Effects of Common Cancer Mutations on Stability

Heat map of reliable electrostatic interaction energy between pairwise amino acid residues of the p53 monomer

The difference in the calculations obtained for the Positive and Negative set of p53 mutations

In the last decades, the quest thereof has been dominated by structural and thermodynamical considerations, where candidate ligands are ranked by their equilibrium constants Kd. This constant, also known as the dissociation constant, describes the fraction of target-proteins that would be bound to the ligand at equilibrium conditions, and in particular, at constant ligand concentration. A schematic picture of protein-ligand binding is given in Figure 1, where it is seen that the equilibrium constant is given by the ratio of the kinetic rate constants koff and kon. From physical chemistry, it is known that Kd is proportional to the Boltzmann constant associated with the free energy difference of the bound and unbound states (Figure 1, left).

Figure 1: Left: schematic picture of the Protein-Ligand (P-L) binding free energy profile. The equilibrium constant Kd is fully described by the free energy difference deltaG of the unbound and bound states, describing the strength of the P-L bound complex. For this reason, Kd has served as the dominant parameter in targeted drug design. However, the binding reaction is almost always accompanied by an energy barrier which is often not negligible, and can highly impact the effectiveness of the candidate ligand in vivo (see text). Right: differential equation accompanying the bimolecular binding reaction, where [P] and [L] denote protein and ligand concentrations, respectively.

While it is true that Kd is a good indicator of binding strength, it has major shortcomings that prove to be detrimental: more than 90% of promising drug molecules fail human trials by off-target toxicity and/or bad overall target selectivity. Indeed, thermodynamic selection based on Kd neglects the existence of a free energy barrier that needs to be overcome during the binding reaction (Figure 1, left). While the final bound state at the target protein may be energetically most favourable, the energy barrier may be sufficiently high that most drug molecules bind to a – potentially toxic – off-target protein with less favourable bound state, but lower energy barrier. To this end, the notion of kinetic selectivity has gained a lot of attention in the latest years, where one tries to obtain the rate constants kon and koff. These parameters hold information about kinetic properties of the protein-ligand interaction, such as the drug residence-time, allowing better profiling of candidate drug molecules and saving costly and time-consuming in vivo experiments.

https://plato.ea.ugent.be/mp/export1.jsp?nr=25223&view=ntpbrPD

Models of drug–target binding. a Schematic diagram of a one-barrier drug–target binding free energy profile. A one-step model with one free energy barrier is used to derive the experimental rate constants. The figure and equations show how the steady-state rate constants relate to the free energy differences shown. The residence time of a drug bound to its target, τ (which is the reciprocal of the rate constant for dissociation of the drug–target complex, k _off), results from the “difference” in free energy between the transition state (TS) and the bound ground state (GS), ΔG _off.

The red arrows indicate that prolongation of the τ can be achieved by stabilizing the GS (increasing the magnitude of ΔG _D), destabilizing the TS (increasing ΔG _on) or a combination of both (i.e.,

b Diagram schematically illustrating different mechanisms of drug binding involving protein conformational changes.
R and R^C denote two different conformations of the protein, the latter requires conformational changes for ligand binding.

These may occur by conformational selection (blue path) or by induced fit upon formation of an encounter complex [RL]^# (red path), or by a combination of the two mechanisms. Binding proceeds through an energetically unfavorable intermediate state (TS in panel A or a local minimum in a 2 (or more)-step binding free energy profile) that, in the conformational selection and induced fit mechanisms, corresponds, respectively, to the R+L or [RL]^# state of the system); the final complex is denoted by [RL].

The gray path and third equation describe the pseudo-one-step binding process shown in (a) is used to derive the experimental rate constants

Thermodynamic profiles of N-HSP90 inhibitors measured by ITC. The enthalpic and entropic components of the binding free energy are shown in a and b for for WT N-HSP90, and the L107A mutant, respectively. The dashed diagonal line (ΔH=−TΔS) divides the plot into two main areas where the enthalpy (gray) or the entropy (red) dominate the binding free energy (ΔG).

Thermodynamic profiles of N-HSP90 inhibitors

The thermodynamic profiles of the binding of the 20 resorcinol ligands to N-HSP90 obtained by isothermal titration calorimetry (ITC) are depicted in Fig. 3 and quantify the energetic differences between two states in equilibrium (free state and bound state).

