Digital Logic Design

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Digital systems are said to be constructed by using logic gates. The basic operations are described below with the aid of truth tables. It will give a low output if either, but not both , of its two inputs are high. The symbol is an EXOR gate with a small circle on the output.

Digital Logic Design - National University

The small circle represents inversion. Also note that a truth table with 'n' inputs has 2 n rows. You can compare the outputs of different gates. You can check this out using a truth table. There are also multiple input gates if you want to know more about them then click on the link below.

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Here are some tutorials using LabVIEW simulations to show the gate functions and some of the different ways that gates can be configured. A component library of signals defining r 1 —r 20 was used in this work Supplementary Table 1.

The pGRR i,j promoter contains two, 20 base-pair bp target sites that match r i and r j respectively. Because the promoter has relatively low expression levels and we wanted its output to have a strong ON output when not repressed, an upstream activating sequence UAS from the strong pGPD promoter 47 was added, forming the base pGRR promoter. It has been shown that RNA device folding can be insulated from surrounding sequence context through computational sequence selection 51 , As a demonstration of the complex circuits possible with our NOR gates, six two-input, one-output digital logic circuits were built by integrating up to five NOR gate cassettes into various selectable loci in the yeast genome Fig.

The circuits were constructed from the 16 guide sequences of the component library that exhibited the strongest repression Supplementary Fig. The truth table for each gate was experimentally obtained by constructing four separate strains, one for each pair of possible input values, in which the corresponding gRNA input signals were expressed from constitutive promoters Supplementary Table 2.

Fluorescence values were collected using flow cytometry of cells growing in log phase. The histograms represent population fraction from three different biological replicates measured during a single experiment and were normalized so that area sums to unity. Fluorescence population ratios of the circuits are included in the Supplementary Table 3. To distinguish circuit state, value bands for digital ON, OFF and Undefined, fluorescence values were determined with the 16 guide sequences and their cognate pGRR promoters used in circuit construction Supplementary Fig.

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For the state of a circuit to be considered ON or OFF we specified that a majority of cell population fall in the expected fluorescence band. Population fraction tables for all circuits can be found in Supplementary Table 3. Circuits containing different NOR gate variants can exhibit a range of behaviours.

For example, 15 versions of the XOR, from Fig. We hypothesize that circuit performance variations are due to expression differences in the pGRR promoters and repression efficiency variations of the gRNA in the individual NOR gates of the circuit. To test the limits of size and complexity our NOR gate circuits can achieve inverter cascades of depth one through seven were composed with NOT gates Fig.

The cascade of depth D was made by the addition of a NOT gate to repress the input stage of the depth D —1 cascade. As seen previously with the two-input logic circuits, there is considerable variability within the ON and OFF states. As cascade depth increased the fluorescence levels of the OFF states for all of the odd depth cascades increased. Similarly, except for the cascade of depth 6, as cascade depth increased the fluorescence levels of the ON states decreased. This suggests a gradual degradation of circuit function as the number of layers increased.

Similar behaviour was also observed for other repression cascades that were constructed Supplementary Fig. Cascades were created with sequential genomic integrations of NOT gates. Fluorescence measurements were taken using flow cytometry. Fluorescence population ratios of the circuits are included in Supplementary Table 3. A model of the cascade, in which each layer is treated as a Hill function, was used to fit the data.

The plot shows the data from one biological replicate. As the number of layers in the cascade increases, signal degradation and increased time to steady state is observed. The model was used to generate the fits for the steady-state and kinetic inducible cascade experiments. To investigate the temporal characteristics of the inverter cascades, we analysed the kinetics of cascades of depth one through four. With increasing cascade depth, a clear delay in output response was evident, with the cascades reaching half-maximal expression at 4.

The dose response curves of the four cascades were also measured after passaging cells over 5 days Fig. Some signal degradation with successive layers was observed Fig. A kinetic model was constructed to capture the behaviour of our synthetic cascades.

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The model combines successive Hill functions to represent simple transcription and repression associated with each gRNA- dCas9-Mxi1 signal. The parameters v d and k d roughly capture expression and repression strengths of the promoters driving each gRNA- dCas9-Mxi1 signal, r d. The parameter L represents the transcriptional leak as a percentage of the maximal expression of a given gate when maximally repressed parameters n and b capture the cooperativity of repression.

The steady-state dose response and kinetic time course for inducible cascade data were both fit to the model Fig. Due to the different growth conditions of the steady-state and kinetic cascade experiments, two separate model fits were generated for each experiment. To address potential model identifiability issues parameter values were constrained based on published biological values Supplementary Table 4.

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The fitting results were found to correlate well with the experimental data. The reported value of L was calculated as the average of the predicted transcriptional leak from the model fits from Fig. To demonstrate the ability of dCas9-Mxi1 to decrease transcriptional leak compared with steric repression via dCas9 , gRNA dose response curves of repression at three pGRR promoter target site positions were performed using dCas9 and dCas9-Mxi1 Fig. At maximal induction, dCas9-Mxi1 represses the promoter to a lower fluorescence level than dCas9 alone at all three positions.

