i

Theoretical and Computational Study of Sulfur Compounds

Reactivity in Prebiotic Chemistry: The Whitesides Network

of Thiols and Thioesters

João Miguel dos Santos Nicolau da Inês

Dissertação para obtenção do Grau de Mestre em

Química

Orientadores: Prof. Luís Filipe Coelho Veiros (IST)

Prof. Josep Maria Bofill Villà (Universitat de Barcelona)

Júri

Presidente: Prof. Maria Matilde Soares Duarte Marques (IST)

Orientador: Prof. Luís Filipe Coelho Veiros (IST)

Vogal: Prof. Adelino Leitão de Moura Galvão (IST)

Setembro de 2017

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Resumo

Actualmente propõem-se como base química das origens da vida um conjunto de reacções

cujos compostos contêm enxofre. Em sistemas biológicos actuais observaram-se reacções que

apresentam comportamentos interessantes relacionados com aspectos da química da vida.

O sistema de reacções proposto é constituído por tióis e tioésteres com um número pequeno

de átomos. Estes tióis e tioésteres são responsáveis pelo comportamento autocatalítico e

autoamplificativo do sistema de reacções. A autoamplificação gerada pelos tióis é ajustada pelos

processos competitivos, nomeadamente: 1) reacção entre maleimida e tióis, no processo de iniciação,

a qual atrasa a autocatálise e 2) a reacção de inibição dos tióis com a acrilamida. Esta última reacção

é a que consome os tióis do sistema. As oscilações que se observam nas concentrações de tióis em

função do tempo são obtidas escolhendo adequadamente as concentrações iniciais de reagentes e

controlando as velocidades espaciais no reactor.

Um feito interessante deste sistema de reacções é o efeito de memória em condições fora de

equilíbrio. Pode observar-se através do fenómeno de histerese que se obtém num intervalo de

velocidades espaciais.

O objectivo principal deste trabalho é modelar este sistema de reacções orgânicas, focando a

formação da ligação amida (troca tiol-tioester seguida de transferência de grupo acilo), troca tiol-

dissulfeto, hidrólise de tioésteres e adições conjugadas 1,4. Utilizando a teoria Hartree-Fock,

calcularam-se as distintas barreiras energéticas do sistema de reacções. A análise das barreiras

energéticas foi conduzida através do modelo de Ligação de Valência.

As constantes de velocidade de reacção obtiveram-se através da Teoria de Estado de

Transição. Estas constantes de velocidade utilizaram-se posteriormente no sistema de equações que

rege a cinética das reacções para se obter o perfil teórico da variação de concentrações das espécies

químicas em função do tempo no ciclo autocatalítico.

Palavras-chave: Pré-biótica, Tióis, Tioésteres, Autocatálise, Histerese, Hartree-Fock

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Abstract

It is hypothesized that a network of organic reactions containing sulfur may have played a role

in the origins of life. Similar complex reactions are observed in biological systems and display

interesting behavior in many aspects of chemical life.

The proposed organic reaction network is composed by small molecules mainly thiols and

thioesters. These thiols and thioesters are responsible of an autocatalytic cycle and auto-amplification.

The resulting auto-amplification of thiols is finely tuned with two competitive processes: first, the trigger

reaction, between maleimide and thiols, delays the autocatalytic event; and second, the inhibition

reaction of thiols with acrylamide. The latter consumes the remaining thiols in the system. Fine-tuned

oscillations in thiol concentration over time can be achieved by modeling the initial concentrations of

reactants and the Continuous Stirred Tank Reactor space velocities. Another interesting feature of out-

of-equilibrium network of this chemical set of reactions is the memory effect. This can be observed by

hysteresis over a range of space velocities.

The main objective of this work is to model this network of organic reactions, namely amide

bond formation (thiol-thioester exchange followed by S to N acyl transfer), thiol-disulfide exchange,

thioester hydrolysis and 1,4 conjugate addition. Ab initio quantum chemical calculations using Hartree

Fock theory are carried out to calculate the distinct energy barriers in the Potential Energy Surface.

Valence Bond theory is used as a tool for a qualitative description and analysis of the nature of the

activation energy between reactants and the transition state.

Furthermore, the reactions rate constants are obtained by Transition State Theory in order to

be introduced in the set of ordinary differential equations for a quantitative description of the

concentration profiles with respect to the time in the autocatalytic cycle.

Keywords: Pre-biotic, Thiols, Thioesters, Autocatalysis, Hysteresis, Hartree-Fock

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Contents

Resumo .................................................................................................................................................... iii

Abstract .................................................................................................................................................... v

List of Tables .......................................................................................................................................... viii

List of Figures ............................................................................................................................................ x

Nomenclature ......................................................................................................................................... xii

1. Introduction ......................................................................................................................................... 1

2. Computational Details ......................................................................................................................... 4

3. General aspects of Sulfur chemistry .................................................................................................... 4

4. Results and Discussion ........................................................................................................................ 6

4.1 Thiolate-thioester exchange.......................................................................................................... 6

4.2 Intramolecular rearrangement ...................................................................................................... 9

4.3 Thiolate-disulfide interchange .................................................................................................... 12

4.4 1,4 Conjugate addition ................................................................................................................ 16

4.5 Thioester Hydrolysis .................................................................................................................... 19

4.6 Numerical modelling of network kinetics .................................................................................... 22

5. Conclusion ......................................................................................................................................... 24

Bibliography ........................................................................................................................................... 24

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List of Tables

TABLE 1: Major vibrational contributions in energy distribution matrix for intramolecular

rearrangment .......................................................................................................................... 3

TABLE 2: pKa values and estimated populations for reactants and cystamine at equilibrium . 6

TABLE 3: Geometrical comparison of distances (d), angle(𝛼, values in degrees), and

dihedral angles (δ, values in degrees) for both thiolate-disulde TS ......................................... 3

