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Robert S Balaban

Publications and source records attributed to Robert S Balaban.

At least 19 recordsLinked to original sources
PubMed2006

Functional consequences of mitochondrial proteome heterogeneity.

Potential functional consequences of the differences in protein distribution between the mitochondria of the rat liver, heart, brain, and kidney, as determined in the companion paper in this issue (Johnson DT, French S, Blair PV, You JS, Bemis KG, Wang M, Harris RA, and Balaban RS. The tissue heterogeneity of the mammalian mitochondrial proteome. Am J Physiol Cell Physiol292: C689-C697, 2006), were analyzed using a canonical metabolic pathway approach as well as a functional domain homology analysis. These data were inserted into the Kyoto Encyclopedia of Genes and Genomes pathway framework to give global and metabolic pathway-specific information on the impact of the differential protein distribution on mitochondrial function. Custom pathway analysis was also performed using pathways limited to the mitochondrion. With the use of this approach, several well-known functional differences between these mitochondrial populations were confirmed. These included GABA metabolism in the brain, urea synthesis in the liver, and the domination of oxidative phosphorylation in the heart. By comparing relative protein amounts of mitochondria across tissues, a greater understanding of functional emphasis is possible as well as the nuclear "programming" required to enhance a given function within the mitochondria. For proteins determined to be mitochondrial and lacking a defined role functional domain BLAST analyses were performed. Several proteins associated with DNA structural modification and a novel CoA transferase were identified. A protein was also identified capable of catalyzing the first three steps of de novo pyrimidine synthesis. This analysis demonstrates that the distribution of nuclear encoded proteins significantly modifies the overall functional emphasis of the mitochondria to meet tissue-specific needs. These studies demonstrate the existence of mitochondrial biochemical functions that at present are poorly defined.

Animals↗
PubMed2006

Modeling mitochondrial function.

The mitochondrion represents a unique opportunity to apply mathematical modeling to a complex biological system. Understanding mitochondrial function and control is important since this organelle is critical in energy metabolism as well as playing key roles in biochemical synthesis, redox control/signaling, and apoptosis. A mathematical model, or hypothesis, provides several useful insights including a rigorous test of the consensus view of the operation of a biological process as well as providing methods of testing and creating new hypotheses. The advantages of the mitochondrial system for applying a mathematical model include the relative simplicity and understanding of the matrix reactions, the ability to study the mitochondria as a independent contained organelle, and, most importantly, one can dynamically measure many of the internal reaction intermediates, on line. The developing ability to internally monitor events within the metabolic network, rather than just the inflow and outflow, is extremely useful in creating critical bounds on complex mathematical models using the individual reaction mechanisms available. However, many serious problems remain in creating a working model of mitochondrial function including the incomplete definition of metabolic pathways, the uncertainty of using in vitro enzyme kinetics, as well as regulatory data in the intact system and the unknown chemical activities of relevant molecules in the matrix. Despite these formidable limitations, the advantages of the mitochondrial system make it one of the best defined mammalian metabolic networks that can be used as a model system for understanding the application and use of mathematical models to study biological systems.

Animals↗
PubMed2006

Tissue heterogeneity of the mammalian mitochondrial proteome.

The functionality of the mitochondrion is primarily determined by nuclear encoded proteins. The mitochondrial functional requirements of different tissues vary from a significant biosynthetic role (liver) to a primarily energy metabolism-oriented organelle (heart). The purpose of this study was to compare the mitochondrial proteome from four different tissues of the rat, brain, liver, heart, and kidney, to provide insight into the extent of mitochondrial heterogeneity and to further characterize the overall mitochondrial proteome. Mitochondria were isolated, solubilized, digested, and subjected to quantitative liquid chromatography-mass spectroscopy. Of the 16,950 distinct peptides detected, 8,045 proteins were identified. High-confidence identification threshold was reached by 1,162 peptides, which were further analyzed. Of these 1,162 proteins, 1,149 were significantly different in content (P and q values < 0.05) between at least 2 tissues, whereas 13 were not significantly different between any tissues. Confirmation of the mitochondrial origin of proteins was determined from the literature or via NH(2)-terminal mitochondrial localization signals. With these criteria, 382 proteins in the significantly different groups were confirmed to be mitochondrial, and 493 could not be confirmed to be mitochondrial but were not definitively localized elsewhere in the cell. A total of 145 proteins were assigned to the rat mitochondrial proteome for the first time via their NH(2)-terminal mitochondrial localization signals. Among the proteins that were not significantly different between tissues, three were confirmed to be mitochondrial. Most notable of the significantly different proteins were histone family proteins and several structural proteins, including tubulin and intermediate filaments. The mitochondrial proteome from each tissue had very specific characteristics indicative of different functional emphasis. These data confirm the notion that mitochondria are tuned by the nucleus for specific functions in different tissues.