Repression via steric hindrance showed promoter positional variations in predicted leak parameter values. The observed positional variation is consistent with previous results In all three positions dCas9-Mxi1 was predicted to have the same or lower leak parameter L.

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  • These data indicate that in the context of our NOR gates, dCas9-Mxi1 confers stronger and more consistent repression than dCas9 alone. Alternative plots comparing dCas9 and dCas9-Mxi1 repression as a function of inducible promoter activation driving gRNA are included in Supplementary Fig.

    The temporal responses of the cascades were predicted from simulations using randomly sampled parameters within the range of the model fit. Parameter values for kinetic simulations were resampled from the model fit using the kinetic time course experimental data.

    Linear regression analysis estimated the slope of the increase in response time per layer to be equal to Increasingly layered cascades show a positive linear relationship between circuit time to half-maximal response and circuit depth, with a slope of The first four data points highlighted in purple are experimental data from Fig. The bins highlighted in orange and yellow contain the predicted L values for the steric repression measurements in Fig. To extrapolate the model to predict the effect of leak on signal degradation for deeper cascades, cascades of various lengths were simulated, with increasing values of L , using randomly sampled parameter sets within the range of dose response experimental fits.

    Here dynamic range is defined as the log fold change of the maximal and minimal response of a cascade,. Signal degradation was found to be largely dependent on the transcriptional leak parameter, L Fig. In this range the performance of the cascade is more sensitive to other parameters in the model. In addition, these data show the significance of reducing NOR gate leak when constructing larger circuits.

    We introduced a class of dCas9 -based modular genetic NOR gates that behave digitally, have low variability and show minimal retroactivity or effects on cell growth. These features made these gates relatively easy to combine into Boolean logic circuits that are among the largest ever built in any organism. In particular, we found that most circuits in Figs 3 and 4 required that only a handful of gate combinations be screened to identify a functional design, and others required only one.

    Table 1 compares our technology with selected published circuits. We measured circuit complexity with a combination of two metrics: the number of gates and the number of connections among gates, allowing us to locate circuits in a two-dimensional plot Supplementary Fig. These complexities compare well with gene circuits developed in Escherichia coli , for example.

    Our NOR gates enabled extremely simple design and construction of large gene circuits. Before genetic circuits can be made much larger, however, many factors that influence the size and complexity of synthetic genetic circuits must be addressed. First, the gates in any framework must be well behaved. Gates can suffer from retroactivity, where a downstream gate affects the behaviour of upstream gates to which it is not connected by design 55 , 56 , In this case it is quite difficult to design large circuits even with CAD because we may not know the source of the retroactivity, how to model it or how to design with it.

    In addition, gates can be highly variable, where the outputs levels of one gate do not match the input levels of the next. Electrical engineers call this an impedance mismatch. A recent paper 22 addressed retroactivity by adding insulators to their gates. By meticulously characterizing the performance each gate, and using CAD, they were able to select compatible subsets of parts out of which they constructed circuits as large as those demonstrated here, despite gate variability. Not all of the circuits predicted to work by the CAD tool functioned correctly, possibly due to residual retroactive effects, requiring the circuits to be screened for function.

    Thus, in our case, the design problem is easy enough that extensive part characterization and CAD tools were not necessary at the circuit level even though CAD tools such as standard DNA editors and secondary structure predictors for RNA were used at the sequence level. Second, the host organism presents many unique challenges. Each organism can be thought of as a different computer operating system. Promoters, for example, in E. Transcriptional regulation in eukaryotes is complex, involving a variety of mechanisms including chromatin remodelling 59 , 60 , 61 , 62 , 63 , and understanding it remains a highly active area of research Thus, directly comparing circuit architectures between organisms, as we did between yeast and E.

    Nevertheless, we believe that because CRISPR-dCas9 functions in mammalian cells 20 , 30 , 31 , 32 , 34 , 48 , and the human Mxi1 repression domain has been used in synthetic contexts to regulate transcription in human cells 30 , 39 , 40 , our NOR gates could be ported into mammalian cells, with difficulties of strain engineering likely dominating. Third, the method by which circuits are constructed and the genetic tractability of the host affects progress toward building large circuits.

    For example, the circuits we present here are all singly integrated into the yeast genome, because plasmid-based systems exhibit cell-to-cell variation in copy number. That made the process of building and testing strains slow, costly and cumbersome and in fact limited our ability to build circuits much larger than those shown here. Larger circuits and large libraries of circuit variants will require that we develop, for example, one-pot assembly methods for large DNA constructs Depending on the technology, such assemblies may be more or less difficult to harness.

    The success or failure of different approaches to building bigger circuits may depend on how well behaved, insulated, simple and scalable the input low-level devices and gates are. Yeast transformations were carried out using a standard lithium acetate protocol The cells were then spun down, supernatant was removed and they were resuspended in H 2 O and then plated on selective agar media.

    Matings of the MATa and MATalpha were performed by coculturing both mating types and plating the culture onto selective agar media. All strains and sequences used in this work are detailed in the Supplementary Data 1.