Mendelian randomization study to evaluate the effects of interleukin-6 signaling on four neurodegenerative diseases

Genetically predicted associations between circulating cytokines and autoimmune diseases: a bidirectional two-sample Mendelian randomization

Objectives

Previous studies have indicated a correlation between cytokines and autoimmune diseases. yet the causality remains uncertain. Through Mendelian Randomization (MR) analysis, we aimed to investigate the causal relationships between genetically predicted levels of 91 cytokines and three autoimmune diseases: Multiple Sclerosis (MS), Systemic Lupus Erythematosus (SLE), and Hashimoto's Thyroiditis (HT).

Methods

A bidirectional two-sample MR approach was utilized to assess the causal relationships between cytokines and MS, SLE, and HT. The datasets included 47,429 MS cases and 68,374 controls, 5,201 SLE cases and 9,066 controls, and 16,191 HT cases with 210,612 controls. Data on 91 cytokines comprised 14,824 participants. Causal analyses primarily employed inverse variance weighted, weighted median, and MR-Egger methods, with sensitivity analyses including heterogeneity and pleiotropy assessment.

Results

Genetically predicted levels of IL-18 (OR = 0.706; 95% C.I. 0.538-0.925), ADA (OR = 0.808; 95% C.I. 0.673-0.970), and SCF (OR = 0.898; 95% C.I. 0.816-0.987) were associated with a decreased risk of MS. IL-4 (OR = 1.384; 95% C.I. 1.081-1.771), IL-7 (OR = 1.401; 95% C.I. 1.010-1.943), IL-10RA (OR = 1.266; 95% C.I. 1.004-1.596), CXCL5 (OR = 1.170; 95% C.I. 1.021-1.341), NTN (OR = 1.225; 95% C.I. 1.004-1.496), FGF23 (OR = 0.644; 95% C.I. 0.460-0.902), and MCP4 (OR = 0.665; 95% C.I. 0.476-0.929) were associated with SLE risk. CDCP1 (OR = 1.127; 95% C.I. 1.008-1.261), IL-33 (OR = 0.852; 95% C.I. 0.727-0.999), and TRAIL (OR = 0.884; 95% C.I. 0.799-0.979) were associated with HT risk. Bidirectional MR results suggest the involvement of CCL19, IL-13, SLAM, ARTN, Eotaxin, IL-22RA1, ADA, and MMP10 in the downstream development of these diseases.

Conclusions

Our findings support causal relationships between certain cytokines and the risks of MS, SLE, and HT, identifying potential biomarkers for diagnosis and prevention. Additionally, several cytokines previously unexplored in these autoimmune disease contexts were discovered, laying new groundwork for the study of disease mechanisms and therapeutic potentials.

The Role of Selected Interleukins in the Development and Progression of Multiple Sclerosis-A Systematic Review

Multiple sclerosis is a disabling inflammatory disorder of the central nervous system characterized by demyelination and neurodegeneration. Given that multiple sclerosis remains an incurable disease, the management of MS predominantly focuses on reducing relapses and decelerating the progression of both physical and cognitive decline. The continuous autoimmune process modulated by cytokines seems to be a vital contributing factor to the development and relapse of multiple sclerosis. This review sought to summarize the role of selected interleukins in the pathogenesis and advancement of MS. Patients with MS in the active disease phase seem to exhibit an increased serum level of IL-2, IL-4, IL-6, IL-13, IL-17, IL-21, IL-22 and IL-33 compared to healthy controls and patients in remission, while IL-10 appears to have a beneficial impact in preventing the progression of the disease. Despite being usually associated with proinflammatory activity, several studies have additionally recognized a neuroprotective role of IL-13, IL-22 and IL-33. Moreover, selected gene polymorphisms of IL-2R, IL-4, IL-6, IL-13 and IL-22 were identified as a possible risk factor related to MS development. Treatment strategies of multiple sclerosis that either target or utilize these cytokines seem rather promising, but more comprehensive research is necessary to gain a clearer understanding of how these cytokines precisely affect MS development and progression.

