Introduction

AnthraFelix is a genetically engineered probiotic that responds to elevated serotonin levels in the colon of IBS-D patients by converting excess serotonin into melatonin. In our Dry Lab efforts, we delved into various aspects of this innovative solution. We constructed ODE models to predict system behavior, allowing us to make informed approximations to simplify the complex dynamics. Additionally, we focused on modeling the serotonin uptake by a bacterial analog of SERT in E. coli, highlighting its significance in improving serotonin uptake compared to passive diffusion. Furthermore, through a mutational analysis of the LasR protein, we identified crucial contact residues essential for binding serotonin. These Dry Lab results played a vital role in supporting our Wet Lab experiments, illustrating how computational modeling and analysis have contributed significantly to advancing the development of the probiotic.

ODE Models for Reaction Dynamics

We have formulated an extensive simplistic model involving the chemical reactions at every step with corresponding ODEs (Ordinary Differential Equations). The mechanism and corresponding ODEs are enlisted in detail in this section.

Distribution of Serotonin into bacterial cells

Serotonin available in the lumen shall be distributed among the bacterial population, for it to be converted into Melatonin.

$S_{e0}$ - initial concentration of extracellular serotonin;

$S_e$- extracellular serotonin concentration at time t;

$S_i$ - intracellular serotonin concentration at time t;

$V_l$ - average lumen volume;

$V_c$ - average E coli cell volume;

$N$ - No. of bacteria in the bacterial population

differentiating both sides w.r.t. time,

This equation is quite general under the assumptions,

1. All cells are identical and equally accessible to serotonin
2. Volumes of cells and media are invariant over time

We may consider the influx of serotonin to be governed by Fick’s law of diffusion.

Translating this to the probiotic system, we say, the rate is proportional to the concentration difference. We approximate the uptake with passive diffusion. This approximation is experimentally valid as illustrated by Schuster et al. [1]

Protein Production

LasR is the quorum-sensing molecule that is expressed under a constitutive promoter. Its concentration at time ‘t’ is governed by its production and degradation.

$L$ - LasR protein concentration;

$\beta$ - protein production rate;

$C_N$ - Plasmid copy number;

$d_1$ - LasR protein degradation rate

Enzyme Production through Hill Kinetics: The enzymes that convert Serotonin to Melatonin are SNAT and COMT. They are expressed under inducible promoter pLasI. pLasI gets induced when the LasR-Serotonin complex binds to it. Due to a conformation change, this promoter is now better recognized by the RNA polymerase.

$\beta$ - maximum protein production rate

$C_N$ - plasmid copy number

$n$ - hill coefficient

$d_2$ - protein degradation rate of SNAT

$d_3$ - protein degradation rate of COMT

$S_i$ - Intracellular serotonin

$LS_i$ - LasR-Serotonin complex

Quorum Sensing

Interaction between LasR and Serotonin is a Protein-Ligand interaction locally. But quorum sensing is an emergent property of this complex interaction where sharp spikes in protein concentrations can be observed whenever certain concentrations of Serotonin are reached. Thus we model this as a chemical interaction.

Catalysis of Serotonin to NAS to Melatonin

A short note on Michaelis-Menten kinetics. The general scheme of enzyme-catalyzed reaction is as follows:

This is the Michaelis-Menten equation. Here $v_{max} = k_2[E_T]$, where $k_2$ is catalytic turnover number and $[E_T]$ is the total Enzyme concentration. $k_M$ is also known as half-maximum concentration which implies that half of the active sites on the enzymes are filled.

In the probiotic system, we have two coupled enzymatic reactions by SNAT and COMT for serotonin-to-melatonin conversion. They are:

• Serotonin N-acetyl Transferase catalyzes Serotonin (S) to N-Acetyl Serotonin (NAS) catalysis.

$ * \frac{dNAS}{dt} = k_1[SNAT]\frac{S}{S + k_{m1}} $

• Caffeic Acid O-methyl Transferase catalyzes N-Acetyl Serotonin (NAS) to Melatonin (M).

