Recombinant Saccharomyces cerevisiae Altered inheritance of mitochondria protein 5, mitochondrial (AIM5)

What is the fundamental role of AIM5 in Saccharomyces cerevisiae mitochondrial function?

AIM5 belongs to the family of proteins involved in altered inheritance of mitochondria, similar to other AIM proteins such as Aim24. These proteins play critical roles in maintaining mitochondrial functionality, particularly in relation to respiratory complexes and the MICOS (Mitochondrial Contact Site and Cristae Organizing System) complex. In yeast cells, AIM proteins were identified through screens for mutants with altered inheritance of mitochondria patterns, indicating their importance in mitochondrial dynamics and distribution . The specific function of AIM5 involves maintaining the structural integrity of mitochondrial membranes and potentially influencing the organization of respiratory chain components, similar to the documented role of Aim24 in respiratory function maintenance.

How do I verify successful deletion or modification of the AIM5 gene in my yeast strains?

Verification of AIM5 deletion or modification requires a multi-faceted approach to ensure complete characterization. First, perform PCR-based confirmation using primers that flank the targeted region, allowing detection of the expected size change caused by deletion or insertion. Second, conduct Southern blot analysis to confirm genomic integration at the correct locus. Third, verify the absence or modification of protein expression through Western blot analysis using specific antibodies against AIM5. Finally, confirm mitochondrial DNA presence through DAPI staining, as shown in studies with related AIM proteins, to rule out complete mitochondrial genome loss . For recombinant strains, additional verification of the introduced sequence integrity through sequencing is essential to confirm the absence of unwanted mutations.

What growth conditions best differentiate wild-type from AIM5-deficient yeast strains?

The most effective differentiation between wild-type and AIM5-deficient strains is achieved through comparative growth assays on fermentable versus non-fermentable carbon sources. Based on observations with related AIM proteins, AIM5-deficient strains would likely display compromised growth on non-fermentable carbon sources such as lactate or glycerol, which require functional mitochondrial respiration . Standard protocol involves spotting serial dilutions (typically 10-fold) of both wild-type and mutant strains on glucose-containing media (YPD) as a control, alongside glycerol/ethanol-containing media (YPGE) to assess respiratory function. Incubate plates at 30°C and monitor growth at 24-hour intervals for 3-5 days. Significant growth differences on YPGE but not on YPD would indicate respiratory deficiency in the mutant strain, suggesting AIM5's involvement in mitochondrial function. Additionally, temperature sensitivity assays at 37°C may reveal phenotypes not apparent at standard growth temperatures.

How should I design experiments to study the interaction between AIM5 and the MICOS complex components?

Designing experiments to study AIM5-MICOS interactions requires a comprehensive approach incorporating multiple complementary techniques. First, establish a tagging strategy using C-terminal or N-terminal epitope tags (such as HA, Myc, or His tags) that minimally disrupt protein function. Based on experiences with other AIM proteins, note that C-terminal His-tagging of certain MICOS components can produce synthetic effects in AIM deletion backgrounds .

Design co-immunoprecipitation experiments using tagged AIM5 to pull down associated MICOS components, followed by Western blot or mass spectrometry analysis. Perform reciprocal experiments with tagged MICOS components to confirm interactions. Include appropriate controls for non-specific binding and validate with yeast two-hybrid or proximity ligation assays.

For functional studies, create a matrix of single and double deletion strains combining ΔAIM5 with deletions of individual MICOS components. Analyze these strains using Blue native gel electrophoresis to examine the integrity of mitochondrial complexes, as demonstrated in studies with Aim24:

This experimental design allows for the detection of synthetic genetic interactions that may reveal functional relationships between AIM5 and specific MICOS components, similar to what has been observed with Aim24 and components like Mic12 and Mic26 .

What approaches should I use to investigate the effect of AIM5 deletion on mitochondrial membrane lipid composition?

To investigate AIM5's impact on mitochondrial membrane lipid composition, implement a comprehensive lipidomic analysis workflow. Begin with isolation of highly purified mitochondria using differential centrifugation followed by density gradient purification to minimize contamination with other cellular membranes. Extract lipids using a modified Bligh and Dyer method with appropriate internal standards for quantification.