Amino Acid Sequence↗
PubMed2006

The mammalian target of rapamycin (mTOR) pathway regulates mitochondrial oxygen consumption and oxidative capacity.

Metabolic rate and the subsequent production of reactive oxygen species are thought to contribute to the rate of aging in a wide range of species. The target of rapamycin (TOR) is a well conserved serine/threonine kinase that regulates cell growth in response to nutrient status. Here we demonstrate that in mammalian cells the mammalian TOR (mTOR) pathway plays a significant role in determining both resting oxygen consumption and oxidative capacity. In particular, we demonstrate that the level of complex formation between mTOR and one of its known protein partners, raptor, correlated with overall mitochondrial activity. Disruption of this complex following treatment with the mTOR pharmacological inhibitor rapamycin lowered mitochondrial membrane potential, oxygen consumption, and ATP synthetic capacity. Subcellular fractionation revealed that mTOR as well as mTOR-raptor complexes can be purified in the mitochondrial fraction. Using two-dimensional difference gel electrophoresis, we further demonstrated that inhibiting mTOR with rapamycin resulted in a dramatic alteration in the mitochondrial phosphoproteome. RNA interference-mediated knockdown of TSC2, p70 S6 kinase (S6K1), raptor, or rictor demonstrates that mTOR regulates mitochondrial activity independently of its previously identified cellular targets. Finally we demonstrate that mTOR activity may play an important role in determining the relative balance between mitochondrial and non-mitochondrial sources of ATP generation. These results may provide insight into recent observations linking the TOR pathway to life span regulation of lower organisms.

Adenosine Triphosphate↗
PubMed2006

Mitochondrial matrix phosphoproteome: effect of extra mitochondrial calcium.

Post-translational modification of mitochondrial proteins by phosphorylation or dephosphorylation plays an essential role in numerous cell signaling pathways involved in regulating energy metabolism and in mitochondrion-induced apoptosis. Here we present a phosphoproteomic screen of the mitochondrial matrix proteins and begin to establish the protein phosphorylations acutely associated with calcium ions (Ca(2+)) signaling in porcine heart mitochondria. Forty-five phosphorylated proteins were detected by gel electrophoresis-mass spectrometry of Pro-Q Diamond staining, while many more Pro-Q Diamond-stained proteins evaded mass spectrometry detection. Time-dependent (32)P incorporation in intact mitochondria confirmed the extensive matrix protein phosphoryation and revealed the dynamic nature of this process. Classes of proteins that were detected included all of the mitochondrial respiratory chain complexes, as well as enzymes involved in intermediary metabolism, such as pyruvate dehydrogenase (PDH), citrate synthase, and acyl-CoA dehydrogenases. These data demonstrate that the phosphoproteome of the mitochondrial matrix is extensive and dynamic. Ca(2+) has previously been shown to activate various dehydrogenases, promote the generation of reactive oxygen species (ROS), and initiate apoptosis via cytochrome c release. To evaluate the Ca(2+) signaling network, the effects of a Ca(2+) challenge sufficient to release cytochrome c were evaluated on the mitochondrial phosphoproteome. Novel Ca(2+)-induced dephosphorylation was observed in manganese superoxide dismutase (MnSOD) as well as the previously characterized PDH. A Ca(2+) dose-dependent dephosphorylation of MnSOD was associated with an approximately 2-fold maximum increase in activity; neither the dephosphorylation nor activity changes were induced by ROS production in the absence of Ca(2+). These data demonstrate the use of a phosphoproteome screen in determining mitochondrial signaling pathways and reveal new pathways for Ca(2+) modification of mitochondrial function at the level of MnSOD.

Animals↗
PubMed2006

The mammalian longevity-associated gene product p66shc regulates mitochondrial metabolism.