Efflux of Melatonin out of the cell

Similar to the Influx of Serotonin we might consider the Efflux of Melatonin as a diffusive process.

Set of ODEs for the Probiotic system

The total set of 9 ODEs: $Eq. (1)$ to $Eq. (9)$

These equations represent the entire system in full detail. However, it is often complicated to solve these many coupled ODEs. Thus we attempted to simplify these ODEs further through some valid assumptions.

Reduced set of ODEs

In this probiotic system, there are multiple interacting variables and processes. Some of these may be fast-changing, while others change comparatively slowly. By assuming Quasi-static equilibrium for the latter, we simplify the system's dynamics, making it easier to analyze and solve. Quasi-static equilibrium implies that certain variables or processes are changing so slowly that they can be considered nearly constant over a relatively short period. In other words, they reach an equilibrium state much faster than other variables, making their dynamic effects negligible. Diffusion, protein production, and intermediate formation reach equilibrium quickly in comparison to Enzyme activity.

Thus treat everything except the SNAT and COMT enzymatic reactions as Quasi-static processes for the sake of simplicity. Thus the following conditions apply owing to their slow change in concentrations.

$\dot{S_e} = 0$, $(\dot{S_i})_{in} = 0$, $\dot{L} = 0$, $\dot{LS} = 0$, $\dot{SNAT} = 0$, $\dot{COMT} = 0$, and $(\dot{M_e})_{eff} = 0$ where $\dot{X} = \frac{dX}{dt}$

Considering these conditions, we can reduce the equations to the following:

Note that for $Eq. (5)$ and $Eq. (6)$, an assumption was that $[SNAT]$ and $[COMT]$ are equal. This is practically valid owing to their similar degradation rates and the fact that they are being expressed under the same promoter-RBS combination.

Thus, the ODEs from $Eq. (1) - Eq. (9)$ are reduced to three ODEs namely $Eq. (10) - Eq. (12)$ that depend only on Enzyme concentrations. By reducing the number of ODEs, we simplified the system's behavior and made it more amenable to analysis and simulation. This is especially valid because the full set of ODEs is computationally challenging and unnecessary.

Solutions of the reduced ODEs

To solve these ODEs, Python's SciPy library was used. [12]

Strength of expression of SNAT and COMT

From the plots of Serotonin, N-acetyl Serotonin, and Melatonin the efficiency of conversion is higher when the enzyme concentration is more thus a strong expression of SNAT and COMT is necessary for efficient conversion from Serotonin to Melatonin.

Cassettes with pLasI promoter and various RBS from “Community Collection” from iGEM parts were designed. Out of these the one with the strongest expression was chosen to be expressed in the model organism.

Modeling the Serotonin Uptake

Uptake through passive diffusion

Fick’s law of diffusion:

$J$ is the flux of the molecule (the amount of substance passing through a unit area per unit time), $D$ is the diffusion constant, and $\frac{dC}{dx}$ is the concentration gradient across the membrane. Approximating this to the probiotic system, we have

$J$ is the influx of serotonin, $A$ is the surface area provided by the cell membrane, $l$ is the thickness of the cell membrane, $S_e$ is extracellular serotonin concentration, and $S_i$ is intracellular serotonin concentration. This equation can be followed from the previous section.

The diffusion constant ($D$) depends on various factors, including the size of the diffusing species, the temperature, and the properties of the membrane (e.g., lipid composition). Smaller molecules typically diffuse more rapidly than larger ones through the same type of membrane.

To estimate the diffusion constant based on the size of the diffusing species, one can use the Stokes-Einstein equation, which relates the diffusion constant ($D$) to the radius ($r$) of a spherical particle:

Where $k$ is Boltzmann's constant, $T$ is the absolute temperature and $\eta$ is the dynamic viscosity of the medium.