Analyze the extracted lipids using liquid chromatography-mass spectrometry (LC-MS/MS) to characterize the complete lipidome, with particular attention to cardiolipin species, phospholipids, and ergosterol content. Based on findings with Aim24, focus on cardiolipin acyl chain composition, as alterations in this parameter may indicate disturbances in membrane organization and potentially implicate tafazzin (Taz1) function .

Experimental comparisons should include:

• Wild-type vs. ΔAIM5 strains

• ΔAIM5 strains complemented with AIM5

• ΔAIM5 strains in combination with tagged MICOS components

• ΔAIM5/ΔTAZ1 double mutants to investigate potential synergistic effects

The resulting data should be analyzed for statistically significant differences in:

• Total phospholipid content

• Phospholipid class distribution

• Cardiolipin fatty acid composition (chain length and saturation)

• Ergosterol content

This multi-parameter analysis will provide insights into whether AIM5 influences mitochondrial membrane lipid homeostasis, potentially affecting membrane fluidity, curvature, and protein complex assembly.

How can I establish a reliable system for measuring mitochondrial inheritance patterns in AIM5 mutants?

Establishing a reliable system for quantifying mitochondrial inheritance patterns requires a combination of fluorescence microscopy techniques and rigorous analytical methods. Create a strain expressing a mitochondrial matrix-targeted fluorescent protein (such as mito-GFP or mito-RFP) in both wild-type and ΔAIM5 backgrounds. Additionally, incorporate a second fluorescent marker (e.g., Spc42-CFP) to visualize spindle pole bodies and determine cell cycle stage.

For time-lapse analysis, culture cells in glucose-limited media to enhance mitochondrial development and immobilize them on concanavalin A-coated glass-bottom dishes. Perform live-cell imaging using a confocal microscope with appropriate environmental controls, capturing images at 3-5 minute intervals for 2-3 hours.

Analyze mitochondrial inheritance using the following parameters:

• Percentage of buds receiving mitochondria at different bud size intervals

• Velocity of mitochondrial movement into buds

• Quantity of mitochondrial mass transferred to daughter cells

• Distribution pattern of mitochondria between mother and daughter cells post-division

Compile data from at least 100 cell division events across three independent experiments. Statistical analysis should include chi-square tests for categorical data and appropriate parametric or non-parametric tests for continuous variables. This approach will provide quantitative insights into how AIM5 influences mitochondrial inheritance during cell division, with particular attention to whether its deletion results in asymmetric distribution patterns characteristic of altered inheritance of mitochondria mutants.

How does the interplay between AIM5 and cardiolipin affect respiratory complex stability in Saccharomyces cerevisiae?

The relationship between AIM5, cardiolipin, and respiratory complex stability represents a complex area requiring sophisticated experimental approaches. Based on observations with related AIM proteins, AIM5 likely influences cardiolipin metabolism and consequently affects respiratory complex stability . To investigate this relationship, implement a multi-layered experimental strategy.

First, employ Blue native gel electrophoresis to analyze respiratory complex and supercomplex formation in wild-type, ΔAIM5, ΔTAZ1 (tafazzin deletion), and ΔAIM5/ΔTAZ1 double mutant strains. Complement with assays measuring individual complex activities using spectrophotometric methods for complexes I-IV and ATP synthase.

Next, perform comprehensive cardiolipin analysis in these strains, focusing on both total cardiolipin content and acyl chain composition using high-resolution mass spectrometry. The typical pattern observed in AIM protein deficiencies is a shift toward longer and more saturated acyl chains in cardiolipin, as demonstrated with Aim24 :

To establish mechanistic links, conduct in vitro reconstitution experiments using purified respiratory complexes with liposomes containing defined cardiolipin compositions. This approach would determine whether specific cardiolipin species altered in ΔAIM5 mutants directly affect respiratory complex stability and activity.

Finally, perform protein-lipid interaction studies using cardiolipin affinity chromatography or microscale thermophoresis to determine if AIM5 directly interacts with cardiolipin or influences other proteins' interactions with this critical phospholipid. This comprehensive approach will elucidate whether AIM5 impacts respiratory complex stability through direct effects on complex assembly or indirectly through modulation of cardiolipin metabolism.

What methodologies are most effective for resolving contradictory findings regarding AIM5's role in different genetic backgrounds of Saccharomyces cerevisiae?