TABLE 4: Theoretical rate constant values for the reactions in gas-phase using

thermochemistry at 298 K ....................................................................................................... 6

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List of Figures

FIG. 1: Hydrolisis of AlaSEt and conjugate addition of thiols to maleimide .............................. 3

FIG. 2: Native chemical ligation and thiol-disulfide exchange reactions .................................. 3

FIG. 3: Conjugate addition of thiols to acrylamide ................................................................... 3

FIG. 4: Thiolate-thioester reaction between AlaSEt and CS .................................................... 6

FIG. 5: Neutral and concerted TS 2. All distances are given in Angstrom ............................... 7

FIG. 6: Hypothetical neutral stepwise transition state.............................................................. 7

FIG. 7: Hypothetical anionic stepwise transition state ............................................................. 7

FIG. 8: Potential energy profile for the thiolate-thioester exchange reaction accounting the

zero point energy correction. Energy of activation relative to reactants in kcal mol-1 with Zero

Point Energy correction. All distances are given in Angstrom ................................................. 8

FIG. 9: Qualitative VB configuration mixing diagram for thiolate-thioester exchange reaction 9

FIG. 10: S → N acyl transfer ................................................................................................. 10

FIG. 11: Potential energy profile for the intramolecular rearrangement reaction accounting

the zero point energy correction. Energy of activation relative to reactants in kcal mol-1 with

Zero Point Energy correction. All distances are given in Angstrom ....................................... 10

FIG. 12: Qualitative VB Configuration Mixing Diagram for the S → N acyl transfer ............... 11

FIG. 13: Thiolate-disulfide exchange reaction. Two molecules of cysteamine are formed in

this two parallel reactions ..................................................................................................... 12

FIG. 14: Potential energy profile for the thiolate-disulfide reaction with EtS- accounting the

zero point energy correction. Energy of activation relative to reactants in kcal mol-1 with Zero

Point Energy correction. All distances are given in Angstrom ............................................... 13

FIG. 15: Potential energy profile for the thiolate-disulfide reaction with 5- accounting the zero

point energy correction. Energy of activation relative to reactants in kcal mol-1 with Zero Point

Energy correction. All distances are given in Angstrom ........................................................ 14

FIG. 16: Qualitative VB State Correlation Diagram for the thiolate-disulfide reaction ............ 15

FIG. 17: 1,4 conjugate addition mechanism present in trigger and inhibition mechanisms,

respectively. First, nucleophilic addition of EtS-, second proton transfer and final tautomeric

equilibrium ............................................................................................................................ 16

FIG. 18: Potential energy profile for the 1,4 conjugate addition reaction with acrylamide

accounting the zero point energy correction. Energy of activation relative to reactants in kcal

mol-1 with Zero Point Energy correction. All distances are given in Angstrom ....................... 17

FIG. 19: Potential energy profile for the 1,4 conjugate addition reaction with maleimide

accounting the zero point energy correction. Energy of activation relative to reactants in kcal

mol-1 with Zero Point Energy correction. All distances are given in Angstrom ....................... 18

FIG. 20: Qualitative VB Configuration Mixing Diagram for the 1,4 conjugate addition of EtS-

reaction with acrylamide ....................................................................................................... 18

FIG. 21: Qualitative VB Configuration Mixing Diagram for the 1,4 conjugate addition of EtS$-

reaction with maleimide ........................................................................................................ 19

FIG. 22: Hydrolysis of AlaSEt to carboxylic acid. The first thiols are generated in this reaction.

............................................................................................................................................................... 19

FIG. 23: TS 8 structure for the hydrolysis reaction. Distance units in Angstrom .................... 20

FIG. 24: Relevant molecular orbitals representations for hydrolysis in TS 8 .......................... 21

FIG. 25: Qualitative VB Configuration Mixing Diagram for the hydrolysis reaction ................ 21

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Nomenclature

PES – Potential Energy Surface

TS – Transition State

TST – Transition State Theory

VB – Valence Bond

NCL – Native Chemical Ligation

RSH – Thiols

CSTR – Continuously Stirred Tank Reactor

IRC – Intrinsic Reaction Coordinate

GS 2 – Gonzales and Schlegel second order

GAMESS – General Atomic Molecular Electronic Structure System

EWG – Electron Withdrawing Group

CT – Charge Transfer

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1. Introduction

An understanding of chemical reactivity begins with an understanding of chemical bonding, the

forces which render atoms aggregated to form molecules. London and Heitler introduced quantum

mechanics into reactivity problems, in chemistry. This approach followed the molecular orbital

description of bonding. As a fruitful consequence, quantitative understanding of bonding led to

satisfactory calculations of energies, optimum bond lengths and geometries1.

Hartree Fock (HF) theory is one of the simplest approximate theories for solving the many-

body Hamiltonian. It is based on a simple approximation to the true many-body wavefunction: that the

wavefunction is given by a single Slater determinant of N spin-orbitals23. By assuming a single-

determinant form for the wave-function, neglects static correlation between electrons. This implies that

states that are poorly described by a single configuration, such as transition structures involving bond

breaking or bond forming, may need to be further improved by post-HF methodologies such as

Configuration Interaction (at least at doubles level – CISD) or Perturbation Theory such as MP2.

It’s also to be noted that the mean field approach of HF methodologies includes an intrinsic

formalism error by ignoring the dynamic correlation between electrons that could be better dealt with

the DFT formalism. Electronic correlation will be introduced in future work for a better description of

the energy barriers.

