A Basket Clinical Study to Assess Glycerol Tributyrate in Patients With Mitochondrial Encephalopathy, Lactic Acidosis, Stroke-like Episodes (MELAS) or Leber's Hereditary Optic Neuropathy-Plus (LHON-Plus)

During the two-month-long baseline lead-in phase, we will acquire the following information, which are part of standard clinical care: 1. Medical history 2. Pregnancy test for subjects of childbearing potential: using a urine human chorionic gonadotropin test 3. Number of hospitalizations in the last 12 months 4. Physical examination 5. 6-minute-walk test 6. Clinical laboratory biomarkers completed and/or interpreted at the CLIA-certified labs at Children's National Hospital: * GDF-15 * FGF-21 * CMP * Hemoglobin A1C * Plasma amino acids * Lactate * Carnitine and acylcarnitine * Urine organic acids and urine analysis 7. Standard 1 hour-long EEG for MELAS subjects 8. Baseline MRI (for subjects with MELAS or LHON-Plus) and MRS (for MELAS subjects) 9. Screen for stroke-like episodes for MELAS subjects 10. Electronic seizure diary for MELAS subjects 11. Motor examination for subjects with MELAS or LHON-Plus 12. Electromyography and nerve conduction velocity for LHON-Plus subjects 13. Ophthalmological examination (fundi, visual field, and visual acuity) for LHON-Plus subjects 14. Snellen chart exam for LHON-Plus subjects 15. Lumbar puncture for LHON-Plus subjects to assess CSF markers for multiple sclerosis-like: * A specific group of antibodies referred to as oligoclonal bands * Myelin basic proteins (MBP) * IgG levels * Levels of inflammasome proteins * Leukocytes count: lymphocytes (B-cells and T-cells), monocytes, macrophages, plasma cells, and granulocytes * CSF/serum glucose ratio 16. Fatigue screen using the Modified Fatigue Impact Scale 17. Quality of Life (QoL) is assessed using the short questionnaire "Neuro-Quality of life" 18. Cognitive assessment using the NIH-Toolbox Cognitive Battery 19. Skin biopsy to assess: * Mitochondrial Genetic Analysis: Quantification of the heteroplasmic levels of MELAS and LHON-Plus mitochondrial variants by long-range PCR followed by massively parallel sequencing done at Baylor Miraca Genetics Laboratories DBA Baylor Genetics, Clinical Diagnostics Laboratory. * Mitochondrial Respiratory Chain Enzyme Analysis: Quantification of enzymatic activity of oxidative phosphorylation (OXPHOS) Complexes by spectrophotometry done by Baylor Genetics. * Mitochondrial Fitness Assays: The mitochondrial fitness of participant-derived dermal fibroblasts are assessed in real-time by live-cell mitochondrial assays using the two world's most advanced automated cell metabolism analyzers and the automated normalization system, Cytation1, from Agilent Technologies Inc., and the three following specialized metabolic assays from Agilent: Mitochondrial Stress Test assay: This assay measures the baseline of the participant's mitochondrial functions by quantifying OXPHOS bioenergetic parameters. The investigators uses this assay to monitor the potential efficacy of oral administration of glycerol tributyrate in participants. Real-Time ATP Rate assay: The investigators use this assay to quantify the pathway-specific ATP rate production from the mitochondrial OXPHOS pathway and the cytosolic glycolytic pathway. Agilent Glycolytic Rate assay: The investigators use this assay to assess the metabolic plasticity between the two main energy pathways, OXPHOS and glycolysis,as well as to correlate one-on-one the glycolytic activity with lactate accumulation. No participants are enrolled in the dose-escalation phase without a complete interpretation of the clinical data from the baseline lead-in phase. As a higher level of safety risk, participants with the pre-existing severe complications, renal failure, arrhythmia, pneumonia with respiratory failure, and/or severe gastroparesis, will be excluded from progressing to the dose-escalating phase. During the six-month-long dose-escalation phase, the investigators will determine the safe participant-specific MTD using the toxicology and clinical data described above. Participants are administered glycerol tributyrate three times a day (tid) dispensed by the Children's National Hospital (CNH) research pharmacy located in the study site (CNH). To initiate the dose-escalation phase, the investigator provides all participants with a one-month supply of 100 capsules, each containing 500 mg of glycerol tributyrate. The initial dose is 1000 mg tid. During the last week of month 1 and subsequent months, the investigators review the clinical and biochemical data for each participant before increasing the oral dose of glycerol tributyrate. Below is the description of the methods to assess for dose-limiting toxicity (DLT) throughout the dose-escalation phase. 