Resolving contradictory findings regarding AIM5 function across different yeast genetic backgrounds requires a systematic approach that accounts for strain-specific genetic modifiers and environmental conditions. First, establish a panel of at least three different background strains (such as S288C, W303, and SK1) and create isogenic ΔAIM5 mutants in each background using identical deletion constructs . This ensures that phenotypic variations stem from background differences rather than construct design.

Conduct parallel phenotypic analyses across all strains under identical conditions, assessing:

• Growth rates on fermentable and non-fermentable carbon sources

• Mitochondrial morphology and inheritance patterns

• Respiratory complex assembly and activity

• Cardiolipin composition and metabolism

• Gene expression profiles through RNA-seq

For genetic background effects, perform quantitative trait locus (QTL) analysis using crosses between strains showing divergent phenotypes. This approach can identify genetic modifiers that influence AIM5-related functions. Additionally, implement synthetic genetic array (SGA) analysis in different backgrounds to identify strain-specific genetic interactions.

Complementation studies represent a critical aspect of this methodology. Express the AIM5 gene from each background strain in all ΔAIM5 mutant backgrounds to determine if strain-specific AIM5 alleles behave differently. Sequence analysis of these alleles and their regulatory regions may reveal background-specific variations affecting function.

Environmental interaction studies should test multiple conditions for each strain:

• Temperature ranges (18°C, 30°C, 37°C)

• Carbon sources (glucose, galactose, glycerol, lactate)

• Oxidative stress levels (H₂O₂, paraquat)

• Growth phase (log, diauxic shift, stationary)

This comprehensive approach will determine whether contradictory findings stem from genetic background effects, environmental conditions, or interactions between the two. The resulting data matrix will provide a foundation for understanding context-dependent functions of AIM5 across different yeast lineages.

How can I design experiments to distinguish between direct and indirect effects of AIM5 on nuclear-encoded mitochondrial protein expression?

Distinguishing between direct and indirect effects of AIM5 on nuclear-encoded mitochondrial protein expression requires a carefully structured experimental approach combining temporal analysis, genetic manipulation, and biochemical techniques. Begin by establishing an inducible AIM5 depletion system using either a tetracycline-repressible promoter or an auxin-inducible degron system. This allows precise temporal control for tracking primary versus secondary effects.

Conduct time-course experiments collecting samples at frequent intervals (0, 30, 60, 120, 240 minutes, 12 hours, 24 hours) following AIM5 depletion and analyze:

• Transcriptome changes using RNA-seq

• Proteome alterations using quantitative mass spectrometry

• Post-translational modifications through phosphoproteomics

• Changes in mitochondrial membrane potential and respiratory activity

Primary (direct) effects would manifest early in the time course, while secondary (indirect) effects would appear later. Cluster analysis of the temporal data will help categorize genes into immediate-response and delayed-response groups.

Implement chromatin immunoprecipitation sequencing (ChIP-seq) or CUT&RUN with epitope-tagged AIM5 to determine whether it directly associates with nuclear DNA or with transcription factors involved in mitochondrial gene expression. For proteins showing altered expression, analyze their promoter regions for enrichment of specific regulatory elements.

To distinguish between transcriptional effects and post-transcriptional mechanisms, employ reporter constructs containing the promoters of affected genes driving fluorescent protein expression. Compare these with constructs containing both promoters and 3'UTRs to capture potential post-transcriptional regulation.

In parallel, analyze retrograde signaling pathways (Rtg1/3, Hap, and stress-response pathways) by creating double mutants of ΔAIM5 with deletions of key retrograde signaling components. If AIM5 acts indirectly through these pathways, deletion of pathway components should suppress some of the transcriptional changes observed in ΔAIM5 single mutants.

Finally, perform metabolomic analysis to identify altered metabolites that might function as signaling molecules between mitochondria and the nucleus. This integrative approach will establish whether AIM5 directly influences nuclear gene expression or acts indirectly through retrograde signaling pathways activated by mitochondrial dysfunction.

What are the optimal parameters for experimental design when studying AIM5 interactions with the yeast mitochondrial genome?

