Interpretation of organizational role of proteins on E. coli nucleoid via Hi-C integrated model

Abstract

Several proteins in Escherichia coli work together to maintain the complex organization of its chromosome. However, the individual roles of these so-called nucleoid-associated proteins (NAPs) in chromosome architectures are not well characterized. Here, we quantitatively dissect the organizational roles of Heat Unstable (HU), a ubiquitous protein in E. coli and MatP, an NAP specifically binding to the Ter macrodomain of the chromosome. Toward this end, we employ a polymer physics-based computer model of wild-type chromosome and their HU- and MatP-devoid counterparts by incorporating their respective experimentally derived Hi-C contact matrix, cell dimensions, and replication status of the chromosome commensurate with corresponding growth conditions. Specifically, our model for the HU-devoid chromosome corroborates well with the microscopy observation of compaction of chromosome at short genomic range but diminished long-range interactions, justifying precedent hypothesis of segregation defect upon HU removal. Control simulations point out that the change in cell dimension and chromosome content in the process of HU removal holds the key to the observed differences in chromosome architecture between wild-type and HU-devoid cells. On the other hand, simulation of MatP-devoid chromosome led to locally enhanced contacts between Ter and its flanking macrodomains, consistent with previous recombination assay experiments and MatP’s role in insulation of the Ter macrodomain from the rest of the chromosome. However, the simulation indicated no change in matS sites’ localization. Rather, a set of designed control simulations showed that insulation of Ter is not caused by bridging of distant matS sites, also lending credence to a recent mobility experiment on various loci of the E. coli chromosome. Together, the investigations highlight the ability of an integrative model of the bacterial genome in elucidating the role of NAPs and in reconciling multiple experimental observations.

Significance

Escherichia coli maintains a macrodomain-separated, well-organized chromosome architecture where multiple proteins are involved in a nucleus-like structure management of chromosomes in bacteria. Such proteins are called nucleoid-associated proteins (NAPs). Some of these bind to chromosomes locally and while others bind in a non-specific manner. However, individual roles of these NAPs in bacterial chromosome organization are obscured by numerous contrasting hypotheses and the need for quantitative characterization. Here we combine computer simulation with multiple experimental inputs and Hi-C data to dissect the organizational role of HU and MatP. The investigations reconcile multiple precedent observations on HU and MatP’s function as drawn from diverse experiments and highlight the role of carefully crafted control simulations in providing mechanistic insights into past experiments.

Introduction

The common eubacteria Escherichia coli has a single circular chromosome with genomic size of ≈4.64 mega-basepairs (Mbp). Although the contour length is $\approx 1.5$ mm, it is packed compactly into a nucleus-like structure called a “nucleoid,” inside a $1.5-2.5\mu$m-long cell. For a long time, the structure and packing of chromosome(s) inside microbial cells and nucleus have raised intrigue and have gone well beyond the old perception of bacteria as a bag of macromolecules (1). Over the last decade, clarity is slowly emerging on the mechanisms and potential factors that various organisms utilize to organize their genomic material.

Evidence from various experiments suggested that multiple proteins are involved in a nucleus-like structure management of chromosome in bacteria (2). Previously, the protein component of the nucleoid was believed to be chiefly RNA polymerase (3). But later studies found more than 200 potential DNA binding proteins in E. coli cells (4). Out of those potential proteins, 10–20 were found to be responsible for nucleoid organization (5). These proteins were called nucleoid-associated proteins (NAPs), which play distinct roles in chromosome organization. A large subset of the NAPs binds non-specifically across the whole chromosome and controls its overall organization.

One such ubiquitously found protein in E. coli is HU (Heat Unstable) (6,7). HU is composed of two subunits, HU$\alpha$ and HU$\beta$ (8). The functional units are hup${\alpha }_2$, hup${\beta }_2$, and hup$\alpha \beta$. Each performs a different physiological function (8). We denote the set of functional units as HU throughout this paper. HU is the histone equivalent present in prokaryotes (9), which plays an important role in DNA compaction and negative supercoiling (10). It does not have any specific motif to which it binds and binds to almost the whole chromosome uniformly. Along with MukBEF, HU is an important factor in chromosome partitioning, and its removal has been observed to have the $\Delta$MukBEF phenotype. The most likely reason for such a phenotype is chromosome misfolding, which changes the expression levels of different genes (11).

Initial studies for understanding the macrodomain (12) organization suggested the presence of MatP, which has 23 specific binding sites in the Ter macrodomain, referred to as matS sites (13). MatP is responsible for insulating Ter from the rest of the chromosome. The functional unit of the protein is a tetramer (14,15). It was originally believed that MatP insulated Ter by cross-linking distant matS site pairs (14) until, recently, it was shown that this is not correct (15,16). Recent investigations show almost negligible change in the organization of Ter upon MatP deletion (17). On the contrary, it was observed the MatP tetramer binds to only one matS site while cross-linking it to a non-matS DNA and that in the absence of matS, MatP can also bind to non-matS DNA (15). It is also known that MatP displaces mukBEF bound to matS sites (18). Cryo-electron microscopy studies show that matS-bound MatP facilitates proper positioning of the DNA inside the MukBEF DNA-entrapment ring. This positioning increases the unloading efficiency of DNA from mukBEF (16), which can explain the displacement of MukBEF by MatP.

In the current investigation, we aim to quantitatively investigate and interpret the role played by two NAPs, namely HU and MatP, each of which respectively represents the mode of “non-specific” and “specific” binding to chromosome. We sought to do so by using a polymer model for the E. coli chromosome. Numerous previous studies (1,19,20,21,22,23,24,25,26) have used experimental data and/or phenomenological methods to propose models for the bacterial chromosome. However, we will use an indigenous polymer-physics-based computer model which has been integrated with recently reported Hi-C interaction maps (17) of the E. coli chromosome for cells under multiple growth conditions and across multiple mutations.

In particular, we develop three-dimensional computer models of E. coli chromosome(s) at 5 kilo-basepair (kbp) resolution under two different growth conditions. Subsequently, we individually compare the derived wild-type (WT) chromosome model with that of single-mutant chromosomes using respective Hi-C interaction maps of cells devoid of one of the NAPs (i.e., either HU or MatP) under similar growth conditions as those of respective WT. The current investigation addresses the following questions on the organizational roles of HU and MatP:

• •What is the impact of deletion of HU on the E. coli chromosome? In particular we reconcile a recent experimental observation (17): how a loss in contact probabilities, seen upon deletion of HU from E. coli cells, can cause nucleoid compaction.
• •How does MatP insulate the Ter macrodomain from the rest of the chromosome? In this context, can precedent mechanism of action of MatP on the Ter domain be put to the test via computer simulations, as posited by previous experiments (14,15)?

Here, we first describe our simulation protocol for modeling the mutant and their respective WT chromosome(s) of E. coli by combining experimental measurements with a polymer-physics-based framework. In the results and discussion section, we consider each mutant chromosome individually and provide a quantitative perspective of the change in chromosomal organization due to deletion of one of the NAPs from the WT chromosome under the same growth conditions. The results are quantitatively explored and used to interpret experimental observations. Finally we present a summary in the conclusion section along with a brief discussion.

Materials and methods

The model

The E. coli chromosome is circular and is 4.64 Mbp in length. We have modeled the chromosome as a self-avoiding, beads-in-spring, homopolymer in a confinement. The role of the confinement is to mimic the cell wall. Therefore, using our model and the simulation protocol, we effectively simulate chromosome(s) inside an E. coli cell. A detailed discussion regarding the confinement and the simulation protocol can be found toward the end of this section. In this study we have explored the role of NAP in the chromosome organization in WT E. coli cells grown at 37°C in Lennox broth (LB) medium and cells grown at 30°C in minimal medium (MM). These are high and moderate growth conditions, respectively. Under such growth conditions, the chromosome replicates rapidly and may even undergo multiple rounds of replication (27). Moreover, the mutants that we have simulated also have similar or more complicated chromosome topology. Therefore, it is important to discuss the generation of individual polymer models that ensure chromosome topology equivalent to experimental ones during simulations. Dr. Virginia Lioy, from the Institute for Integrative Biology of the Cell, Paris (the lead experimentalist of Hi-C experiments (17)), generously shared the experimental measurements of the chromosome contents, the nature of chromosome architecture, and cell dimensions of WT (and mutant) chromosomes under multiple growth conditions (Table 1), which have remained integral for modeling the respective chromosome conformations.

Table 1.

Details of cell sizes and chromosome contents for each system simulated

Cell type	Temperature (°C)	Growth medium	Cell length ($\mu$m)	Ori/Ter (approx.)	G	No. of chromosomes	No. of replication oriCs	$w$
WT	37	LB	2.48a	3.6	3.6	2	2	0.3
WTcontrol	37	LB	5.3	5.5	5.5	3	2	0.3
WT	30	MM	3.05	1.8	1.8	1	1	0.5
$\Delta$HU	37	LB	5.3	5.5	5.5	3	2	0.3
$\Delta$MatP	30	MM	3.08	1.8	1.8	1	1	0.5

^aThe cell length has been taken from (28).