Previous studies have determined that mice with a homozygous deletion in the adapter protein p66(shc) have an extended life span and that cells derived from these mice exhibit lower levels of reactive oxygen species. Here we demonstrate that a fraction of p66(shc) localizes to the mitochondria and that p66(shc-/-) fibroblasts have altered mitochondrial energetics. In particular, despite similar cytochrome content, under basal conditions, the oxygen consumption of spontaneously immortalized p66(shc-/-) mouse embryonic fibroblasts were lower than similarly maintained wild type cells. Differences in oxygen consumption were particularly evident under chemically uncoupled conditions, demonstrating that p66(shc-/-) cells have a reduction in both their resting and maximal oxidative capacity. We further demonstrate that reconstitution of p66(shc) expression in p66(shc-/-) cells increases oxygen consumption. The observed defect in oxidative capacity seen in p66(shc-/-) cells is partially offset by augmented levels of aerobic glycolysis. This metabolic switch is manifested by p66(shc-/-) cells exhibiting an increase in lactate production and a stricter requirement for extracellular glucose in order to maintain intracellular ATP levels. In addition, using an in vivo NADH photobleaching technique, we demonstrate that mitochondrial NADH metabolism is reduced in p66(shc-/-) cells. These results demonstrate that p66(shc) regulates mitochondrial oxidative capacity and suggest that p66(shc) may extend life span by repartitioning metabolic energy conversion away from oxidative and toward glycolytic pathways.

Adaptor Proteins, Signal Transducing↗
PubMed2006

Multi-photon excitation microscopy in intact animals.

Two-photon excitation fluorescence microscopy and backscattered-second harmonic generation microscopy permit the investigation of the subcellular events within living animals but numerous aspects of these experiments need to be optimized to overcome the traditional microscope geometry, motion and optical coupling to the subject. This report describes a stable system for supporting a living instrumented mouse or rabbit during endogenous reduced nicotinamide adenine dinucleotide and exogenous dye two-photon excitation fluorescence microscopy measurements, and backscattered-second harmonic generation microscopy measurements. The system was a modified inverted LSM510 microscope (Carl Zeiss, Inc., Thornwood, NY, U.S.A.) with a rotating periscope that converted the inverted scope to an upright format, with the objective located approximately, 15 cm from the centre of the microscope base, allowing easy placement of an instrumented animal. An Olympus 20x water immersion objective was optically coupled to the tissue, without a cover glass, via a saline bath or custom hydrated transparent gel. The instrumented animals were held on a specially designed holder that poised the animal under the objective as well as permitted different ventilation schemes to minimize motion. Using this approach, quality images were routinely collected in living animals from both the peripheral and body cavity organs. The remaining most significant issue for physiological studies using this approach is motion on the micrometre scale. Several strategies for motion compensation are described and discussed.

Acrylic Resins↗
PubMed2006

Maintenance of the metabolic homeostasis of the heart: developing a systems analysis approach.

The heart is almost unique in the body with a constant requirement to conduct work well beyond the normal maintenance of cellular integrity. With this constant workload, it is not surprising that cardiac energy conversion is highly specialized to maintain a constant supply of energy. This maintenance of cellular metabolites during alterations in workload has been termed metabolic homeostasis. Here we discuss our efforts to understand the cellular and mitochondrial control network that orchestrates the metabolic homeostasis of the heart. This begins with a better definition of the metabolic pathways, acute posttranslational control sites, and proper kinetic evaluation of the reaction steps in the intact mitochondrial environment. First, a quantitative model of mitochondrial energy conversion is presented and demonstrates several serious gaps in our knowledge of this process. Toward filling these gaps, screens of the entire mitochondrial proteome have been conducted to establish the metabolic pathways that need to be considered. In addition, the dynamic phosphoproteome of intact mitochondria, using 2D gel electrophoresis coupled to (32)P labeling, has revealed a remarkably extensive protein phosphorylation network throughout the mitochondrial metabolic network that has essentially been overlooked. Initial studies on evaluating the functional significance of these protein phosphorylations and the kinase-phosphatase system involved will be reviewed. One of the major deficits in the consensus quantitative model of oxidative phosphorylation to explain intact mitochondria activities is in complex I, where even the initiation of Nicotinamide Adenine Dinucleotide (reduced) (NADH) oxidation is problematical using in vitro kinetic data. Studies will be described where the NADH binding and oxidation kinetics at complex I in the intact mitochondria were determined using fluorescence lifetime and enzyme dependent-fluorescence recovery after photo-oxidation (ED-FRAP) techniques. These later studies suggest that matrix NADH binding characteristics are much different (>10(3) binding constant errors) than isolated proteins. In addition, complex I is far from equilibrium and may play an important role in regulating the rate of reducing equivalent delivery to the cytochromes.