Associations of the circulating levels of cytokines with risk of amyotrophic lateral sclerosis: a Mendelian randomization study

BACKGROUND

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disorder that is accompanied by muscle weakness and muscle atrophy, typically resulting in death within 3-5 years from the disease occurrence. Though the cause of ALS remains unclear, increasing evidence has suggested that inflammation is involved in the pathogenesis of ALS. Thus, we performed two-sample Mendelian randomization (MR) analyses to estimate the associations of circulating levels of cytokines and growth factors with the risk of ALS.

METHODS

Genetic instrumental variables for circulating cytokines and growth factors were identified from a genome-wide association study (GWAS) of 8293 European participants. Summary statistics of ALS were obtained from a GWAS including 20,806 ALS cases and 59,804 controls of European ancestry. We used the inverse-variance weighted (IVW) method as the primary analysis. To test the robustness of our results, we further performed the simple-median method, weighted-median method, MR-Egger regression, and MR pleiotropy residual sum and outlier test. Finally, a reverse MR analysis was performed to assess the possibility of reverse causation between ALS and the cytokines that we identified.

RESULTS

After Bonferroni correction, genetically predicted circulating level of basic fibroblast growth factor (FGF-basic) was suggestively associated with a lower risk of ALS [odds ratio (OR): 0.74, 95% confidence interval (95% CI): 0.60-0.92, P = 0.007]. We also observed suggestive evidence that interferon gamma-induced protein 10 (IP-10) was associated with a 10% higher risk of ALS (OR: 1.10, 95% CI: 1.03-1.17, P = 0.005) in the primary study. The results of sensitivity analyses were consistent.

CONCLUSIONS

Our systematic MR analyses provided suggestive evidence to support causal associations of circulating FGF-basic and IP-10 with the risk of ALS. More studies are warranted to explore how these cytokines may affect the development of ALS.

Mechanisms of Xiong-Pi-Fang in treating coronary heart disease associated with depression: A systematic pharmacology strategy and in vivo pharmacological validation

BACKGROUND

Coronary heart disease (CHD) and depression are very common and often co-existing disorders. Xiong-Pi-Fang (XPF), a therapeutic classical traditional Chinese medicine (TCM) formula, has shown satisfactory efficacy in treating CHD associated with depression. However, its mechanism of action is still unknown.

PURPOSE

To employ a systematic pharmacology approach for identifying the action mechanisms of XPF in treating CHD associated with depression.

METHODS

We used a systematic pharmacology approach to identify the potential active mechanisms of XPF in treating CHD with depression. Potential active compounds in XPF and the diseases targets were screened using relevant databases to build corresponding pathways, following the experiments that were conducted to confirm whether the presumptive results of systemic pharmacology were correct.

RESULTS

Network pharmacology predicted 42 key targets and 20 signaling pathways involved in XPF-mediated treatment, with IL-6/JAK2/STAT3/HIF-1α/VEGF-A pathway significantly affected. The common influences were hypothalamic-pituitary-adrenal axis (HPA axis) and glucocorticoid signaling, validated through chronic unexpected mild stress (CUMS) with isoprenaline (ISO) for inducing CHD within the depression model in rats. In addition, XPF intake reduced depressive-like behaviors and improved ECG ischemic changes. Furthermore, XPF exerted some anti-inflammatory effects by inhibiting the interleukin-6 (IL-6) induced phosphorylation of janus kinase 2 (JAK2) and signal transducer and activator of transcription 3 (STAT3), ultimately downregulating hypoxia-inducible factor 1-α (HIF-1α) and vascular endothelial growth factor-A (VEGF-A) activation. The dysfunctional HPA axis feedback loop was also regulated, which enhanced the glucocorticoid receptor (GR) expression. In contrast, it improved glucocorticoid resistance by reducing the mineralocorticoid receptor expression.

CONCLUSIONS

Suppressing IL-6 release and maintaining the HPA feedback loop balance could be the primary mechanism of XPF against CHD with depression. The significance of the IL-6 and HPA axis identified indicates their potential as essential targets for CHD therapy with depression.

Anti-IL-6 therapies in central nervous system inflammatory demyelinating diseases

Current treatments for central nervous system (CNS) inflammatory demyelinating diseases (IDDs) include corticosteroids, plasma exchange, intravenous immunoglobulin, and immunosuppressant drugs. However, some patients do not respond well to traditional therapies. In recent years, novel drugs, such as monoclonal antibodies, targeting the complement component C5, CD19 on B cells, and the interleukin-6 (IL-6) receptor, have been used for the treatment of patients with refractory CNS IDDs. Among these, tocilizumab and satralizumab, humanized monoclonal antibodies against the IL-6 receptor, have shown beneficial effects in the treatment of this group of diseases. In this review, we summarize current research progress and prospects relating to anti-IL-6 therapies in CNS IDDs.