Chromosome model for WT cells grown at 37°C in LB

WT cells grown at 37°C in LB medium each have two chromosomes. Each chromosome has primary and secondary replication forks (27) as can be seen from Fig. 1 a. For ease of referencing, we shall denote such cells as WT37LB. The average chromosome content for WT37LB has been denoted by its genome equivalent (G) (27). The G value for a cell is calculated as $G=\frac{\text{amount}\text{of}\text{DNA}\text{in}\text{the}\text{cell}\text{in}\text{bp}}{4.64\times {10}^6\text{bp}}$. As per experimental observations (27), WT37LB E. coli cells have G = 3.6. Thus a typical cell would have two chromosomes with a total of 8 oriCs and 2 dif regions. A chromosome inside such cells would be very similar to the polymer model of the chromosome(s) shown in Fig. 1 a. Moreover, the Ori/Ter ratio data shared by Dr. Lioy reports an Ori/Ter ratio of ≈3.6 for WT37LB (Table 1). Therefore, we argue that the Ori/Ter ratio is good metric to estimate the average chromosome content of a model cell.

Figure 1.

Chromosome topologies for different wild-type (WT) and mutant cells showing primary and secondary replication forks. (a) Chromosome topology for WT cells grown at 37°C in LB medium. It consists of two chromosomes each with secondary replication forks. The cell has a total of G = 3.6. (b) Chromosome topology for WT cells grown at 30°C in MM medium. It consists of one chromosome with a single replication fork and a total of G = 1.8. (c) Chromosome topology for HU-devoid cells grown at 37°C in LB medium. It consists of three chromosomes each with secondary replication forks. The cell has a total of G = 5.5. (d) Chromosome topology for MatP-devoid cells grown at 30°C in MM medium. It consists of one chromosome with a single replication fork and a total of G = 1.8. To see this figure in color, go online.

Chromosome model for WT cells grown at 30°C in MM

WT cells grown at 30°C in MM have an Ori/Ter ratio of ≈1.8 (Table 1). For ease of referencing, we label such cells as WT30MM. We therefore use G = 1.8 for WT30MM cells. For moderate growth media, such as MM, it is unlikely to have a very rapid chromosome replication that can generate secondary replication forks. However, G $>$ 1 suggests ongoing replication, thereby necessitating the presence of a replication fork in the model. Therefore, we model the chromosome for WT30MM cells as a circular beads-in-spring polymer with one branch as shown in Fig. 1 b.

Chromosome model for HU-devoid cells

The HU mutant cells, where HU was not present, were grown at 37°C in LB medium. For ease of referencing, we label such cells as $\Delta$HU. It was experimentally observed for $\Delta$HU that the cells had multiple chromosomes in them with the most prominent number of chromosomes being 3 (17). The Ori/Ter ratio for $\Delta$HU was experimentally determined by Dr. Lioy to be ≈5.5 (Table 1). Using that as an estimate for G and following the experimental observations, we use three chromosomes in each $\Delta$HU model cell. Each such chromosome has, therefore, $G=\frac{5.5}{3}=1.83$. We have also modeled each chromosome to have secondary replication forks as shown in Fig. 1 c.

Chromosome model for MatP-devoid cells

MatP-devoid cells, here on to be referred to as $\Delta$MatP, were grown in MM at 30°C. The experimental Ori/Ter ratio for such cells were determined to be ≈1.8 (Table 1), similar to that of WT30MM. Therefore the chromosome topology for $\Delta$MatP was similar to that of WT30MM, as shown in Fig. 1 d.

Determination of the number of beads for a polymer model

As discussed earlier, we use beads-in-spring homopolymers of varying topology to simulate chromosome(s) inside an E. coli cell. For proper simulation of the chromosome(s) in an E. coli cell, we have incorporated Hi-C contact probability matrices for WT and mutant cells in the polymer model. Details on how the Hi-C contact probability was incorporated into a model are discussed later in this section. On that note, the number of beads in such a polymer model and the resolution of our model is determined by its $G$ value and the resolution of the Hi-C contact probability matrix encoded. In the experimental study (17), the Hi-C matrices reported have a bin size of 5 kbp. Therefore, each polymer bead in the simulations represent 5 kbp of the chromosome(s), which sets the resolution of our model to 5000 basepairs per bead. For an unreplicated chromosome, the number of beads $\left(N\right)$ would then be $\frac{4.64\times {10}^6\text{bp}}{500\text{bp}}=928$ (referred to as $N_0$) beads. However, the cases explored in this study all have chromosomes that have partially replicated, i.e., $G>1$. For such cases the number of beads $=N_{0}G$, rounded off to the nearest integer.

Determination of size of each bead

As we have modeled the chromosome as self-avoiding beads-in-spring polymers, each bead of the polymer has a finite size $\left(\sigma \right)$. The size of each bead is determined on the basis of the cell volume, the chromosome volume fraction $\left(f_r\right)$, and the number of beads in the model $\left(N=N_{0}G\right)$. The size of a bead can be calculated using $\sigma ={\left(\frac{6f_r{r}^2}{G{N}_0}\left(\frac{4r}{3}+l\right)\right)}^{\frac{1}{3}}$, where $r$ is the radius of the E. coli cell while $l$ is the length of the cell without the end-caps. The derivation can be found in supporting methods. The lengths for each cell used in this study have been reported in Table 1 and mostly were determined via microscopy by Dr. Lioy. For all cells, an average diameter of $0.84\mu \mathrm{m}$ has been used, which is a typical cell diameter for almost all E. coli cells (29,30). The size of each bead also sets the length scale for simulations. Therefore, all simulations length units are in terms of $\sigma$.

Building a Hi-C integrated force field for the chromosome

The complete Hamiltonian for the Hi-C integrated chromosome model employed here is given by Eq. 1:

$$H=V_{adj}+V_{conf}+V_{nb}+V_{Hi-C}\text{.}$$ (1)

Below, we describe each of the constituent potential terms.

Generic potential terms

The force field for a polymer starts with the bonds between its adjacent beads. Here, adjacent beads of the polymer have been connected using strong harmonic springs with force constants denoted by $k_{adj}$ (= 300 $k_{B}T{\sigma }^{-2}$), and the equilibrium distance among adjacent beads has been set to $\sigma$. The potential between two adjacent polymer beads is given by Eq. 2.

$$V_{adj}\left(r_{i,i+1}\right)=\frac{1}{2}{k}_{adj}{\left(\left|\overrightarrow{r_{i+1}}-\overrightarrow{r_i}\right|-\sigma \right)}^2\text{.}$$ (2)

We have modeled the excluded volume interaction among non-adjacent polymer beads using volume exclusion potential $\left(V_{nb}\left(r\right)\right)$ via the repulsive part of Lennard-Jones potential given by Eq. 3.

$$V_{nb}\left(r\right)=\{\begin{array}{cc}A{\left(\frac{\sigma }{r}\right)}^{12}& \text{if}r<=2.0\sigma \\ 0& \text{otherwise}\end{array}\text{,}$$ (3)

where $A$ determines the strength of repulsion. Here $A=1.0k_{B}T$ has been used.

To introduce spherocylindrical confinement mimicking the E. coli cell wall, we use a confinement potential $\left(V_{conf}\right)$ that restricts the polymer(s) within a capsule-shaped volume. The size of the confinement for a polymer model depends on the cell length $L$ (including the end-caps) and cell radius $r$, which are employed as per the experimental inputs on WT and mutant cells (Table 1). The potential function for the confining potential is given by Eq. 4, where $k_{conf}=300k_{B}T{\sigma }^{-2}$ and $R_0$ is the center of the confinement. Thus the confining potential acts only if a bead crossed the cell wall or confinement.

$$V_{conf}\left(\overrightarrow{r_i}\right)=\{\begin{array}{cc}\frac{1}{2}{k}_{conf}{\left(\left|\overrightarrow{r_i}-\overrightarrow{R_0}\right|\right)}^2& \text{if}\left|x_i\right|>R\text{or}\left|y_i\right|>R\text{or}\left|z_i\right|>L\\ 0& \text{if}\left|x_i\right|\le R,\left|y_i\right|\le R,\left|z_i\right|\le L\end{array}\text{.}$$ (4)

Modeling Hi-C contact probabilities as harmonic restraints

The Hi-C contact probabilities have been hypothesized to be proportional to physical distances among regions of the chromosome (31) as per Eq. 5:

$$P=K{D}^{\nu }\text{.}$$ (5)

For converting the Hi-C contact probabilities as distances, we propose that $K=\sigma$ and $\nu =-1$. The choice of $\nu =-1$ has been made because for a contact probability $=1$, the corresponding distance among the beads come out to be $\sigma$, which is the minimum distance of approach for any two beads of the polymer which represents the chromosome. Distances closer than $\sigma$ face an energy penalty as per Eq. 3. Therefore, Eq. 5 reduces to Eq. 6.

