Mitochondrial Inheritance Calculator

This page accompanies the BioExplorer Mitochondrial Inheritance Calculator, an educational mtDNA heteroplasmy transmission model. The calculator is NOT a clinical disease-risk calculator.

It computes the probability that a modeled offspring heteroplasmy exceeds a user-defined comparison value, given the measured maternal heteroplasmy and a single-step binomial sampling model of the mitochondrial bottleneck.

BioExplorer · Genetics Interactive Tool

Mitochondrial Inheritance Calculator

Educational mtDNA heteroplasmy transmission model. Predict the probability that a modeled offspring heteroplasmy exceeds a user-defined comparison value, given the measured maternal heteroplasmy and a single-step binomial sampling model of the mitochondrial bottleneck. Not a clinical disease-risk calculator.

Maternal variant status The mtDNA variant status of the mother. This is NOT mapped to a heteroplasmy value; the heteroplasmy is a separate input below.

Worked examples

Maternal heteroplasmy fraction (0 to 1) The mother’s measured heteroplasmy fraction, from a validated assay. The grammar rejects 1e-1, abc, 1.5; only 0, 0.X, .X, 1, and 1.0...0 are accepted.

Comparison value (greater than 0, at most 1) User-defined comparison value. The model outputs P(modeled offspring heteroplasmy > cutoff). Not a clinical threshold. Must be greater than 0.

Bottleneck size (30 to 1000) The effective sample size N for the binomial sampling model. The default is 200 (an illustrative value within the application-supported range [30, 1000]).

Trait label (optional) Recorded for context only. The calculator does not validate the label’s notation, identity, or clinical significance.

Sample tissue (optional) Recorded for context only; the model assumes the entered value is the maternal sampling pool.

What is mitochondrial inheritance?

Mitochondrial DNA (mtDNA) is inherited from the mother. The mother’s mtDNA population is a mixture of molecules; some carry a particular variant and some do not. The fraction of variant-bearing molecules is called the heteroplasmy fraction, h. The supported range is h in [0, 1]; the homoplasmic endpoints h = 0 (no variant) and h = 1 (all variant) are valid edge cases.

The mother’s offspring does not inherit her full mtDNA population; instead, a small subset is sampled through a process called the mitochondrial bottleneck. The offspring’s heteroplasmy is a sample from a distribution centered on the mother’s heteroplasmy but with substantial variance, because the sample size is small relative to the mother’s mtDNA population.

The BioExplorer Mitochondrial Inheritance Calculator implements a single-step binomial sampling model of this bottleneck. The binomial sampling is a simplified representation of one mother-to-offspring transmission event; it is not a complete biological mechanism.

The model computes, for a given maternal heteroplasmy, a comparison value c, and an effective bottleneck size N, the probability that the modeled offspring heteroplasmy exceeds c. The output is a probability in [0, 1], NOT a probability of clinical disease.

The math

Given maternal heteroplasmy h_m, bottleneck size N, and comparison value c, the modeled offspring heteroplasmy h_o is sampled as:

h_o ~ Binomial(N, h_m) / N

The probability that h_o exceeds c is the upper-tail probability of the Binomial(N, h_m) distribution:

P(h_o > c) = sum_{k = k_min}^{N} C(N, k) * h_m^k * (1 - h_m)^(N - k)

where k_min is the smallest integer k such that k/N > c. With the BigInt exact rational computation, k_min = floor(c * N) + 1 in exact arithmetic.

For upper-tail probabilities at least 0.5, the implementation uses the complementary lower tail with Math.expm1 to avoid floating-point cancellation. The defensive error guard rejects non-finite or non-positive values from the complementary path.

The model is a single-step representation of one mother-to-offspring transmission event. It is not a Kimura random-drift distribution. It is not a multi-generation cumulative bottleneck. It does not incorporate tissue variation, penetrance, mosaicism, or de novo mutation rate. See the “What this calculator does not do” section below for the full list.