Assuming Serotonin is a sphere of radius $r$, we can estimate $r$ using the formula:

where $M$ is the molar mass of serotonin, $N_A$ is Avagadro’s Number and $\rho$ is the density of serotonin in compound form. Assume $\rho = 1.0 \space g/cm^3$ (Since most organic molecules have densities in the range of $0.8 - 1.4 \space g/cm^3$).

where $r \approx 0.531 \: nm$. $k_{diff}$ can be estimated using the following formula:

pH dependence of Diffusion rate

Serotonin has an $NH_2$ group that gets protonated in aqueous media and protonated serotonin ($5HT^+$) cannot cross the non-polar lipid bilayer. Since Serotonin is a weak acid with an estimated pKa of 9.2, we have the fraction of protonated and unprotonated molecules using the Henderson-Hasselbalch equation:

If $\chi_+$ and $\chi$ denote the fraction of protonated and unprotonated Serotonin, we have:

We can see that as pH increases, the fraction of unprotonated serotonin ($S_e^0$) dominates the fraction of protonated one ($S_e^+$).

When pH is neutral (7.2), we have $\chi \approx 1\%$. When pH is slightly acidic like it is in the gut (around 6.2), we have $\chi \approx 0.1\%$. So, the substrate for diffusion keeps decreasing as pH decreases. This causes a very weak diffusion of serotonin into the bacteria inside the gut.

Points to note:

• Serotonin in aqueous form is polar in nature and its passive diffusion across the non-polar lipid bilayer membrane is expected to be much less. This is apparent from the study done by Byeon et al. [5] Only a little of the 1mM serotonin is converted to Melatonin.
• For this reason, we employ a serotonin transporter protein that is a bacterial homolog of SERT (CUW_0748) - from the study made by Hoffman et al. [6] to help serotonin get inside the bacterial cell more efficiently.

Serotonin Transporter protein

Functional mechanism of Serotonin reuptake transporters (SERTs) [9]: They are dependent on extracellular $Na^+$ and extracellular $Cl^-$. Unlike $Na^+$, $Cl^-$ can be at least partly substituted for by $NO_2^-$, $Br^-$, and other anions. Intracellular potassium ($K^+$) is also used in the process but can be replaced by other ions, most notably hydrogen ($H^+$). The driving force for the energetically unfavorable transport of serotonin is the $Na^+$ influx down its concentration gradient. The $Na^+/K^+$ pump ($Na^+/K^+$ ATPase) maintains the extracellular $Na^+$ concentration as well as the intracellular $K^+$ concentration. $Na^+/K^+$ ATPase pumps three $Na^+$ ions out for each two K+ ions pumped into the cell. The electrical potential produced, in addition to creating the $Na^+$ concentration used by the transporter protein, also leads to the loss of $Cl^-$ ions from the cell which are also used in transport.

According to the present model of the SERT function, the first step occurs when $Na^+$ binds to the carrier protein. Serotonin, in its protonated form ($5HT^+$), then binds to the transporter followed by $Cl^-$. Chloride ions are not required for $5HT^+$ binding to occur but are necessary for net transport to take place. The initial complex of serotonin, $Na^+$, and $Cl^-$ creates a conformational change in the transporter protein. The protein, which begins by facing the outside of the cell, moves to an inward position where the neurotransmitter($5HT$) and ions are released into the cytoplasm of the cell. Intracellular $K^+$ then binds to the SERT to promote reorientation of the carrier for another transport cycle. The unoccupied binding site becomes, once again, exposed to the outside of the cell, and the $K^+$ is released outside the cell.

From here on we refer to the bacterial homolog of SERT (cuw0748) as SERT for the sake of convenience.

• Protonated serotonin binding to SERT

$ Na^{+}_e + SERT \xrightarrow{k_1} Na^{+}SERT \xrightarrow{k_2, 5HT^{+}_e} [5HT^{+}]Na^{+}SERT \xrightarrow{k_3, Cl^{-}_e} Cl^{-}[5HT^{+}]Na^{+}SERT $

• Influx of serotonin

$ Cl^{-}[5HT^{+}]Na^{+}SERT \xrightarrow{k_4} SERT^{'}Na^{+}[5HT^{+}]Cl^{-} \xrightarrow{k_5} SERT^{'} + Na^{+} + 5HT^{+}_{i} + Cl^{-} $

• Efflux of potassium ions

$ SERT^{'} + K^{+}_{i} \xrightarrow{k_6} SERT^{'}K^{+} \xrightarrow[flip \: + \: efflux]{k_7} SERT+ K_e^+ $

Thus following ODEs govern the uptake of Serotonin.