$$P=\frac{\sigma }{D}$$

$$\Rightarrow D=\frac{\sigma }{P}\text{.}$$ (6)

Here, $P$ is a $N_0\times N_0$ experimental contact probability matrix and D is its corresponding “Hi-C derived” distance matrix. Therefore, the experimental contact probability between two beads $i$ and $j$ of the polymer model is given by $P_{ij}$. The distance that needs to be maintained during simulations between beads $i$ and $j$ is given by $D_{ij}$. Therefore for P_ij $=1,D=\sigma$ and for $P_{ij}=0,D_{ij}=\infty$.

$$V_{HiC}\left(r_{ij}\right)=\frac{1}{2}{k}_{ij}{\left(D_{ij}-r_{ij}\right)}^2\text{.}$$ (7)

A harmonic restraint potential models the interaction between two beads $i$ and $j$, with an equilibrium distance = $D_{ij}$ (Eq. 7). These springs that maintain the Hi-C-derived distances among beads are labeled “Hi-C bonds” hereafter. However, we also varied the force constants of these Hi-C bonds with their contact probability as per Eq. 8:

$$k_{ij}=k_0{e}^{-\frac{{\left(r_{ij}-D_{ij}\right)}^2}{w}}\text{,}$$ (8)

where $k_0$ determines the upper limit to the strength of the Hi-C bonds and $w$ is a parameter that needs to be optimized for each Hi-C contact probability matrix. Details regarding the optimization have been discussed further in this section.

Therefore, the lower is the contact probability between two beads $i$ and $j$, the lower is the extent to how strongly their Hi-C-derived distance is being maintained. At $P_{ij}=0,D_{ij}=\infty$ and $k_{ij}=0$. Thus, chromosome regions having low contact probabilities are not held strongly by Hi-C bonds while high contact probability regions are very rigidly held together. It should be noted that we have not introduced any Hi-C bonds among the bead pairs that satisfy the following conditions: 1) beads of the polymer which are adjacent to each other as they are already connected via bonds; 2) beads that belong to different replication forks of the same chromosome because here we assume that it is much easier to create a contact within the replication fork rather than cross-replication fork and, moreover, cross-replication fork contacts can also hinder chromosome segregation; 3) beads belonging to the unreplicated chromosome region and the beads belonging to replication forks—here the reason is same as in point 2, since it will be easier to generate intra-replication fork contacts because the regions are genomically much closer than the unreplicated region and the replication fork regions; 4) beads belonging to different chromosomes; 5) if $k_{ij}<{10}^{-3}$. The last condition thus reduces the number of Hi-C contacts that are finally encoded drastically (Table S1) without any significant effect on the chromosome conformations, also resulting in much faster simulations.

For all the simulations performed, $k_0=10k_{B}T{\sigma }^{-2}$ has been used. We have kept the value of $k_0$ much lower than $k_{adj}$, as $k_0$ mostly denotes protein-mediated contacts between regions of the chromosome. The majority of such contacts are not due to covalent linkage between regions of the chromosome and thus are much weaker than the covalent linkages between DNA nucleotides that form the bonds between adjacent beads of a polymer model.

In Eq. 8, $w$ determines the width of the Gaussian. Thus, a high $w$ would lead to stronger Hi-C bonds even for low contact probability regions. Since it effects the relative strengths of the Hi-C bonds, variation in $w$ has a profound effect on the simulated chromosome structure and thereby on the Hi-C contact matrices calculated from simulations. Therefore, it needs to be optimized for each Hi-C contact probability matrix. We optimize $w$ as described in supporting methods.

Simulation details

For each cell type we have discussed, 200 simulations have been performed with different initial structures. Each simulation consisted of 2 steps: 1) an energy minimization; 2) a production run using stochastic dynamic simulations as per Eq. 9:

$$m_i\frac{d^2{r}_i}{d{t}^2}=-m_i\gamma \frac{d{r}_i}{dt}+F_i\left(r\right)+{\eta }_i\text{,}$$ (9)

where $m_i$ is the mass of the ith particle, $r_i$ is the coordinate of the ith particle, $F_i$ is the force on the ith particle, $\gamma$ is the friction coefficient, and ${\eta }_i$ is a Gaussian random noise on particle obeying the fluctuation-dissipation theorem given by Eq. 10,

$$⟨{\eta }_i\left(t\right){\eta }_j\left(t^{\prime }\right)⟩=6m_i\gamma k_{B}T\delta \left(t-t^{\prime }\right){\delta }_{ij}\text{.}$$ (10)

For both of the above steps, Hi-C interactions were considered. The time step for step 2 was 0.002 ${\tau }_{\text{SD}}$ where ${\tau }_{\text{SD}}=\frac{m_i}{{\gamma }_i}=4.8\times {10}^{-14}$ s. Each production simulation has been run for 2.5 $\times {10}^6$ steps. The output frequency was set to 1000 steps. Thus, we obtain a total of 2500 frames from which only the last 2000 frames have been used for further analysis.

For investigation into the mobility of various Ter loci, the last frame from the stochastic dynamics simulations were used to run Brownian dynamics simulations as per Eq. 11. Each such simulation consisted of 2.5 $\times {10}^7$ steps with a time step of ${10}^{-4}{\tau }_{BD}$ where ${\tau }_{BD}=\frac{3\pi \eta {\sigma }^3}{k_{B}T}=12.4$ s. The output frequency was set to 10,000 steps. Thus, we obtain a total of 2500 frames from which only the last 2000 frames have been used for further analysis.

$$\frac{d{r}_i}{dt}=-\frac{1}{\gamma }{F}_i\left(r\right)+{\eta }_i\text{,}$$ (11)

where $r_i$ is the coordinate of the ith particle, $F_i$ is the force on the ith particle, $\gamma$ is the friction coefficient, and ${\eta }_i$ is a Gaussian random noise on particle obeying the fluctuation-dissipation theorem given by Eq. 12,

$$⟨{\eta }_i\left(t\right){\eta }_j\left(t^{\prime }\right)⟩=\frac{6k_{B}T}{\gamma }\delta \left(t-t^{\prime }\right){\delta }_{ij}\text{.}$$ (12)

Generation of simulated contact probability matrix from trajectory

Using the last 2000 frames of kth simulation, we generate a distance matrix $D^k$ whose distances have been averaged over the number of frames. We generate the final simulated distance matrix $D_{\text{sim}}$ by averaging over those matrices:

$$D_{\text{sim}}=\frac{1}{n}\sum _{k=1}^n{D}^k\text{.}$$ (13)

Similarly, we also generate $P^k$ as per Eq. 14, which is the simulated contact probability matrix for the kth simulation:

$$P_{ij}^k=\frac{\sigma }{D_{ij}^k}\text{.}$$ (14)

The simulated probability matrix $P_{\text{sim}}$ is an average over $P^k$ (Eq. 15):

$$P_{\text{sim}}=\frac{1}{n}\sum _{k=1}^n{P}^k\text{.}$$ (15)

We have used n = 200, i.e., we have used 200 simulations for the averaging.

List of software

In the current study we have used only “free and open source software,” listed below.

GROMACS (32,33), VMD (34), Python (35), Numpy (36), Scipy (37), Matplotlib (38), MDAnalysis (39,40), Jupyter (41).

Results and discussion

In our protocol to model bacterial chromosome(s) we encode self-avoiding homopolymer(s) with Hi-C contact probability matrix (Fig. 2). We hypothesize that the probabilities would be inversely proportional to distances among polymer beads. We incorporate springs into the model so as to maintain those distances. However, we also make sure that regions with high contact probabilities are held more tightly by the springs than regions with low contact probabilities. To speed up simulations, we also neglect introduction of a spring if its stiffness is very low (<${10}^{-3}$). To obtain an ensemble of chromosome conformations, we generate 200 random polymer conformations as the initial states. In each such conformation, adjacent beads are connected by strong harmonic bonds (see materials and methods). The distance restraints are introduced using harmonic bonds between non-adjacent beads, whose equilibrium bond distances and force constants are calculated using Eqs. (6) and (8) and the conditions described in materials and methods. We then perform stochastic dynamic simulations with excluded volume interactions to obtain an ensemble of equilibrated polymer conformations.

Figure 2.

Schematic of the method used to generate an ensemble of final chromosome structures. (a) Contact probability matrix from Hi-C experiment for WT E. coli. (b) Contact probability matrix from Hi-C experiment for mutant E. coli. (c) Initial configurations. (d) Chromosome after equilibration of an energy minimized conformation for WT. (e) Chromosome after equilibration of an energy minimized conformation for mutant. Distances from equilibrium conformations were converted to a contact probability matrix; the simulated and the experimental matrices are compared and the simulated matrix is used for further analysis. The cell walls shown in the figures represent the confinement used during simulations. To see this figure in color, go online.