Free Energy Calculations

As a reward for the highly intensive computation, the results of free energy calculations ought to be reliable and almost quantitative. The main advantages over faster scoring functions are that the free energy calculations include both the energetic (i.e., potential energy and solvation energy) and entropic (i.e., dynamics/flexibility of both protein and ligand, and solvent effects) contributions, and require no case-by-case parameter fitting

Anyway, the accurate prediction of binding free energy using the calculation methods, despite being an ambitious goal, would revolutionize their applications in basic research and in drug design and discovery.

Free energy calculations rely on the fundamental relationship between Helmholtz free energy F and the partition function Z:
F = −k_BTlnZ

where k_B and T is Boltzmann’s constant and temperature, respectively. When the system is treated in terms of the classic approximation of statistical thermodynamics, the partition function can be expressed as configurational integral:

where h is Planck’s constant, N is the number of atoms or particles in system, and N! is only present for indistinguishable particles.

The latter describes the interactions between the various atoms in system (i.e., potential function). The difference in free energy between two states A and B can be expressed as a ratio of their partition functions:

If the conformational sampling is carried out under constant temperature and pressure conditions (isothermal-isobaric ensemble), the Gibbs free energy can be obtained.

[Insights into Protein–Ligand Interactions: Mechanisms, Models, and Methods]

Free energy calculations of the protein-ligand binding try to compute the binding free energies based on the principles of statistical thermodynamics.

[Insights into Protein–Ligand Interactions: Mechanisms, Models, and Methods]

[Some Binding-Related Drug Properties are Dependent on Thermodynamic Signature]

Thermodynamic profiles for three pairs of HIV-1 proteinase inhibitors that vary by only a single group: (a) KNI-10033-KNI-10075 pair within which an apolar group thioether on KNI-10033 is replaced by a polar group sulfonyl to form KNI-10075; (b) KNI-10052-KNI-10054 pair within which an apolar methyl group is replaced by a polar hydroxyl group; and (c) KNI-10046-KNI-10030 pair within which a hydrogen atom on the former is replaced by an apolar methyl group to form the latter. The binding free energy (∆G), enthalpy (∆H), and entropy (T∆S) are shown

[Freire, E. The binding thermodynamics of drug candidate. In Thermodynamics and Kinetics of Drug Binding; Keserü, G.M., Swinney, D.C., Eds.; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2015; pp. 1–13.]

[Lafont, V.; Armstrong, A.A.; Ohtaka, H.; Kiso, Y.; Mario Amzel, L.; Freire, E. Compensating enthalpic and entropic changes hinder binding affinity optimization. Chem. Biol. Drug Des. 2007, 69, 413–422.]

[Kawasaki, Y.; Freire, E. Finding a better path to drug selectivity. Drug Discov. Today 2011, 16, 985–990.]

NBD-556 is a competitive inhibitor of CD4 characterized by a binding affinity of 3.7 μM. Despite the small size, NBD-556 binds with a thermodynamic signature that resembles that of CD4 (ΔH = -24.5 kcal/mol, -TΔS = 17.1 kcal/mol at 25 °C

dH, kcal/mol

dH, kcal/mol

-TΔS, kcal/mol

-TΔS, kcal/mol

The thermodynamic signatures of sCD4 and NBD-556 at 25°C. The large conformational structuring of gp120 triggered by CD4 binding is reflected in a thermodynamic signature characterized by an unusually large favorable change in enthalpy and a very large unfavorable entropy change. Except for a lower affinity, the binding of NBD-556 to gp120 is also associated with enthalpy and entropy changes similar to those observed for CD4. ΔG is represented by blue bars, ΔH by green bars and -TΔS by red bars.

Free energy calculations of protein-ligand complexes

The entropy change accompanying a chemical reaction is defined as
the difference between the sum of the entropies of all the products and
the sum of the entropies of all reactants.
the entropy change is given by:
dS = (cSc + dSD + • • •) - (aSA + bSB+ • • )
where SA, SB, etc., are the entropies per mole of the various species.

When the entropies of the individual substances correspond to a state of
unit activity they are called standard entropies and they are designated by
the symbol S°.