The principle of activation, that is, the postulate that only those molecules with combined

energy equal or greater than some critical value can react, is likewise a statistical concept, but the

actual value of this critical energy depends on electronic changes in the reacting molecules and

cannot be found without a knowledge of quantum laws2. The Whitesides3 reaction network was

subjected to analysis by means of the Potential Energy Surface (PES), within the Born-Oppenheimer

approximation, allowing the calculation of the activation energy for each reaction.

Additionally, the rate constants of the Whitesides3 reactions were calculated by theoretical

methods in the gas-phase using Transition State Theory (TST).

The reagent molecule(s) are supposed to be in thermodynamic equilibrium with the Transition

State (TS) which passes to products at a specific frequency and it is only applied to single microscopic

rate constant as a result of collisions of two molecules (or unimolecular reactions) to render a

configuration of maximum potential energy.

Valence Bond (VB) theory formalism decomposes chemical systems into a linear combination

of chemically meaningful structures (molecular states), in which the electrons occupy localized orbitals

by combining relevant atomic orbitals. Therefore, VB looks for the probability of finding a molecule at a

given molecular state. A VB correlation diagram, which traces the VB configurations along the

reaction coordinate, and by mixing of configurations, projects the root cause of the energetic barrier,

the nature of the transition state, and the origins of reaction intermediates4. Thus, VB approach is

followed in all reactions study in order to create elements of reasoning that can serve experimental

chemists to describe reactivity trends.

2

Thioesters are involved in biochemistry as derivatives of coenzyme A, participate in

pantetheine acyl carrier protein in biosynthesis of fatty acids and intermediates during hydrolysis of

peptide bonds by cysteine proteases5. The importance of thiol-thioester reactions can be coupled with

hydrolysis of thioesters. In this way, there will be a competition between the two reactions.

Participation of thioesters in the origin of life may be associated with constructive processes where

small reagents build larger molecules and with the ability to concentrate and sequester molecules of

biological importance. Additionally, the network of organic molecules must also be able to store and

transfer energy6. This increase in complexity of molecules must be regulated and it is precisely where

hydrolysis is introduced to compete effectively as a destructive reaction.

Intramolecular rearrangement - subsequent to thiol-thioester exchange - is the second stage

of Native Chemical Ligation (NCL). NCL is responsible for the synthesis of peptides from smaller

fragments with a C-terminal thioester and a fragment that carries an N-terminal cysteine residue. It

was shown by Dawson7 and coworkers that the addition of thiols can be used to modulate the

reactivity of the peptide-𝛼-thioester by thiol-thioester exchange.

Moreover, thiol-disulfide interchange may also play a role in the origins of life and it is the final

reaction of the autocatalytic production of thiols in this model. In biology, thiol-disulfide interchange is

the rate determining step in the folding process of proteins to form structural disulfide bonds9. Disulfide

bonds between cysteine residues are also determinant in the tertiary and quaternary structure of

proteins, enzymes and hormones. Thiol-disulfide interchange may regulate enzyme activity because

the cleavage of this bond in many proteins turns out in loose activity. Regulation of enzyme activity

due to the cleavage of disulfide bond may be associated with thiol-disulfide interchange reactions8.

In the present work, it was proposed to study a set of biologically relevant organic reactions

that present some interesting features as autocatalysis, bistability and oscillatory behavior. The

reactions network is complete with an initial (trigger) and final (inhibition) conjugate addition of the

produced thiols (RSH) over time. The triggering reaction is very quick and so, the production of thiols

is delayed until all maleimide is consumed. Similarly, as the autocatalytic process develops, there will

be an exponential growth of thiols and acrylamide will react with the formed thiols to slowly inhibit thiol

production.

Control theory enables to probe and model the reactions dynamics that take place in a

continuously stirred tank reactor (CSTR) that can simulate a cell for this purposes. Feedback and

control are universal processes that affects a single cell microbes or even a multicellular complex

system that can be a condition for a definition of life. Cells are in a constant state of feedback and

response to numerous stimuli, which some are self-regulated10.

For the sake of comprehension of the reader, this complex network of thiols and thioesters can

be divided into the following processes:

I. Trigger - Generation of RSH by hydrolysis of L - alanine ethyl thioester and

destruction of RSH by conjugate addition to maleimide (see Fig.1).

3

FIG. 1: Hydrolisis of AlaSEt and conjugate addition of thiols to maleimide

II. Positive Feedback - autoamplification by autocatalysis: RSH generates a

positive feedback loop via thiol-disulfide interchange and native chemical ligation (see Fig.2).

FIG. 2: Native chemical ligation and thiol-disulfide exchange reactions

III. Negative Feedback - inhibition of RSH by conjugate addition to acrylamide

(see Fig.3).

FIG. 3: Conjugate addition of thiols to acrylamide

IV. Refill - Compounds 1, 2, 9, 10 are fed into the reactor continuously.

V. Washout - all compounds are removed by the outlet port of the reactor.

The goal of this work is to model the amide bond formation (thiol-thioester exchange followed

by S to N acyl transfer), thiol-disulfide interchange, thioester hydrolysis and 1,4 conjugate addition. By

means of Hartree-Fock theory it is investigated the PES to calculate the energy barriers. Valence

4

Bond theory is used as a tool to describe its origins. Finally, the free energy of activation will allow the

calculation of rate constant for each reactions in order to solve the set of differential equations that

governs the kinetics of this network.

2. Computational Details

Ab initio quantum mechanical gas-phase calculations were performed using GAMESS

program11. Optimizations employed the Quadratic Approximation algorithm and all stationary points

were characterized by computing the Hessian matrix. The electronic structure calculations are based

in Hartree Fock theory capable of studying closed shell systems. In order to properly describe the

sulfur chemistry, it was used a split valence basis function, namely a 6-31G** basis set. More

specifically, this uses six primitive functions for core orbitals and doubly-split functions combining

contracted basis functions of three primitive functions with one uncontracted basis function for valence

orbitals. Polarization functions must be added to reasonably sized bases in order to avoid non-

physical results and incorrect descriptions of the polarity of the molecule. Polarization of the valence-

shell of sulfur is crucial to incorporate the anisotropic nature of molecular orbitals originating from

chemical bonds. One can question also the non inclusion of diffuse functions to study anions in a more

reliable way. For the sake of time constrains, the diffuse functions, solvation and electronic correlation

were left for future calculations.

