their implications in antibody production and emergent patterning

Introduction

Overview

Proteins such as mechanosensitive channels [9] or proteins in the electron transport chain [10] couple two different regions separated by the lipid bilayer by sitting on the membrane and directing the flow of molecules into or out of the cell, thus benefiting or driving chemical gradients. After showing our findings on the sequence-dependent effects of this protein-DNA interaction, I will discuss our results in more detail by relating the data we have collected to the known information about the physical mechanism of the binding and cutting effect, as well as reflect on how our findings give us a better understanding of the unequal frequency of creation of particular combinations of genes that code for antibodies.

Figure 1.1: Examples of proteins with coupling functions. Cells utilize a range of proteins with coupling functions

Antibody production starts with cutting and pasting within

In the case of the human Igκ locus, the 12RSSs (purple) are adjacent to the V gene segments, while the 23RSSs (orange) are adjacent to the J gene segments. Dotted lines indicate a large part of the DNA region where no gene segments are found.

Figure 1.3: Arrangement of antibody-encoding gene segments in the Igκ locus on chromosome 2 in humans

Working as a collective to create organization

The empirical cumulative distribution of measured PC lifetimes (black lines) is shown for representative endogenous sequences (A) as well as for synthetic RSS with single-point changes in the heptamer (B), spacer (C) or nonamer (D). ) region. Concentration profiles of the analytical solution for the initial conditions (A)c(r,0) =c0, (B) c(r > R0,0) = c0 and (C) c(r > R0,0) = c0exp (−r2/ 2λ2) with the steady-state solution and the first non-zero eigenvalue solution (purple line), the first three non-zero eigenvalue solutions (blue), the first five terms (red), and the first twelve terms (green).

Figure 1.8: Comparison of myosin, kinesin, and dynein motors. While myosin motors walk along actin filaments, kinesin and dynein walk along mi-crotubules

Sequence-dependent dynamics of synthetic and endogenous

Abstract

Little quantitative information is known about the contributions of individual RSS positions over the course of the RAG-RSS interaction. We find that some rarely used endogenous gene segments can be directly mapped to poor RAG binding on their adjacent 12RSSs.

Introduction

Despite this comprehensive characterization of the interaction, little is known about how a given RSS sequence affects each step of the RAG-RSS reaction. We discuss the implications of our findings in the context of our understanding of the molecular details of the RAG-RSS reaction.

Figure 2.1: Schematic focusing on the initial steps of V(D)J recom- recom-bination. (A) The RAG complex composed of RAG1 (purple) and RAG2 (green) binds to the 12- and 23RSSs (dark purple and orange triangles, re-spectively) neighboring gene segments (sho

Results

This RSS also had one of the broadest residence time distributions of all synthetic RSSs studied. Endogenous RSSs of Vκgene segments show different efficiencies of PC formation and cleavage.

Figure 2.2: Sample data output of TPM. By tracking the root mean square displacement (RMSD) of the tethered bead position undergoing restrained Brownian motion, we discern when the DNA tether is (A) in the unlooped state, (B) in the PC (looped) state, and

Discussion

In contrast, certain deviations from the consensus nucleotide at the last four positions of the heptamer or in the nonamer reduced the frequency of PC formation. As previously mentioned [14], a YR combination at the 3' end of the spacer in 12RSS is favorable for DNA binding, consistent with our data.

Materials and methods

These fluctuations are likely due to the diffusion of microtubules in the flow cell, as SI Fig. We note that since our advection diffusion (using u for concentration here) is of the form

Grid FRAP patterning reveals a dispersive effect in the bulk

Abstract

We photobleach a network pattern into a network of highly connected fluorescent microtubules to observe the rearrangement of filaments in the bulk of the network as they contract to form an aster. Analysis of fluorescent squares shows that while there is a linear shrinkage of microtubules toward the center of the network, the microtubules that make up the fluorescent squares also exhibit a local dispersive effect.

Introduction

Nevertheless, the use of photobleaching to investigate the movement of the key players in active systems is still sparingly applied in the field and is less common in systems where the filament network contracts to organize over a smaller volume and increase density by orders of magnitude. . In such cases of network compaction, bleaching regions can occur within the bulk of the network.