WT E. coli cells grown under different growth conditions share similar traits of chromosome organization

While the main purpose of the present investigation is to characterize and interpret the effect of mutational perturbation on the genomic organization of E. coli chromosome, we initiated our study by simulating WT counterpart. A careful, first-hand characterization of WT chromosome would serve as key benchmarks for later comparison with the mutants. The availability of Hi-C contact probability maps of two NAP mutant chromosomes (17) at two different growth conditions ($\Delta$HU at 37°C in LB medium and $\Delta$MatP at 30°C in MM) necessitated the investigation of corresponding WT chromosome under these conditions. Accordingly, in this study we have simulated WT E. coli cells for two different growth conditions: 1) WT E. coli cells grown at 37°C in LB medium (labeled as WT37LB) and 2) WT E. coli cells grown at 30°C in MM (labeled as WT30MM).

To ascertain the chromosome architecture and chromosome contents, we considered the Ori/Ter ratio or genomic equivalent (G) (see materials and methods for definition and details in accounts by Bremer and Denis (27)). The growth conditions, considered in this work, are high growth and moderate growth conditions, respectively. E. coli cells in high growth conditions have multiple chromosomes inside its cell, each undergoing multiple rounds of replication before the cell divides (27), giving rise to a value of $G>1$. To properly model such a situation, we use a forked circular polymer topology to model the chromosome with replication forks. We also place two chromosomes inside the cell boundary as G = 3.6 (Table 1) for WT37LB, which means that on average there are two chromosomes present inside an E. coli cell.

For WT30MM the Ori/Ter ratio, which is a good estimate for the G value of a cell, was used to model the chromosome. For moderate growth conditions, we assumed that the chromosome does not contain secondary replication forks. However, for WT30MM, G = 1.8 (Table 1), which suggests that the chromosome is undergoing replication. Therefore, we model the chromosome with a single replication fork. A summary of the chromosome contents, cell sizes, and polymer topology is provided in Table 1 and discussed in detail in materials and methods. However, we shall not delve into the chromosome organization of WT37LB in the current study. We had previously explored the chromosome organization and loci positioning for WT37LB at different stages of chromosome replication using the modeling protocol discussed in the methods section of a prior publication (42). In the previous study we showed that for WT37LB E. coli cells, the current model is capable of reconciling multiple preceding experimental investigations such as oriC and dif loci positioning during replication (43), site-specific recombination frequency (12), and several other properties of the WT E. coli chromosome. Here we shall first perform a comparative study of the chromosome organization between WT E. coli cells grown under different growth conditions, followed by exploration of the role of two NAPs, HU and MatP, on the chromosome organization of E. coli.

Fig. 3, a and b show representative conformations for WT37LB and WT30MM, respectively. A stark difference in their chromosome content is evident in these conformations.

Figure 3.

(a) Representative chromosome conformation for WT37LB obtained from simulations. The macrodomains have been color coded as per the legend provided below. (b) Representative chromosome conformation for WT30MM obtained from simulations. The macrodomains have been color coded as per the legend provided above. (c) Comparison of simulated and experimental Hi-C contact probability matrices for WT37LB. The upper triangle represents simulated Hi-C matrix while the lower diagonal represents the experimental Hi-C contact probability matrix. (d) Comparison of simulated and experimental Hi-C contact probability matrices for WT30MM. The upper triangle represents simulated Hi-C matrix while the lower diagonal represents the experimental Hi-C contact probability matrix. (e) 3D density correlation matrix for WT37LB. (f) 3D density correlation matrix for WT30MM. The cell walls shown in the figures represent the confinement used during simulations. To see this figure in color, go online.

In both cases we observe that oriCs have moved toward the cell poles while dif loci are predominantly at or near mid-cell (Fig. S2), which is consistent with previous experimental observations (43,44). For WT37LB, however, there are two Ter macrodomains, each belonging to one of the partially replicated chromosomes, while both dif loci remain near mid-cell (Fig. S1 a). This causes a polar orientation for the oriCs and dif belonging to the same chromosome. For the unreplicated Ter macrodomain in WT30MM, we observe that dif is, grossly, situated at mid-cell (Fig. S1 b). Thus we argue that the chromosome conformations obtained using our protocol recapitulated quite well the localizations of oriCs. We were also able to obtain the experimentally observed locations of Ter macrodomain(s) (mid-cell) without the need of any external imposition (45) for both the growth conditions discussed here and, with less accuracy, the orientation or organization of the rest of the macrodomains.

To check whether the Hi-C contacts were properly maintained in the simulations, we compare the simulated and their respective experimental Hi-C matrices for WT37LB and WT30MM (Fig. 3, c and d, respectively). For both the cases we observe a very high degree of similarity between the simulated and Hi-C contact probability matrices. To quantify the similarity between the experimental and the simulated matrices, we calculate the Pearson correlation coefficient values between the experimental and simulated matrices (see supporting methods). The Pearson correlation coefficients between the simulated and experimental Hi-C contact matrices for WT37LB and WT30MM are 0.88 and 0.91, respectively. To further justify our claims that the contacts are properly maintained, we plot the difference matrices relative to experimental counterpart (Fig. S2, a and b). From the difference matrices, it can be seen that most values for both WT37LB and WT30MM are near zero (signified by their low color intensities). We also plot the distribution of the absolute values of the differences in Fig. S2, c and d, from which we can see that the difference in probabilities for WT37LB and WT30MM lies around 0.05, which is very low. Therefore, the high correlation values between simulated and experimental matrices and the low error in the simulated matrices quantitatively provide evidence that the Hi-C contacts are properly maintained during the simulations for WT37LB as well as WT30MM.

We also plot the mean contact probability as a function of genomic distance obtained from experimental and simulated contact probability matrices (Fig. S3). For both cases, namely WT37LB (Fig. S3 a) and WT30MM (Fig. S3 b), we observe that simulated P(s) is lower than the experimental P(s) for shorter genomic distances, i.e., low values of s. Conversely, at high genomic distances, i.e., at higher s values, the trend is reversed. These results occur mainly due to the reasons discussed below.

The cause of simulated P(s) being lower than the experimental one is due to the assumption that each 5000 basepairs of DNA, represented by beads of the polymer model, interact among themselves via pure repulsion. Such an assumption causes nearby beads to spread out more than what experiments suggest. This causes decreased simulated P(s) with respect to the experimentally observed values at low values of genomic separation (s). However, these interactions fall off very quickly with spatial separation among regions of the chromosome and do not affect the long-range interactions among them. Finally, the reason for the simulated P(s) values at high genomic separations to be higher than what the experiment shows is due to the presence of a finite volume that is available to the chromosome to reside in, which is defined by the cell wall. As we assume that the distances among regions/beads of the chromosome are inversely proportional to the contact probabilities among them, for the P(s) curves to match even more closely, the distances among many beads should have been very large to yield lower simulated P(s) values. Such contact probabilities appear as zero or near-zero values in the experimental matrix. However, due to the confining effect of the cell wall, any two regions of the chromosome can have a maximum, finite distance between them. This causes a slight enhancement in contact probabilities and consequently in P(s) values at large genomic separations for the P(s) values obtained from simulations when compared with the ones obtained via experiments. We had also noted this in our previous two articles.(42,46).

A key hallmark of the organization underlying E. coli chromosome is its self-segregation into four distinct macrodomains (Ori, Ter, Left, Right) and two non-structured right and non-structured left domains (12,13,47,48). While we have previously explored the macrodomain organization for WTLB37 at multiple replication stages (42), here we intended to compare how this trait is maintained across two growth conditions. Toward this end we analyzed three-dimensional (3D) density correlation for all macrodomain pairs given by $Corr\left(d_1,d_2\right)$, where $Corr\left(\right)$ is the Pearson correlation function and $d_1,d_2$ are 3D densities of any two macrodomain pairs. The 3D density correlation is a measure of how much overlap is present between any macrodomain pair. As the cell lengths and chromosome contents for WT37LB and WT30MM are very different, their corresponding chromosomes might have different extents of macrodomain segregation. However from Fig. 3, e and f, we can see that for both growth conditions the extent of macrodomain segregation remains practically unaltered. With the differences in the cell volumes (1.22 $\mu {\mathrm{m}}^3$ and 1.53 $\mu {\mathrm{m}}^3$, respectively), the macrodomain segregation can be unaffected if the chromosome in WT37LB is more compact with respect to the chromosome in WT30MM. The chromosome compaction can be quantifiably evident from the full width at half maximum (FWHM) values obtained from the chromosome linear densities (Fig. S4, a and b). FWHM provides us with a metric that is proportional to the extent of cell length occupied by the chromosome(s), which is equal to the density along the long axis (49). The FWHM value of linear densities of chromosome is an indication of the extent of compaction the chromosome has undergone. Lower FWHM corresponds to higher compaction and vice versa. Thus, the data suggest that the WT37LB chromosome is more compact than the WT30MM chromosome. Therefore, we recapture the experimental observation (50) that the DNA inside the E. coli cell is compacted or expanded based on the balance of the cell volume and the cell’s DNA content. We hypothesize that such changes in compaction are performed by E. coli to avoid large changes in the volume fraction of the chromosome during replication.