For each TS, Intrinsic Reaction coordinate (IRC) was conducted by the second-order method

of Gonzales and Schlegel (GS2) to connect reactants and products. This approach is based on implicit

trapezoid method that combines an explicit Euler step with an implicit Euler step.

All resulting structures (except TS) were shown to be minima by confirming that all harmonic

frequencies were real; the transition states were shown to contain only one imaginary frequency. The

difference in enthalpic energy (in kcal mol-1) is computed at 298 K using the thermochemistry

computations in the GAMESS11 program.

The set of ordinary differential equations were solved numerically using the built-in ode45 in

Matlab12 program. The general code was developed by Whitesides and co-workers.

All 2-D representations were carried out in Chemdraw program, while the 3-D structures and

molecular orbitals were obtained by Wxmacmolplt13 software.

3. General aspects of Sulfur chemistry

Sulfur nucleophiles compared with oxygen nucleophiles are larger in size and hence, the

solvation is not so strong as in protic solvents. This effect in aqueous media enhances thiolates strong

5

nucleophilicity in comparison with alcohols. RS- anions are more reactive than RO- anions towards

electrophilic centers even displaying lower electronegativity. Thiolate anions will be surrounded by H-X

dipoles arranged in a way that are higher chances of displaying parallel dipoles resulting in repulsion

and therefore, the solvation energy decreases. Also the decrease in entropy will be greater due to the

attachment of the solvent molecules, reducing the freedom of motion14. Nevertheless, it is expected

different rates of reaction in solution than in the gas phase.

Greater reactivity of large nucleophilic atoms is not only linked to solvation effects. Larger

atoms have greater polarizability, the electron cloud is easily distorted, providing a greater degree of

electron density to the substrate increasing the steric strain at the transition state. The Lewis base

uses its unshared pair of electrons to displace the leaving Lewis base with its bonding pair.

Swain and Scott15 suggest that nucleophiles with nonbonding electrons highly polarizable

display long distance interactions in transition state, reducing the energy necessary for the transition

state and increasing the reaction rate by displaying less electrostatic repulsion. In fact, the reasons

underlying a good nucleophile are more complex and wide. This substitution reaction is simply an

acid-base reaction and the implicit relation between basicity and nucleophilicity must be taken in

consideration. The negative potential around sulfur atom suffers a larger charge redistribution as a

result of the presence of a proton. This contributes for a lower basicity because of the more diffuse

charge cloud, producing a lower negative potential.

The rate of reaction for thiolates depends highly on the distance to the partial positive charge

of the electrophile (carbonyl carbon or β-carbon double bond assisted by EWG) and the negative

charge on sulfur. This can be view in terms of electrostatic potential that lowers the overall energy of

the two charges separated at a distance. Pauli exclusion principle operation play a role in the

repulsion felt by electrons of the two centers and its effects are higher than simple electronic repulsion

for shorter distances16. Another important factor is the orientation of non-bonding electrons in sulfur

atom. The electrostatic repulsion felt by the leaving group is smaller. High polarization in sulfur

chemistry may be explained by the existence of low-lying excited states. This low energy orbitals are

easily accessible and can accommodate electrons in the transition state by mixing of orbitals and thus,

producing polarity.

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4. Results and Discussion

4.1 Thiolate-thioester exchange

Thiolate-thioester exchange describes the reaction between a thioester and a thiolate to

produce another thioester and thiolate as products belonging to a class of organic reactions that

reversibly generate covalent bonds in water17.

FIG. 4: Thiolate-thioester reaction between AlaSEt and CS-

Optimum conditions were set by Whitesides and his co-workers3 with near neutral pH 7.5-8

and at room temperature (25°C) allowing this reaction to take place in biological medium6. Based on

the pKa value for cysteamine (CSH) the estimation for thiol/thiolate populations at equilibrium can be

calculated. Thiolate has a significantly lower molar percentage between 0.001-0.1 in the solvent3.

Therefore, four different routes can be considered as potential mechanisms to model the

reaction:

I. Anionic concerted mechanism - the nucleophile is the CS- and EtS- the

leaving group (see Fig. 4). This mechanism is considered to be the dominant due to a lower

energy pathway and it will be subject to study in more detail.

II. Neutral and concerted mechanism - attack of the sulfur atom of CSH at the

carbonyl carbon of AlaSEt and simultaneously departure of EtSH (see Fig. 5).

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FIG. 5: Neutral and concerted TS 2. All distances are given in Angstrom.

III. Neutral stepwise mechanism - additional proton transfer after sulfur attack

to the carbonyl (see Fig. 6).

FIG. 6: Hypothetical neutral stepwise transition state

IV. Anionic stepwise mechanism - sulfur atom of CS$- attacks the carbonyl

carbon to form a tetrahedral intermediate, and subsequently ethanethiolate anion leaves (see

Fig. 7).

FIG. 7: Hypothetical anionic stepwise transition state

The stepwise transition state mechanisms 3 and 4 were not located in this work. Analysis of

the optimized structures for ionic concerted transition state reveals an enthalpy of activation ) of

10.83 kcal mol-1. Thiol-thioester exchange (neutral) requires an enthalpic activation of 66.43 kcal mol-1.

It is worthy to notice that the energy barrier in 1 is relatively small, which can be overcome by means

of thermal activation of the process and dominates over the neutral specie.