Figure 3.1: Concept of fluorescence recovery after photobleaching (FRAP). (A) A laser shines on a sample of red fluorescent molecules in order to bleach the molecules within its path, (B) leaving behind a circular pattern within which all of the particles

Results

Over a minute after photobleaching (middle column), the unit cells shrink toward the center of the grid as the photobleached lines appear thinned. Data for unit cells toward the outer edges of the grid are truncated when the cells appear to merge with each other.

Figure 3.2: Photobleaching a grid pattern onto the contracting mi- mi-crotubule network

Discussion

We discuss the implications of the model–observation disagreement in more detail in the Discussion section. A schematic of the assembly process of tethered beads, as explained in the manuscript Materials and Methods, is shown in Fig.

Figure A.1: Tethered bead preparation process. Tethered beads are first assembled by adding anti-digoxigenin from Sigma-Aldrich into the flow cell chamber by gravity flow and left to incubate for at least two hours

Data analysis: Extracting all relevant information from bead

Using the remaining values of the shuffled vector, calculate the reference quantity of interest m(simulation). Rather than reporting a single value, we can determine the probability distribution of the parameter cleave.

Figure A.2: Sample bead trajectories for beads that have passed all filters in one replicate

Posterior distributions of the endogenous sequences

Specifically, we used Hamiltonian Markov chain Monte Carlo as implemented in the probabilistic programming language Stan [8]. The code used to examine this distribution can be accessed on the paper's website or GitHub repository.

The top-to-bottom order of endogenous RSSs is the same as their order from left to right in Fig. A.7A and A.7C show that RAG forms the most frequently paired complex with the reference sequence and the G-to-T change at the eleventh position of the reference spacer sequence when the reaction occurs in Ca2+.

Figure A.6: Posterior distributions of the cutting probabilities as de- de-rived in Section A.2.3 for the endogenous 12RSSs studied

Coding flank contributions

Thus, we compared the C-to-A change at spacer position 1 in the reference sequence to the V4-55 coding arm. Thus, we find that for most endogenous RSSs studied, the coding arm has little effect on the overall RAG-RSS interaction.

Figure A.9: V4-55 12RSS (grey) and C-to-A change at spacer position 1 (blue) comparison of looping frequency, posterior distribution of the cutting probability and ECDFs of PC lifetimes for PCs that cut, those that unloop, and both.

Cloning a different 12RSS in plasmids

B.2(B) shows the normalized mean intensity of the microtubule fluorescence channel, but in the absence of microtubules. eq. B.80 shows that the steady-state concentration profile is a Gaussian distribution with standard deviation λ.

Table A.1: Table of endogenous 12RSS sequences. The 6 base pairs before the heptamer, known as the coding flank, is changed in the endogenous RSS studies and is included here

Endogenous RSS sequences

Synthetic and endogenous 12RSS primer sequences

Protein purification

Nickel-bound HMGB1 is then washed with more binding buffer before washing with buffer containing low imidazole concentration. Washed HMGB1 is then eluted through the column with elution buffer containing higher concentration of imidazole.

Materials and methods

The coverslip is placed on top of the parafilm with pressure applied to flatten the film. The laser performs the photobleaching of the microtubules in a grid pattern by passing through a cylindrical lens array.

Fig. B.1 gives a general idea of the layout of the microscopy components.

Unit cell segmentation and fluorescence preservation in subse-

If the total intensity is less than 99% of the original intensity, we continuously add a single-pixel thick layer around the unit cell until the unit cell eventually falls within 99% of the original intensity. Unit cell centroids, areas, and fluorescence intensities are then calculated over the pixel-weighted center of the entire contracting network after this intensity-adjusted treatment for all the unit cells.

Projector effects on microtubule fluorescence intensity

Imaging of a unit cell ends when it is found to overlap with another unit cell during the fluorescence intensity correction scheme, as this indicates that the unit cells are beginning to merge and will no longer be distinguished at the next time point. Blue shaded region represents one standard deviation in the mean intensity (normalized by the same initial mean value). B) Mean intensity of the same fluorescence channel in the absence of microtubules.