The compaction of the nucleoid we captured and the overall chromosome conformation in E. coli is a result of complex interactions between regulatory elements such as promoters and repressors and structural elements such as NAPs. Intrigued by the structural properties of the E. coli chromosome and the insights that our method can provide, in the current work we sought to obtain insights into the role of HU and MatP (which binds specifically to matS sites in Ter) in maintaining the nucleoid architecture. In the following, we provide key insights into the individual role of HU and MatP in governing the structural aspects of E. coli chromosome and discuss our results in the light of preceding experiments.

Dissection of the impact of HU protein in chromosome organization

One of the most abundant and highly conserved NAPs in prokaryotes is the protein HU composed of Hup$\alpha$ and Hup$\beta$ subunits encoded by the genes hupA and hupB, respectively. It is the histone equivalent found in prokaryotes and condenses the chromosome rendering it more compact (51). It is known to be distributed uniformly throughout whole E. coli chromosome (52), binding non-specifically to DNA-stabilizing “protein-mediated” DNA loops (7). The non-specific nature of binding of this protein across chromosome raises the question as to its potential role on the chromosomal organization. Upon deletion of HU from the E. coli cells (17), microscopy images indicated (17) that $\Delta$HU (i.e., devoid of HU) cells would have more compact chromosomes with more filamentous cells and with chromosome segregation defects. The Hi-C interaction map for $\Delta$HU, as derived by Lioy et al. (17), was also observed to be sparser than that of its corresponding WT, suggesting significant loss in contact probabilities in the mutant. However, in the light of the significant loss in contact probabilities in Hi-C interaction matrix in $\Delta$HU cells, the experimentally observed relative compaction of chromosomes upon deletion of HU from bacterial cell raises intrigue. For a closer understanding of the role of HU, we decided to develop a numerical model of the $\Delta$HU chromosome by integrating the respective Hi-C interaction matrix with a polymer-based model and contrasted the same against WT chromosome.

Simulations recapture nucleoid compaction and chromosome segregation defects upon HU deletion

The availability of Hi-C interaction maps (17) for both WT and $\Delta$HU chromosomes at 37°C in LB medium encouraged us to derive computer models for both of them under the same growth conditions so that these could be compared at par. Our modeling efforts ensured that individual cell lengths and the chromosome contents of WT and $\Delta$HU cells used for the simulations are commensurate with experimentally observed average cell sizes at 37°C in LB medium (Table 1). In accord with the cell-length data and the Ori/Ter ratio provided by Lioy corresponding to 37°C in LB medium (Table 1), we have modeled the WT cell encapsulating two chromosomes (Fig. 1 a) while the HU-devoid cell contains three chromosomes (Fig. 1 c). All chromosomes in both cases have primary as well as secondary replication forks (Fig. 1, a and c). For the HU mutant cells, a G value (see materials and methods) of 5.5 was used as per the Ori/Ter ratio observed for $\Delta$HU cells. Since it contains three chromosomes, the G value for each chromosome is 1.83. On the other hand, as per the experimental inputs, contrary to a $\Delta$HU cell, WT cells grown under the same conditions (37°C in LB medium), on average, have two chromosomes in a cell each with primary and secondary replication fork corresponding to a G value of 3.6 (27). Apart from the different chromosome contents, it is also noteworthy that WT (2.48 $\mu$m) and $\Delta$HU (5.3 $\mu$m) cells (Table 1) have considerably different cell lengths (by a factor of more than two). All of these parameters and Hi-C interaction maps were integrated in the polymer-based frameworks (see materials and methods), and 3D conformations of WT and $\Delta$HU chromosome were modeled at the same resolution (5 kbp).

In the previous section, we already validated the derived computer model for WT by comparing the Hi-C matrix calculated from the simulations with its respective experimental matrix (Fig. 3 c). Therefore to validate the model for $\Delta$HU chromosome(s), we compared the simulated and the experimental Hi-C contact probability matrices for $\Delta$HU in Fig. 4 a. The correlation values for WT and $\Delta$HU are 0.88 and 0.89, respectively (Figs. 3 c and 4 a). The values suggest that for both WT and $\Delta$HU, the experimental contacts are properly maintained in the simulated cells. Fig. 4, b and c showcase representative conformations of the chromosome(s) present in a WT cell grown at 37°in LB medium and its corresponding $\Delta$HU mutant, respectively. A significant difference in chromosome contents and cell sizes is evident from these figures. The cell sizes and chromosome contents depicted in the representative conformations are equivalent to the experimentally observed values by Lioy et al. (17) as discussed previously. Using these conformations, we further quantify the effect of deletion of HU on the overall chromosome organization of E. coli.

Figure 4.

(a) Comparison of simulated (upper triangle) and experimental (lower triangle) Hi-C contact probability matrices for $\Delta$HU cells grown at 37°C in LB medium. The matrices have been enhanced by taking an element-wise square root to increase the contrast. The capsule-shaped boundary is representative of the cell wall. (b) Representative chromosome structure from simulation for WT cells. (c) Representative chromosome structure from simulation for $\Delta$HU cells. The capsule-shaped boundary is representative of the cell wall. The cell walls shown in the figures represent the confinement used during simulations. To see this figure in color, go online.

For a quantitative comparison of relative organization of WT and $\Delta$HU chromosomes, we analyzed their individual axial density profiles (Fig. 5 a). The linear densities have been calculated upon scaling them with respect to the cell’s long axis to make the linear densities from different cell lengths comparable. The chromosome localization into separate cell halves can also be seen in Fig. 5 a. In particular, the linear densities indicate that the two chromosomes in the simulated WT cells are properly segregated. The linear densities were used to quantify the extent of segregation by calculating an overlap score between any two chromosomes. The overlap score between two chromosomes is calculated as

$$\text{overlap}\text{score}=0.5\left(Corr\left(d_1,d_2\right)+1\right)\text{,}$$

where $Corr\left(\right)$ is the Pearson correlation function, and $d_1$ and $d_2$ are linear densities of the chromosomes we want to calculate overlaps for. Therefore for complete overlap, the score is 1 while for no overlap, the score is 0.

Figure 5.

(a) Comparison of chromosome linear densities between WT cells and $\Delta$HU cells, both grown at 37°C in LB medium. The full width at half maximum (FWHM) values are reported in the plot legend. (b) Overlap score between the two chromosomes in WT cells calculated from the linear densities shown in (a). (c) Overlap score among the three chromosomes in $\Delta$HU cells calculated from the linear densities shown in (a). (d) Comparison of sizes of each macrodomain between WT cells and $\Delta$HU cells, both grown at 37°C in LB medium. The size has been quantified by calculating DNA content weighted radius of gyration (R_g) for individual macrodomains. Please see supporting methods for further details. (e) The FWHM values obtained from linear densities are denoted in a bar plot for a better comparison. To see this figure in color, go online.

The overlap scores for WT and $\Delta$HU chromosomes are provided in Fig. 5, b and c. The low overlap score in case of the WT chromosomes (as denoted by dark-blue shading along the off-diagonal axis) suggests minimal inter-chromosome overlap or proper chromosome segregation in WT cells. However, from Fig. 5 c, we can see higher chromosome overlap scores (as denoted by light-blue shading along the off-diagonal axis in Fig. 5 c) in the case of adjacent chromosomes in $\Delta$HU cells. Furthermore, we also calculated the size (see materials and methods for metric of size) of each macrodomain and individual chromosomes for both WT and $\Delta$HU cells, as shown in Fig. 5 d and Table S2. The size of each macrodomain, except Ori, is found to increase in $\Delta$HU, indicating that the HU-devoid chromosomes would have larger macrodomain sizes. To show that simulations properly recapture the experimental observation that in $\Delta$HU cells nucleoid “compaction” was observed, we measure the FWHM of the linear density profiles of individual nucleoids in both WT and $\Delta$HU (Fig. 5 e). From the FWHM values, we find that the average width of the chromosome’s axial density is lower in $\Delta$HU (average FWHM = 0.31) than that in WT cells (average FWHM = 0.43), indicating relative compaction along the scaled cell long axis, without any condensation of the chromosome. Together, the larger extent of overlap, as measured in our model, provides evidence in support of the chromosome segregation defects in $\Delta$HU cells, as originally shown from experimental microscopic images (17).

