile of the thermogram at [L]tot兾[P]tot = 0.5 (Figure 6) is modified and two maxima are present in the heat capacity curve. From Figure 6B it clearly emerges that the bimodal unfolding behavior at subsaturating conditions is basically due to the quite different denaturation temperatures of N and NL. The concentration of N begins to drop at about 55 C and its conversion to U accounts for the first endotherm. The unfolding of NL and the consequent release of L only begin at around 65 C. Thus the initial consumption of N occurs without substantial modification of NL concentration. From 65 to 70 C both native species contribute to the unfolding process.
Vol. 82 No. 1 January 2005
•
Journal of Chemical Education
91
In the Classroom
B—Effect of Protein Concentration at Constant Ligand/Protein Mole Ratio Figure 7A shows the unfolding process for an identical ligand兾protein mole ratio [L]tot兾[P]tot = 0.5 but protein concentration varies. Even when [L]tot兾[P]tot remains constant, it is possible to obtain different thermograms ranging from a symmetric to a bimodal when [P]tot goes from 104 M to 103 M. Figures 7B and 7C show the redistribution course of species for each situation. The data can be interpreted in a way similar to that in cases II and VA. Even when the [L]tot兾[P]tot ratio is an important variable in the system, it should be noticed that the calorimetric output varies according to the absolute values of [L]tot and [P]tot, and therefore the analytical concentration of at least one of the components has to be known. Conclusions In this article we present a comprehensive theoretical description of thermal protein unfolding coupled to ligand binding. While the thermodynamic concepts are independent of the method used to monitor protein unfolding, we have chosen differential scanning calorimetry as a tool for
examining the unfolding process. The approach allows prediction of an expected thermogram and modeling of the probable protein–ligand interaction. The model includes the probability of ligand interaction with a single site on the protein in either the native, the unfolded, or both conformations simultaneously. The simulated thermogram allows the generation of the temperature course for the different species during thermal unfolding. Monitoring the evolution of the species concentration during unfolding is a powerful tool for understanding the chemical equilibria that define the process. Several common cases in the protein–ligand interaction field have been discussed. We show the influence of the absolute concentration of both the protein and the ligand on the shape of the thermogram for the same ligand兾protein mole ratio. This fact indicates the significance of providing data on the final concentration as well as on the ligand兾protein mole ratio used to define the calorimetric output unequivocally. The model is versatile and adaptable enough so as to introduce variations in external variables (e.g., protein and ligand concentrations) as well as in inner ones (e.g., unfolding enthalpy, binding enthalpy, association constant, and changes in heat capacity). Acknowledgments MSC holds a doctoral fellowship from Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET). SAD and GDF are Career members of CONICET. This work was supported by CONICET, Agencia Córdoba Ciencia, FONCYT, and SeCyT-UNC. Helpful discussion with N. Wilke, O. R. Camara and B. Maggio are gratefully acknowledged. Literature Cited
Figure 7. Effect on thermogram shape of protein concentration: (A) simulated thermograms for protein unfolding coupled to ligand binding to native protein for the same value of [L]tot/[P]tot = 0.5, (B) species distribution profile corresponding to [P]tot = 0.1 mM, and (C) same as B but [P]tot = 1 mM. Concentration normalization was carried out as in Figure 3. See Table 1 for simulation parameters.
92
Journal of Chemical Education
•
1. Rezvan, H.; Nasiri, S.; Mousari, K. Arch. Irn. Med. 2001, 4, 10–13. 2. Waldron, T. T.; Murphy, K. P. Biochemistry 2003, 42, 5058– 5064. 3. Lumry, R.; Biltonen, R. Biopolymers 1966, 4, 917–944. 4. Crothers, D. M. Biopolymers 1971, 10, 2147–2160. 5. Schellman, J. A. Biopolymers 1975, 14, 999–1018. 6. McGhee, J. D. Biopolymers 1976, 15, 1345–1375. 7. Brandts, J. F.; Lin, L.-N. Biochemistry 1990, 29, 6927–6940. 8. Shrake, A.; Ross, P. D. Biopolymers 1992, 32, 925–940. 9. Straume, M.; Freire, E. Anal. Biochem. 1992, 203, 259–268. 10. Plotnikov, V. V.; Brandts, J. M.; Lin, L.-N.; Brandts, J. F. Anal. Biochem. 1997, 250, 237–244. 11. Chowdhry, B.; Leharne, S. J. Chem. Educ. 1997, 74, 236–240. 12. Privalov, P. L. Adv. Protein Chem. 1979, 33, 167–241. 13. Sturtevant, J. M. Ann. Rev. Phys. Chem. 1987, 38, 463–488. 14. Privalov, P. L. In Protein Folding; Creighton, T., Ed.; W. H. Freeman: New York, 1992; pp 83–126. 15. Dill, K. A.; Shortle, D. Annu. Rev. Biochem. 1991, 60, 795–825. 16. Makhatadze, G. I.; Privalov, P. L. J. Mol. Biol. 1990, 213, 375– 384. 17. Privalov, P. L.; Makhatadze, G. I. J. Mol. Biol. 1990, 213, 385– 391. 18. Freire, E. Meth. Enzymol. 1995, 259, 144–168. 19. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in Fortran, 2nd ed.; Cambridge University Press: New York, 1992; pp 402–448.
Vol. 82 No. 1 January 2005
•
www.JCE.DivCHED.org