Data analysis

To more carefully calculate the network contraction rate and determine the extent of the credibility of the calculated rate, we use a Bayesian approach. From each (α, v0) sampled, we compute the mean µ=α r+v0 for 0≤r ≤R, where R is the distance of the farthest centroid from the network center and report the median and 95% credible region for kl . each distance r as shown in fig.

Deformation of a square due solely to contraction

In this case, we can compare the area of the square before and after the deformation. Thus we find that the area of the unit cell undergoing only contraction would decrease by (1−α∆t)2 after a time period ∆t.

Figure B.3: Schematic of unit cell contraction due purely to the advec- advec-tive velocity field

Microtubule length extraction

This contrasts with the results we present here, where the area of the fluorescent unit squares remains constant during the contraction process, suggesting a mechanism that microtubules spread against the global contraction. Here we see that for most of the work performed, the MTs had lengths between 1 − 3 µm with a median length between 1.5 − 2 µm.

Motor constructs

Putative MTs are skeletonized after removing objects too close to the edge of the image or too small. As a final step before measuring lengths, we removed any microtubules that appeared to cross.

Measuring motor speeds and their effects on contraction rate

Yet we find that despite the dramatic increase in contraction rate, the area of unit cells remains constant on average. contraction rate of individual unit cells = 0.0016 s 95% credible region. contraction rate of individual unit cells = 0.0014 s 95% credible region. contraction rate of individual unit cells = 0.0072 s 95% credible region. contraction rate of individual unit cells = 0.0065 s 95% credible region. individual unit cells mean pure contractile across unit cells. individual unit cells mean pure contractile across unit cells. individual unit cells mean pure contractile across unit cells. individual unit cells mean pure contractile across unit cells. Top row) Contraction velocity versus radius for unit cell centroids with most likely fit of contraction velocity (red line) and 95% credible region (shaded area) and (bottom row) unit cell area as a function of time for (A) Ncd236 (B) Ncd281, (C) K401 expressed in insect cells, and (D) K401 expressed in bacteria.

Fig. B.6 shows the effects of the different motor speeds on contraction speed as a function of distance from the center of the contracting network and nor-malized area as a function of time

The recovery of a typical FRAP-like disc is time-sensitive in

Again, the analytical solution matches the simulations of the same initial conditions shown in the figure. This makes sense since the steady state function, which is the eigenfunction of the PDE, is orthogonal to the chosen eigenfunction.

Figure B.7: Radial advection-diffusion for various initial conditions.

Sturm-Liouville Theory

We further argue that by the Sturm-Liouville theory all integrals in the summation vanish, except for the case where i = h. To determine the initial conditions of the steady-state coefficient term, we would instead multiply by the weighting function and the steady-state eigenfunction -r.

Figure B.10: Zeros of k for λ 2 2 k 2 1 F 1

Numerically solving advection-diffusion equations with COM-

To do this, we specify the coordinates where we define the minimum and maximum values of x and y based on the center of the pixel-weighted grid, as discussed in Appendix B.2, and the image dimensions. Fortunately, according to the geometry we specify, we will not take any part of the image outside the region of interest.

Gibbs phenomenon in analytical solutions and mesh granular-

For visualization purposes, the appearance of the meshes used for the defined geometry are shown as insets in the upper right corner of the respective subfigures. The concentration profile is from a line trace along the horizontal axis from the origin of the geometry to the boundary.

Figure B.11: Gibbs phenomenon for analytical solutions. Concentration profiles of the analytical solution for the initial conditions (A) c(r, 0) = c 0 , (B) c(r > R 0 , 0) = c 0 , and (C) c(r > R 0 , 0) = c 0 exp(−r 2 /2λ 2 ) with the steady-state s

Parameter sweeping and P´ eclet numbers

B.13 shows the concentration along the x-axis extending from the origin to the boundary at r = 10 µm and as depicted by the purple line in the t = 0 graph in Fig. Conversely, decreasing the diffusion constant which increases the P “Eklet number maintains the oscillatory pattern of the concentration profile as the advection pushes the material toward the origin.