Worked examples

The calculator includes 11 numbered worked examples: 10 numerical examples (Examples 1-4, 6-11) and one paternal non-transmission explanation (Example 5). The numerical examples are available as one-click presets in the calculator above.

Example 5 is rendered via the “Show paternal non-transmission panel” button and is not a numerical preset, because the explanation is about a model assumption, not a binomial-tail result. Each numerical example has a hand-verified reference value.

Example 1: h=0.30, c=0.70, N=200. P = 4.97 × 10⁻³² (essentially 0; the upper tail is far above the mean).
Example 2: h=0.50, c=0.50, N=200. P = 0.4718 (less than 0.5 because the strict-inequality lower bound floors at 101).
Example 3: h=0.50, c=0.80, N=200. P = 4.16 × 10⁻¹⁹ (essentially 0).
Example 4: h=0.65, c=0.60, N=200. P = 0.9195.
Example 5: Paternal non-transmission explanation (rendered separately in the UI).
Example 6: h=0.65, c=0.60, N=1000. P = 0.9994 (tighter variance at larger N).
Example 7: h=0.10, c=0.999, N=1000. P underflows (positive but too small to represent).
Example 8: h=0.90, c=0.99999999999, N=30. P = 0.0424 (BigInt boundary: the all-variant outcome is included because 30/30 > 0.99999999999).
Example 9: h=0.5, c=0.001, N=1000. P > 99.99% (near-1 upper tail; v0.6 regression for the v0.5 overflow).
Example 10: h=0.95, c=0.8, N=200. P > 99.99% (100% rule: non-exact value that rounds to 100.00% at 2 decimals is shown as >99.99%, not 100%).
Example 11: h=0.03, c=0.001, N=30. P = 0.5990 (kMin=1 lower-tail regression; the v0.6 condition kMin > 1 short-circuited P(K=0)).

Paternal non-transmission

Under the v1 calculator’s standard maternal-inheritance model, paternal mtDNA contribution is set to zero. The father contributes no mtDNA to the modeled offspring heteroplasmy in the model, regardless of his own heteroplasmy. The modeled offspring heteroplasmy depends only on the mother’s mtDNA population and the bottleneck.

This is a model-scoped assumption. The calculator does not assert a universal mechanistic claim; it adopts the conventional modeling assumption that the modeled offspring heteroplasmy depends only on the mother’s mtDNA population. For the human evidence base supporting this assumption, see the references below.

Sources and further reading

Sutovsky P, Moreno RD, Ramalho-Santos J, Dominko T, Simerly C, Schatten G. Ubiquitin tag for sperm mitochondria. Nature. 1999;402:371-372. DOI: 10.1038/46466. (Note: the 1999 study examined non-human mammals; the human evidence is from later work.)
Lee W, et al. Molecular basis for maternal inheritance of human mitochondrial DNA. Nature Genetics. 2023. PMID: 37723262. (Human mechanism; identifies mtDNA elimination during late spermatogenesis.)
Wonnapinij P, Chinnery PF, Samuels DC. The distribution of mitochondrial DNA heteroplasmy due to random genetic drift. American Journal of Human Genetics. 2008;83(5):582-593. DOI: 10.1016/j.ajhg.2008.10.007. (Background only; not used to validate the v1 quantitative formula.)
Stewart JB, Chinnery PF. The dynamics of mitochondrial DNA heteroplasmy: implications for human health and disease. Nature Reviews Genetics. 2015;16(9):530-542. (Canonical review of the bottleneck model and clinical implications.)
Carelli V, Ross-Cisneros FN, Sadun AA. Mitochondrial dysfunction as a cause of optic neuropathies. Progress in Retinal and Eye Research. 2004;23(1):53-89. PMID: 14766317. (LHON review.)
Finsterer J. Leigh and Leigh-like syndrome in children and adults. Pediatric Neurology. 2008;39(4):223-235. PMID: 18805359. (Leigh syndrome review.)
GeneReviews Mitochondrial Disorders Overview. NBK1224. https://www.ncbi.nlm.nih.gov/books/NBK1224/
GeneReviews LHON. NBK1174. https://www.ncbi.nlm.nih.gov/books/NBK1174/
GeneReviews MELAS. NBK1233. https://www.ncbi.nlm.nih.gov/books/NBK1233/

Related resources

BioExplorer Y-Linked Inheritance Calculator: a sister tool for Y-linked (holandric) trait probability.
BioExplorer Punnett Square Calculator: a tool for general Mendelian inheritance patterns.
BioExplorer Genetics Glossary: definitions of heteroplasmy, mitochondrial bottleneck, penetrance, and other terms used in this article.