One way to visualize the interaction between loci pairs as a function of their genetic distance (distance based on the position of the bead pair on the genome) is a plot of average contact probability for regions separated by particular genomic distances (P(s)) versus genomic distances of separation(s) (17,53). Comparison of mean contact probability as a function of genomic distance, i.e., P(s) versus s curves (Fig. 6 a) provides a better comparative account of short-range and long-range contacts between WT and $\Delta$HU cells. At genomic separation below 340 kbp, the contact probability in the $\Delta$HU chromosome (blue line in Fig. 6 a) are slightly enhanced than WT chromosome (red line in Fig. 6 a). This causes slight compaction in the chromosomal regions separated by low genomic distances in HU-devoid cells. However, at longer genomic separations, we see a crossover in contact probability, with the long-range contacts in HU-devoid chromosome being weaker than that in WT. The same effect can also be seen from the difference matrix (Fig. 6 b). The red regions in the difference matrix denote enhanced contacts in $\Delta$HU while blue regions denote diminished contacts. It can be seen that regions near the diagonal (genomically close) have their contact probabilities enhanced in $\Delta$HU. Regions farther away from the diagonal are mostly blue, emphasizing the loss of long-range contacts. The prediction of weaker long-range interaction and short-range compaction in $\Delta$HU cells by the present model is consistent with experimental observations (17) where short-range interactions were enhanced and long-range contacts were diminished upon HU removal.

Figure 6.

(a) Comparison of mean contact probability versus genomic distance plots for WT and $\Delta$HU calculated from simulated contact matrices. The dashed vertical line signifies the genomic distance after which the mean contact probabilities for $\Delta$HU become lower than that of WT. (b) Enhanced difference matrix between WT and $\Delta$HU. The enhancement was performed by taking an element-wise square root while preserving the sign of the elements from the original difference matrix. For example, if an element is $-a$, the corresponding value after enhancement would be $-\sqrt{a}$. Macrodomains are demarcated by dashed black lines. To see this figure in color, go online.

Overall, via our model and concurrent analysis of the data from simulations, we have been able to recapture, quantify, and characterize the effect of removal of HU from WT cells. The model indicates that HU removal actually compresses the chromosome at a short length scale while reducing long-range interactions, altogether present in a more filamentous cell. The phenotype for HU removal is similar to that of MukBEF deletion, and it has been proposed that HU and MukBEF cooperate to promote interactions at the mega-basepair level (17). However, we think that the sole effect of such a phenotype is due to misregulation of gene expression because of absence of HU, as has been proposed previously (17). More detailed investigations are, in any case, required to unravel the mechanism of phenotypic similarity between HU and MukBEF deletion and to ascertain whether HU and MukBEF cooperatively promote very-long-range interactions within the chromosome. However, as per the experimentally observed values of contact probabilities, a decrease in the long-range contact probabilities was observed upon deletion of HU (17). Thus there appear to be two conflicting observations made via two different experiments on the same system: 1) microscopy reveals a “compaction” in the nucleoid in $\Delta$HU; 2) Hi-C reveals a decrease in long-range contact probabilities which should have rather expanded the chromosome. This expansion can be observed from the spatial distance versus genomic distance plots for the WT and $\Delta$HU cases (Fig. S5). The expansion is due to the loss in long-range contacts, which causes regions of the chromosome, which are genomically distant, to be not bound closely. Therefore they drift apart, resulting in increased intra-chromosome distances and an expanded chromosome. This is in agreement with the experimental observations whereby for all macrodomains except Ter, a severe loss in contact probabilities was observed after 300 kbp, while in Ter the same loss was observed after 50 kbp. Fig. S5 shows that for almost all genomic distances, spatial distances are higher in $\Delta$HU with respect to WT. We think that this clash of experimental observations occur due to the different cell lengths and chromosome contents present in the WT and $\Delta$ HU cells during the experiments. However, a situation where cell sizes and chromosome contents for both WT and $\Delta$HU are same cannot be realized experimentally. Therefore, we perform in silico control simulations to realize such a situation to observe and characterize the effects of HU deletion.

Confinement and chromosome content controls nucleoid compaction in $\Delta$HU cells

As mentioned earlier, the previous simulations of WT and $\Delta$HU cells had different cell sizes and chromosome contents. Such a situation introduces different extents of confinement and self-crowding effects, which are important factors in governing chromosome organization inside the cell (1,26,54). Therefore, to enforce the same confinement and self-crowding effects in both WT and HU chromosomes, we performed a control simulation on the WT chromosome. In the control simulations we ensured the same cell size and chromosome contents in WT as that of HU, i.e., the WT cell is also filamentous with three chromosomes. We denote the control WT simulations as WT^control. Thus, now the only difference in WT^control and $\Delta$HU simulations is the encoded Hi-C matrix. We encode the Hi-C contacts by converting them into distances using Eq. 14 and by maintaining those distances among different bead pairs via the introduction of harmonic springs among them. The stiffness of the springs was determined by Eq. 8. During insertion of the springs, we made sure not to incorporate springs among the following bead pairs: 1) inter-replication fork beads; 2) replication fork-unreplicated chromosome beads; 3) inter-chromosome beads; 4) wherever the stiffness was lower than ${10}^{-3}$. In Eq. 8, $w$ is a parameter that affects the reproducibility of the encoded contact probability matrix and has been optimized for individual systems. All non-adjacent beads interact via repulsive interactions. A confining potential has also been implemented so as to enclose the chromosomes within a volume which is commensurate with experimentally observed cell sizes. These interactions have been described in detail in our previous articles (42,46). The $w$ value used for WT simulations has been kept the same for WT^control, ensuring the same extent of Hi-C contacts being encoded also in WT^control.

The representative chromosome structures for WT^control and $\Delta$HU are shown in Fig. 7 a. To quantitatively compare the WT^control and $\Delta$HU chromosome organizations, we recalculated the linear densities, overlap scores, and macrodomain sizes. The comparison of linear densities (Fig. 7 b) and FWHM values (Fig. 7 c) between WT^control and $\Delta$HU chromosomes actually suggests that the $\Delta$HU chromosomes seem more expanded than WT^control, contrary to the previous observation involving WT and $\Delta$HU (which suggested otherwise). A comparison of chromosome overlap scores between WT^control and $\Delta$HU (Fig. 7 d) indicates that the chromosome segregation defects are higher in $\Delta$HU with respect to WT^control. We can also see from Fig. 7 e that all macrodomain sizes are drastically larger in HU than in WT^control, further strengthening our observations that with respect to WT^control, in HU chromosome packing is much less dense.

Figure 7.

(a) Representative snapshots for WT^control (top) and $\Delta$HU (bottom) chromosomes. (b) Linear density along the cell long axis for WT^control and $\Delta$HU. (c) FWHM comparison for WT^control and $\Delta$HU. (d) Comparison of overlap scores among chromosomes in WT^control and $\Delta$HU. The upper triangle contains overlap scores are for WT^control, and the lower triangle contains overlap scores for $\Delta$HU. (e) Sizes of macrodomains for WT^control and $\Delta$HU. The cell walls shown in the figures represent the confinement used during simulations. To see this figure in color, go online.

These results highlight the importance of considering the role of cell size and chromosome contents on the E. coli chromosome organization. The control simulations of WT brought forth the latent effect of HU on the chromosome and how its deletion effects the chromosome organization. Removal of HU causes chromosome expansion due to the loss in long-range intra-chromosome contacts. Such losses in contacts are also reflected in the Hi-C contact probability matrix for the HU mutant cells. These observations further enhance the validity of our claims on the role of HU in chromosome organization. Considering the fact that a situation such as that of WT^control is challenging to generate experimentally, this emphasizes the role that carefully crafted computer experiments can play in dissecting the origin of chromosome organization defects in mutant cell.

Exploring insulation of Ter macrodomain MatP

MatP is a crucial protein for cell division and chromosome segregation. It is known to bind specifically to the 23 sites (referred as matS sites) in the Ter macrodomain of the E. coli chromosome (13). Through various experiments, it has been shown that MatP insulates Ter from the rest of the chromosome (55). Currently, two working mechanisms have been proposed for Ter macrodomain insulation by MatP protein, based on structural studies (14,18) and Hi-C experiments (17), the first of which is that the insulation of the Ter macrodomain is orchestrated by forming MatP tetramers and by bridging distant matS sites (14). On the other hand, the second mechanism suggests that the insulation of the Ter macrodomain takes place by excluding MukBEF condensin from the Ter macrodomain. Since MukBEF forms long-range contacts which, as per the second mechanism, are excluded by MatP from Ter, Ter interactions should be limited within itself (17,18). However, recent studies show that the first mechanism, whereby matS-bound MatP dimers tetramerized to bridge distant matS sites, is not possible (15,16). In the following section, we attempt to explore the organization of Ter and the rest of the chromosome upon deletion of MatP. Next, using a few control studies, which cannot be realized in vivo, we show that MatP does not bridge distant matS sites via tetramer formation. These data lend more credence to the current model as well as to the previous experimental observations regarding the mechanism of MatP in Ter organization.

Exploring the effect of MatP deletion at genome scale

The access to Hi-C data (17), chromosome content and cell dimensions as shared by Dr. Lioy (Table 1) for both WT cells and MatP-devoid cells at 30°C in MM prompted us to provide a spatially resolved picture on the effect of MatP removal on chromosome conformation by developing a 5-kbp-resolution polymer-based computer model of $\Delta$MatP and its respective WT E. coli cell grown at 30°C in MM. As per the cell size and the Ori/Ter ratio data shared by Dr. Lioy, we have modeled both the mutant (i.e., $\Delta$MatP) and the WT cells having a single chromosome with one replication fork. Both WT and $\Delta$MatP cells were grown at 30°C in MM. Therefore, we modeled their chromosomes as per the polymer topology in Fig. 1, b and d, respectively.