Again, in a reaction where all the substances involved are
at unit activity dS is written dS0, and the latter is the standard entropy
change of the reaction.
One way of obtaining these is through the third law of thermodynamics.

ENTROPY CHANGE IN CHEMICAL REACTIONS

Li and Deber [1] used circular dichroism (CD) data to rank order helical propensity of proteins within membranes. Residues such as Ile, Val and Thr, which usually exist as β-sheets in an aqueous environment, prefer an α-helical conformation in lipid membranes. Thus, the helical propensity of amino acid residues correlates with the hydrophobic nature of the side chain

Felitsky et al. introduced the use of a new parameter called “average area buried upon folding” (AABUF) [2] that explains both local contacts and long-range interactions. AABUF was used to study folding of apomyoglobin and provided additional insight into hydrophobic collapse and early folding events.

[1] A measure of helical propensity for amino acids in membrane environments
[2] Modeling transient collapsed states of an unfolded protein to provide insights into early folding events

This principle, called the third law of thermodynamics, states that the entropy of all pure crystalline solids may be taken as zero at the absolute zero of temperature.

The importance of the third law lies in the fact that it permits the calculation
of absolute values of the entropy of pure substances from thermal
data alone.

THE THIRD LAW OF THERMODYNAMICS

Further, since the third law states that for
any pure crystalline substance S = 0 at T = 0
then for any such substance the equation may be integrated
between this lower limit and any temperature T to yield:

St, known as the absolute entropy of the solid, is always a positive quantity.

All that is necessary for integration of this equation is a knowledge of the heat capacities of the solid from T = 0 to any desired temperature T

The integral in Eq. above is evaluated graphically by plotting either Cp
vs. In T or Cp/T vs. T and determining the area under the curve between
T = 0 and any temperature T. This area is then the value of the integral
and hence of ST. In practice heat.capacities are usually measured from
approximately 20°K to temperature T, and extrapolation is resorted to
from ca. 20°K to T = 0.


Such extrapolations are generally made by use of the Debye third power law for the heat capacity of solids at low temperatures, namely,

EVALUATION OF ABSOLUTE ENTROPIES

This expression substituted into Eq. above yields

and hence on integration between T=0 and Ti, the lower limit of the heat capacity data, we get

Since Cp = a(T)^3, then the value of ST1 is equal to one-third of the value
of Cp at temperature T1

A plot of Cp vs. log10 T for anhydrous sodium sulfate is shown in Figure. The area under the curve between T = 14° and
T = 298.15°K is 15.488, while the area from T = 0 to T = 14° is 0.026. Hence the absolute entropy per mole of sodium sulfate at 298.15°K is

Absolute entropies of substances that are liquid or gaseous at room temperatures can also be obtained with the third law.

Heat capacity of Na2S04 at various temperatures.

Absolute entropies are usually calculated and tabulated for 25°C and
unit activity. Values of these thermodynamic quantities in the standard
state are available at present for most elements and for many compounds.
Some of these are listed in Table:

USE OF ABSOLUTE ENTROPIES

STANDARD ABSOLUTE ENTROPIES OF ELEMENTS
AND COMPOUNDS AT 25°C
(Entropy units per gram atom or mole)

Suppose the entropy change is required for the reaction:
C(s, graphite) + 2 H2(g) + l- 0,(g) = CH30H(1)

In a similar manner may be calculated AS0 values for other reactions at 25°C provided the necessary absolute entropies are known. To obtain the entropy changes at temperatures other than 25°C:

Although entropy can be employed to measure the tendency of systems
to undergo change, under conditions most frequently encountered it is
not as convenient a quantity to use as the so-called free energy functions
The Helmholtz free energy of any system, A, is defined as A = E - TS

where E and S are, respectively, the internal energy and entropy of a
system. Since E, T, and S depend only on the state of the system, A
must also be a state function. Consequently, when the system passes
from one state to another, the change in A must be given by

THE HELMHOLTZ FREE ENERGY

Equation (2) gives the most general definition of dA. Under isothermal
conditions, when T2 = T1 = T, this equation reduces to

dA = A 2 — A i= dE - (T2S2 - T1S1) (2)

dA = dE - TdS (3)

Equation (3) allows a physical interpretation of dA. Since under isothermal conditions TdS = qr ,we have

dA = dE - qr

Hence at constant temperature the maximum work done by a system is
accomplished at the expense of a decrease in the Helmholtz free energy
of the system. This is why A is sometimes called the maximum work
content of a system.