Energy distribution matrix found in Pulay analysis at transition state shows two additional

vibrational modes in the neutral concerted mechanism corresponding to torsional modes. The extra

modes can be the root cause for higher activation energy corresponding to the concerted nucleophilic

attack and proton transfer between the two sulfur atoms. The stretching mode concerning S20-C1 (see

Figures 5 and 8) is commonly shared in both mechanisms but the vibrational contribution in the neutral

form is lower.

Thiolates are favored in terms of lower activation energy as result of higher electron density,

therefore the study of anionic species prevailed upon neutral thiols in further reaction mechanisms.

8

Bell-Evans-Polanyi (BEP) principle states that reactions can be described in terms of bond-

breaking and bond-forming process and the progress of the reaction can be visualized by the

energetics of bond-breaking and bond-forming along the reaction coordinate14. The exothermicity of

the reaction is -7.66 Kcal mol-1, upon calculation of the standard enthalpy of formation. As the reaction

becomes less exothermic, the reactant-like structure moves along the reaction coordinate changing its

distances of resulting transition state. Therefore, Hammond postulate does not apply to the description

of the anionic reaction mechanism due to a transition state that resembles products instead of

reactants-like.

FIG. 8: Potential energy profile for the thiolate-thioester exchange reaction accounting the zero

point energy correction. Energy of activation relative to reactants in kcal mol-1 with Zero Point Energy

correction. All distances are given in Angstrom.

In TS 1 (see Fig.8), the shorter distance S20-C1 is attributed to weaker nucleophile-electrophile

interaction of CS- 18. The angle formed by S12-C1-O11 in the TS is 105.3 degree, which is in good

agreement with the theoretical angle for a nucleophile approach on a trigonal unsaturated moiety of

107-109 degree. Sulfur p-orbital and carbonyl - orbital interaction is favored within this range.

Variations in the angle are caused by electrophile specific repulsive and attractive electrostatic and

Van der Waals interactions22. According to Corbett17, the difference in electronegativity in the

nucleophile influences the HOMO-LUMO energy difference. The calculated energy gap between

frontier molecular orbitals relative to the neutral and anionic species is 13.69 and 5.99 eV,

respectively. This confirms that thiols are poor nucleophiles.

Examination of ionic Valence Bond (VB) structures provides information on the reactivity of

covalent bonds. Ionic structures are simply secondary VB configurations of polar covalent bonds and

its influence must be investigated.

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FIG. 9: Qualitative VB configuration mixing diagram for thiolate-thioester exchange reaction

Fig. 9 displays the VB configuration mixing diagram (VBCMD) containing the reactants,

products, promoted states and the “foreign” excited states. Reactants and product states are localized

in active bonds, whereas the promoted states are obtained from electronic excitations and bonds that

do not make part of the active bonds. Fundamental curves are built up from the ground states and σ-

charge transfer (σ-CT) state that are able to describe this single-step reaction. The mechanism is

provided by a direct backside σ attack. The “concertedness” of this process is ruled by σ -CT state and

π-CT lying close in energy. Because of low energy difference between these two states, the reaction

proceeds in a single step and the tetrahedral intermediate does not take part of the mechanism of the

reaction. In gas phase, the anionic intermediate cannot be stabilized. One possible explanation is

given by the fact that the large electron cloud of sulfur atoms increases the repulsion to such high

levels that is not possible for carbonyl carbon atom to coordinate simultaneously to two sulfur atoms.

One can also question if this intermediate is stable in aqueous media by solvent interaction. Given the

small barrier for the concerted process and a possible low stabilization by solvent, this intermediate

may not be found.

4.2 Intramolecular rearrangement

Native chemical ligation (NCL) is one of the most used chemoselective strategies for the

formation of a peptide bond. This method takes advantage of the high nucleophilicity of the thiolate

anion, as well as its ability as a leaving group. It consists in the following elementary steps: the

unprotected peptide-α-thioester reacts with another unprotected peptide containing an N-terminal

cysteine residue by thiol-thioester exchange yielding an intermediate. It is followed by a quick and

entropically favorable intramolecular rearrangement (S → N acyl transfer, see Fig.10) yielding an

amide bond at the ligation site7.

10

FIG. 10: S → N acyl transfer

For a successful intramolecular rearrangement to take place, the amine moiety must attack

the carbonyl to form a five-membered cyclic transition state.

The equilibrium of the S → N / N → S acyl transfer ratio is thermodynamically favored,

pushing the equilibrium towards the amide product. Intramolecular reactions are entropy reduction-

facilitated via the loss of the translational entropy, which accompanies the bringing together of the

reactants. However, using different conditions and methodology, the S → N acyl transfer can be

reversed in order to synthesize thioesters by a different approach19. Harding and Owen reported that

thioesters with an hydroxyl group, under dilute alkali conditions, isomerize to the oxygen ester with

high yield compared with the hydrolysis process20.

For the intramolecular rearrangement, the mechanism proceed by a concerted and neutral

transition state TS 3 (see Fig.11).

FIG. 11: Potential energy profile for the intramolecular rearrangement reaction accounting the

zero point energy correction. Energy of activation relative to reactants in kcal mol-1 with Zero Point

Energy correction. All distances are given in Angstrom

The nucleophilic attack of thiolate proceeds via single TS 3 with an enthalpy of activation of

40.9 kcal mol-1. Notice that this high kinetic barrier is compensated thermodynamically by means of

the standard enthalpy of formation with a value of -54.5 kcal mol-1. Such high barrier may be attributed

11

to an increase of steric effects during the formation of the 5-membered ring in TS 3, increasing the ring

tension. In aqueous media, the proton transfer can be easily mediated by the solvent, thus lowering

the energetic cost of the overall reaction.

