Measurement of in-vivo chromosome conformations (structures) in single cells is a major technolog... more Measurement of in-vivo chromosome conformations (structures) in single cells is a major technological goal of structural biology. If one could identify many genetic loci in a microscope image despite the limited palette of fluorescent colors used to label them, then the conformation could be solved at some resolution by 'connecting the dots'. Computational tools for making this reconstruction are expected to produce near-perfect reconstructions when the number of fluorescent colors is high enough, irrespective of the number of loci assayed. Here we report the first experimental test of the performance of these reconstruction algorithms and check their ability to reconstruct experimentally-measured conformations. We also demonstrate the experimental metrics needed to assess reconstruction quality. Our results indicate that current sequential FISH experiments may be close to the point where the reconstructions are nearly flawless at some distance scales.
Certain biological processes, such as the development of cancer and immune activation, can be con... more Certain biological processes, such as the development of cancer and immune activation, can be controlled by rare cellular events that are difficult to capture computationally through simulations of individual cells. Information about such rare events can be gleaned from an attractor analysis, for which a variety of methods exist (in particular for Boolean models). However, explicitly simulating a defined mixed population of cells in a way that tracks even the rarest subpopulations remains an open challenge. Here we show that when cellular states are described using a Boolean network model, one can exactly simulate the dynamics of non-interacting, highly heterogeneous populations directly, without having to model the various subpopulations. This strategy captures even the rarest outcomes of the model with no sampling error. Our method can incorporate heterogeneity in both cell state and, by augmenting the model, the underlying rules of the network as well (e.g., introducing loss-of-f...
We previously published a method that infers chromosome conformation from images of fluorescently... more We previously published a method that infers chromosome conformation from images of fluorescently-tagged genomic loci, for the case when there are many loci labeled with each distinguishable color. Here we build on our previous work and improve the reconstruction algorithm to address previous limitations. We show that these improvements 1) increase the reconstruction accuracy and 2) allow the method to be used on large-scale problems involving several hundred labeled loci. Simulations indicate that full-chromosome reconstructions at 1/2 Mb resolution are possible using existing labeling and imaging technologies. The updated reconstruction code and the script files used for this paper are available at: https://github.com/heltilda/align3d.
The ability to directly observe the molecular motion of single molecules in real-time provides in... more The ability to directly observe the molecular motion of single molecules in real-time provides insights that are not feasible with bulk assays. To date, the highest-precision single-molecule measurements have been obtained using optical tweezers, which can measure motor protein procession with ~300 pm spatial resolution and time scales of ~1 ms (refs. 1,2). Here we present single-molecule picometer-resolution nanop-ore tweezers (SPRNT), a method for monitoring the motion of DNA and conformational changes of processive nucleic-acid-binding proteins as the nucleic acid passes through a nanopore. SPRNT detects nucleic acid motion relative to the enzyme that processes it with a precision of ~40 pm on timescales shorter than a millisecond. We use SPRNT to observe two distinct substates in the ATP hydrolysis cycle of a helicase. SPRNT draws upon the concept of nanopore DNA sequencing 3. In nanopore sequencing, a nanometer-sized pore is formed between two chambers filled with an ionic solution (Fig. 1a and Supplementary Fig. 1). Upon application of an electrostatic field, an ion current flows through the pore and draws single-stranded DNA (ssDNA) into the pore. The presence of DNA nucleotides in the pore's constriction modulates the ion current. A motor enzyme is used to move the ssDNA through the pore at speeds of 1–100 nt/s, thereby enabling the ion current to be correlated with the DNA sequence 4,5. Here we use a mutated Mycobacterium smegmatis porin A (MspA) 6 , which has a short, narrow constriction capable of resolving individual DNA nucleotides (Fig. 1b) 4,7. We find that the exquisite base sensitivity of MspA allows for precise measurement of the position of the DNA inside the pore and thereby enables study of the motion of DNA through proces-sive enzymes. Such measurements can be used to infer conformational Techniques for measuring the motion of single motor proteins, such as FRET and optical tweezers, are limited to a resolution of ~300 pm. We use ion current modulation through the protein nanopore MspA to observe translocation of helicase Hel308 on DNA with up to ~40 pm sensitivity. This approach should be applicable to any protein that translocates on DNA or RNA, including helicases, polymerases, recombinases and DNA repair enzymes. changes of enzymes and kinetic stepping parameters. Figure 1c shows raw ion current data. Each current level represents a single-nucleotide (nt) step of the motor enzyme phi29 DNA polymerase (DNAP) along the DNA strand and the current magnitude corresponds to the sequence of the DNA passing through the pore's constriction (Fig. 1d) 4,7. Each level can be resolved with submillisecond accuracy and pico-ampere (pA) precision (Supplementary Fig. 2). For some