These constants $k_1, k_2,..., k_7$ are very specific to bacterial SERT (cuw0748) and need to be experimentally determined for an accurate model. Due to a lack of parameter studies on cuw0748, this model cannot be extrapolated further.

For the sake of prediction and further extrapolation, we may approximate the kinetics of SERT with its NSS (Neurotransmitter sodium symporters) homolog in bacteria - the MhsT transporter.

MhsT is an NSS member from Bacillus halodurans. The estimated parameters for SERT assuming it is similar to MhsT are given. The parameters are taken from Malinauskaite et al. [4]*

Using Michelis-menten equation,

Passive diffusion vs Facilitated Transport

ODEs for serotonin uptake through passive diffusion:

where $X^0$ stands for unprotonated form (and $X^+$ for protonated form). If $S_e$and $S_i$ are total extracellular and intracellular serotonin concentrations respectively,

$S_e^0 = \chi \cdot S_e$ and $S_i^0 = \chi \cdot S_i$

Similarly, ODEs for the case when a functional transporter protein is present can be given by:

This qualitatively establishes that there is a necessity for Transporter protein for efficient uptake of Serotonin in the gut environment. One could use the above equations along with the estimated parameter to quantitatively verify the same.

Mutational Analysis of LasR Protein

The quorum-sensing molecule that is being employed in the probiotic system is very sensitive to serotonin by the standards of levels of serotonin in the gut lumen. The LasR variant activates the plasI promoter at around 0.1uM [8] while gut lumen serotonin levels might vary anywhere between 10 uM to 100 uM. Usually, greater than 100 uM in IBS-D patients.[16][17][18] Thus a less sensitive lasR variant would be a great addition to the project. To achieve this goal we did a mutational impact analysis on contact residues of Serotonin in the LasR-Serotonin complex.

Simulating the interaction between LasR and Serotonin

Obtaining the structures

We obtained the PDB structure of LasR from the RCSB Protein Data Bank (PDB id: 3IX3) [13] and the SDF file of Serotonin from here. LasR protein was prepared for docking by removal of heteroatoms, waters, and identical chains using PyMol software.

LasR - Serotonin docking

Let’s refer to the original LasR protein as the “wild-type” protein. The prepared wild-type LasR monomer and Serotonin were set for docking in the CB-Dock2 [14][15] server. Given the three-dimensional (3D) structure of a protein and a ligand, CB-Dock2 can predict their binding sites and affinity. It runs AutoDock Vina in the back end.

5 binding pockets with Vina scores, as follows, were identified.

We consider the pocket C1 with the lowest Vina score for further docking.

Identification of Contact Residues

The CB-Dock2 server identified 16 contact residues of Serotonin with LasR. They are

LEU36 TYR56 TRP60 ARG61 TYR64 ASP73 THR75 VAL76 TRP88 TYR93 PHE101 ALA105 LEU110 VAL111 THR115 SER129

Note that the indexing of amino acids is relative to the utilized PDB file. It can vary with predicted PDB files at later stages, so direct comparison must be avoided.

Point mutations in Contact Residues

Wild-type LasR is converted to a FASTA file using the pdb2fasta tool. Point mutations in the FASTA file were generated using Python for normalizing the index and editing the sequence. The respective amino acids (for eg. L in the case of LEU36) were replaced with Alanine (A). Alanine is the common substitute residue to perform mutation studies as it lacks a functional side chain.

In total 16 mutant FASTA files were generated. The structures of these 16 mutants were predicted using the Swiss Model tools.

Mutant Docking

Each of the 16 mutants was docked to Serotonin and their respective Vina scores are as follows.