In TS3 (ν = i 82.22 cm-1) the C1-N15 bond is partially weakened and the bond length is

enlarged from 1.36 Å to 1.54 Å. The S12-C1 distance is 2.61 Å and shows that this is a late transition

state due to the nature of the product stability. This reaction is exothermic by -13.6 kcal mol-1.

TABLE 1: Major vibrational contributions in energy distribution matrix for intramolecular

rearrangement

Table I gives the information concerning which modes are vital in TS3 by means of Pulay

analysis. The proton transfer is accomplished throughout the IRC procedure. The assisted proton

donation by the positively charged amine moiety it is essential to stabilize the thiolate. First, because

the N15-H17 distance is 1.01 Å and remains unchanged from reactant to products. Second, the torsion

angle contributions involve the right positioning of the carbonyl for a tetrahedral geometry to

accommodate the entering sulfur with an angle of 114 degree. This angle influences the orientation of

sulfur lone pair of electrons to interact with the carbonyl π* orbital.

Valence bond diagrams are helpful to understand the reactivity mechanisms with simple

valence bond structures.

FIG. 12: Qualitative VB Configuration Mixing Diagram for the S → N acyl transfer

In Fig.12, structure 7 does not provide a low energy pathway for the TS3, especially in the gas

phase, due to steric effects during the formation of the 5-membered ring. The boat-type configuration

adopted in TS3 by structure 7 also increase the energy in comparison to a more stable chair-type

12

conformation. It is also expected that the solvent will decrease largely the TS 3 energetic barrier due

to the fact that charge is not present in reactants nor products, hence the energy in TS3 and the

activation energy must decrease.

4.3 Thiolate-disulfide interchange

Disulfide bond plays an essential role in biological processes. Reversible creation/disruption of

the S-S bond in cellular systems is a non equilibrium dynamic process and is governed kinetically, not

thermodynamically9. Fig. 13 shows an SN2 type nucleophilic substitution of a thiolate in disulfides with

another thiolate.

FIG. 13: Thiolate-disulfide exchange reaction. Two molecules of cysteamine are formed in this

two parallel reactions

Depending on the pKa of the environment, the neutral and anionic form are present. Assuming

the pKa extracted from previous work and, according to Whitesides and co-workers, the molar ratio of

ionic/neutral species are presented in table II.

TABLE 2: pKa values and estimated populations for reactants and cystamine at equilibrium

Based on the relative populations and given the dramatic differences in nucleophilicity, the

present study will focus on the above species. Therefore, the effect of pH is important to establish the

13

kinetics of the thiol-disulfide interchange. Protonation-deprotonation are usually fast and can be

treated as a pre-equilibrium assumption9.

1)

2)

In this way, the apparent rate constant will be pH dependent described by equation (3),

3)

where, k1 is pH independent. Thus, the kinetics of thiolate-disulfide exchange is intrinsically

related to the pH media, and an optimum value is found when most of the thiol is deprotonated. Thiol-

disulfide interchange reaction has not been observed experimentally8. The reason must be attributed

to the dramatic difference of nucleophilicity.

Thiolate-disulfide interchange reactions are favored approximately by three orders of

magnitude in aprotic solvents rather than in water9. The theoretical argument is based on the more

delocalized negative charge in the transition state. Investigation on the geometry of the transition state

for the reaction of CSSC with two different nucleophiles was chosen to compare the reactivity of both

thiolates 4 and 5. The reaction Fig. 13 summarizes both thiolate-disulfide exchange reactions involved

in the autocatalysis of thiols. The transition state models predict, as expected, a concerted mechanism

for both reactions.

FIG. 14: Potential energy profile for the thiolate-disulfide reaction with EtS- accounting the zero point

energy correction. Energy of activation relative to reactants in kcal mol-1 with Zero Point Energy

correction. All distances are given in Angstrom

14

The enthalpy of activation for reactants 5 and 4 are 21.89 (see Fig. 15) and 17.01 (see Fig.

14) kcal mol-1, respectively.

FIG. 15: Potential energy profile for the thiolate-disulfide reaction with 5- accounting the zero point

energy correction. Energy of activation relative to reactants in kcal mol-1 with Zero Point Energy

correction. All distances are given in Angstrom

The pKa values of the nucleophiles are in agreement with Wilson and co-workers21

observations based on Brønsted equation. Higher pKa values for attacking thiolates are related to

higher rate.

The potential energy surface consists of an entrance and exit ion-dipole complex. In TS4 and

TS5 the steric effects are small to describe the barriers, mostly, when the difference is mainly localized

in the alkyl substitution at carbon β to sulfur. All sulfur atoms are bonded to a -CH2- moiety displaying

very low steric hindrance. This factor can influence positively the orientation of the electronic lone pair

directed along the axis of the covalent bonds. The p-orbital (HOMO) of the incoming sulfur must

interact with the σ* orbital (LUMO) of the S-S disulfide bond. The relative higher barrier in TS5 is

presumably due to steric effects of substituents at the carbon β to sulfur.

TABLE 3: Geometrical comparison of distances (d), angle (𝛼, values in degrees), and dihedral

angles (δ, values in degrees) for both thiolate-disulfide TS.

15

The SN2 reaction geometry of the transition state is given in table III. It summarizes the

important distances, angle and dihedral angles of TS 4/TS 5 by comparing distances and angle in the

incoming and outgoing sulfur moieties along the axis. The more symmetrical TS 4 shows almost

identical distances between sulfur atoms and it is 1 degree closer to ideal 180 degree, in comparison

to TS 5. In order to avoid electronic repulsion between the sulfur substituents, the dihedral angle,

must be the closest to 90 degree. For this reason, the energy barrier in TS 4 is lower.

Experimental evidence based on Brønsted coefficients points that the charge distribution is

higher in the two terminal sulfurs is confirmed by computational results8. The negative charge is

accumulated in the sides, while the central sulfur possesses a positive charge.