Animals↗
PubMed2005

Mitochondria, oxidants, and aging.

The free radical theory of aging postulates that the production of intracellular reactive oxygen species is the major determinant of life span. Numerous cell culture, invertebrate, and mammalian models exist that lend support to this half-century-old hypothesis. Here we review the evidence that both supports and conflicts with the free radical theory and examine the growing link between mitochondrial metabolism, oxidant formation, and the biology of aging.

Aging↗
PubMed2005

Distribution of mitochondrial NADH fluorescence lifetimes: steady-state kinetics of matrix NADH interactions.

The lifetimes of fluorescent components of matrix NADH in isolated porcine heart mitochondria were investigated using time-resolved fluorescence spectroscopy. Three distinct lifetimes of fluorescence were resolved: 0.4 (63%), 1.8 (30%), and 5.7 (7%) ns (% total NADH). The 0.4 ns lifetime and the emission wavelength of the short component were consistent with free NADH. In addition to their longer lifetimes, the remaining pools also had a blue-shifted emission spectrum consistent with immobilized NADH. On the basis of emission frequency and lifetime data, the immobilized pools contributed >80% of NADH fluorescence. The steady-state kinetics of NADH entering the immobilized pools was measured in intact mitochondria and in isolated mitochondrial membranes. The apparent binding constants (K(D)s) for NADH in intact mitochondria, 2.8 mM (1.9 ns pool) and >3 mM (5.7 ns pool), were on the order of the estimated matrix [NADH] (approximately 3.5 mM). The affinities and fluorescence lifetimes resulted in an essentially linear relationship between matrix [NADH] and NADH fluorescence intensity. Mitochondrial membranes had shorter emission lifetimes in the immobilized poo1s [1 ns (34%) and 4.1 ns (8%)] with much higher apparent K(D)s of 100 microM and 20 microM, respectively. The source of the stronger NADH binding affinity in membranes is unknown but could be related to high order structure or other cofactors that are diluted out in the membrane preparation. In both preparations, the rate of NADH oxidation was proportional to the amount of NADH in the long lifetime pools, suggesting that a significant fraction of the bound NADH might be associated with oxidative phosphorylation, potentially in complex 1.

Animals↗
PubMed2005

Measurement of skeletal muscle perfusion during postischemic reactive hyperemia using contrast-enhanced MRI with a step-input function.

The regional distribution of skeletal muscle blood flow was measured during postischemic reactive hyperemia using Gd-DTPA contrast-enhanced (CE) MRI. The release of an occlusive thigh cuff was used to deliver a step-input of contrast concentration that was coincident with the onset of reactive hyperemia. A first-order tracer kinetic equation was used to estimate the unidirectional influx constant, Ki (ml/100 g/min), and the distribution volume of Gd-DTPA in the tissue, v(e), from T1-weighted images acquired with saturation recovery (SR) steady-state free precession (SSFP) and spoiled gradient-echo (SPGR) protocols. The capillary permeability surface (PS) area increased significantly during reactive hyperemia, which facilitated rapid extraction of Gd-DTPA during the first pass. Regional muscle group studies from 11 normal volunteers yielded blood flow (Ki) values of 108.3 +/- 34.1 ml/100 g/min in the gastrocnemius, 184.3 +/- 41.3 ml/100 g/min in the soleus, and 122.4 +/- 34.4 ml/100 g/min in the tibialis anterior. The distribution volumes (v(e)) in the corresponding muscle groups were respectively 8.3% +/- 2.1%, 9.3% +/- 1.9%, and 7.9% +/- 1.8% from the kinetic model, and 8.8% +/- 2.4%, 9.1% +/- 1.9%, and 7.2% +/- 1.4% from tissue relaxometry studies. Bulk blood flow studies in the same volunteers using phase-contrast velocimetry (popliteal artery) yielded significantly lower flow values, but with a correlation coefficient R2 = 0.62 and P = 0.004.