The Hi-C interaction matrix simulated from the computer models of WT and $\Delta$MatP chromosomes (Figs. 3 d and 8 a) indicate close similarities between experimental and simulated matrices, thereby suggesting proper maintenance of intra-chromosome contact probabilities in the simulations. From the linear densities and FWHM for WT and $\Delta$MatP (Fig. 8 b), it can be seen that the chromosome slightly expands in the long axis of the chromosome upon removal of MatP. This expansion is caused by a slight loss in long-range interactions in $\Delta$MatP. However, such an expansion is not discernible from the structures of the chromosomes from simulations (Fig. 8, c and d). Moreover, very similar chromosome conformations in WT and $\Delta$MatP chromosomes highlight the fact that overall macroscopic chromosome structure remains almost unperturbed even after MatP deletion.

Figure 8.

(a) Comparison of simulated (upper triangle) and experimental (lower triangle) Hi-C contact probability matrices for $\Delta$MatP cells grown at 30°C in MM medium. (b) Chromosome linear density comparison between WT and $\Delta$MatP. (c) Representative chromosome structures from simulation for WT cells. (d) Representative chromosome structures from simulation for $\Delta$MatP cells. (e) Difference matrix between WT and $\Delta$MatP. The green circles highlight the Ter-Right and Ter-Left interactions in the difference matrix. The differences have been enhanced by taking a square root over the magnitudes of each value while keeping their signs intact. (f) Comparison of collision between Ter and Right macrodomains in WT and MatP mutant. (g) Comparison of collision between Ter and Left macrodomains in WT and MatP mutant. The cell walls shown in the figures represent the confinement used during simulations. To see this figure in color, go online.

For exploration of the effect of MatP deletion on a genome level, we calculated the size of each macrodomain in the WT and the mutant (Fig. S6 a). It can be seen that sizes have increased in the mutant for all macrodomains and also for the whole chromosome (Table S2), though only slightly. This suggests that upon MatP deletion, the chromosome has expanded slightly although the contact probability curves (P(s) versus s) (Fig. S6 b) suggests that in terms of contact probabilities, there are negligible changes upon MatP deletion. For a more quantitative characterization of the changes in the contact matrix due to MatP deletion, we calculated the difference matrix between $\Delta$MatP and WT (Fig. 8 d). The difference matrix (Fig. 8 e) carries a signature of an increase in the extent of interactions with neighboring macrodomain with Ter in MatP-devoid chromosome, indicating enhancement in contact probabilities between Right-Ter and Left-Ter macrodomains (highlighted by circles in Fig. 8 d). Interestingly, these enhanced contacts with the neighboring macro domains of the Ter is consistent with previous site-specific recombination assay experiments for MatP mutant (13), where it was observed that upon MatP deletion, Ter collided more with its flanking macrodomains, hinting at probable disruption of Ter insulation by MatP. To ascertain the same in simulations, we calculated the fraction of colliding beads between Ter-Right and Ter-Left macrodomains from the simulated trajectories of WT and $\Delta$MatP chromosomes (see supporting methods for details of calculation of fraction of colliding particles). As plotted in Fig. 8, f and g, we find that the fraction of collisions between Ter and neighboring beads of flanking macrodomain (i.e., Right and Left) has increased in $\Delta$MatP with respect to WT, recapturing the observations in experiments of Mercier et al. (13).

Ter macrodomain shows higher loci mobility in $\Delta$MatP

Fig. 9, a and b show representative conformations of the Ter macrodomain in WT and $\Delta$MatP cells, respectively. We can see that their overall organizations are unaffected. However, higher collision between Ter and its flanking macrodomains in the mutant suggests a disrupted Ter organization. Previous experimental reports have shown that deletion of MatP increases the dynamics of the DNA loci in Ter (13,56). Therefore, we hypothesize that deletion of MatP does not cause a disruption in Ter conformational organization but rather leads to increased Ter mobility. Via fluorescence microscopy, Javer et al. (57) have measured the diffusion of multiple loci scattered throughout the E. coli chromosome. Of those loci, ter2, ter4, and ter6 are of particular interest in the context of loci mobility in the Ter macrodomain and the impact of MatP deletion on them. Thus to quantify the possible effect of MatP deletion on local, temporal mobility and fluctuations of the Ter macrodomain, we calculated the mean square displacement (MSD), given by $MSD\left(\tau \right)=⟨{\left|\overrightarrow{r}\left(t+\tau \right)-\overrightarrow{r}\left(t\right)\right|}^2⟩$ where $⟨\dots \text{.}⟩$ represents time average and $\tau$ is the lag time. We plot the MSD versus lag time for ter2 (Fig. S7), ter4 (Fig. S8), ter6 (Fig. S9), and the matS sites (Fig. 9 c) in WT and $\Delta$MatP cells by making use of a large ensemble of trajectories obtained via Brownian dynamics simulation (see materials and methods, Eq. 11, and Eq. 12 for details of the Brownian dynamics simulations).

Figure 9.

(a) Representative chromosome conformation for Ter in WT cells. (b) Representative chromosome conformation for Ter in $\Delta$MatP cells. (c) MSD versus time plot for matS sites in WT (red) and $\Delta$MatP (purple) cells in log-log scale. (d) Diffusion constants $\left(D\right)$ for matS sites, ter2, ter4, and ter6 loci for short lag time. (e) Diffusion exponents $\left(\alpha \right)$ for matS sites, ter2, ter4, and ter6 loci for short lag time. To see this figure in color, go online.

The MSD versus time plots indicate that all loci belonging to the Ter macrodomain (matS, ter2, ter4, and ter6) diffuse faster upon removal of MatP (Fig. 9 c), hinting at a relatively more flexible Ter macrodomain in the mutant. A power law fitting of the MSD versus time profiles has been performed as per the equation

$$MSD\left(\tau \right)=6D{\tau }^{\alpha }\text{.}$$

The fits provided the diffusion coefficients $\left(D\right)$ and the diffusion exponents $\left(\alpha \right)$ for all these loci. We find that the slower and subdiffusive dynamics of loci in the Ter macrodomain, as predicted in the current simulation, is consistent with the previous coordinate-dependent loci tracking measurements of mobility (57). Intriguingly, we can see from Fig. 9 d that all loci diffuse more in the mutant as signified by the higher $D$ values of the loci in $\Delta$MatP (Tables S3 and S4). Additionally, Fig. 9 e depicts that not only do all Ter loci diffuse with higher $D$ in MatP-devoid chromosome but their diffusive exponents also have changed from being subdiffusive (signified by $\alpha <1$ in WT) to normal diffusion (signified by $\alpha \approx 1$) in the mutant. This shows that upon deletion of MatP, the Ter macrodomain is more mobile. Therefore, we conclude that in the absence of MatP, a more mobile Ter is responsible for the increased collisions between Ter and its flanking macrodomains, which was observed in experiments (13) as well as simulations (Fig. 8 e).

Interpretation of possible mechanism of Ter insulation by MatP

Having characterized the modulation of the insulation of Ter from the rest of the chromosome in WT and $\Delta$MatP cells, we test the existing mechanism underlying the role of MatP in the same. Prior experimental investigations proposed two plausible mechanisms of action of MatP. In the first mechanism, MatP dimers first bind to matS sites. Next the matS-MatP₂ complex tetramerizes to form (matS-MatP₂)₂, i.e., matS-bound tetrameric MatP (14). This would cause distant matS sites to come in close proximity to each other. A schematic of the mechanism described above is presented in Fig. 10 a. To test the validity of this mechanism, we calculated the probability distribution of distances among matS sites (Fig. 10 c), ter2-ter4 loci (100 kbp apart) (Fig. 10 d), and ter2-ter6 loci (350 kbp apart) (Fig. 10 e). In all these distance profiles the red lines represent distances measured for WT while the purple lines represent distances measured for $\Delta$MatP. The distance distributions appear to be very similar for WT and the mutant for all the loci distances. If distant matS sites would have been bridged by MatP, as per the mechanism discussed above, we should have seen significant difference in the distance distributions between WT and $\Delta$MatP.

Figure 10.

(a) Cartoon representation of the mechanism whereby matS-bound dimeric MatP tetramerizes to bring genetically distant matS sites spatially closer, thereby insulating Ter. We label this as mechanism 1. (b) Cartoon representation of the mechanism whereby MatP excludes MukBEF bound to matS sites. Exclusion of MukBEF most likely causes Ter to lose its interaction with Right and Left macrodomains, thereby insulating Ter. We label this as mechanism 2. (c) Distribution of distances among matS sites. (d) Distribution of distances between ter2 and ter4 loci. (e) Distribution of distances between ter2 and ter6 loci. To see this figure in color, go online.