Valence bond state correlation diagram presents the Heitler-London mixing structures 1-4.

The ground state at the reactant geometry is 1 which gets gradually destabilized as the S1-S2 bond is

homolyzed and the three electron overlap repulsion increases in S3-S2 interaction.

FIG. 16: Qualitative VB State Correlation Diagram for the thiolate-disulfide reaction.

Structure 2 represents the excited state and interchanges with 1 along the reaction coordinate

as a result of one-electron transfer from the thiolate to the S1 sulfur, resulting in a triplet excitation. The

charge transfer states σ-CT are closer to ground states mostly due effective electron delocalization

which is expressed by a lower energy profile in the transition state.

16

4.4 1,4 Conjugate addition

The conjugate addition of thiolates to acrylamide and maleimide (see Fig. 17) displays very

different kinetic and thermodynamic behavior in the Whitesides3 network of reactions.

FIG. 17: 1,4 conjugate addition mechanism present in trigger and inhibition mechanisms,

respectively. First, nucleophilic addition of EtS-, second proton transfer and final tautomeric

equilibrium.

Sustainable oscillations are dependent on the trigger and inhibition mechanisms that control

the thiol production.

When the electron density of a carbon-carbon bond is reduced by strongly electron-

withdrawing substituents, nucleophilic addition turns to be possible. Conjugation of a double bond to a

carbonyl group transmits the electrophilic character of the carbonyl carbon to the β-carbon of the

double bond. These conjugated carbonyl are called enones or 𝛼, β unsaturated carbonyls. Usually, in

conjugate addition, the rate-determining step is the nucleophilic addition2.

1,2 addition nucleophile adds to the carbon which is in the one position. The hydrogen adds to

the oxygen which is in the two position. In 1,4 addition the nucleophile is added to the carbon β to the

carbonyl while the hydrogen is added to the carbon 𝛼 to the carbonyl. During the addition of a

nucleophile there is a competition between 1,2 and 1,4 addition products and it is the nature of the

nucleophile that mostly dictates which mechanism is favored.

Thiolates are weak bases and therefore, the preferred 1,4 addition dominates. This means

that the stability of carbonyl group is guaranteed and the reaction is controlled thermodynamically.

The model proposed only concerns the nucleophilic attack by thiolate and it assumes that

there is a proton assisted mechanism to the formed carbanion.

17

FIG. 18: Potential energy profile for the 1,4 conjugate addition reaction with acrylamide

accounting the zero point energy correction. Energy of activation relative to reactants in kcal mol -1 with

Zero Point Energy correction. All distances are given in Angstrom

As usual, the reactions undergo a single transition state or concerted mechanism. Enthalpy of

activation in TS 7 (see Fig.18) is 27.25 kcal mol-1, while there is a sharp drop in TS 6 (see Fig.19) with

an enthalpy of activation of 4.34 kcal mol-1. This energetic difference must be investigated by

electronic effects in the transition state. In both cases, the attacking thiol is the same, the main

difference is related to conjugation effects in acrylamide (10) and maleimide (9). Maleimide is an anti-

aromatic heterocyclic molecule with two carbonyl π-bonds, one methylene π bond and the electronic

p-lone pair of nitrogen. This conjugation lowers the activation barrier and stabilizes the resulting

carbanion structure 11a. Acrylamide displays planarity but only possesses one π bond conjugated with

one carbonyl π bond and the p-lone pair of nitrogen. This has a dramatic behavior change in both,

energy barrier and product stabilization. Initial H-bond stabilization by the amine may also contribute to

a larger activation. The resulting carbanion cannot successfully stabilize the negative charge at 𝛼-

carbon by conjugation.

18

FIG. 19: Potential energy profile for the 1,4 conjugate addition reaction with maleimide

accounting the zero point energy correction. Energy of activation relative to reactants in kcal mol -1 with

Zero Point Energy correction. All distances are given in Angstrom

Thermodynamically, there is an equilibrium between structures 9 + 4- and 11 and it is a

endothermal reaction by 0.66 kcal mol-1. In TS 7 the reaction equilibrium is more displaced to the

thermodynamic more stable reactants and the endothermicity of reaction was calculated to be 25.54

kcal mol-1.The thermodynamics of the system is incomplete due to the stabilization of the proton-

assisted mechanism in solution by the solvent and tautomeric equilibrium. For this reason, the values

presented here are kinetically more reliable than thermodynamically.

The transition state geometry is slightly different in terms of nucleophile-electrophile distance

and planarity. TS 7 shows a C1-S11 distance of 2.22 Å compared with 2.30 Å in TS 6. The

approximation of attacking sulfur along the reaction coordinate towards maleimide distorts the

planarity of the ring by 10 degree compared with 2 degree in the case of acrylamide.

Valence bond theory was used, once again, as a tool to understand the quantum chemical

aspects that generate energy barriers in transition state.

FIG. 20: Qualitative VB Configuration Mixing Diagram for the 1,4 conjugate addition of EtS-

reaction with acrylamide

Figure 20 and 21 show that thiolates add to the β-carbon in a concerted mechanism with no

further stabilization of structures 2, 7, 5. Despite of no further stabilization of the π-CT, the carbonyl

19

plays an important role in electron delocalization. Conjugate addition implies the formation of a σ-bond

and the partial π-bond-breaking.

FIG. 21: Qualitative VB Configuration Mixing Diagram for the 1,4 conjugate addition of EtS$- reaction

with maleimide

Despite of similar charge transfer excitations, TS 6 has an additional carbonyl moiety capable

of higher stabilization. The presence of an electron withdrawing group, as the 𝛼-NH / 𝛼-NH2 moieties

may raise the LUMO orbital energy of the carbonyl by n → π* interaction. This delocalization leads to

some degree of charge separation and polarization of the amide.