sequence contexts there is a large change in ion current when the DNA moves by 1 nt. For example, the ion current levels associated with a sequence of DNA containing an abasic site (marked by an " X ") has a change in current equal to ~16 pA when the DNA moved by 1 nt (Fig. 1e). If the DNA were to move within MspA by a distance of about one tenth of a nucleotide, a linear interpolation would have the observed current change by about one tenth of the change in current, or ~1.6 pA. Coupling the ion-current to the DNA position allows us to measure the position of DNA in MspA to precision much smaller than 1 nt. The scales in Figure 1e, which show the conversion of current to displacement, use a cubic spline to approximate the ion current between levels measured at 1 nt intervals. Using this distance scale, we relate the uncertainty of ion current levels to the uncertainty of the DNA position in the pore. For the ion current levels depicted in Figure 1e a position uncertainty as small as 0.06 nt can be resolved, corresponding to a distance uncertainty of ~40 pm. We assume an inter-phosphate distance of 690 pm (refs. 8,9) and 88–95% DNA-elongation. Next, we changed the elongation of DNA by altering the electrostatic force applied to the DNA. While DNA was moved by phi29 DNAP in single-nucleotide steps, we applied driving potentials of 140 mV and 180 mV. Changing the voltage (and thereby the force on the DNA) alters the elongation of DNA between the motor enzyme and pore constriction and shifts the position of nucleotides within MspA's constriction (Fig. 1f). Figure 1g displays the levels for data taken at the two voltages with cubic spline interpolants overlaid. The location of the splines' peaks shift between the different voltages. After normalizing the current amplitudes, we find that the spline for levels taken at 180 mV can predict the levels at 140 mV, when the spline is shifted 0.29 ± 0.03 nt (Fig. 1h). Exploring DNA elongation with voltages between 100 mV and 200 mV indicated that the DNA elongation was consistent with experimental force-stretching curves for ssDNA 8,9 for forces in the range ~20–40 pN (Supplementary Fig. 3 and Supplementary Discussion 1). These results show that the spline is a reasonable prediction of currents between levels seen at 1 nt intervals. We evaluated the precision of SPRNT using Hel308 of Thermococcus gammatolerans EJ3 (hereafter Hel308), which is an ATP-dependent Ski2-like superfamily II (SF2) helicase/translocase that unwinds duplex DNA in the 3′ to 5′ direction. Hel308 is conserved in many archaea and eukaryotes, including humans 10. With a known crystal structure, Hel308 is a good system for understanding processive SF2 helicases 11. The current patterns we observed were qualitatively similar to those observed with phi29 DNAP (Fig. 2a,b). However, when Hel308 moved
Measurement of in-vivo chromosome conformations (structures) in single cells is a major technolog... more Measurement of in-vivo chromosome conformations (structures) in single cells is a major technological goal of structural biology. If one could identify many genetic loci in a microscope image despite the limited palette of fluorescent colors used to label them, then the conformation could be solved at some resolution by 'connecting the dots'. Computational tools for making this reconstruction are expected to produce near-perfect reconstructions when the number of fluorescent colors is high enough, irrespective of the number of loci assayed. Here we report the first experimental test of the performance of these reconstruction algorithms and check their ability to reconstruct experimentally-measured conformations. We also demonstrate the experimental metrics needed to assess reconstruction quality. Our results indicate that current sequential FISH experiments may be close to the point where the reconstructions are nearly flawless at some distance scales.
Certain biological processes, such as the development of cancer and immune activation, can be con... more Certain biological processes, such as the development of cancer and immune activation, can be controlled by rare cellular events that are difficult to capture computationally through simulations of individual cells. Information about such rare events can be gleaned from an attractor analysis, for which a variety of methods exist (in particular for Boolean models). However, explicitly simulating a defined mixed population of cells in a way that tracks even the rarest subpopulations remains an open challenge. Here we show that when cellular states are described using a Boolean network model, one can exactly simulate the dynamics of non-interacting, highly heterogeneous populations directly, without having to model the various subpopulations. This strategy captures even the rarest outcomes of the model with no sampling error. Our method can incorporate heterogeneity in both cell state and, by augmenting the model, the underlying rules of the network as well (e.g., introducing loss-of-f...
We previously published a method that infers chromosome conformation from images of fluorescently... more We previously published a method that infers chromosome conformation from images of fluorescently-tagged genomic loci, for the case when there are many loci labeled with each distinguishable color. Here we build on our previous work and improve the reconstruction algorithm to address previous limitations. We show that these improvements 1) increase the reconstruction accuracy and 2) allow the method to be used on large-scale problems involving several hundred labeled loci. Simulations indicate that full-chromosome reconstructions at 1/2 Mb resolution are possible using existing labeling and imaging technologies. The updated reconstruction code and the script files used for this paper are available at: https://github.com/heltilda/align3d.