Algorithms↗
PubMed2004

Skeletal muscle NAD(P)H two-photon fluorescence microscopy in vivo: topology and optical inner filters.

Two-photon excitation fluorescence microscopy (TPEFM) permits the investigation of the topology of intercellular events within living animals. TPEFM was used to monitor the distribution of mitochondrial reduced nicotinamide adenine dinucleotide (NAD(P)H) in murine skeletal muscle in vivo. NAD(P)H fluorescence emission was monitored ( approximately 460 nm) using 710-720 nm excitation. High-resolution TPEFM images were collected up to a depth of 150 microm from the surface of the tibialis anterior muscle. The NAD(P)H fluorescence images revealed subcellular structures consistent with subsarcolemmal, perivascular, intersarcomeric, and paranuclear mitochondria. In vivo fiber typing between IIB and IIA/D fibers was possible using the distribution and content of mitochondria from the NAD(P)H fluorescence signal. The intersarcomeric mitochondria concentrated at the Z-line in the IIB fiber types resulting in a periodic pattern with a spacing of one sarcomere (2.34 +/- 0.17 microm). The primary inner filter effects were nearly equivalent to water, however, the secondary inner filter effects were highly significant and dynamically affected the observed emission frequency and amplitude of the NAD(P)H fluorescence signal. These data demonstrate the feasibility, and highlight the complexity, of using NAD(P)H TPEFM in skeletal muscle to characterize the topology and metabolic function of mitochondria within the living mouse.

Animals↗
PubMed2004

NAD(P)H fluorescence imaging of mitochondrial metabolism in contracting Xenopus skeletal muscle fibers: effect of oxygen availability.

The blue autofluorescence (351 nm excitation, 450 nm emission) of single skeletal muscle fibers from Xenopus was characterized to be originating from mitochondrial NAD(P)H on the basis of morphological and functional correlations. This fluorescence signal was used to estimate the oxygen availability to isolated single Xenopus muscle fibers during work level transitions by confocal microscopy. Fibers were stimulated to generate two contractile periods that were only different in the PO2 of the solution perfusing the single fibers (PO2 of 30 or 0-2 Torr; pH = 7.2). During contractions, mean cellular NAD(P)H increased significantly from rest in the low PO2 condition with the core (inner 10%) increasing to a greater extent than the periphery (outer 10%). After the cessation of work, NAD(P)H decreased in a manner consistent with oxygen tensions sufficient to oxidize the surplus NAD(P)H. In contrast, NAD(P)H decreased significantly with work in 30 Torr PO2. However, the rate of NAD(P)H oxidation was slower and significantly increased with the cessation of work in the core of the fiber compared with the peripheral region, consistent with a remaining limitation in oxygen availability. These results suggest that the blue autofluorescence signal in Xenopus skeletal muscle fibers is from mitochondrial NAD(P)H and that the rate of NAD(P)H oxidation within the cell is influenced by extracellular PO2 even at high extracellular PO2 during the contraction cycle. These results also demonstrate that although oxygen availability influences the rate of NAD(P)H oxidation, it does not prevent NAD(P)H from being oxidized through the process of oxidative phosphorylation at the onset of contractions.

Animals↗
PubMed2004

Absolute myocardial perfusion in canines measured by using dual-bolus first-pass MR imaging.

PURPOSE: To compare fluorescent microsphere measurements of myocardial blood flow (MBF) with qualitative, semiquantitative, and fully quantitative measurements of first-pass perfusion at magnetic resonance (MR) imaging. MATERIALS AND METHODS: Coronary artery occlusion or intracoronary adenosine infusion was successfully performed in 16 beagles; both procedures were performed simultaneously in one animal. MBF was assessed at microsphere analysis. First-pass myocardial perfusion MR imaging was performed during a dual-bolus administration of gadopentetate dimeglumine (0.0025 mmol/kg followed by 0.10 mmol/kg). The absolute myocardial perfusion at MR imaging was calculated by using Fermi function deconvolution methods. Qualitative, semiquantitative, and absolute myocardial perfusion MR imaging measurements were compared with microsphere MBF measurements by using paired t tests, linear correlation, and Bland-Altman analysis. RESULTS: Fully quantitative (ie, absolute) analysis of MBF at MR imaging correlated with microsphere MBF measurement (r = 0.95, P <.001) across the full range of blood flow rates encountered (from 0 to >5.0 mL/min/g). Similar close correlations were observed in endocardial and epicardial segments (representing approximately 0.85 g of the myocardium). With modest increases in MBF, qualitative measurements plateaued in the hyperemic zones. Semiquantitative measurements did not correlate with MBF as well (r = 0.69-0.89); they plateaued around 3.0 mL/min/g. CONCLUSION: Dual-bolus MR imaging enabled accurate measurement of absolute epicardial and endocardial perfusion across a wide range of blood flow rates (0 to >5.0 mL/min/g). Use of qualitative MR imaging measures such as the contrast enhancement ratio led to substantially underestimated hyperemic blood flow measurements.