4.5 Thioester Hydrolysis

The acyl group of a thioester can be transferred to a water molecule in a hydrolysis reaction,

resulting in a carboxylate. In Fig. 22, it is presented a SN2 reaction between a hydroxyl anion and

AlaSEt that yields a carboxylic acid and the leaving thiolate anion.

FIG. 22: Hydrolysis of AlaSEt to carboxylic acid. The first thiols are generated in this reaction.

Thioester hydrolysis can be acid or base mediated. However, the base catalyzed reaction

favors the thiolate-thioester competition mechanism in solution that is needed for the autocatalytic loop

to proceed more efficiently. Therefore, it is very important to keep in mind that the kinetics of

hydrolysis is pH dependent.

20

The nucleophilic attack of hydroxyl anion towards the thioester proceeds via single TS 8

without barrier. It is a surprising result but it is important to remember that is a gas-phase calculation.

The formed carboxylic acid shows to be a very stable product in comparison to a more labile C-S bond

in the thioester molecule. The calculated standard enthalpy of formation is -57.96 kcal mol-1. Due to

such high exothermal reaction, the transition state resembles the reactants, as referred in Hammond

postulate.

FIG. 23: TS 8 structure for the hydrolysis reaction. Distance units in Angstrom

In TS8 (see Fig. 23), the C1-S7 bond is just slightly weakened by 0.1 Å. This may be

associated with a long nucleophile interaction. The O20-C1 distance is 2.4 Å and it is more common in

soft bases as the thiolate anion.

It was found that the two frontier molecular orbitals, HOMO-LUMO, have 5.06 eV energy gap.

As a consequence, a better interaction is confirmed by the O20-C1-O3 angle of 109.41 degree.

21

FIG. 24: Relevant molecular orbitals representations for hydrolysis in TS 8

Valence bond theory allows to make an interpretation of the nature of the energetic barrier in

TS 9 by analysis of the promoted states 2, 3, 5, 6, 7.

FIG. 25: Qualitative VB Configuration Mixing Diagram for the hydrolysis reaction

Fig. 25 puts in evidence the energy differences in σ-CT π-CT in order to accommodate the

one-electron excitation provided by the electronic lone pair of hydroxyl nucleophile. It is clear that the

dominant mechanism is a direct backside attack in the C-S bond and it is enhanced by the carbonyl π*

conjugation. The formation of the tetrahedral intermediate is once again avoided. The explanation may

be given by the energetic difference of supra-LUMO to LUMO orbital and a greater electron cloud

22

surrounding sulfur atom. The last effect produces a greater degree of electron density, together with

oxygen, resulting a high increase in steric strain in TS 8.

4.6 Numerical modelling of network kinetics

The analogies between a cell and a continuous stirred tank reactor (CSTR) allows simulation

of the cellular prebiotic dynamics. A set of ordinary differential equations were solved numerically by

means of Matlab12 code used by Whitesides et al3.

4)

10)

11)

9)

12)

13)

5)

6)

7)

8)

23

The network dynamics should display bistabily and oscillatory behavior as a consequence of

the triggering, auto-amplification and inhibition balance.

This set of differential equations can be solved for different space velocities (FνV) and initial

concentrations of [AlaSEt]0, [CSSC]0, [mal]0 and [AAm]0. Compound 11 stands for AlaS(CH2)2NH2. The

space velocities are dependent on the initial concentrations in order to achieve sustained oscillations

in thiol (RSH) concentrations. Therefore, if one fixes the initial concentrations, there will be a transition

from dumped oscillations to sustained oscillations for a range of space velocities.

The values for the theoretical rate constants (k) were calculated under thermodynamic

formulation of transition state theory:

14)

where, kB is the Boltzmann constant, h is Planck's constant and T is the Kelvin temperature.

The free energy of can be divided into contributions from enthalpy of activation, , and

entropy of activation, . The units correction factor to distinguish an unimolecular reaction from a

bimolecular is introduced by M, the molarity. It vanishes for a unimolecular reaction due to its

molecularity (m).

TABLE 4: Theoretical rate constant values for the reactions in gas-phase using

thermochemistry at 298 K

Deviations from the experimental rate constants are attributed to solvent interactions with

reactants and TS complexes, which affect the activation energies. The pH dependence is also

determinant and controls the ratio of anionic/neutral species in solution. This factor is of great

importance when the rate of hydrolysis around neutral pH is very small compared with Kent ligation. In

order to observe thiol concentration oscillations, the conjugated addition must have the greatest rate

constant in order to trigger the autocatalysis. The first thiolate is formed in the hydrolysis, which

enables the thiolate-disulfide reaction with CSSC and formation of CSH in the network. However, all

thiols are inactive by reaction with maleimide. Once is consumed, the autocatalytic loop is activated

and the thiol population increases but the conjugate addition to acrylamide will inhibit the thiol

population. Therefore, the inhibition rate constant must play a gradual role in the dynamics with a

small rate constant.

24

5. Conclusion

The results in Hartree-Fock level of theory show that all mechanisms studied are concerted via

a single TS. Factors like sulfur size, polarizability and nucleophilic strength influence its reactivity

reflecting the non-observed π-CT mixing. Intermediates may not be able to be stabilized in the gas-

phase due to the electronic repulsion in tetrahedral intermediates, for the case of nucleophilic attack

on carbonyl. One can imagine that the absence of intermediates is an important feature of sulfur

reactivity that avoids side reactions in the origins of life.

In future work, the introduction of solvent and electronic correlation must be taken in

consideration to proper describe the activation energies. Concentration profiles in autocatalytic cycle

must be introduced in future work, with proper energy barriers calculations that lead to more accurate

rate constants.

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