Designing experiments to study AIM5 interactions with the mitochondrial genome requires optimization of several critical parameters to ensure reliable and reproducible results. Based on established methodologies for studying mitochondrial proteins in S. cerevisiae, implement the following optimized protocol:

For mitochondrial DNA (mtDNA) maintenance studies, utilize a combination of quantitative PCR and Southern blotting to assess mtDNA copy number and integrity. Optimize DNA extraction protocols specifically for mitochondrial DNA using DNase I treatment to remove contaminating nuclear DNA prior to mitochondrial lysis. Select at least three mitochondrial genome loci (representing different regions) and three nuclear loci as controls for qPCR analysis.

For direct interaction studies, optimize crosslinking conditions if employing ChIP approaches for mitochondrial proteins. Use formaldehyde at 1% concentration for 15 minutes at room temperature, followed by quenching with 125 mM glycine. During immunoprecipitation, include additional steps to reduce non-specific binding, such as pre-clearing lysates with protein A/G beads and using BSA as a blocking agent.

When analyzing respiratory function, measure oxygen consumption rates under multiple substrate conditions to distinguish between effects on different complexes of the respiratory chain. Standardize cell numbers and ensure measurements are taken during logarithmic growth phase when mitochondrial function is most active. Include appropriate controls such as antimycin A or CCCP to establish baseline and maximum respiratory capacity.

For genetic analysis experiments, utilize the established VDE-initiated recombination system, which has been effectively employed to study genomic recombination in S. cerevisiae . This system allows for controlled induction of recombination events and precise measurement of crossover and non-crossover outcomes at specific genomic locations. The optimal experimental design would include:

• Integration of VRS (VDE recognition site) at multiple genomic locations

• Inclusion of both wild-type and ΔAIM5 strains

• Analysis of both crossover and non-crossover events

• Quantification using Southern blot analysis following the methodology described in the literature

This optimized experimental design accounts for the specific challenges of studying mitochondrial genome interactions while providing robust controls to distinguish AIM5-specific effects from general perturbations to mitochondrial function.

How should I interpret conflicting results between in vivo and in vitro studies of AIM5 function?

Interpreting conflicting results between in vivo and in vitro studies of AIM5 function requires a systematic analytical framework considering multiple factors that might contribute to these discrepancies. First, evaluate methodological differences that could explain the conflicting results. Consider the complexity of the cellular environment versus purified systems, differences in protein concentrations, and the absence of spatial organization in vitro. Additionally, document differences in experimental conditions including pH, salt concentration, temperature, and redox state.

Conduct systematic bridging experiments to reconcile conflicting results. For example, if purified AIM5 shows different activities in vitro than observed in vivo, perform cellular fractionation studies to create increasingly complex in vitro systems. Start with purified AIM5, then add purified mitochondrial membranes, then use crude mitochondrial extracts, and finally utilize semi-permeabilized cells. This step-wise approach can identify which cellular components are needed for native AIM5 function.

Examine post-translational modifications that may be present in vivo but absent in vitro. Analyze AIM5 using mass spectrometry to identify phosphorylation, acetylation, SUMOylation, or other modifications. Create phosphomimetic mutants to test whether specific modifications reconcile in vitro results with in vivo observations.

Consider protein interaction partners that may be absent in vitro. Perform co-immunoprecipitation studies to identify AIM5-interacting proteins in vivo, then test whether adding these partners to in vitro assays alters AIM5 activity. This approach has proven valuable in studies of other mitochondrial proteins where complex formation is essential for function.

Finally, analyze the time scales of the experiments. In vitro studies typically measure immediate biochemical activities, while in vivo studies often capture steady-state outcomes after regulatory feedback loops have engaged. Time-course experiments in both settings can help determine whether apparent contradictions reflect true functional differences or simply different temporal snapshots of AIM5 activity.

Presenting the data in a comparison table can help identify patterns in the discrepancies:

This comprehensive approach acknowledges that both in vitro and in vivo systems have limitations and strengths, and that reconciling conflicting results often leads to deeper mechanistic insights.

What statistical approaches should be used to analyze the effects of AIM5 mutations on mitochondrial membrane potential and respiratory chain activity?

Analyzing the effects of AIM5 mutations on mitochondrial membrane potential and respiratory chain activity requires robust statistical methods appropriate for the complexity and variability of these measurements. Implement a multi-layered statistical approach that addresses biological variability, technical replication, and appropriate hypothesis testing.

For experimental design, utilize a minimum of three biological replicates (independent cultures) with at least three technical replicates per biological sample. This nested design allows for partitioning variance between biological and technical sources. When comparing multiple AIM5 mutations, implement a randomized block design to control for day-to-day variations in measurement conditions.