Association Between C-Reactive Protein and Risk of Amyotrophic Lateral Sclerosis: A Mendelian Randomization Study

Background: Until now, the relationship between C-reactive protein (CRP) levels and amyotrophic lateral sclerosis (ALS) risk has not been fully established. It is necessary to assess whether there is a causal relationship between C-reactive protein levels and ALS risk. Objective and Methods: We aimed to determine whether CRP has causal effects on risk of ALS. In this present study, summary-level data for ALS (20,806 cases and 59,804 controls) was obtained from large analyses of genome-wide association studies. For instrumental variables, 37 single nucleotide polymorphisms that had been previously identified to be related to CRP levels were used, including 4 SNPs of conservative CRP genetic variants and 33 SNPs of liberal CRP genetic variants. MR estimates were calculated using the inverse-variance weighted method, supplemented by MR-Egger, weighted median, and MR-PRESSO methods. Results: There was no significant causal relationship between genetically predicted CRP levels and ALS risk (OR = 1.123, 95% CI = 0.963-1.309, p = 0.139) and results for the conservative CRP instruments were consistent (OR = 0.964, 95% CI = 0.830-1.119, p = 0.628). Pleiotropic bias was not observed in this study. Conclusions: This study suggests that genetically predicted CRP levels may not be a causal risk factor for ALS.

A review of Mendelian randomization in amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis is a relatively common and rapidly progressive neurodegenerative disease that, in the majority of cases, is thought to be determined by a complex gene-environment interaction. Exponential growth in the number of performed genome-wide association studies combined with the advent of Mendelian randomization is opening significant new opportunities to identify environmental exposures that increase or decrease the risk of amyotrophic lateral sclerosis. Each of these discoveries has the potential to shape new therapeutic interventions. However, to do so, rigorous methodological standards must be applied in the performance of Mendelian randomization. We have reviewed Mendelian randomization studies performed in amyotrophic lateral sclerosis to date. We identified 20 Mendelian randomization studies, including evaluation of physical exercise, adiposity, cognitive performance, immune function, blood lipids, sleep behaviours, educational attainment, alcohol consumption, smoking and type 2 diabetes mellitus. We have evaluated each study using gold standard methodology supported by the Mendelian randomization literature and the STROBE-Mendelian randomization checklist. Where discrepancies exist between Mendelian randomization studies, we suggest the underlying reasons. A number of studies conclude that there is a causal link between blood lipids and risk of amyotrophic lateral sclerosis; replication across different datasets and even different populations adds confidence. For other putative risk factors, such as smoking and immune function, Mendelian randomization studies have provided cause for doubt. We highlight the use of positive control analyses in choosing exposure single nucleotide polymorphisms (SNPs) to make up the Mendelian randomization instrument, use of SNP clumping to avoid false positive results due to SNPs in linkage and the importance of multiple testing correction. We discuss the implications of survival bias for study of late age of onset diseases such as amyotrophic lateral sclerosis and make recommendations to mitigate this potentially important confounder. For Mendelian randomization to be useful to the amyotrophic lateral sclerosis field, high methodological standards must be applied to ensure reproducibility. Mendelian randomization is already an impactful tool, but poor-quality studies will lead to incorrect interpretations by a field that includes non-statisticians, wasted resources and missed opportunities.

Body Mass Index, Interleukin-6 Signaling and Multiple Sclerosis: A Mendelian Randomization Study

Objectives

We explored whether genetically predicted increased body mass index (BMI) modulates multiple sclerosis (MS) risk through interleukin-6 (IL-6) signaling.

Methods

We performed a two-sample Mendelian randomization (MR) study using multiple genome-wide association studies (GWAS) datasets for BMI, IL-6 signaling, IL-6 levels and c-reactive protein (CRP) levels as exposures and estimated their effects on risk of MS from GWAS data from the International Multiple Sclerosis Genetics Consortium (IMSGC) in 14,802 MS cases and 26,703 controls.