1. Disease-specific assessment: * For participants with MELAS, there are two measurable and reliable biomarkers for MELAS-specific upper threshold of the effect of the investigational drug: 1) plasma lactate levels greater than three times the normal levels; and 2) blood glucose levels above 200 mg/dl (11.1 mM). In addition, general toxicity is assessed in participants with MELAS as described in the criteria detailed below, which are shared by all participants. If general toxicity and/or MELAS-specific upper threshold of plasma lactate levels and blood glucose levels, MELAS participants will not be escalated to the next planned dose by 500 mg tid but rather re-treated at a one-dose concentration lower than the dose at which Grade 3 toxicity is encountered. * For participants with LHON-Plus, there are no similar reliable biomarkers for assessing such upper threshold. Therefore, these subjects will be closely monitored for general toxicity. 2. General toxicity assessment: The clinical investigators evaluate toxicity using the Common Terminology Criteria of Adverse Events (CTCAE) version 4.0 3 grading scale. * Dose-limiting toxicity (DLT) is defined as any of the adverse effects (AE) listed in Section 5.3.1.11 "Toxicity Monitoring" graded on the CTCAE v4.03. AE is considered possibly related to the investigational drug that occurs any time from the initial dose of glycerol tributyrate, when at grade 3 or higher, or worsening of baseline status as defined by increase of at least 2 grades, if baseline grade is less than or equal to 1. participants who develop Grade 3 or higher toxicity are re-treated at a one-dose concentration lower than the dose at which Grade 3 toxicity is encountered. * In the absence of DLT or in the case of CTCAE grade 1 or 2 toxicity, dose of glycerol tributyrate is escalated to the next planned dose by 500 mg tid. Doses are increased to the next planned dose by 500 mg tid every month until month 6 or prior if the participant-specific DLT is reached based on toxicity data using the CTCAE grading scale, as defined above. If participants reach their MTD prior to month 6 of the dose-escalating phase, they immediately enter the clinical phase at the fixed participant-specific MTD, defined as a one-dose concentration lower than the dose at which Grade 3 toxicity is encountered. At the conclusion of the dose-escalation phase, a skin biopsy will be performed on all participants prior to the onset of the clinical phase at fixed participant-specific MTD. The participant-specific dermal fibroblasts will be derived to determine the genetic and mitochondrial bioenergetic parameters for each participant at the outset of the clinical phase. The 12 month-long clinical phase at fixed participant-specific MTD starts at the conclusion of the 6-month-long dose-escalation phase and is divided into two 6-month-long periods. This 12-month-long time-frame is necessary to capture disease-specific clinical symptoms, to collect preliminary evidence of efficacy of glycerol tributyrate using disease-specific biomarkers, and to assess possible clinical outcomes demonstrating clinical benefit of glycerol tributyrate. At the outset, mid-phase, and end of the 12 month-long clinical phase, participants will undergo three skin biopsies to assess the potential efficacy of glycerol tributyrate on: 1. OXPHOS bioenergetic parameters 2. the clinical and biochemical target biomarkers. Throughout the clinical phase at fixed MTD, we will implement the same safety assessment for DLTs than for the dose-escalation phase. At the end of the 12-month-long clinical phase at fixed participant-specific MTD, the investigators will discharge the participants after performing a follow-up study during which non-serious adverse events or serious adverse events will be recorded for 7 or 30 days, respectively, after the last day of study participation. Capsules containing glycerol tributyrate (500 mg) will be administered orally to all participants three times a day with an 8-ounce glass of water on an empty stomach: morning, noon, and evening during the dose-escalation phase and the clinical phase at fixed subject-specific MTD of the study. Compliance will be assessed with an electronic log/diary where participants will record on a daily basis time, date, and pill counts. Participants will be asked to bring back all the bottles of glycerol tributyrate to subsequent visits to assess compliance. Compliance will be considered satisfactory with 80% of planned doses logged in. Participants will be specifically monitored for the occurrence of the following Adverse Events (AEs) graded based on the CTCAE v4.03: * Dizziness * Syncope * Concentration impairment * Fatigue * Fever * Nausea * Vomiting * Diarrhea * Hypoglycemia * Hyperglycemia * Lactic acidosis The investigators will review any AEs in person during the scheduled visits. The participants will also fill out a survey on their electronic diary to make it easier to capture any AEs. A Data and Safety Monitoring Board (DSMB) committee has been formed and includes five independent members: a metabolic physician, neurologist, bioethicist, a clinical trialist, and a lay person as a non-voting member. The DSMB committee will review safety data on an ongoing basis, meet biannually or ad-hoc if the need arises. This additional oversight provided by a DSMB committee provides further protection to the study participants during the basket clinical trial for MELAS and LHON-PLus.