Results, Analysis, and Interpretation

The scoring function of AutoDock Vina is a measure of binding affinity between the ligand and the protein. The higher the Binding affinity higher the absolute value of the score. Further info on Vina Scoring Function [10]. Note that the plot is exp(Vina-score) vs mutants. Since Vina-score is negative the plot with the highest exp(Vina-score) will have the least absolute value.

From the results, it appears that when certain residues in the LasR protein are mutated from Tyrosine (Y) to Alanine (A), there is a significant decrease in binding affinity with serotonin. These residues play a crucial role in the binding of LasR to serotonin, likely due to their aromatic nature.

Here are some conclusions and insights you can draw from these results:

1. Aromaticity is important: Tyrosine (Y) is an aromatic amino acid, characterized by its aromatic rings. Aromatic residues often play a critical role in binding interactions due to their ability to form π-π stacking and other aromatic interactions. When these aromatic residues are mutated to non-aromatic Alanine (A), it disrupts these interactions, leading to a decrease in binding affinity.
2. Specific residues are crucial: Not all aromatic residues have the same impact on binding affinity. For example, TYR56 and TYR64 have lower binding affinities when mutated to Alanine compared to the wild-type LasR, suggesting that these specific Tyrosine residues are particularly important for serotonin binding in comparison to other aromatic amino acids like Tyrosine at TYR93 and Phenylalanine at PHE101.
3. ARG61 and ASP73: These residues showed higher binding affinities when mutated to Alanine. This could suggest that they might have unfavorable interactions with serotonin in the wild-type LasR, and their removal improved the binding affinity.
4. Conservation of binding: Some residues like LEU36, TRP60, and TRP88 showed binding affinities similar to the wild-type LasR when mutated to Alanine. This indicates that these specific residues may not be as critical for serotonin binding or that other compensatory interactions are occurring.

In summary, one can say targeting Tyrosine residues at TYR56 and TYR64 would be beneficial in producing LasR mutants with lesser affinity to Serotonin. This eventually allows to creation of a quorum-sensing bio-switch with less sensitivity toward serotonin. This is better suited for gut environments than wild-type LasR.

FASTA files of the proposed variants with lesser sensitivity to Serotonin:

                
                    >TYR56
                    FLELERSSGKLEWSAILQKMASDLGFSKILFGLLPKDSQDYENAFIVGNAPAAWREHYDR
                    AGYARVDPTVSHCTQSVLPIFWEPSIYQTRKQHEFFEEASAAGLVYGLTMPLHGARGELG
                    ALSLSVEAENRAEANRFMESVLPTLWMLKDYALQSGAGLAFEH
                    >TYR64
                    FLELERSSGKLEWSAILQKMASDLGFSKILFGLLPKDSQDYENAFIVGNYPAAWREHADR
                    AGYARVDPTVSHCTQSVLPIFWEPSIYQTRKQHEFFEEASAAGLVYGLTMPLHGARGELG
                    ALSLSVEAENRAEANRFMESVLPTLWMLKDYALQSGAGLAFEH
                
              

Figure 7: TYR56 mutant complex

Figure 8: TYR64 mutant complex

It is to be noted that, though this analysis gave curious insights, further modeling needs to be done in order to settle with final conclusions. Molecular Dynamics is a good place to start with. However, due to time constraints, we are going to report only Protein modeling and docking studies.

References:

[1] Schuster Martin, Li Christina, Smith Parker and Kuttler Christina 2023 Parameters, architecture, and emergent properties of the Pseudomonas aeruginosa LasI/LasR quorum-sensing circuit J. R. Soc. Interface. 20:20220825
http://doi.org/10.1098/rsif.2022.0825

[2] Wang, H. H., Isaacs, F. J., Carr, P. A., Sun, Z. Z., Xu, G., Forest, C. R., & Church, G. M. (2009). Programming cells by multiplex genome engineering and accelerated evolution. Nature, 460(7257), 894–898. https://doi.org/10.1038/nature08187
https://bionumbers.hms.harvard.edu/bionumber.aspx?id=106028