To this extent, as a proof of concept, we carried out a set of control simulations whereby we cross-linked matS sites (those which are not already connected via “Hi-C bonds”) that are genetically separated by at least 100 kbp. The distances among the matS sites that were cross-linked in the control simulations were modeled using Eq. 16:

$$d_{matS}=\sigma +\eta \text{,}$$ (16)

where $\sigma =1$ and $\eta$ is a random number with the bounds (0, $0.1\sigma$). The force constants for these extra cross-links were calculated using Eq. 8. The resulting trajectories derived from these control simulations were processed to calculate the probability distribution of distances among matS sites, ter2-ter4 loci, and ter2-ter6 loci for the control simulations. The simulated distance distributions obtained from this control “cross-linking” simulation are plotted (blue curve) in Fig. 10 c and d and Fig. 10 e to compare them with those obtained from WT and $\Delta$MatP. The control simulations suggest a most probable distance of ≈150 nm among matS sites (see peak in blue plot of Fig. 10 c) had these been ideally cross-linked. Here it is important to briefly discuss the experiments performed by Crozat et al. (15). From their experiments they probed the mode of binding of MatP to DNA in the Ter macrodomain. They found that MatP binds to DNA always in the tetrameric form. MatP can, in practice, bind to both matS motif and non-matS DNA, but the matS-MatP complex is much more stable. However, they observed that MatP-bound matS almost always remained cross-linked with a non-matS DNA. The investigation also argues that the MatP-induced shortening of distances between matS site pairs is only 30 nm, as compared with a 100-nm shortening of those distances if MatP cross-linked distant matS sites. Interestingly in our WT “cross-linking” simulations, where we have actually cross-linked matS sites which are at least 100 kbp apart, the decrease in the distances among matS sites we observe is ≈112 nm, which is in quantitative agreement with the experimental observations (15). This corroboration with already present experimental studies validates our control simulations and provides confidence to compare its results with those of WT and $\Delta$MatP. Upon comparison of the distances for matS sites, ter2-ter4, and ter2-ter6 among control (i.e., the one with cross-linked matS sites), WT, and the mutant, we observe that these loci are mutually more separated in both WT and $\Delta$MatP than the control simulations. Therefore it is evident from these comparisons (Fig. 10, c–e) that the proposed cross-linking mechanism is not correctly predicting the role of MatP in Ter insulation and hence must not be correct.

However, in another mechanism it was observed that insulation of Ter is caused by displacement of MukBEF from matS sites by MatP. MukBEF is a condensin and the only SMC (structural maintenance of chromosomes) present in E. coli (58,59). MukBEF promotes formation of chromosome loops (60), thereby allowing long-rang intra-chromosome interactions. In the absence of MatP ($\Delta$MatP situation), MukBEF can bind to matS (60), allowing Ter to interact with its flanking macrodomains. Signatures of Ter interacting with its flanking macrodomains have been captured via site-specific recombination assay experiments (13) and were also observed in contact probability matrices obtained via chromosome capture techniques (17), and such signatures are also present in our current simulations. In the presence of MatP (WT cells), MukBEF is displaced from matS sites, as MatP has a higher binding affinity toward matS (60) than MukBEF. Removal of MukBEF causes Ter to lose its long-range interactions, thereby insulating it from the rest of the chromosome. A schematic of the second mechanism is presented in Fig. 10 b. This mechanism does not inherently require matS sites to be cross-linked for Ter insulation. On that note, it was also observed by Crozat et al. (15) that MatP does not promote bridging of distant matS sites. On the contrary, it was observed that MatP tetramers bind to one matS and one non-matS DNA. Similar distance distributions of matS sites for WT and $\Delta$MatP along with breaking of Ter insulation suggests that matS bridging is not required for Ter insulation and that removal of MatP does not change much in Ter conformation but rather affects Ter mobility. We think that, as per mechanism 2 (Fig. 10 b), upon mutation by removal of MatP, intra-Ter contacts are lost and contacts between Ter-Right and Ter-Left are introduced. This leads to a net decrease in the number of Ter-Ter contacts. Thus, Ter is now not being very tightly held together with respect to the WT scenario. This results in a more mobile Ter macrodomain, which shows up as higher diffusion constants and exponents of matS sites as well as other Ter loci (Fig. 9, c–e). However, the intricacies of the MatP-mats-MukBEF interactions cannot be understood from the current model owing to its relatively low resolution and also to the fact that the proteins have not been modeled explicitly. Questions pertaining to the details of such interactions need to be probed by more detailed simulations with atom-level resolutions.

Conclusion

The current investigation elucidates the conformational aspects of organization and maintenance of E. coli chromosome as imparted by NAPs HU and MatP. By integrating a polymer-physics-based model with a recently published Hi-C interaction matrix of WT and the NAP-devoid mutants of E. coli, we simulated the structural aspects of E. coli’s chromosome as governed by HU and MatP. For a realistic comparison, we meticulously incorporated experimentally determined cell dimensions and average replication status of the chromosome(s) of WT and different mutants into our model. Close correspondences between experimentally hypothesized notions about E. coli chromosome organization and simulated WT chromosome conformations under two different growth conditions (WT30MM and WT37LB) were established via comparison of Hi-C interaction matrix, which served as a reference for subsequent comparison with NAP-devoid chromosome. The simulated conformational ensembles developed at both growth conditions capture the key hallmark of macrodomain segregation of WT chromosome. Upon deletion of HU, the chromosome appeared to be relatively more compact, with an increase in the short-range interactions but decreased long-range ones. It also shows a higher extent of inter-chromosome overlap, which would translate to segregation defect in HU-devoid chromosome. However, it was not sufficient to explain the reduction in the intra-chromosome contact probabilities in the mutant. A control simulation in such circumstances helped to interpret that the relative change in the cell dimension due to removal of the HU actually contributes significantly toward the overall change in chromosome organization and extent of compaction. Therefore, although the chromosome might appear to have been relatively compact upon HU deletion in the experiments, simulations support that the true role of HU is to promote intra-chromosome interactions leading to a more densely packed chromosome (61). On the other hand, simulation of MatP-devoid cell predicted very marginal expansion of the chromosome as well as for each macrodomain. Individual macrodomain properties remained grossly similar to those of the WT counterpart under the same growth conditions. This suggests a weak effect of MatP on global genomic organization. However, notably the simulation predicted that the interactions and collision frequencies between Ter and its flanking macrodomains (Right and Left) would be considerably enhanced in $\Delta$MatP mutant relative to WT. The simulated trajectories predicted a systematically higher dynamical mobility of key loci in the Ter macrodomain (ter2, ter4, ter6, and matS sites) of $\Delta$MatP chromosome than of WT chromosome. These observations imply that MatP would help the Ter macrodomain to remain insulated from the rest of the chromosome. This provides direct evidence in support of an earlier observation based on Hi-C matrix (17) and site-specific recombination assay experiments for MatP mutant (13). Apart from lending credence to preceding experiments, the simulations were useful in refuting an existing hypothesis underlying the mechanism of MatP’s role in Ter insulation (14). With regard to Ter disorganization due to MatP deletion, our simulation did not observe any significant increase in average distances between distant loci present in the Ter macrodomain (ter2-ter4, ter2-ter6, and matS sites) in $\Delta$MatP mutant compared with that of WT. Via design of control simulations, in which matS sites were kept mutually tethered, we were able to show that the distance distribution among matS sites in such scenarios are significantly different from that in a WT chromosome, thereby predicting that MatP does not insulate the Ter macrodomain via cross-linking matS sites and supporting the experimental observations (15,16,17).

Collectively, going beyond the experimental hypothesis, the spatially resolved models have provided key insights into the role of two individual NAPs. Using our protocol and data on other mutants or even on multiple mutations, one can gain structural and visual insights into the role of such protein in E. coli chromosome organization. The model also provides flexibility for designing situations (e.g., control studies) which cannot be otherwise easily realized via experimental setup. With regard to all the results and the scope of our current work, the current model is limited by the resolution of Hi-C interaction matrices (which is at present 5 kbp). Therefore, multiple binding sites for a NAP, which are only a few basepairs long, can be present in one bead. This leads to the current model being unable to answer questions specific to the role of NAPs in gene regulation or the change in the local structure of the chromosome attributable to the mutations. Nevertheless, we see very good corroboration between experimental and simulation results that highlights the robustness of our model to capture changes in the chromosome organization from Hi-C alone. Lastly, the current work has been largely successful in determining and quantifying the effects of HU or MatP deletion on the overall structure of the chromosome. Future directions would include increasing the resolution of the model further either by using higher-resolution Hi-C data or via an integrative modeling approach where one can include multiple experimental data in a single model.

Data and software availability

Data can be made available upon request. Software used for the current investigations are all free and open source. A list of software used can be found in materials and methods.

Author contributions

A.W., A.G., and J.M. conceived the project; A.W. performed the simulations; A.W., A.G., and P.B. analyzed the data; A.W. and J.M. wrote the manuscript with help from A.G. and P.B.

Editor: Helmut Schiessel.