For membrane potential measurements using fluorescent dyes (such as JC-1, TMRM, or Rhodamine 123), collect data at the single-cell level using flow cytometry or quantitative microscopy. This generates distribution data rather than simple means. Apply the following statistical approaches:

• For normally distributed data: Use mixed-effects ANOVA with mutation type as a fixed effect and biological replicate as a random effect. Follow with appropriate post-hoc tests (Tukey's HSD) corrected for multiple comparisons.

• For non-normally distributed data: Apply non-parametric alternatives such as Kruskal-Wallis tests followed by Dunn's test with Benjamini-Hochberg correction for multiple comparisons.

For respiratory chain activity measured via oxygen consumption, enzyme activities, or Blue native gel band intensities, implement regression analysis to examine dose-response relationships:

$y = \beta_0 + \beta_1x_1 + \beta_2x_2 + ... + \beta_nx_n + \epsilon$

Where y represents the measured activity, x variables represent experimental factors (mutation status, substrate concentration, etc.), and β coefficients quantify the effect sizes.

For complex datasets involving multiple mutations and conditions, employ multivariate approaches:

• Principal Component Analysis (PCA) to identify patterns of covariation across measurements

• Hierarchical clustering to identify mutations with similar phenotypic profiles

• Partial Least Squares Discriminant Analysis (PLS-DA) to identify variables that best separate mutation groups

Power analysis is critical for determining appropriate sample sizes. Based on preliminary data, calculate the sample size needed to detect a biologically meaningful effect (typically 20-30% change in respiratory activity) with 80% power at α = 0.05. This typically requires 6-8 biological replicates for measurements with moderate variability (CV ≈ 15-20%).

Finally, implement bootstrap or permutation tests when comparing complex distributions between wild-type and mutant strains, as these methods make fewer assumptions about the underlying data distribution and can provide more robust p-values for challenging biological datasets.

How can I differentiate between primary defects in AIM5 function and secondary responses in mitochondrial gene expression patterns?

Differentiating between primary defects in AIM5 function and secondary responses in mitochondrial gene expression requires a multi-faceted analytical approach combining temporal studies, conditional expression systems, and comprehensive data analysis. Implement the following integrated strategy:

First, utilize a tightly controlled inducible expression system for AIM5, such as the tetracycline-repressible promoter system. This allows for precise temporal control over AIM5 depletion. Conduct high-resolution time-course experiments sampling at multiple timepoints (15, 30, 60, 120, 240 minutes, 8, 16, and 24 hours) following AIM5 repression. At each timepoint, perform parallel RNA-seq and proteomics analysis to track changes in both transcriptome and proteome.

Primary effects of AIM5 deficiency will manifest early in the time course and should display consistent directionality across the time series. Secondary effects typically appear later and often show transient or oscillatory patterns as cellular compensation mechanisms engage. Apply time-series clustering algorithms such as STEM (Short Time-series Expression Miner) or WGCNA (Weighted Gene Correlation Network Analysis) to categorize genes into temporal response patterns.

Create a gene regulatory network model using algorithms such as ARACNE or CLR (Context Likelihood of Relatedness) to identify the most likely direct targets of AIM5. Validate these predictions using chromatin immunoprecipitation (if AIM5 has DNA-binding properties) or RNA immunoprecipitation (if it affects RNA stability).

To distinguish between transcriptional and post-transcriptional effects, compare mRNA levels with corresponding protein levels at each timepoint. Calculate protein-to-mRNA ratios to identify genes where post-transcriptional regulation predominates. For genes showing discordant mRNA and protein patterns, investigate potential mechanisms such as altered translation efficiency or protein stability.

Finally, compare the AIM5 depletion signature with known stress response signatures in yeast, including the retrograde response, unfolded protein response, and oxidative stress response. Genes appearing in these canonical pathways after AIM5 depletion likely represent secondary adaptive responses rather than direct AIM5 targets.

Present your findings in a comprehensive temporal heat map showing gene expression changes over time, clustered by response pattern. This visualization approach efficiently communicates the distinction between immediate primary effects and delayed secondary responses in your system.

What analytical frameworks best resolve the complex data from experiments examining AIM5's role in respiratory complex assembly?