Results

In univariable MR analyses, genetically predicted increased BMI and IL-6 signaling were associated with higher risk of MS (BMI: odds ratio (OR) = 1.30, 95% confidence interval (CI) = 1.15-1.47, p = 3.76 × 10-5; IL-6 signaling: OR = 1.51, 95% CI = 1.11-2.04, p = 0.01). Furthermore, higher BMI was associated with increased IL-6 signaling (β = 0.37, 95% CI = 0.32,0.41, p = 1.58 × 10-65). In multivariable MR analyses, the effect of IL-6 signaling on MS risk remained after adjusting for BMI (OR = 1.36, 95% CI = 1.11-1.68, p = 0.003) and higher BMI remained associated with an increased risk for MS after adjustment for IL-6 signaling (OR = 1.16, 95% CI =1.00-1.34, p = 0.046). The proportion of the effect of BMI on MS mediated by IL-6 signaling corresponded to 43% (95% CI = 25%-54%). In contrast to IL-6 signaling, there was little evidence for an effect of serum IL-6 levels or CRP levels on risk of MS.

Conclusion

In this study, we identified IL-6 signaling as a major mediator of the association between BMI and risk of MS. Further explorations of pathways underlying the association between BMI and MS are required and will, together with our findings, improve the understanding of MS biology and potentially lead to improved opportunities for targeted prevention strategies.

Educational Attainment and Ischemic Stroke: A Mendelian Randomization Study

Observational studies have evaluated the potential association of socioeconomic factors such as higher education with the risk of stroke but reported controversial findings. The objective of our study was to evaluate the potential causal association between higher education and the risk of stroke. Here, we performed a Mendelian randomization analysis to evaluate the potential association of educational attainment with ischemic stroke (IS) using large-scale GWAS datasets from the Social Science Genetic Association Consortium (SSGAC, 293,723 individuals), UK Biobank (111,349 individuals), and METASTROKE consortium (74,393 individuals). We selected three Mendelian randomization methods including inverse-variance-weighted meta-analysis (IVW), weighted median regression, and MR–Egger regression. IVW showed that each additional 3.6-year increase in years of schooling was significantly associated with a reduced IS risk (OR = 0.54, 95% CI: 0.41–0.71, and p = 1.16 × 10^–5). Importantly, the estimates from weighted median (OR = 0.49, 95% CI: 0.33–0.73, and p = 1.00 × 10^–3) and MR–Egger estimate (OR = 0.18, 95% CI: 0.06–0.60, and p = 5.00 × 10^–3) were consistent with the IVW estimate in terms of direction and magnitude. In summary, we provide genetic evidence that high education could reduce IS risk.

Joint Analysis of Genome-Wide Association Data Reveals No Genetic Correlations Between Low Back Pain and Neurodegenerative Diseases

Background: We aimed to explore the genetic correlation and bidirectional causal relationships between low back pain (LBP) and three neurodegenerative diseases, Alzheimer’s disease (AD), Parkinson’s disease (PD), and amyotrophic lateral sclerosis (ALS).

Methods: Summary-level statistics were obtained from genome-wide association studies of LBP (n = 177,860), AD (n = 63,926), PD (n = 482,730), and ALS (n = 80,610). We implemented linkage disequilibrium score regression to calculate heritability estimates and genetic correlations. To investigate possible causal associations between LBP and three neurodegenerative diseases, we also conducted a bidirectional two-sample Mendelian randomization (MR) study. Inverse variance-weighted MR was employed as the primary method to generate overall estimates, whereas complementary approaches and sensitivity analyses were conducted to confirm the consistency and robustness of the findings.

Results: There was no evidence of genetic correlations between LBP and AD (Rg = −0.033, p = 0.766). MR analyses did not support the causal effect of LBP on AD (OR = 1.031; 95% CI, 0.924–1.150; p = 0.590) or the effect of AD on LBP (OR = 0.963; 95% CI, 0.923–1.006; p = 0.090). Likewise, this study failed to identify genetic correlations between LBP and two other neurodegenerative diseases. MR results of the associations of LBP with PD and ALS, and the reverse associations, did not reach Bonferroni-corrected significance.

Conclusion: The study did not support genetic correlations or causations between LBP and three common neurodegenerative diseases, AD, PD, and ALS in the European population.