The ability to directly observe the molecular motion of single molecules in real-time provides in... more The ability to directly observe the molecular motion of single molecules in real-time provides insights that are not feasible with bulk assays. To date, the highest-precision single-molecule measurements have been obtained using optical tweezers, which can measure motor protein procession with ~300 pm spatial resolution and time scales of ~1 ms (refs. 1,2). Here we present single-molecule picometer-resolution nanop-ore tweezers (SPRNT), a method for monitoring the motion of DNA and conformational changes of processive nucleic-acid-binding proteins as the nucleic acid passes through a nanopore. SPRNT detects nucleic acid motion relative to the enzyme that processes it with a precision of ~40 pm on timescales shorter than a millisecond. We use SPRNT to observe two distinct substates in the ATP hydrolysis cycle of a helicase. SPRNT draws upon the concept of nanopore DNA sequencing 3. In nanopore sequencing, a nanometer-sized pore is formed between two chambers filled with an ionic solution (Fig. 1a and Supplementary Fig. 1). Upon application of an electrostatic field, an ion current flows through the pore and draws single-stranded DNA (ssDNA) into the pore. The presence of DNA nucleotides in the pore's constriction modulates the ion current. A motor enzyme is used to move the ssDNA through the pore at speeds of 1–100 nt/s, thereby enabling the ion current to be correlated with the DNA sequence 4,5. Here we use a mutated Mycobacterium smegmatis porin A (MspA) 6 , which has a short, narrow constriction capable of resolving individual DNA nucleotides (Fig. 1b) 4,7. We find that the exquisite base sensitivity of MspA allows for precise measurement of the position of the DNA inside the pore and thereby enables study of the motion of DNA through proces-sive enzymes. Such measurements can be used to infer conformational Techniques for measuring the motion of single motor proteins, such as FRET and optical tweezers, are limited to a resolution of ~300 pm. We use ion current modulation through the protein nanopore MspA to observe translocation of helicase Hel308 on DNA with up to ~40 pm sensitivity. This approach should be applicable to any protein that translocates on DNA or RNA, including helicases, polymerases, recombinases and DNA repair enzymes. changes of enzymes and kinetic stepping parameters. Figure 1c shows raw ion current data. Each current level represents a single-nucleotide (nt) step of the motor enzyme phi29 DNA polymerase (DNAP) along the DNA strand and the current magnitude corresponds to the sequence of the DNA passing through the pore's constriction (Fig. 1d) 4,7. Each level can be resolved with submillisecond accuracy and pico-ampere (pA) precision (Supplementary Fig. 2). For some sequence contexts there is a large change in ion current when the DNA moves by 1 nt. For example, the ion current levels associated with a sequence of DNA containing an abasic site (marked by an " X ") has a change in current equal to ~16 pA when the DNA moved by 1 nt (Fig. 1e). If the DNA were to move within MspA by a distance of about one tenth of a nucleotide, a linear interpolation would have the observed current change by about one tenth of the change in current, or ~1.6 pA. Coupling the ion-current to the DNA position allows us to measure the position of DNA in MspA to precision much smaller than 1 nt. The scales in Figure 1e, which show the conversion of current to displacement, use a cubic spline to approximate the ion current between levels measured at 1 nt intervals. Using this distance scale, we relate the uncertainty of ion current levels to the uncertainty of the DNA position in the pore. For the ion current levels depicted in Figure 1e a position uncertainty as small as 0.06 nt can be resolved, corresponding to a distance uncertainty of ~40 pm. We assume an inter-phosphate distance of 690 pm (refs. 8,9) and 88–95% DNA-elongation. Next, we changed the elongation of DNA by altering the electrostatic force applied to the DNA. While DNA was moved by phi29 DNAP in single-nucleotide steps, we applied driving potentials of 140 mV and 180 mV. Changing the voltage (and thereby the force on the DNA) alters the elongation of DNA between the motor enzyme and pore constriction and shifts the position of nucleotides within MspA's constriction (Fig. 1f). Figure 1g displays the levels for data taken at the two voltages with cubic spline interpolants overlaid. The location of the splines' peaks shift between the different voltages. After normalizing the current amplitudes, we find that the spline for levels taken at 180 mV can predict the levels at 140 mV, when the spline is shifted 0.29 ± 0.03 nt (Fig. 1h). Exploring DNA elongation with voltages between 100 mV and 200 mV indicated that the DNA elongation was consistent with experimental force-stretching curves for ssDNA 8,9 for forces in the range ~20–40 pN (Supplementary Fig. 3 and Supplementary Discussion 1). These results show that the spline is a reasonable prediction of currents between levels seen at 1 nt intervals. We evaluated the precision of SPRNT using Hel308 of Thermococcus gammatolerans EJ3 (hereafter Hel308), which is an ATP-dependent Ski2-like superfamily II (SF2) helicase/translocase that unwinds duplex DNA in the 3′ to 5′ direction. Hel308 is conserved in many archaea and eukaryotes, including humans 10. With a known crystal structure, Hel308 is a good system for understanding processive SF2 helicases 11. The current patterns we observed were qualitatively similar to those observed with phi29 DNAP (Fig. 2a,b). However, when Hel308 moved
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