Следовательно, при постоянной температуре максимальная работа, совершаемая системой, достигается за счет уменьшения свободной энергии Гельмгольца.
Вот почему А иногда называют максимальной работой системы.

The maximum work a process may yield is not necessarily the amount
of energy available for doing useful work, even though the process is
conducted reversibly. Of the total amount of work available, a certain
amount has to be utilized for the performance of pressure-volume work
against the atmosphere due to contraction or expansion of the system
during the process.

THE GIBBS FREE ENERGY

For any pure substance A is most conveniently expressed in terms of T and V as the independent variables:

Equation shows the dependence of A for a pure substance dn both the temperature and volume, with the individual effects of these variables

Максимальная работа, которую может произвести процесс, не обязательно равна сумме энергии, доступной для совершения полезной работы, даже если процесс проводится обратимо. Из общего объема имеющихся работ определенное количество должно быть использовано для выполнения работы давление-объем против атмосферы из-за сжатия или расширения системы во время процесса.

For a process taking place reversibly at constant temperature and pressure, and involving a volume change from V1 to V2,
the work done against the atmosphere is P(V2 — Vi) = PdV.

Since this work is accomplished at the expense of the maximum work yielded by the process, the net amount of energy available for work other than pressurevolume against the confining atmosphere must be

Net available energy at T and P

To bring out more precisely the nature of the maximum net energy
available from a process, let us define another state function F, called the Gibbs free energy, by the relation F = H - TS

The change in F between two states of a system will be, therefore,

and when the temperature is constant

An alternate, but equivalent, way of defining F is through the relation

F = A + PV

where A is the Helmholtz free energy, and P and V are the pressure and volume of the system.

which at constant pressure becomes

dF=dA+PdV

The equivalence of the two definitions may be shown by inserting Eq's. We obtain thus

Hence the total maximum work wm:

where dqr is the infinitesimal quantity of heat absorbed in a process taking place under reversible conditions at temperature T. In the case of a finite reversible change at constant temperature, dS becomes AS, dqT becomes qr

Therefore, for any isothermal reversible process in which an amount of heat qr is absorbed at temperature T, the entropy change involved is simply the absorbed heat divided by the absolute temperature. When qr is positive, i.e., heat is absorbed, AS is also positive, indicating an increase in the entropy of the system. On the other hand, when heat is evolved qT is negative and so is dS, and the system experiences a decrease in entropy.

Следовательно, для любого изотермического обратимого процесса, в котором количество тепло qr поглощается при температуре T, связанное с этим изменение энтропии представляет собой просто поглощенное тепло, деленное на абсолютную температуру. Когда qr положителен, т. е. происходит поглощение тепла, AS также положителен, что указывает на увеличение энтропии системы. С другой стороны, когда выделяется тепло, qT отрицательно, как и AS, и в системе происходит уменьшение энтропии.

The physical significance of dF at constants T and P may be obtained as follows: At constant temperature TdS = qr. Again, when the pressure is also constant, dH = dE + PdV.

dF = dE + PdV - qr
= -(qr - dE-PdV)

But, by the first law qr — dE = wm, and, therefore,

Good design is obvious. Great design is transparent.

dF = -(wm -PdV)

dF represents the maximum net energy at constant T and P available for doing useful work, the net available energy under the specified conditions results from a decrease in the free energy content of the system on passing from the initial to the final state.

It is customary to refer to the Gibbs free energy simply as the free
energy. We shall follow this procedure, and append the designation Gibbs
or Helmholtz only when necessary for clarity.
Like H, F is most conveniently expressed in terms of T and P as
independent variables.

dF представляет собой максимальную чистую энергию при постоянных T и P, доступную для совершения полезной работы, чистая доступная энергия в указанных условиях является результатом уменьшения содержания свободной энергии в системе при переходе от начального к конечному состоянию.

Свободную энергию Гиббса принято называть просто свободной энергией. Мы будем следовать этой процедуре и добавим обозначение Гиббса или Гельмгольца только тогда, когда это необходимо для ясности, подобно H, F удобнее всего выражать через T и P как независимые переменные.