Growth Differentiation Factor 15 Is Associated With Alzheimer's Disease Risk

Background

Previous observational studies have suggested that associations exist between growth differentiation factor 15 (GDF-15) and neurodegenerative diseases. We aimed to investigate the causal relationships between GDF-15 and Alzheimer’s disease (AD), Parkinson’s disease (PD), and amyotrophic lateral sclerosis (ALS).

Methods

Using summary-level datasets from genome-wide association studies of European ancestry, we performed a two-sample Mendelian randomization (MR) study. Genetic variants significantly associated (p < 5 × 10^–8) with GDF-15 were selected as instrumental variables (n = 5). An inverse-variance weighted method was implemented as the primary MR approach, while weighted median, MR–Egger, leave-one-out analysis, and Cochran’s Q-test were conducted as sensitivity analyses. All analyses were performed using R 3.6.1 with relevant packages.

Results

MR provided evidence for the association of elevated GDF-15 levels with a higher risk of AD (odds ratio = 1.14; 95% confidence interval, 1.04–1.24; p = 0.004). In the reverse direction, Mendelian randomization suggested no causal effect of genetically proxied risk of AD on circulating GDF-15 (p = 0.450). The causal effects of GDF-15 on PD (p = 0.597) or ALS (p = 0.120) were not identified, and the MR results likewise did not support the association of genetic liability to PD or ALS with genetically predicted levels of GDF-15. No evident heterogeneity or horizontal pleiotropy was revealed by multiple sensitivity analyses.

Conclusion

We highlighted the role of GDF-15 in AD as altogether a promising diagnostic marker and a therapeutic target.

Effect of plasma vitamin C levels on Parkinson's disease and age at onset: a Mendelian randomization study

BACKGROUND

Until now, epidemiological evidence regarding the association between vitamin C intake (both diet and supplements) and Parkinson's disease (PD) remains inconsistent. Hence, it is necessary to establish the causal link between vitamin C levels and PD, and further develop effective therapies or prevention.

METHODS

We selected 11 newly identified plasma vitamin C genetic variants from a large-scale plasma vitamin C GWAS dataset (n = 52,018) as the effective instrumental variables, and extracted their corresponding GWAS summary statistics from PD (33,674 PD cases and 449,056 controls) and PD age at onset (AAO) (n = 28,568). We then performed a Mendelian randomization (MR) study to evaluate the causal association of plasma vitamin C levels with PD and PD AAO using inverse-variance weighted (IVW), the weighted median, MR-Egger, and MR-PRESSO test.

RESULTS

We did not observe any significant association between genetically increased vitamin C levels and PD. Interestingly, we found a reduced trend of PD AAO (1.134 years) with 1 SD genetically increased vitamin C levels using IVW (beta = - 1.134, 95% CI: [- 2.515, 0.248], P = 0.108). Importantly, this trend was further successfully verified using both weighted median and MR-Egger. Each 1 SD genetically increased vitamin C levels could reduce PD AAO 1.75 and 2.592 years using weighted median (beta = - 1.750, 95% CI: [- 3.396, - 0.105], P = 0.037) and MR-Egger (beta = - 2.592, 95% CI: [- 4.623, - 0.560], P = 0.012).

CONCLUSIONS

We demonstrated the causal association between genetically increased plasma vitamin C levels and reduced PD AAO in people of European descent. Randomized controlled trials are required to clarify whether diet intake or supplement, or both could reduce the AAO of PD.

Circulating Interleukins and Risk of Multiple Sclerosis: A Mendelian Randomization Study

Background

Previous research have implicated critical roles of systemic inflammation in the development of Multiple Sclerosis (MS). But the causal relationship between interleukins (ILs) and MS has not been fully elucidated.

Objective

In this study, we applied Mendelian randomization (MR) approaches to address the causal associations between genetically determined circulating levels of ILs and the risk of MS.

Methods

Genetic instruments for circulating IL-1 receptor antagonist (IL-1Ra), IL-2 receptor α subunit (IL-2Rα), IL-6, IL-16, IL-17, and IL-18 were obtained from recently published genome-wide association studies (GWAS). Summary-level data for MS were obtained from the International Multiple Sclerosis Genetics Consortium. MR analyses were performed using the R software (version 3.6.1, The R Foundation) and the TwoSampleMR package.