Resolving complex data from respiratory complex assembly experiments requires sophisticated analytical frameworks that integrate multiple data types and account for the hierarchical nature of complex assembly. Implement a multi-tiered analytical approach combining structural biology principles with systems biology methods.

Begin with a component-level analysis examining individual subunits of respiratory complexes using quantitative proteomics data. Calculate stoichiometric ratios between subunits within each complex and identify imbalances that may indicate assembly defects. Compare these ratios between wild-type and ΔAIM5 strains to identify specific steps in the assembly process affected by AIM5.

For Blue native gel electrophoresis data, implement densitometric analysis with curve deconvolution to resolve overlapping complex bands. Quantify the proportion of fully assembled complexes versus assembly intermediates in wild-type and mutant strains. For complex density data, present results as normalized ratios:

Next, apply dimension reduction techniques such as Principal Component Analysis (PCA) or t-SNE to identify patterns in the multivariate dataset comprising multiple complex measurements. This approach can reveal whether AIM5 affects all complexes similarly or has specific effects on particular assemblies.

For time-resolved assembly experiments using pulse-chase labeling, implement kinetic modeling to determine rate constants for each assembly step. Compare these kinetic parameters between wild-type and mutant strains to identify the specific assembly transitions affected by AIM5. Present these data as kinetic curves with fitted rate constants.

Integrate structural information about respiratory complexes using constraint-based modeling approaches. Map quantitative data onto known structural models of respiratory complexes to visualize which structural regions are most affected by AIM5 deletion. This approach can distinguish between effects on core structural subunits versus peripheral or regulatory components.

Finally, implement Bayesian network analysis to infer causal relationships between AIM5 activity, membrane lipid composition, and respiratory complex assembly. This probabilistic approach can distinguish direct effects from indirect consequences and identify the most likely mechanisms by which AIM5 influences complex assembly.

This multi-layered analytical framework transforms complex experimental data into mechanistic insights about AIM5's specific role in respiratory complex assembly, providing a foundation for targeted follow-up studies.

How should I reconcile contradictory findings about AIM5's interaction with the MICOS complex across different experimental approaches?

Reconciling contradictory findings regarding AIM5's interaction with the MICOS complex requires a systematic meta-analytical approach that considers methodological variations, experimental conditions, and biological context. Implement the following structured reconciliation framework:

First, create a comprehensive inventory of all experimental approaches used to study AIM5-MICOS interactions, including co-immunoprecipitation, proximity labeling, genetic interaction screening, and functional assays. For each method, document critical parameters such as detergent type and concentration, salt conditions, pH, temperature, and whether crosslinking was employed. These factors significantly influence the detection of transient or weak interactions typical of membrane protein complexes.

Next, perform weighted analysis of evidence based on methodological strengths and limitations. Assign higher weight to methods that preserve native conditions (e.g., in vivo crosslinking followed by mass spectrometry) compared to those requiring extensive purification. Create a contingency table categorizing positive and negative interaction findings by method type:

Implement reciprocal testing strategies to resolve contradictions. If AIM5 fails to pull down MICOS components but MICOS components pull down AIM5, this suggests asymmetric accessibility of epitope tags or conformation-dependent interactions. Test multiple tagging configurations and both N-terminal and C-terminal tags to resolve such discrepancies.

Consider dynamic and condition-dependent interactions. Test AIM5-MICOS interactions under various physiological states such as fermentation versus respiration, different growth phases, and stress conditions. Interactions may be transient or occurring only under specific metabolic conditions, explaining apparently contradictory findings.

Examine domain-specific interactions through truncation or point mutation analysis. Create a panel of AIM5 constructs with systematic deletions or mutations and test each for MICOS interaction. This approach can identify specific interaction domains and explain why some experimental approaches detect interactions while others do not.

Finally, implement Bayesian probability updating to synthesize evidence across studies. Start with a prior probability of interaction based on computational predictions, then systematically update this probability with each experimental result, weighted by methodological strength. This approach provides a quantitative measure of confidence in the interaction despite contradictory individual findings.

Present the reconciled model as a context-dependent interaction map showing conditions under which AIM5-MICOS interactions occur and the strength of evidence supporting each interaction. This nuanced presentation acknowledges the complexity of protein interactions in membrane environments and provides a framework for designing definitive experiments to resolve remaining contradictions.