A minus sign denotes, therefore, that the reaction tends to proceed spontaneously. When the tendency is from right to left, however, net work equivalent to dF has to be absorbed in order for the reaction to proceed in the direction indicated, and dF is positive. A positive sign for dF signifies, therefore, that the reaction in the given direction is not spontaneous. Finally, when the system is in equilibrium, there is no tendency to proceed in either direction, no work can be done by the system, and hence dF = 0.

These three possible conditions for the free energy change of a process at constant temperature and pressure may be summarized as follows:

When a catalyst like platinized asbestos is introduced, however, the reaction
proceeds with explosive violence. Even with a catalyst the reaction
would have been impossible had not the potentiality to react been present.

Однако при введении такого катализатора, как платинированный асбест, реакция протекает сo взрывной силой. Даже при наличии катализатора реакция была бы невозможна, если бы не существовала возможность реакции.

The arrows indicate the directions the reaction tends to follow spontaneously for the given sign of the free energy change.

A negative free energy change for a process does not necessarily mean that the process will take place. It is merely an indication that the process can occur provided the conditions are right.

Platinized asbestos is a catalyst material obtained by permeating asbestos fibers with finely divided platinum, usually via the chemical method. It is a white fibrous solid containing around 5% platinum metal by weight.
Platinized asbestos used to be sold in the past by chemical suppliers, but nowadays it's getting harder to find since most asbestos-containing products have been phased out. It is very toxic and irritant and should be handled with care. Inhalation of fine particles will lead to severe lung problems, while skin or tissue contact will cause irritation or dermatitis.
Uses

1. Platinised asbestos is used as a catalyst in the manufacture of H2SO4.
2. Platinised asbestos helps in the formation of SO3, from S02 and O2.

It is the sign of the free energy change which determines whether the
potentiality to react exists, and it is the magnitude of the free energy
change which tells us how large that potentiality is.

The term represents the heat interchange between the system and its surroundings when the process is conducted isothermally end reversib

When dH is greater than dF, qr is positive and energy is absorbed as heat from the surroundings. On the other hand, when dF is greater than dH, qr is negative and heat is evolved to the surroundings. Finally, in the special case when
dH = dF, heat is neither absorbed nor evolved by the system, and hence ther is no change in entropy.

— TdS or

The difference between the work so obtained and the heat which would have been liberated had the reaction been carried out completely irreversibly, as in an open beaker,
is given by the Gibbs-Helmholtz equation, and is equal to either

amount of heat qr

dF equations are useful not only for calculating the free energy change at any temperature T, but also for evaluating dS and dH.
dS is readily obtained by differentiation with respect to temperature at constant pressure of the dF expression in accordance with Eq.

Cp is the heat capacity per mole

An approach to the apolar molecule-water interaction was adopted by
W. Kauzmann. Rather than focus on the formation of crystalline hydrates, he considered the thermo dynamics of transferring an apolar residue from an apolar solvent to water. For example, he asked what the free energy change would be in transferring methane from mole fraction x in benzene to mole fraction x in water. This kind of approach basically aims at determining whether the apolar groups would prefer to reside on the protein surface—and thus interact with water—or bring themselves together in the interior of the protein—and thus create an apolar environment for themselves.

Unitary and cratic contributions to free energy of transfer

Lets concider a standard free energy change

dG°=-RTlnK

The dependence of dG° on the standard state is a purely statistical effect that arises from the expression for the partial molal entropy; consider the partial molal entropy Sa of A:

where Xa is the mole fraction of A. (We are considering dilute solutions, and therefore we are ignoring activity-coefficient effects.)
The term — RInXa is called the cratic contribution to the entropy; it is a purely statistical term arising from the mixing of A with solvent molecules.
This contribution is independent of the chemical nature of A.

The term S'a is called the unitary contribution; it reflects the characteristics of A itself and its interaction with solvent.

The standard entropy change for the reaction becomes:

Equation above is the usual expression for the partial molar entropy. It can easily be derived by starting with the total differential for the Gibbs free energy:

DERIVATION OF EXPRESSION FOR PARTIAL MOLAR ENTROPY

Introductory physical chemistry textbooks derive the following relationship:

is the standard chemical potential at Xi = 1.
Using this relationship, and differentiating the preceding expression, we obtain

where Xm is the mole fraction of a molecule when its concentration is
1 mole/ liter. Because the water concentration is 55.6 molar in dilute aqueous solution, the cratic contribution to the entropy change is about — Rln56= — 8 cal /(mol deg) at 300 K, this corresponds to a cratic contribution to the free energy of about — 2.4 kcal/ mole.