Results

Genetic predisposition to higher circulating levels of IL-2Rα were significantly associated with MS risk. The odds ratio (OR) was 1.22 (95% confidence interval [CI], 1.12-1.32; p < 0.001) per one standard deviation increase in circulating IL-2Rα levels. There was a suggestive association of circulating IL-1Ra with MS risk (OR, 0.94; 95% CI, 0.88-0.99; p = 0.027). The other ILs were not associated with the outcome.

Conclusion

Our results indicated that circulating IL-2Rα was causally associated with risk of MS.

Impact of serum calcium levels on total body bone mineral density: A mendelian randomization study in five age strata

BACKGROUND & AIMS

Mendelian randomization (MR) studies have reported the causal association between serum calcium levels and bone mineral density (BMD). The results showed that genetically increased serum calcium levels in individuals with normal calcium levels did not increase BMD and could even reduce BMD. However, whether there are differences in the association between serum calcium and BMD in different age strata remains unclear.

METHODS

We selected eight serum calcium genetic variants with genome-wide significance (P < 5.00E-08) as the potential instrumental variables. We conducted an MR analysis to evaluate the impact of serum calcium levels on total body BMD in five age strata, 0-15, 15-30, 30-45, 45-60, and ≥60 years, using large-scale serum calcium (61,079 individuals) and total body BMD genome-wide association study (66,628 individuals) datasets. For pleiotropy analysis, we used a manual method and four common statistical methods, namely the MR-Egger intercept, MR-PRESSO, heterogeneity, and Steiger filtering tests. For MR analysis, we selected four MR methods, namely inverse-variance weighted, weighted median, MR-Egger, and MR-PRESSO. In addition to the univariable MR analysis, we conducted a multivariate MR analysis taking into account the effect of serum parathyroid hormone levels.

RESULTS

Univariable MR analysis using the inverse-variance weighted method indicated that per 0.5-mg/dL increase (about 1 standard deviation) in serum calcium levels was statistically significantly associated with reduced total body BMD only in the ≥60 years stratum (effect estimate (beta) = -0.545, 95% confidence interval (CI): -0.892 to -0.198, P = 0.002). The weighted median regression (beta = -0.446, 95% CI: -0.821 to -0.094, P = 1.40E-02) and MR-PRESSO (beta = -0.545, 95% CI: -0.892 to -0.198, P = 0.022) MR methods further supported this suggestive association. The multivariable MR analysis also found a significant association between increased serum calcium levels and reduced total body BMD in the ≥60 years stratum (beta = -0.547, 95% CI: -0.934 to -0.16, P = 0.006).

CONCLUSIONS

Our results provide genetic evidence that increased serum calcium levels did not improve BMD in the general population and that the elevated serum calcium levels in generally healthy populations, especially in adults older than 60 years, may even reduce the BMD. Our results are comparable with those of recent MR findings.

Relationships between accelerometer-measured and multiple sclerosis: a 2-sample Mendelian randomization study

BACKGROUND

Observational studies suggest that physical activity (PA) can independently modify the risk of developing multiple sclerosis (MS).

OBJECTIVE

To investigate the causal effect of PA on MS by Mendelian randomization (MR) approaches.

METHODS

Through a genome-wide association study including 91,105 participants from UK Biobank, we obtained 5 single-nucleotide polymorphisms (SNPs) associated with accelerometer-measured PA (P < 5 × 10^-8). Summary-level data for MS were obtained from a meta-analysis, incorporating 14,802 subjects with MS and 26,703 healthy controls of European ancestry. MR analyses were performed using the inverse-variance-weighted method, weighted median estimator, and MR-PRESSO method. Additional analyses were further performed using MR-Egger intercept and Cochran's Q statistic to verify the robustness of our findings.

RESULTS

We failed to detect a causal effect of PA on MS (OR, 0.60; 95% confidence interval [CI], 0.30-1.20; P = 0.15) per in the random-effects IVW analysis. Additional MR methods yielded consistent results. MR-Egger regression suggested no evidence of horizontal pleiotropy (Intercept = 0.14, P = 0.21) and there seemed no substantial heterogeneity (I² = 29.8%, P = 0.22) among individual SNPs.

CONCLUSION

Our findings suggest that enhancing PA might not modify the risk of developing MS independent of established risk factors.