[3] DiRienzo, J. M., Nakamura, K., & Inouye, M. (1978). The outer membrane proteins of Gram-negative bacteria: biosynthesis, assembly, and functions. Annual review of biochemistry, 47, 481–532. https://doi.org/10.1146/annurev.bi.47.070178.002405 https://bionumbers.hms.harvard.edu/bionumber.aspx?s=n&v=0&id=109060

[4] Malinauskaite, L., Quick, M., Reinhard, L., Lyons, J. A., Yano, H., Javitch, J. A., & Nissen, P. (2014). A mechanism for intracellular release of Na+ by neurotransmitter/sodium symporters. Nature structural & molecular biology, 21(11), 1006–1012. https://doi.org/10.1038/nsmb.2894

[5] Byeon, Y., & Back, K. (2016). Melatonin production in Escherichia coli by dual expression of serotonin N-acetyltransferase and caffeic acid O-methyltransferase. Applied microbiology and biotechnology, 100(15), 6683–6691. https://doi.org/10.1007/s00253-016-7458-z

[6] Hoffman, J. M., & Margolis, K. G. (2020). Building community in the gut: a role for mucosal serotonin. Nature reviews. Gastroenterology & hepatology, 17(1), 6–8. https://doi.org/10.1038/s41575-019-0227-6

[7] Back, K., Tan, X., & Reiter, R. J. (2016). Melatonin biosynthesis in plants: Multiple pathways catalyze tryptophan to melatonin in the cytoplasm or chloroplasts. Journal of Pineal Research, 61(4), 426-437. https://doi.org/10.1111/jpi.12364

[8] Knecht, L. D., Mittal, R., Liu, X. Z., Daftarian, P., Deo, S. K., & Daunert, S. (2016). Serotonin Activates Bacterial Quorum Sensing and Enhances the Virulence of Pseudomonas aeruginosa in the Host. EBioMedicine, 9, 161-169. https://doi.org/10.1016/j.ebiom.2016.05.037

[9] DiRienzo, J. M., Nakamura, K., & Inouye, M. (1978). The outer membrane proteins of Gram-negative bacteria: biosynthesis, assembly, and functions. Annual review of biochemistry, 47, 481–532. https://doi.org/10.1146/annurev.bi.47.070178.002405

[10] Trott, O., & Olson, A. J. (2010). AutoDock Vina: improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading. Journal of computational chemistry, 31(2), 455–461. https://doi.org/10.1002/jcc.21334

[11] MATLAB. (2010). version 7.10.0 (R2010a). Natick, Massachusetts: The MathWorks Inc.

[12] Van Rossum, G., & Drake Jr, F. L. (1995). Python reference manual. Centrum voor Wiskunde en Informatica Amsterdam.

[13] ** https://doi.org/10.2210/pdb3IX3/pdb

[14] Yang Liu, et al. CB-Dock2: improved protein-ligand blind docking by integrating cavity detection, docking and homologous template fitting. Nucleic Acids Research, 2022.

[15] Xiaocong Yang, et al. FitDock: protein-ligand docking by template fitting. Briefings In Bioinformatics, 2022.

[16] Knecht, L. D., O'Connor, G., Mittal, R., Liu, X. Z., Daftarian, P., Deo, S. K., & Daunert, S. (2016). Serotonin Activates Bacterial Quorum Sensing and Enhances the Virulence of Pseudomonas aeruginosa in the Host. EBioMedicine, 9, 161–169. https://doi.org/10.1016/j.ebiom.2016.05.037

[17]Miwa J, Echizen H, Matsueda K, Umeda N. Patients with constipation-predominant irritable bowel syndrome (IBS) may have elevated serotonin concentrations in colonic mucosa as compared with diarrhea-predominant patients and subjects with normal bowel habits. Digestion. 2001;63(3):188-94. doi: 10.1159/000051888. PMID: 11351146.

[18]healthy individualsErspamer, V. (1966). Occurrence of indolealkylamines in nature, in 5-hydroxytryptamine and related indolealkylamines (V. Erspamer, ed.).