Animals↗
PubMed2004

High-resolution imaging reveals a limit in spatial resolution of blood flow measurements by microspheres.

Density of 15-microm microspheres after left atrial application is the standard measure of regional perfusion. In the heart, substantial differences in microsphere density are seen at spatial resolutions <5 ml, implying perfusion heterogeneity. Microsphere deposition imaging permits a superior evaluation of the distribution pattern. Therefore, fluorescent microspheres (FMS) were applied, FMS deposition in the canine heart was imaged by epifluorescence microscopy in vitro, and the patterns were observed compared with MR images of iron oxide microspheres (IMS) obtained in vivo and in vitro. FMS deposition in myocardial slices revealed the following: 1) a nonrandom distribution, with sequentially applied FMS of different color stacked within the same vessel, 2) general FMS clustering, and 3) rather large areas devoid of FMS (n = 3). This pattern was also seen in reconstructed three-dimensional images (<1 nl resolution) of FMS distribution (n = 4). Surprisingly, the deposition pattern of sequentially applied FMS remained virtually identical over 3 days. Augmenting flow by intracoronary adenosine (>2 microM) enhanced local microsphere density, but did not alter the deposition pattern (n = 3). The nonrandom, temporally stable pattern was quantitatively confirmed by a three-dimensional intermicrosphere distance analysis of sequentially applied FMS. T2-weighted short-axis MR images (2-microl resolution) of IMS revealed similar patterns in vivo and in vitro (n = 6), as seen with FMS. The observed temporally stable microsphere patterns are not consistent with the notion that microsphere deposition is solely governed by blood flow. We propose that at high spatial resolution (<2 microl) structural aspects of the vascular network dominate microsphere distribution, resulting in the organized patterns observed.

Adenosine↗
PubMed2004

NADH enzyme-dependent fluorescence recovery after photobleaching (ED-FRAP): applications to enzyme and mitochondrial reaction kinetics, in vitro.

NADH enzyme-dependent fluorescence recovery after photobleaching (ED-FRAP) was evaluated for studying enzyme kinetics in vitro and in isolated mitochondria. Mass, optical, and nuclear magnetic resonance spectroscopy data were consistent with the UV NADH photolysis reaction being NADH --> NAD* + H+ + e-. The overall net reaction was O2 + 2NADH + 2H+ --> 2NAD+ + 2H2O, or in the presence of other competing electron acceptors such as cytochrome c, NADH + 2Cyt(ox) --> NAD+ + H+ + 2Cyt(red). Solution pH could differentiate between these free-radical scavenging pathways. These net reactions represent the photooxidation of NADH to NAD+. Kinetic models and acquisition schemes were developed, varying [NADH] and [NAD] by altering NADH photolysis levels, for extracting kinetic parameters. UV irradiation levels used did not damage mitochondrial function or enzymatic activity. In mitochondria, [NADH] is a high affinity product inhibitor that significantly reduced the NADH regeneration rate. Matrix NADH regeneration only slightly exceeded the net rate of NADH consumption, suggesting that the NADH regeneration process is far from equilibrium. Evaluation of NADH regeneration in active mitochondria, in comparison to rotenone-treated preparations, revealed other regulatory elements in addition to matrix [NADH] and [NAD] that have yet to be fully characterized. These studies demonstrate that the rapid UV photolysis of NADH to NAD is an effective tool in evaluating the steady-state kinetic properties of enzyme systems. Initial data support the notion that the NADH regeneration process is far from equilibrium in mitochondria and is potentially controlled by NADH levels as well as several other matrix factors.

Animals↗