FAQs

Is this calculator a clinical disease-risk calculator?

No. The BioExplorer Mitochondrial Inheritance Calculator is an educational model that computes the probability that a modeled offspring heteroplasmy exceeds a user-defined comparison value. It is NOT a probability of clinical disease. Clinical penetrance depends on additional factors the calculator does not model: the specific mtDNA variant, the tissue distribution, the age of the offspring, the sex of the offspring, nuclear-genome modifiers, and environmental factors.

What if my heteroplasmy is measured in a different tissue than the bottleneck sampling pool?

The model assumes the entered value represents the maternal sampling pool. The calculator records the sample tissue for context only. If your measured value is from blood and the bottleneck samples from a different tissue, the model’s assumption may not hold. A clinical genetic counselor can help interpret the result.

What is the bottleneck size N?

The bottleneck size N is the effective sample size for the binomial sampling model. The application supports illustrative values from 30 to 1000. The default is 200, an illustrative value within that range. The default is NOT quoted from any single publication. If you have a per-variant estimate, override the default.

Can I use this for a syndrome threshold?

The v1 calculator does not include syndrome threshold presets. Published thresholds (e.g., for LHON, MELAS, MERRF, NARP, Leigh) are heterogeneous and mutation-specific. A threshold that works for one mutation may not work for another. The v1 calculator uses a user-defined comparison value with explicit educational labeling. Consult a clinical genetic counselor for syndrome-specific interpretation.

Why does the result say “P > 99.99%” instead of a higher value?

The result card shows “P > 99.99%” when the modeled probability is non-exact but rounds to 100.00% at 2 decimal places. This is the 100% rule: a non-exact value that would render as 100.00% is shown as >99.99% to avoid the misleading “100% probability” claim. The exact “100%” is reserved for the h=1, c<1 endpoint, where the modeled offspring heteroplasmy is exactly 1 by definition.

About the calculator

What this calculator does: computes the probability that a modeled offspring heteroplasmy exceeds a user-defined comparison value, given the measured maternal heteroplasmy and a single-step binomial sampling model of the mitochondrial bottleneck.

What this calculator does NOT do:

Clinical disease risk. A probability of modeled offspring heteroplasmy exceeding a comparison value is NOT a probability that the child will develop clinical disease. The output is labeled accordingly.
Mitochondrial disorders caused by nuclear-gene variants. These follow autosomal dominant, autosomal recessive, or X-linked inheritance, not the proposed maternal model. The v1 calculator applies only to confirmed mtDNA variants.
Tissue-specific heteroplasmy. Blood, urine, and muscle heteroplasmy are different in a single individual. The v1 calculator treats heteroplasmy as a single number h, with an optional sampleTissue field for context only. The model assumes the entered value represents the maternal sampling pool.
Multi-generation cumulative bottleneck. A probability is not a heteroplasmy and cannot be reused as the next generation’s input. The v1 calculator produces a one-generation result.
A clinically validated bottleneck size. N is a user-overridable hypothetical parameter. The default N = 200 is an illustrative value within the application-supported range [30, 1000]; it is not a clinical measurement.
Per-mutation or per-syndrome penetrance. The v1 calculator does not include a syndrome dropdown or a “disease threshold” concept.
Reproductive technology modeling. Mitochondrial donation, pronuclear transfer, and spindle transfer use different sampling assumptions and require a separate calculator.

The BioExplorer Mitochondrial Inheritance Calculator is provided for educational use. It is not a substitute for professional medical advice, diagnosis, or treatment.