If a different standard state and different concentration units were chosen, a different contribution would result. The unitary change in entropy, dSu, thus is obtained from:

An example of separating neutral mutations from oncogenic mutations in calculated numbers

The fact is that the yi values for Negative Set practically coincide with the obtained average value; as a result of the difference between the average and yi values, we get a very small value tending to zero.

Neutral Mutations

Oncological mutations

WOW! affect

Difference in calculated characteristics for Positive and Negative sets of P53 protein mutations.

To determine the correlation coefficient, we use Boolean variables and the Fechner coefficient.
rb(integr) is a Fechner coefficient

Сalculated data obtained for two sets of mutations. Plot of differential entropy changes for two data sets. The graphs show Boolean variables and the final Fechner coefficient.

The graphs for the derivatives of the ddG value are shown on the graph on the left, the graph on the right shows an area with less data scatter. As can be seen from the graph on the left, the spread of points from the Positive data set is much more significant than from the Negative data set.

In 2018 an estimated 1.7 million patients in the US will be diagnosed with cancer, of these roughly 1.5% will have the p53(Y220C) mutation, or >25,000 patients per year.

Carbazole alkaloids natural products are mostly isolated from higher plants of Rutaceae family and major components of the Clausena genus. With the isolation of carbazole core from coal tar in 1872 and the description of the antimicrobial murrayanine in 1965, the interest on these alkaloids began. Since then, natural-occurring carbazole alkaloids have been reported to exhibit a broad pharmacological profile

Rutaceae family

Over 50% of p53 proteins present missense mutations, generating a defective protein in high levels in cells due to the impairment of MDM2 mediated negative feedback, which is responsible for p53 degradation The tumor cell growth inhibitory potential of aminocarbazoles was ascertained in human colon adenocarcinoma HCT116 and melanoma A375 cell lines expressing wild-type (wt) p53

Comparative calculated graphs of the measure of change in differential entropy for various structures of the P53 protein, taking into account Positive mutations

Enlarged area of the comparison graph in the area of greatest change

Calculation graphs for various physical quantities taking into account mutations in the p53 protein

С220

E258

G266

G105

F109

F113

Three-dimensional structure of the p53 protein indicating the amino acid residues, the replacement of which significantly affects the change in the calculated physical parameters

Our research team is interested in Positive mutations that exhibit higher affinity for a small molecule inhibitor.
We will select Positive mutations for which the calculated physical quantities will be as follows:
a decrease in the values of Kd and lg(cond(W)), as well as a negative entropy value TdH

1

The second important aspect of the study is the analysis of structure changes by analyzing the calculated data for various mutations.

2

PK9284

Calculation diagram of a monomer with one chemical molecule

The three-dimensional diagram of the P53 protein contains the indicated amino acid residues with the largest difference in the calculated data for two similar small chemical molecules

Click "Block Editor" to enter the edit mode. Use layers, shapes and customize adaptability. Everything is in your hands.

Tilda Publishing

calculated data: TdH
Between the p53 Core Domain with small inhibitors

Comparison of the results obtained for various small chemical molecules when binding to the P53 protein

Click to ZOOM it!

• The body converts inorganic arsenic into the breakdown product (metabolite) called dimethylarsinic acid (DMA). DMA is also found in such foods as fish, poultry, fruits and grains. NHANES results found DMA and arsenobetaine to be the major components of urinary total arsenic levels. Arsenobetaine is a non-toxic inorganic arsenic form that comes from fish and seafood.

Finding measurable amounts of arsenic in urine does not mean those levels cause an adverse health effect. Biomonitoring studies on levels of arsenic provide physicians and public health officials with reference values. These reference values help experts determine if people have been exposed to higher levels of arsenic than are found in the general population. Biomonitoring data can also help scientists plan and conduct research on exposure and health effects.

PDB: 7V97
Arsenic-bound p53 DNA-binding domain mutant V272M